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MICROCOPY RES')LUTION TEST CHART
NATIONAL BUREAU Of SiANOAROS-196l-A
MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU
or
STANDARDS-1963-A
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Technical B,tll2tin No. 998 • January 1950
•
Partitioning Method of Genetic Analysis
Applied to Quantitative Characters of
Tomato Crosses 1
By LERoy Powlms, senlor geneticist, and 1.. F. LOCKE, horl'iculturist, Bureau oj
Pia nt industry, Soils, and .Agricultural Engineering, Agrlcllitural Research
AdministraUon, United Slalcs Deportmcnt, oj Agriculture, and .r. C. GARUETT,2
assistant extension horticulturist, Ok/ahol/!a Agricultural and llfechanical College
CONTENTS
Introduction. ______________ .. _ ___
Materials and general methods___ _
Experimental procedure and re­
Puge
1
2
S\~ts_______________________
4
Percentage of flowers that set
fruiL ______ ._______________
4
Period from seedinp; to first fruit
ripe and its cOlllPonent charRCtcr:::.._____________________ 11
Weight per fruit and its component characters_ _ _ ______ __ 24
Interrelations of cl1fwacters _ _ _ _ _ 38
•
Page
Variances of period from seeding
to first fruit ripe and its com­
pOIlent characters, and vari. an~es of weight per loeule ____ 45
D1SCUSSI01L__ __ ____ _ _ _ _ _ _ _ _ __ _ __ 48
De~ign of experiment, and pro­
cedures and methods used in
analyzing data______________ 48
Number of major gene pairs
differentiating characters_ __ _ _ 51
Interactiolls____ _ _ ___ _________ 51
SUlllmary_ _ _ _ _ __ ___ _ _____ ____ _ _ 54
Literature cited_________________ 55
INTRODUCTION
Tests by Lockc 3 at the Southern Great Plains Field Station, Wood­
wnn[, Okla., demonstrated that the Porter variety of tomato (Lyco­
l)eJ'sicon esc1dentum 1Jill.) has exceptional fruit-setting capacity. No
othel' variety grown at ",Yoodward approaches it in this respect.
However, the fruits of this variety are entirely too small for commer­
cial production. It was decided to attempt to combine, by hybridiza­
tion, the frui t-setting cap~"ity of Porter with desirable cha.racteristics
of commercial vnrieties. l~welopmental-genetic studies of percentage
of fiO\'r'ers tha~!'\et fruit,,JReriod from seeding to first fl'Uit ripe, and
weight pel' i'ru' ~ r~se.r,iIJal to intelligent and efficient execution of a
breeding prog
Vilth
tlgmatoes in the Great Plains region. This
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1, 1949. FOI'IJlC'r1y StU~lIt ~ista~ U. S. Southern Great Plains Field Station. Unpublished ¢,-ta'a:J
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TECHNICAL BULLET1N 998, U. S. DEPT. OF AGRICULTURE
bulletin reports findings from such studies. It presents new proce­
dures and methods employed in experiments and in analysis of data~
livhich should be helpful in other research projects in the same field.
•
MATERIALS AND GENERAL METHODS
F'onderosa (P 2) was the tomato variety used in crosses with the
Porter (PI) variety to produce the hybrid populations. Hybridizing
to obtain the F, Rnd backcross populations and self-pollinating to
obtain the F2 and parental populations were done at the Cheyenne
Horticultural Field Station, Cheyenne, Wyo. The hybridization work
WitS conducted in gl'eenhouses during the winter. Both female and
male parents were bagged. In all cases, the same plants crossed to
produce the F, population were used to produc(' seed for the backcross
populn,tions and self-fertilized to produce the parentnl populations.
Likewise the lJ\ plants used in backcl'Ossing were selfed to produce the
F2 population. Tbl.} mateI"ial was grown at the Southern Great Plains
Field Station during the summer of 1941.
'1'11c symbol B, here signifies that the progeny indicated resulted
from bnckcrossing the F, to the designated pm·ent. The term "pene­
trancp" as used here denotes the percentage of individuah in any
given class of tbe frequency distributions. This use of the term
b"oadcns its meaning somewhat beyond that originally given by
Timofceff-Ressovsky (22).4
The dependent characters studied and their components are as
follows:
Pereentagc of floll-ers that set fruit.
Period froll! seeding to first frtlit{l)eriOd from seeding to first bloom.
ripc _________________________ Period from first bloom to firat fruit set.
Period from first fruit ~ct to first fruit ripe.
.It
f·t
{l'\umbcr of lorllies per frllit.
WClgl
per rUI ---------------- Weight pe.lol'ule.
Percentage of flowers that set fruit was determined as follows~
Each day from the time the first plants began to bloom, June 6,.
through the week of August 18, two inflol'escences (whenover avail­
able) thnt began to bloom on that day were tagged with the date.
'I'll(' flowers on eaeh of these inflorescen('('s were counted and were
examined weekly until fruit had set or nbscission had taken place.
Then, the, total number' of flowers pC!' inflorescence and the number
that set fmit were r('corded. The data were taken and recorded on
the basis of the individual inflorescence and were entered in the record
book fOl' the week in which the first flower of the given infiorescence
bloomed. A vel"llge number of flowers examined per plant, for both
parents and all generations, was 76. The (lata fOl' aU the component
characters of period from seeding to first f[1.1it ripe were. taken on the
basis of 3-day periods. Weight per fruit li-ild numbet of locules were
determined from two fruits taken at random from ~ll('h plant. All
dnta were taken nnd recorded on the bnsis of the individual plant.
The genetic design of the experiment elnployed il.11 the difrerent
populations that could be obtained f!'Om tile two parents and the F
by crossing and self-rollination: PI, B, to F r, ~'\, F 2, B, to P2, and P2:"
(14). 'rhe statisti{'a design was a randomized compl?te block. Ten
f
Italic numbers in parcntheses refer to Literature Cited, p.
55~
•
•
GENETIC ANALYSIS OF TOMATO CROSSES
•
•
3
blocks of nine plots each werel used. Each plot contained 24 plants.
In each block, one plot each was grown of the PI, Fh and P 2 popula­
tions, and two plots each were grown of the BI to Ph F 2 , and BI to
P 2 populations. 'l'he nine items were randomized wit,hin each block.
The plants were spaced 5 feet withm rows and 5 fee.t between rows.
Plants that did not survive transplanting to the field were replaced,
but data. taken on the replants were not used in the study.
The means, variances,. correlation coefficients, partial standard re~
gression coefficients, and relative percentages of the variances of the
dependent. characters accounted for by regression were calculated
from the individual-plant data in all cases. Detailed and condensed
frequency- distributions were used only in estimating the number of
gene paIrs differentiating the two parents as regards any given
character.
The. standard methods of analyzing such data, those descl"ibed by
Snedecul' (21), were followed. Because of the nature of genetic data,
certnin modifications (12, 13) of these standard methods were neces­
sary to make them applicable. The 'method used to estimate the
genetic and environmental vllrinnces of the scgrcgatin!? gcne1'lltiom
(BI to PI, BI to 1">2, and 11'2) is cssentially that described Oy the seniOl
authol' in an eadier publication (15). The PI, 11'11 and P 2 population!
were employed in estimating the environmental varianc<ls. In som(
cllses in whICh both phenotypic and genic dominance were complete,
the BI to PI populntion also was employed for this purpose. It was
found that fOI' some chnracters the reilltion between the means and
the environmental vaI"illnces WIlS 10gaI"itlunic rather than linear. In
such instances, the moans and cnvironmental variances (total vari­
ances) of nonsegregating generntions (PI' ]i\, and P 2) were transformed
to logarithms in estimating the environmental variances of the segre­
gnting generations. However, the Ilntilogndthms are gh'en in the
tables. In studying the developmental relations of the cha1'llcters by
means of correlation coefficients, partial standard regression coeffi­
cients, and l'eliltive percentages of the variances of the dependent
characters accounted for by regression, transformation of the original
dtltn, WIlS necessary in some cases. For example, in studying the rela­
tions between number of locliles, weight per locule, and. weight per
fruit. the ol'iginal individuill-plllnt data were transformed to loga­
rithms. The fOl'luula used for ctllculuting the rcilltive pel'centage of
the va!'iance of a dependent chlll'llcter a('counted for by regression is
(nJ l b'YI.23) 100, in which rlJI is the coefficient of correlation between
the dependcnt vtlriable and the designated independent variable and
b'11t.23 is tIl(} partial stl1ndllrd measure rcgression coefficient. The inter­
relations of some of the chal'llcters were anulyzed by determining the
percentage of individuals combining Ilny two dosil'llble cIlaracters
being studied. Details of this method hu'.e been published (18).
New methods and pI'ocedurcs used in the analyses Ilre gh'en and
illustrated ill the section entitled "Expel'imental Procedure and
Results."
In all comparisons made when interpreting the data and drawing
conclusions, tests of significllnce were made, usulllly by tho stnndard
methods (2.1). Unless othcl'\\'isc stilted, thc odds were at lCllst 19 tc
1 agninst the noted diffcl'(\l1('es being due to chance. In some of tho
anulyses, significtlncc was lested by methods developcd by W. 1'.
4
TECHNICAL BULLETIN 998, U. S. DEPT. OF AGRICUL1'URE
Federer, of the Statistical Laboratory, Iowa State College, and
now in ~rocess of publication.
EXPERIMENTAL PROCEDURE AND RESULTS
PERCENTAGE OF Fl.OWEHS THAT SET }'RUIT
•
'rho. meaus and varinnc!.'s for pet'centnge 01 flowers that set fmit
are given in tH,blc 1. 'rho. stnndat'(l (.'rrors of the means are not given
because the data WCl'e transformed t') logarithms in conducting tests
of significance. In the Itl1ltlys(.'s that follow, it is necessllry to recognize
both phenotypic and genic dominance ("I, 16).
l\IAGNlTUDE QIo' CHARACTER D1FFEItENCE
From the meitH values lis led in tnbIc 1, it cnn he determined that
51.9 percent mOre of the flowers of Porter tomato thltIl of thosc of
Pondcrosa lOlllitto set fruit.
TAIH,E
(Illtl nIlmuers oj individulIls Jor differellt 1107J1111lti07ls
e;mlllilUd Jor perc(,l1/age of flowers lltill scl/rllit
1.-111caIlS, vltrliUtcl!s,
Varlallce
I'O(lulatioll
l\1(1un
- - - - - - - - IlltliyldUlIls
'l;;r"o[ron-I
llI~ntlll
a.ond'Ic
~xlllllincd
•
DOMI:-IXNCI;:
If p\U'lIotypic dominnnce is intrl'lllC'Cliate (no domilUtnco), the
menu of thr .P't for nil.)' ehnl'ac(rl' equnls 01' dosdy lI,ppl'oxillllttcS
t.he rWl'l'age of lhe IllNlllS of the two pnl'enis, In this insLnnce, tbe
u.Yl'l'ngc of thel!lCIUlS of the two pllI'('nts fOl' pc/'cenbtge of ilow('rs
thnt st't fruit is 27,8, Ilnd the menn of lIw l!\ fOl' this chamelf'[' is 28,5.
The close similnl'ity of U\('se two Ynlul'S shows thttt phenotypic
domin!LncP. WIIS inl(,l'lIlI'dint(\, If gNlic dOlllinltnee WflS intel'llwdinte
also ttntl t1wl'r W('l'r 110 inl('I'nll('lk intt'ra('tions of tilt' gNH'S-tJmt is,
if the efj'l'ets WPI't' Ildditin~-tll('n it would be t'xpl'ett'cl tim!; tll(' lll('ltn
of til(' 13 1 to :POl'tl'1' would equn.l th(' nW'l'lIge of the lTI('iUlS of Port('l'
Ilnd Ii\, the lllrllil of the Fz would ('qual thnt of tht' ]1\, lLHd lhe lllrltn
of the H, to Ponderosa would t'qunL the n,v('rnge of the meuns of Lhe
Fl and POnd('I'OSIL, The L\wordienl Hwans eu\enllll('d on this basis
11['(' as follow:;; HI to 1'o/'l('l', 4.1.2; l~\, 28 i5 i ilnd HI to Pondl'/'osn,
15,2. By compnring UI<'SC figtU'l'S with t.hose in tnbln I, it clIn be
seen t hnt HI(' mngni I tldl' of the n1\'lln of the 131 to POl't('I' is t hn,t
expr{'trd, htl t t h(, IlH'lInS of tit(' l~ nnd l he 13 1 to Pond('/'osa lIl'e dOSl'l'
tlwn (lXP('('(Nl to tilt' .1l1NlIl of Pondrl'ostl., For (his r('!tsoll, lind
since tlte ml'llil of t he' 1<\ is inlt'l'llH'd into b\'lw('('11 lhe meallS of \.ho
•
GENE'l'IC lh"'iALYSIS OF TOMATO CROSSES
5
two pt11'ents, multiple-factor inheritance must have been involved
and both intct'llllelic and inLraallelic interactions must have opere,ted
to produce the results noted, In such a situation genic domine.nce
may 01' may not be intN'mediate. The. irlternllclic internctions \'{ere
such that the effecti \~eness of the genes tending to produce a high
seL (' . fruit dimini!'hed as genes tending to produce a low set of fruit
incrcased in tll(\ genotype,
If g('nic domillunce WtlS intcrmediaJe find thcl'e were no interallelic
intcrilctions of the genes, it would be expNlted that the genetic
varinnce of the Bl to Porter and that of the Bl to Ponderosa would not
difft'r 1l11lterlltlly in lllngllitude, On the OtlH:~l' hand, if the effectiveness
of the genu's tending to produce a high Sl't of ft'LIit dill1inishcd~ as
genes tC'llding to pI:Oducc n low set of fmit incrensed in the. genotype,
then tlte genetic val'innce of the Bl to Porter wouI:d be expected to
ex('eNI thiLt of lit(' Bl to Ponderosl1. The Yilriances (Lp,ble 1) support
the lnt(el' postulation,
•
In annlyzing the data to asccrtain the number of mnjor gene pairs
diffl'I'C'ntillting the pOl'ents, it WIlS ueC't'ssilry to set up a hypothesis
as to th(' numher of gl.'lle puil's illyoh-cd and to detcrmine the pheno­
typt'S of the g!'notypes, the pl'llci.mnc('s of these phellotypes, tho
PWPOl'tiOll of caeh in tho thcoretieHl population) and, finally, the
yaVdity of lhe hypothesis,
,A~} f'xaminnlion of til!:' vnlues given in tnbln 1 shows that tho mean
of E\ is not signifiC'll1ltly cliff('I't'ut fl'om the average of menns of
thr t.wo pn.rcufs lll1d that tIl(' meun of Br to PorlcI' is not significuntly
difl'f'rt'nt ft'om lhe t'wcl'nge of means of 1i\ nnd Porter. This indicntes
thnt ('If('ets of thc gC']leg were additi\'e both within and between gene
puirs. Howe\'('I:, lhe mean of Bl to Ponderosa is lcss thnH the aVCl'Ilge
of m('1tns of 1'1 and Pon<icrosn, This indicntes that ('£recis of
gent's wen' not lhe SHIUe lhroughout ttll genotypes, but thnt g~'Iles
tending to in('l'ense pl'I:('entngt' Qf flowel's setting fruit 1111d a gn~nter
erft'ct in gl'ltotypl'S of HI to POI·tel' than in gl'notypes of BI to Pon­
del'():3Il. 'l'ltl'se ,'estIll" teud to show that efr'.!cts of the gN1C$ were
nd(Lilin in. illl genol:YI)(>s hn,ving at INlst OIl(' domilUlllt gene in ench
of tilt' W'llC pairs. illld that c\omini1l1t g('lleS lind !L gl'cllter effect in
tlU',;C' gt' I1otypt's thiUl they did in genotypes hn\'ing nt least one gene
pill I' 1'('('(Is;~,in'.
Frolll titblt' :2 it ('lInbe S('C'Il tIutt 21.5 pcrC'ent of the plnnts; of Porter
and 9,1 IWrCt'nL or tht, plants of BI to Portpl' werc illllong those of
Whldt no Pl'r('('Jtt O.t' mOI'(' of the flowers set fruil. Thus (9,1-+21.5)100
Ot' 42.S Pl'l'('Pltt of the plnats of the BI to Port!'r bC'ha\'(~d like pIllnls of
Po I'll'r wi til l'(',;peet to the 60-69 nnd 70-ol'-morc classes. If cq LIni effects
of tlt(' g(lJl(l pilirs nn' assumed, this is not consislent with the assumption
thn,t l'{\'l'{'ts of titt' g(l.IlCS WC'l'e nddili\'e in genotyp('S of the 131 to PortCl'.
HOW('YPI', if OIlP gl'Itl' pn il' hud npproximn.teiy HS gl'pnt all ('freet as lllC
othN' gl'lt(. pnil's eombined, tltis high proportion of plants in the 60-69
and 7(}-or-InOI'(' classes would be, expected.
A :;tudv of tLlC' meuns nne! vnriultct's of table 1 shows tliM probably
'ffi0I'(' thn'n one OI: two mnjol' gl'IW pn.il's difJ:rl'l'ntiat('d the pnl'cnts as
t"('gHnl;:; Pl'l.'cl'lttngl' of {!OWl~I'S that set {I'uit:. These 1ll():lItS !mc! vlU'i­
•
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6
TECHNICAL BULLETIN 098, U. S. DEPT. OF AGRICULTURE
2.-Theoretical arid obtained frequency distributions, x2 valulls for testing
goodness of fit; degrees of freedom, ant! values of P for percerltage of flowers that
8et fruit
TABLE
FruQucney distribution by peroontage o( ftowers tbat
set (ruit
Population
0.0
Porter:
Obtained •••••
1'heoreticllL •.
81 to portl'r:
Obtained •• _••
Theoretlc..L ••
FI:
Obinined •••••
1'lIeoreliool. ••
Perctlll
0.19.0
10.0- 20.0- 30.0- 40.0- 50.0- fJ().O­ 70.0
or
lU.O ~'9.0 39.0 ~9.0 ~9.0 69.0 marc
Per·
Per·
Per·
Per·
Ctllt
ulil
Ctllt
De·
grees
x'
at
t'l'C'
dam
Plies be·
tWl'Cn­
-- ---- -- ------ -- -_.
Per·
CtIIt
Per·
ttlll
Ctlll
ctIIl
ctlll
0
0
4.3
8.9
24.2
26.7
ro.O
37.3
18.1
3.~
3.6
2.8
13.0
14.7
25.7
30.1
29.2
29.7
16.8
35.8
35.3
4.7
7.2
0
0
0
0
0
0
0
0
0
0
Per·
Per·
and 0.02.
5.6 }1O.552
4
O.o.~
9.1
5.9
0
0
} 0.688
6
0.30 nod 0.20.
0
0
0
0
0
0
} 0.600
3
1).10 and 0.05.
8.6
7.S
3.1
~.O
0
0
0
0
}10.550
6
0.10 lind 0.05.
19.~
21.~
0
0
0
0
8.2
14.0
61.3
4:1.5
0
0
15.5
23.1
32.9
32.3
25.1
lD.8
14.8
13.0
4.8
9.1
5:!.9
47.9
30.S
33 .,
8.S
7.0
1.7
2.8
0
0
0
0
0
0
0
0
} 9.640
4
0.05 nnd 0.02.
Obtllinctl ..... 46.6
1'hcorotiooL.. 33.0
61. i
1.7
2.9
0
0
0
0
0
0
0
0
0
0
0
0
} 6.042
2
0.05 nnd 0.02.
F,:
Obtaln"t!.....
1'htloret!caL •.
DI to Ponderosa:
Obtllined .....
'l'hcorotlool."
ollderosu:
•
M.I
!tIlCCS,. and the frequency distributions ])('csented in table 2, were
studied to dott'rmine whether they fit til? hypothesis that the parents
were difl'erentiated by fom mnjol' gene pairs. In Porter, these 9:enes
nre symbolized ns AABBGGDD,~ in Ponderosa, as aabbccdd. (8ince
phenotypic dominnnce wus intel'll1edintc, Ilssignment of the cnpital
lettel's to Porter was arbitrary.) The procedures nnd methods are
new nnd therefol'c tu'e emphasized and illustrated. The method of
annlysis is termed "the partitioning method," because the means,
Yitl'iances, and fr('quency distributions of the scgl'egnting generations
nre pal'titioned into their components on the basis of the genotypes
of these gcncrittions.
The genetic hypothesis tested. was that the parents were differen­
tiated by fOUl' majol' gene puil'S, the effects of the genes were additive,
the offects of the genes tending to produce a higher percentnge of
flowers that set fruit ,\'ere great('r in those genotypes having at leust
one dominant gene in ench of the four g(,lle pairs, one of the gene
pnil'S had as grent nn effect as the three othel'S combined, and not only
phonotypic but nlso genic dominllIlce wns intermediate.
In order to partition the backcross nnd F2 populations into their
components, it wns necessary to have an estimate of the effect that a
gene contributes. Results already stated tended to show that the
dominant genes hnd a greater effect in the genotypes having at leas'~
one dominant gene present in each gene pair. The effects of a single
gene in those genot,ypes were determined from the Porter and Fl
population means by the following pl'Ocedure:
From table 1 it can be seen that the mean of Porter is 53.8 percent
and that the mean of FI is 28.5 percent. These two populations
differ by four dominant genes. Therefore the total effect of these
four genes on the mean was 53.8-28,5 percent, or 25.3 percent. The
gene contri'buting as much as the three other genes combined is
•
•
7
GENETIC ANALYS]S OF TOMATO CROSSES
designated the A gene. Its contribution was 25.3 percent +- 2, 01'
12.65 percent. The total effect of the three other genes (B, G, and
D) was 12.65 percent, and the effect of anyone of them was 4.217
percent.
The effect of the dominant genes in those genotypes having botih
genes in Itt leltst one of the four gene pltirs recessive WitS estimat€ld
from the menns of theI!\, BI to Ponderosa, nnd Ponderosa population!).
The procedme wns ItS follows:
The HI to Ponderosn populntion possessed one genotype (AaBbGcDcl)
that hilS a dominant gt'ne in each gene pnir. This is the genotype of
the l!\, Itnc! in cstimnting the effect of a single domillnnt gene it:s
cfrects mllst be subtmcted. From table 1 it cnn be seen that the mean
of tho HI to Ponde!"Oslt population .is 9.7 percent. The least lllunber
of illdividullls I1('Cessnl'y for a populn,tion having all genotypes of .the
backcross is 16. ~illce the nvemge of such n populntion is 9.7 percen~"
the estimated total is (16) (9.7) pel'cent, or 155.2 percent, The pel'­
ccnta&e cOlltl'ibuted by the AaHbCcDd nnd aabbccdd gellot~pes to t.hils
total IS 28.5+1.9 (menn of FI+meun of Pondel'osn). tiubtl'actm~;
this cOlltl'ibution from the totnl of the theol'eticnl HI to PonderosliL
populntion gi Vl'S the percentage 124.8. This is the theOl'etical totn.}
{Ol' the l'l'llIllining 14 geI'iotypes of the theoretical HI to Ponderost:1
popullltion, and tbe men,n is 8.914 percent. The difference between
this menn nnd the Illl'llll of PondNosn is 7.014 percent. Since thest:!
14 g('notypes difrel' {!"Om the genotype ofPontieroslt, 011 un ltvel'llge"
by 2 dominllnt genes, the elred of foul' genes is twice this sum, oJ:'
14.028 percent. ~ince the cfrect of the A gene equals tho effed of til(!
othel' genes combincd, it is 7.014 percent and Lhe cfrect of B, G, or D
is 2.338 percen t.
The thl'on'tienl means given in tnble 3 w('I'e obtnined by stl1rting
with 1.9 for the genotype aabbccdd, IlClding 7.014 fOI' each A gene und
2.~~;~8 1'01' ('neh H, C, 01' l) gene until the gcnotype whose mel1il WI1S
under considNltlion lind Ilt Imst one domillllnt gene in encil of the
foul' gene pnirs, nnd therl'nfter IHlding 12.65 for ('Itch A gene and
4,217 fOI' ench H, e, 01' D gene. The means of the 81 diffcrent geno­
types of the F2 Itnd the 1(i genotypes of each of the H, populations
f01'1ll 11Il nlTHY of IS di(\\'l'ent vnlues.
The first is stub-(~oIUIl1Il entries of tlthle 3 need some explnnl1tioll.
In most insttl!1(,(,S, eneh !.'11[.ry I"l~pr('sents n group of genotypes. For
('Xllmpll', genotype ..:L-1BUCCVll I'epresents Il group including also
AIlIWCcVD nnt! AABbCCJ)l). Two gellotypeg WCl'P listed together
if thl'Y I"{'pn's(>ntp(i two gl'oups of gpnolypes luwing the snme mean.
li'or exnrnple, 18.:3 is till' Ifl('illl fol' the group l'eIH'('Sented by AABbccdcl,
whIeh inellllh's ulso AAbbCcdd Ill1d AAbbccDd, Ilnd fOl" the group
]"epr!'senll'd by AaBBCCcld, which indlldes also .l.'laBBccDD I1nd
AabbC( 'lJ]).
The grnml-total Ylll'iilll('l'S listed in tnble 3 were enlcull1ted ill Il,
nU1IHlt'r dl's('rilwd in [til l'nl"liN' publication (15) by the senior Iluthor"
The llH'fU1S iLnd obtnilH'tl gmnd-tolnl vlll"inm'ps for USI) ill, the f01"llwl:it
•
•
y= 1I11;+b nre gin\l1 in lnhle 4.
•
Fsc of the formula
m=(?b -V7+
1
:£1-);3
'!L1.=V.
.2 +1h =.?h)+-3 yiddNI
the ynlue 1.646, I1nd use of the formula
XI -.r~ I,2-):3
.
b=l(VI-mJ"I)+(Y2-m.r2)+(Y3-m.r3)]+-3 yi('lded the vnlue 15.318. \
00
1-3
t.oj
o
TAlIl,}]
3.-Theoretical t'alttcsJor gelloiY7lf'8 of 131 to Porler, F2 , a1ll1 8 1 to Pond~ro8(t alld calculated means andJfequency diMrilJll(ions of the8e
S pO/lulaliOlls jor 1)ercclltagc oj .flowers that set fruit
--.--.~-
..<-------
I
OcnotypeOf popllilition
---
;\!cun o<
.........
<
...
I
•••••
.............. .
Ail IIbrclJJJ ....... ~.
AA/I/lccdd~.~
... ~
~~~
A .. lllbccdd lind Aft llIlC('tId . ..... ~ .......... <0.
Aa/l/orcJ)j) nnd AAMrrdd
....
AfllIbCcdd 1 nnd au III1Cd)]) ....................
«
..............
AafJbcctld~llnd f1l1l1lJ('c:dd.~ •• ~ ............... .
Aabbeedd' ul1(l O(JIII1Ccdcl...........
a"JJbeedd , ..................................... ..
<. . . . . . . . . . . . . ""l1bmld , .......................................
anbbwld' ~ ,« . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
III IQ l'ortcL..., ............................... .
........................................... ..
.DI to ]·onuerosn .................................
toPorlce (lOpulnlion.
10 I'outlcrosu populution.
PtfU111
5:1.8 110:l.h73
JO.1lI2
40.6
96.000
9.8-1,7
45.4
OO.Olil ~
9.409
41.2\. S:1.1:J:1
9.118
36.9
iG.055
S.721
32.7
69.112
8.315
:!ii.a
(;2.229
i.SS9
25.:1
56.962
7.541
22. II
5:1.011
7.281
20.0
4D.2'_~1
7.010
1S.:1
45.<I~IO
6.741
]5.9
·1\.489
0.441
13.6
37.i04
0.140
11.S
33.918
5.&24
8. 9
~'9. W7
5.47·j
6.«
26.182
5.117
4.2
22.2:11
4. i15
1.9
18.445
4.295\
41.2 ...................,
21.11.......... ..........
9. i.......... ..........
. . . . . . . , . ••
.... "
AaIU/CO)d I ............ <.
I J'roscnl in lJl
'l'f~scnt ill III
I
$tn~dHrd;
,Vnrmllt'C lde"mllon!
Parrllt. , Pactll!
,-I a lib eel)d u .. <' •• , . . . . . .
A:l IlI/CCdd ....... • ~<
-----<
I
I
l'rcqllcney distrlhution b)' ~rccntag(l of flowers that:oel fruit
Grand·
I tal '
0.0
I
0.1-9
J
I
~
100191 :!O-29
;In·39
1--1------1- - - - - -
.·IAllnCC'J)D l ... ~ ......................... '"~<
~1 ... II/1CCj)df......
~
...1.tlIIlCcJJd I. .,~ . .~.
~ .~
AAlIb('c/id llnd Au fIlJCC])f) l~ . . . . . . . . . . .
AaflIlCCf)J 1.
• .... ' •• H ' "
}"
Oran(l·
totlll
'
40-19
50-59
6/H9
Proportion of­
0
0
0
.1
.:1
.9
2.1
3. i
6.4
10.6
17.2
2fl.4
3S.tl
52.5
04.:!
GO. 0
6:1.4
.1
20.9
4i.9
.1
.4
1.0
2.5
6.0
13.1.
22.1
30.7
311.8
4U.0
56.0
57.3
51.9
40.0
25.1
10.9
2.9
~ 2.7
32.3
33.2
2.2
4.11
9.9
1S.9
31.1
4:1.5
49.0
49.1
H.6
30.0
2<1.7
14.5
6.7
2.1
.4
0
0
14•. 7
19.8
7.0
~?o~~
llJ
,
1
¥.
-------!~.3
_1.1
33.9
42.6
43.7
35.:i
24.2
15.5
8.7
4.0
1.4
.4
.1
0
0
0
0
30.1
13.0
2.3
:!5.0
40.0
38.6
29.2
17.0
6.11
2.5
• fl
.a
.1
0
0
0
0
0
0
0
2'J.7
7.8
.5
~3.9
.5.4
H.6
6.3
1.8
.3
.1
0
0
0
0
0
0
0
0
0
0
]6.8
3.2
0
12.6
5.7
1.9
.4
.1
0
0
(J
0
0
0
0
0
0
0
0
0
5.1
.7
0
~
;
til
Percent' perUTlI! Pacml! Pactnt Pcrctnl PaulII Peru"t Pactlll Pactllt Percent
0
0
0
1.0
7.9
20.7
37.3
21.li
6.6
6.25
0
0
0
0
0
0
0
.1
.2
.:1
.7
1.4
2.7
5.4
10.2
19.2
3:1.7
0
2.2
9.1
~
r.:
1.9
.5
.1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.8
.1
0
Percent
Z
0.390625
IS.Z5
2.34~75O
co
18.15
4.68/500 co
12.50
3.906250 t)Q
18. i5
4.687500
18.75
9.3i5OOO
6.25
6.250000 ~
........
1.171875 ........
4.687(JOO !1l
.,..._._
5.S.~9375
..._....
4.687500
••••••••
10.1552.'iO
18.75
14.002!JOO IS.75
10. 54!l875 12.50
8.593750
18.75
5.859375 18.75
2. 343i5O 6.25
.300625 .................... ~ ._.......__• ____• __ o
, ... o. __ . . . ._ . . . . . . .
l:r:1
~
~ ~
r.:
c:l
t"
~
;
t.oj
GENE'l'IC ANALYSIS OF TOMA'l'O CROSSES
9
Thus Lhe gmnd-totnl vnrinnco of the second ll1NLIl of tuble 3 is (49,6)
(1.646)-H5,318, Ot' O(j,O(jO, The oUwr vlll'ittnees of lnblc 3 wem
cnlcuhlled .in It similtll' mlllUH~I', as Wt'l'O till' {lslimnlNI gmnd-toLl11
Ylu'hmc('s of lllblu 4, The file\; t.hat the obi.uilll'd and th(1 estimnted
gt'lI.nd-lolll.l. vtll'inncl's of tuble 4 do 1I0t difl\'I' significllntly ullows one
to pinto considl'mblc confid('ncc ill the gt'lltld-fo"lnl vnl'iIlIlCl's of Lnble
3,
Thc slnn<iHI't! d('vialions gi\'l'n in tnbl0 a 111'(\ (Ilich fOl' It singh" dell'!'­
minnlion, 'rhe lhl'ol'l'liclII fl't~qltl'IH'Y distl'ibutions listNI in Lnble :3
W{'I.'O caklllnlt't! from 1,\1(\ mCllns lind slnndul'(l. devinlions givoll jll lhis
lltblc Hud SIIl'PPlll'd's lahll's of the nOl'mnl pl'Olmbilit,y inll'gml. (~co
})elll'son (10),) In del('I'milling tl\(' pel'('('nlltg(\ of tho populnLion
('xpt'ell'd in n ny gi "Pil duss, t.lH' lowest VltillO of t.ho following column
hending of the' fl'NllIeltey disll'iblltions WIIS lIsed, lhl' 1'('IISOn fOl' this
1>1'0('('dlll'(' bl'ing lhlll nny plttnt hll\'illg il \'lIllle IOWl1I' thnn the lowl'st
\'lllllO of t.lH' ('olulIln h('ILCling \\'Us pitwl'd in tho pl'er.('<iing cluss, li'or
exnr.nplc, it plnllL Itfl\'illg tl\(l ynillo 10,09 wOllld be plttecd ill Lito 10-19
•
TAnl,~~ 4.- J[t'all'~J (,rulld-Iolnl I.'(/""nll(,("~, flnci '~!lmb(Jls Ull'rcof
j{OllWS
Ihlll sei fruil,
/01' Porler, ".\,
lor
(luti Po"dcl'II.~a
71crcCIllagc of
•
rlnss, Ill'IlC,t" in dl'l(\I'lllinin~ tl\(~ (h(,(H.'pU('nl fn'qlH'Jl(',Y fol' t,he 10-1!)
«:litss Hnd for lil(' ~'\aUb(,c1Jrl gl'lLotYIH' of lithic ;), 20,0 is suhLl'lIctcd
from til(' 1l)('1l!l (2H,5) of titis ~l'n()t,VI)(' lind thp I'NHtiting \'111110, 8,5,
is dh'idl'd by thp eOrl'('SpOlldill~ standard dp\'illt ion, 7,HSO, to give Lho
Y!litH' 1.0X,
From. (itt' lahl('s o[ no 1'11111 I probnbility ini!'gl'lll cited
i1ho\'{' il WIIS found tlmt for all J' Yfdul' of l.OH, 1/2(1 +(1,) ('((lIllls O,SHO,
lI('IH'l', HU.O P('I'('pnL of tll(' populitliOIl f('l1l)(',)'oll<1 the IO-~I!) dllSS, IIlId
\·1,0 1)(II'('pnt [l'l1 into this dnss 01'10\\'('1' e1IlSSl'S, SineC' only O,!) ])(,I'('(\lIt
[('11 into 10\\'l'l' ('ll1ss('s, 1 h(' t h('on't it'll I l'XIH'd (It! lH'r(,(,Il(Il~l' of Lhe popu­
lation [or dnss I() \ \l i;-; I:U.,
Titl' [11('01'('1 i('ld p('n'('ntll~(,s lhn.l phillIs o[ individunl ~('not~'PQS uro
o[ til\' two hn('[.::!'ross populntiolls, lind titt' ('Ol'l'('spondillg Ii~ul'l,t\ [01' the
}t'~ POPUllllioll, III'(' lisl('([ ill tltt' Illst t\\'o columns (If lnhlL':3, TIIPso
\'fLltl('S \\'PI'l' Illllitipli!'d hy till' ('orl'('sp(lll(lin~ fn'l(lll'lwy-dislribution
"nllll's diyidpd by 100, lind the I'('sulting \'IIItH's W(,I'(' Slllllllll'd JOI' ('n(~h
('OIUIllIl to o\Jtuin tll(' (h<'ol'pli('nl fI'P{fUl'IH',\' dist l'ibutiollS of 1hl' HI t.o
I'OI'(PI', 1,\, lind. BI to l'olldl'l'lH';I) populn 1i(\lIs ~i n'lI in t it(, In..''lli 1111'('0
lilH'S o[ tnhll' a,
Fol' l'xnmplp, thl' tit('or(,tienl P(,I'(,(,ltln~(' of till' 131
to Portl'I' popllintion ilt ('Inss 70 01' 11101'(, is (i5.{i)(O.()02f,) 1 (1.0) (0, (875)
•
+(O,;»lO,lS7:i)+(O,I)(O.12;iO),
01'
O.H,
Tilt, tll('()l'lltienl Hnd oi>lnill('(1 fl'Pqlll'lH'Y distl'ibut ions, x2 \'nhll's for
t('stit\g goodlH'sS of fit, d{'~I'('l's of fl'('l'dom, lind ndill's of P lIre giY('1l
g·131.GO ··50--2
10
TECHNICAL BULLETIN 998, U, S, DEPT, OF AGRICULTURE
in table 2, The eud classes have beon combined with adjoining classes
so that nt lcnst 10 individuttls nrc expected in ench class, In nU cnses
the x2 vnlues W()J'O enlculated fl'om the actual numbers given Il,s totals
in tltble 1, TllI.I numbl'l' of individunls in each cluss is I'eadily obtained
from thesn totals, Tho values for POl'ter and Pondcl'osa al'o somo.,
what SIll aileI' thnn would bo expected owing to chnllce, if odds of
19: 1 IU'O nccepted 11S the standlml of stnLislienl signitlclulcc, This
would indicate in both Cl1Sl'S tlll1t the obtained frequency dist,l'ibutiolls
IU'O not quile normal.
Also tho P ynIuo for the BI to Ponderosa
population is slightly Sll1nllOl' than. would be expected owing to ('\umee,
The fit bl\twccn.lhe theol'etical and thcobtuined fOl' the]\ and li'2 popuInlions is fnil' and thl1t for the BI to POl't(lr populat,ion is good, Ac­
cording lo SlINl ('CO l' (131), extl'cme (low or high) pel'ccnl,ages do not
follow the n01'llULI CUI've, The thcol'etieal ft'cquency distl'ibution hns It
highel' vfllue thnn lhp obtained in t,he lowest class fOl' Ute 11\ ]1't, !tnd
BI to Pond()l'OSll populations, and the l'eyerse is true fOl' the Pondel'Oslt
populat ion, By combining lhe 0,0 and 0,1-9 clllsses, 11 good fit is
obtained fOl' the BI to Pon(\Nosn nnd POlltll'I'OSI1 populations, It is
('vidN\t Lhnt the difl'el'cnces between the obtained n.nd the theol'cticnl
fl'oquency distl'ibutions IlI'n due to tho fnct lhnt tho distribution of
pel'C(mtnges in \,lit' forlllel' is not q lIiie normnl.
'I'll(' tlt('ol'(\ticnI1ll('lllls fot' the segl'l'gating populntions, giYl'n as t,lH~
lnst, thrt'O VltlU(\S in lhe SN~OIl(1 column of tnble 3, wel'e obtnined by
Laking the ti1eol'cLiclll pel'ct1nt:nge of the 1l1Pltn fOl' Clteh genotypo
J'ep!,(ls('ntod ill It gin'n pOpUhLtiOlL ILnd Slimming, 1i'01' ('xilmple, (,ho
theol'('t,i('nl n\('lln IWl'Cl'ntagl' fOl' thn HI to POI'Lt'l' is (0,0625)(5:3,8) +
+
+
+
+
+
(0,1875)(41).6)
(0,1875)(45.4)
(0,1250)(41.2)
(O,1875)(:3G,!))
(0.1875)(32,7)
(O,OH25)(28,5), 01' 41.2. Tlw oblnilwd m('ltns of
lable 1 nl'c in ('\ose ngl'ecn1l'nt; wit It lhe t1H'ol'clienl I11pnns of In1>lo 3.
This would lutVt\ to be 11'11(' of the HI to POll(\el'osn, lwcitusp the ob­
•
•
I1l('UIl of this popllll1 Lion Wl1S IlsNl to detel'lnino Ow e/I'(>ds of It
g(IIH',
TIll'n, the dntll substnntiale the hypolht'st's thltt the pltl'('nls \\'1'1'0
(\ifl'f'l'l'Iltinll'd by fOlll' IlllljOI' g('II(' pl1il's, Uw efl'pels of Ow g('ll{'S W(lI'O
nddilin' within C't'I'Ln.in gl'oups of gpnotypl.'s, th!.' t'fl'pc\.s of tbt' genes
l(\nding to pl'odu('p f~ hi~b(lJ' pel't't'ntn~e of flowrl's thllt, St't, fl'lIit,w(,I'e
gl'pnll'l' ill thos(' g'('/IoLypps Jmvillg' nt, }Past 011(\ domillllllL gf'llf\ ill (,llcll
of lilt' four g('nC' pHil'S, Ollt' of tht' gPlw pnil's had ns gl'Pltt nil ('f1'{'('t as
tit(' tltl'l'P Ot\\(11' puil's (.olllbint'd J Illlt! both ph t'llot,ypic alld g('llie domi­
ntHl(:C' \\'('1'(' int('L'Il1Nliftlc.
tained
sin~dt'
INTEHACTIONS OF GENES
TIll' illll'l'Il(~tions of the gt'IH'S 'Wt'I'p sueh I.hnt n,IlY givl'll g('IH' did not
hn\"(' llll' snn\(' dl'IP'('(' of efl'('('t. in nl! ~(,Ilot"y\ws, 'rhos!' gCIIl'S t.ending
to iJH'I'('ILS(1 II\(' IW)'C'l'lllllg(' of 1l0wt'J's thllt spL fruit hnd n. gl'l'lIJt'r pffl'ct
itt g('llotypps hn\'ing at least one sllch gt'll(\ pn'st'llt, ill (,lIeh of 11[(\ four
pnil's, This shows tlmL 1Il(' (,ffeets of lilt' g<'IWS w(,I'e ('.ulllllllllivt' but
not sll'i('tly ndd iIh tit I'oughou t til(' rnng(' of g'I'IlOtypPS, 'rhe t'il'('Ct3
of gPIH'S \\'(,I't' not, Ntunl, b(,(,l1l1s(\ the LIA gt'IH'S had all t'ffN',L as gl'ent
us lhe ('olnbill('ti (lfI'cets of the (,hrt'e oLhel' puil's of g(lllt'S,
T
('
•
11
GENETIC ANALYSIS OF TOMATO CROSSES PERIOD FnO~1 SEEDING TO FIRST FnUIT RIPE AND
•
•
•
ITs
COMPONENT CHARACTERS
)IAGNITUDE OF CHARACTER DIFFERENCES AND DOMINANCE
For period from seeding to first fruit ripe Itnd its tllt'eo component
chanlcters, the mugnitude of the chltl'l~cter differences among popula­
tions can be derived from the values in table 5, In comparison with
PondCl'OSIL, Pot'tOl' averaged 12,1 days less in period from seeding to
first bloom, 30,6 days less in period from first bloom to first fruit set,
and 14.4 days less in period from first fmit set to first fruit ripe, or
57.1 days l('ss ill period from seeding to first fruit ripe,
The rllCalls of table 5 provide information on phenotypic domin.ance,
'l'he differences between the means of the first five j)opplations for
pel'iod from seeding to first bloom are not statistically signHi.cuut
when considered collectively j this constitutes rather convincing evi­
dence thnt phenotypic domirlltuce of a shorter period WitS complete,
11'01' period from first bloom to iirst fruit set, the difference between
the ml'nns of Portcl' and BI to Porter is 1.1 days, as compared with a
30,(j-dl~Y din'crence between the menns of Porter and Ponderosa,
'rhCSQ ligures, togelhcl' with those of the same table showing that the
Il1csm or POI'lel' anti th(\ mean of the Fl do not differ significantly, are
cOllvincing evidence thnt phenotypic dominance for period from first
bloom to first fruit set was ttt lenst nlmost, complete, For period
from first fruit set to fiest fwit ripe the menns of Porlor, BI to Porter,
nn.d the 11'1 do not difrer significantly, Agnin." phenotypic dominance
wns ulmost, if not. ('ntil'ely, ('omplete, Since the componen.t chnracters
of pm'iod from seeding to fil'st Il'uit ripe wcre nt least almost completely
domillnnt pill'llOtypiclllly, it Wlls to be expC'cted that this character,
nlso, would show nlmost complete, if not complete, phenotypic domi­
1lI11l('C, EXllmination of the means of Porter, Bl to Poder, the Fit
flnd PonderOS!1 r('\'Nll stich to be the CflSe, Although the difference
of .1.:3 tlilYS belwl'('n lIw meltn of Porter an.d thnt. of the HI to Porter
is sUttistic'nHy signifiellllt, it is smllil in comparison with the difl'Cl't'nce
lwl\\+('('n the l1H'llns of Porter und PonderOsft, 57,1 dilYS, 'fhl'sC YI1lucs
al'(.' in ngr('('ml'lll with those rl'porkd pr('viollsly (14, 17, 20) for a
numbt'l' of hybJ'ids it\\'oh'ing severn I VIll'ictil's of tomnto, Hence,
plH'll.otypil' domilUHI('(' of It shorter pl'rioci fl'om seeding to fir'st fruit
rip!' SPl'll1S to I)p Ute l'ull' rl1l1\('t' thun Lhl' exct'plioll in tomMo hybt'ids,
Thl' n1pltns Ilnd YIU'iitnc('s gin'll in lItblt' 5 provide some informn,Lion
on gl'nic domin/lIH'C (inll'llullt'lic int(,l'llctions) (18), Some genes
tenrling to prodUCt' [t ('t'l'luin cllltl'llctCl' may show intc1'Illlcli(! lind intra­
nlll'lie inlt'l'aetiolls in til(' 111nnnl'r dl'scribl'd by Jones (9) 01' sho\\' intl'lL­
filll'lie inll'l'lH'liolls in the manner descl'ibNI by Enst (2) j othel' genes
tending to produce tIl{' snrne e1l1u'uctN' mn)' be partially recl'ssiYo (1(j)
01' mlly sho\\' nO dorninnncc, pn.rLi~ll dominnnce, Ol' compll'lc domi­
nftnc('; nnd yet all mny intC'I'Hct to giV'l' eomplctl', or TH'ndy eompJete,
phenotypic domillllll(,C nnd in some ('USl'S helc'l'osis, If genic domi­
Il(Ul('P wert' int'olllpletl' Itnd both pn!'l'nts enl'l'i('d nL lellst some pll1'­
tinll\' l'C'('('ssin' gPllt' puil's, the O'l'MS invoh'N\ would pt'oduce pheno­
typic segl'egntes in the HI to P~'t(,l'i find ('\'Pl1 though the mllgllitudo
of lhl' m('uns obUlinNI would bl' due to int0l'Il11l'lic intl'rlldion. of the
gl'IlI'S, tll{' gC'llctic ynl'illllCl' of the B\ to pOt'trr would be significitut,
t.:)
5.-j\[eans and their standard deviations, variances, and conde/lsed frequency distributions (expressed in. percentage of population) for
period from seeding to first fruit ripe and its :3 component characters
[Symbols: X; m~an; Ii, stan.iard dC\'ialion oC the mean; {T•• en\'ironmental \'arianee; l't, genetic \"ariancej
TABLE
X±8,
Porter.......................
III to I'orter.................
F I . . . . . . . . . . . . . . . . . . . . . . . . . ..
F,..... '0"
..................
III to Ponderosa.............
Ponderosa•••••••••••••••••••
P~riod
Period from seeding to first bloom
DaV$
1"",
1',.
Dav.
0.9:£:02ii'
8 O± .If.l
-0. ZH
1....... ..."~ __
I'
26, 0!l9
25. 194
r.........
Vt
IT.
X±Si
fQ~3I,··Da.vl...
JlO.fi±LlHI
60, 78.
Jl3,/l±l.OO9
110. 7±1. 0-12
41. 771
JlO. 3±1. 0.18 i 35,'f.o
11!.9±l.Of>31 4S OOS
12'2. 7±1. 155
129.478
Cram first bloom to first
fruit set
7~O±. ~321
12.5± .847
2O,4±.700
37~5±1.821
DuVI
Dav,
8348 .•••••.•••
19.005
0.G.32
16,[,73 ...... '...
57,3:l6
!!G. 804
124.628
53.5!13
270.293
I
Period Cram secding to 1lrst
bloom
104 days
j:.~~~~~~~~=::==:::=:::=====:::==::=::::=
F .........................................
BI to Ponderosa..........................
Ponderosa................................
107-143
days
116-164
duys
Period Crom first bloom to
1lrst Cruit set
9-30
6 days
days
33-102
days
I
1'.
Period from seeding to first frult
ripe
30,4::!;c .389
31.3± .452
32,2± .904
36.5±1.353
44.6±2.356
I
23.411
2.474
22 nos ..........
32 328
!!G 881
83.311. 29.214
377.354 ..........
45-57
days
97.4
99.6
100.0
9S.0
97.2
995
0
.2
0
.7
2.1
9.5
73.0
63.1
67.4
43.6
19.4
4.3
I
I
27.0
36.9
32.6
51.8
53.S
38.0
0
0
0
4.6
21.8
57.7
100.0
99.S
98.3
94.3
81.S
52.4
Jr.
Vt
E
DaV'
DaV'
Dav.
Z
147.7±0.993
152. 0±1. 087
149,6±1.886
155. 0±1. 209
168,8±1.576
20-1.8±2.5OO
00-111
days
146 days
0
.2
1.7
4.2
13.4
28.3
0
0
0
1.5
U/
19.3
70.0
51.1
68.2
44.7
11.1
0
149-170
days
~
?l
173-188
days
191-242
duys
.---.--Percent I Percent Percent
30.0
44.0
27.5
40.5
44.1
4.1
8
44.439 ••••••••
74.722.
10.47i <0
66.119 .......... <0
92.107
66. S63 00
172.077
65.039 330.756 I'crlod Crom seeding to first Crull tipo
I---I---I---I---I---I---I---!---I
Percent Pacent Percent Percent Percent Perccnt Percent Percent Percent Pa-unl
2.6
.2
0
1.3
.7
0
X:i:,;
1
Ferlod Crom first fruit set to
first Cruit ripe
42 days
~
\:!j
~
Vt
Dav.!~
Dav,
30. 2±0. 521
29.624 .........
Condensed (rC(IUenc), distributions
I'opulution
a
Period from first fruit set to first
Crult ripe
1"±8;
a~
Z
....
:\Ieans, stand'lrd deviations. !lnd mri:mctlS
Population
,.::
~
0
4.9
{.3
13.0
35.2
13.0
ot?'j
"C
:.=
~
>
o
::d
0
()
0
0
C1
1.S t"
9.6 1-3
82.9
~
I:!l
l1'he 3·day intermls in which the data were recorded have been c<,,,dcnsed into the classes shown by the colunm subheadings.
•
GENETIC A...'lfALYSIS OF
TO~IATO
OROSSES 13
In case of complete
•
01' nearly complete genic dominance, the genetic variance of the B\ to Porter would fluctuate about 0, would not be
statistically signi1-icant, llnd ill most cases would be small in comparison
with the geuet.ic variunces of the F2 and the BJ to POXldcrosa. 'l'he
genetic. YUl'in,necs of the BI to Porter, the F 2 , and the B t to Ponderosa
for period from seeding to first bloom ure those expected OIl the bnsis
of cOIllplete genic dominance, For period from first bloom to first
fruit set, period hom first fruit set to first fl'uit ripe, and pcdod from
seeding to first fruit ripe the genetic val'iances of these three popula­
tions IU'C those expccted OIl the basis of complete or nearly complete.
gcnic dominanco,
NO~lBEIl
•
The fiuding that phenotypic dominnnce wns completo, 01' nearly so,
and tho means, val'iances, and condensed frcquency distl'ibutions,
collccti vely I pI'ovido information concel'lling the llUlll,ber of major gono
pnirs diflm'l\lltinting period [!'Om seeding to first fl'uit l'ipe a,nd its
compommt duu'neLeI'S, In annlyzillg these ynlues, it is nccessnl'Y to
I'ollwmbel' thlLt we Itre dNlling with those gencs having major effects.
'l'his is brought out UH)rc clcil.l'ly as the discussion procceds. In case
of complet(l 01' 1\('I\l'ly complete plU:'llOtypic nnd genie dominance,
scgt'('gntion would be disecl'niblp only in tIl('. F2 and the BI to
})oudcI'osa, Only the I'ecessivt' gencs of the majol' geno pah's
involved would tend to increllse the m('uns of theRe two popuhtiiollS
appreciflbly,
l'~mlOD
FROM SEJi:DINO TO "IR8T nLOOM
The fnet thnt the means of the F2 find the BI to Pondel'osa for
p('l'iod fl'om sN'<iing to first bloom IU'(' not significantly difl'Cl'el1,1i from
those of the PI mul Porter iudieutes that a numbm' of genes woro
iuvolYNt in difl'l'I'cn.UnJing this cllll1'netcl', As shown previously, the
g('IU'S tending to product; a ShOl'tN' period wCI'e n1most if noli com­
plelely dominan.t; nne! these gC'l1l'S WC1'e epistfitic to Hle nonnJle1ic
t'C'('{'ssiv(' all'eeting the StllllC' chtll'neLot', 'rhe dati~ al'e examincd to
sep if [hpy lit these. premises.
Thu thl'()I'C'.ticnl IllNU\S [mel ! hcol'('[i('111 perccntugC's of individuals
in lhe third cn,tl'gol'y of thC' condensed fl'OqUQHCY distributions (tnble
5) nrc gi\'en in table G, On thC' b[\sis of the gpnetic hypothcsis nd­
vlttHwd nnd of n. olw-fuctor-pnir dif}'C'!'('!l(,(" it would be ('xpeclcd that
0,75 of thC'[i'!I population wou1d hI' homozy~ous 01' hrtl'l'ozygolls dom\­
nauls nnd 0,25 of lll(, :F2 populttlion would he l'e('C'ssiYe8, Thon, tho
th('ol'el.icnl m('[llt fOl' lh(' F~ would be etlleulttll'd by use of the formula
(15 1)(0,7;,») (P2) (0,25), .in whiel\ P L is thr l1lNUl of the dominant
pt1l'C'nt Hm\ P2 is the nieiln of the r('(~l'ssiYc parent, It' it is kept in
mind thn.t thl' frnetionn,l pnlts ot' lil(' 1'OI'lI1Ull1- Vltl'y !lecol'ding io the
nllmbcl' of gC'IW pairs inYolyC'd and tltC' g('!lC'I'nlion lIn(/('1' eonsiderntion,
lit" fOl'mulHs for culeulnting 1.11(. Oth('I' tlll'ol'f'tir'ni JlINLllS nrc l'enrlily
(\('I'ind. \Y'ltl'll I. 11(1s(' thl'on'Lieul l11('n115 nre ('omIHtl'ed with l he cor­
l'l'sponding obla.ilH'd m~nns (tnbh' 6), it if', fippn.l'Pllt thut tho best fit
is obtnitlN\ fl'om el\{('ulntions bnsec\ on t\w hypothrsis that tho p!lrents
W01'e difl'l'l'('lltitltrd by thl'Cl' major g('flO pairs,
+
•
Ol' MAJOR GENE P.UltS DIFFEltEN'tIATING PARENTS
14
TECHNICAL BULLETIN 998, U. S. DEPT. OF AGRICULTURE
T,\BLE 6.-TMo7'etical values for period from seeding 10 first bloom 0/ individual!
tn 146- 10 164-day class (third category of condensed frequency distribution,
table 5)
.
[Calculations based on hypothesis that indicated number of gene pairs differentiate the parents and that
genes for earliness arc compltltely dominant (both phenotypically and genically) aud epistatic to reces­
sives affecting this character]
Mean for--
•
Individuals In-
Number of gene pairs
F2
Hypothetical:
1.................... _ •••••••••••••••••••••
2••••••••••••.••••••••••••••••••••••••••••••
3...........................................
Actual................................, ••••••••
Dag8
113.6
111.4
110.8
110; ,1:1::1. 038
BI to Pon·
derosa
Daus
1l0.7
!13.6
112.1
111.0::1:1.053
BI to Pon·
derosa
F2
Perunt
2.4
Percent
4.8
2.4
1.2
2.1
.0
.1
.7
It. remains to oe seen w hethcr the condensed frequency distributions
fit the values calculated on the basis of this hypothesis. Theoretical
percentage of the F2 population in the 146- to 1M-day dass was cal­
culated by use of the formula percentage of the F2=(F~)(P~)100, in
which F~ is the theoretical percentage, expressed as a decimal fraction,
of the recessive genotype in the F2 population and P~ is the penetrance,
expressed as a decimal fraction, of the recessive genotype for the indi­
en,ted class, obtained direetly from the table 5 value for the recessive
parent (Ponderosa). Again, the formulas for calculating the other
theoretical percentages are readily derived. By comparing the theo­
retical and obtained means in table 6, it can be seen that the best fit
is obtained from calculations based on the hypothesis that the two
parents were differentiated by three major gene pairs.
'This brings us to a consideration of the genetic variances. Theo­
retical genetic variances of the F2 and BI to Ponderosa populations
have been calculated according to the hypothesis that the parents, as
regnrds period from seeding to first bloom, were differentiated by three
gene pu;irs and thnt the genes contributed by Porter were completely
dominant nnd in addition were epistatic to the nonallelic recessives
affecting this chamcter. The procedure involved calculating theo­
retical populations. According to the genetic hypothesis set forth,
0.984375
•
(Pr) of the F2 population would have a mean of 110.6 days
(PI) from seeding to first bloom, and the remaining 0.015625
(p~)
would have one of 122.7 days (P2')' Since the number of individuals
(n) in the F2 was 455, the number of individuals having a theoretical
mean of 110.6 days
i48, and
(Ptn) 'would be (0.984375)' (455), which equals
the number having a theoretical mean of 122.7 days
(p~n)
would be (0.015625) (455), which equals 7. The theoretical genetic
variance of the F2 and that of the Bl to Ponderosa population were
•
GENETIC
A...~ALYSIS
OF TOMATO CROSSES
15
calculated, by applying the standard formula, as 2.223 and 16.079
respectively. These values are considerably less than those obtained
(table 5). (When these theoretical genetic variances al'e being
interpreted, it must be kept in mind that the interactions between
~enotypcs and those between genes and environment are not included.
Sec section cntitled "Variances of Period from Seeding to First Fruit
Ripe and its Componellt Characters, and Variances of Weight per
Locule.")
The fact thu,t the theoretical genetic variances are considerably less
than the gfmeLic varinnccs obtained indicated that minor geIles were
invol ved in difl'erentiating the two parents as regards period from
seeding to first b100m. '1'he genetic variances and the eetailed fre­
quenty distributions furnish some illfol'mn,tion concerning these minor
genes. :First, as the genetic variance for the BI to Porter population
i5 not sttttistically signiiicttnt, it is ov-ieient that PortoI' contributed
w·ne:! that prohibited the cxpl'ession of these minor genes in the Bl
to Purt!'r. The rl'combination and distribution of these minor genes
.among individuals of the 1.\ and BI to Ponderosa populations were such
ns not to shift the menlls of those populations away from the mcans of
Porter and tho BI to Porter. Since these mi110r genes affected the
variallces, tllPY would be. expected to affect the frequency distributions.
If our supposition is correct, the individuals would not be so closely
grouped about the mean as the individuals of the Porter, Bl to Porter,
and 1\ populations. The detailed frequency distributions would have
mOl'C indi \'idunls in the lower twd higher valued classes. Examination
of the detailed frequency distributions revealed such to be the case.
The x 2 value for testing whetlllH' the difl'erences in the detailed
Ireq uency distributions are statistiL:tLlly significant is 157.696, which,
when tested by the formula ...j2X2- ...j2n-l (Fisher (5)), was found
to be highly significant.
In summary, the means, variances, and condensed frequency dis~
tdbutions prove tlmt thre!' major gene pairs difl'erentiated the parents
as regards period from seeding to first bloom.
•
•
PEIUOD
FRO~1
FIUST
DI~OOM
TO }<'IRST FRUIT SET
The means and their standard errors, variances, and condensed fre­
'q uency distributions for period from first bloom to first fruit set are
given in lable 5. Examination of the means and variances revealed
phenotypic dominlLnce of a shorter period. The means contribute
only suppl!'mentnTY evidence as to how many gene pairs differentiated
the two pilrents in this respect.
If phenotypic domiuance was complete, as indicated by the mcans,
then the frequency distributions for the Porter, BI to Porter, and FJ
populations would be expected not to differ materinlly. v\Then the x2
test for goodness of fit Wits applied to the numbers (not percentages),
a vaIut) of 3 .676 Wi1S obtained, which has 2 degrees of freedom, since there
t"1re no indivillunls in the third class as regards these three populiltions.
This value doC's not rench significance. Hence, the clttta al'C intcrpreted
as supporting the hypothesis that phenotypic dominance was complete,
or so nCttdy complete as to justify considering tlU"1t the Porter, BI to
POl'ti.·t·, !lnd FI popUlations haye the snme penetrallccs for all elasses
Df the condenst'd ft't!quency distributions. Examination of the fl'e­
•
16
TEUHNICAL BULLE'fIN 998, U, S, DEPT. O.F AGRICULTURE
quency distributions for period from first bloom to first {['uit set gh"cn
in table 5 shows that the percentagcs of theF2 , B, to Ponderosa, and
Pondcr'oslL populations falling into the 33- to l02-dny cluss IU'C 4.6,21.8,
ancl57.7, respectively, Thcsc yalups arc not in ng['ppm('nt with the
nssumption that Porter and Pondcl'osn, ns rcgnrds this chnrnetcr, werc
diffcrentiated by on~' 0[' two pair's of frrctOl.~. '.I'he tlworeticnl ~enotypcs based On the hypotlH'sis lhllt Po['ter and Ponc\crosn, i\'('['P dilfer­
entiated by titrcc gCllc pnirs us ['egards period from {jrst bloom to
first fruit S(lt nrc givPll in lnbk 7.
In detcrmining phenotypes lind their penctl'llllCeS, usually it is
<lasicr to Stlll't with reccssivcs. Longel' p(lriocl from first bloom to
first fruit set hns becn shoWIl to b(l ['ccessin and is the conll'llsted
character possessed by tll(' Ponderosa plIl'pnt. The penetl'll\1cc of
Ponderosa for the 33- to 102-day class is 57,7 (tnble 5). '['he PCI'­
centngp of th(' BI to Pondel'oRa populn.tion fulling into this rlnss is
21.8, This is 37.8 pel'cent of 57.7 find is the perc('ntnge of the BI to
POllclN'OSft popul!ttion expectNI to hn\Tc I;he slime nvcrngc pt'nctl'llnces
as POndeI'OSH. 'nw InsL tbl'('e ge'noty{>es of the BI to POlllit'I'osa in
table 7 com pORe :~7.5 percC'ut of the population, nud with the possible
exception of tilt' Aabbcc gC'llotype 1l1'C' thp closest gl'lleticnlly to Pon­
derosa. II' lh('sc three gellot.YP('S do 11n\Te the SlIlnc p('netr:ll1cc fOl'
the 33- to 102-du.y clnss fiS Ponderosfi, the titC'oretienl percell tugc of
thc F2 populnlion f'!tlling illto this ('1!1ss call be ('Itieulat('(l. Since both
phellotypiC' lind genie domillnn('e WP['P fonnd to bp compktc·, tlte gen­
otyp<,s of till' F2 (tnule' 7) that would iJtWP titpse ppnetl'flllc('s firc
a(LBRcc, aaHbcc, (wbbCe, aabbCc, and aczbbcc nnd are given the pheno­
'1',\ HI.I' 7.-'!'heorrli(·ol
[/('/IOI!lprs
(Iud 71hellol!lpl's (1 dijTcrl'nl pOJlI(I(ltioll.~. Imsed
on
•
•
lhe h!lpolhesis t/tat J>orll'r Illld Ponr/I'rosa arf' rlijTere'liliall'd /ly 3 /l/ojor (Ielle ]lairs
(IS rC(lards period /roll/ Jirsl /dOO/ll 10 fir.~l fruit sel
Pnrtrr (P,)
1',
A.lflHCC
Au/JI,Cc
Il, to I'ort"r
G~notYl'l'
I'hrnotyl't'
O~Il()I~'p~
AA /I nee Porll'r,
A.l/WCe
AANllec P, nUll F, illlt'r· ..1.1 HIJCc
Jllrtll:llr,
rio,
fl.lIll1rr
du,
,·I.lI!IJCC
!ln,
A.l/UICC
.·I.II'/Iec
do.
do,
.. 1.·lhIJCC
• LI/)/'('r
F"
.,"l~ tlll'i'('l
AuH/J("('
.luHf'er
PondrrOS;1 (1',)
flItfJI1CC
F.,
Ph~llolyp(l
I'orl~r.
1',IInri I'.
inlerlll~tIlal~,
do.
Fl tlnd P::!
,10,
inl('rm(ld~ll ..l .
tin.
F'l and 1'2 intt.'rUH·dhhl~ I·',. FI and p, intt.'rIuC'<iiato. do. Au'u)er
.'\u/)ll(·r,
IlllflBCC
unl1HCc
IIIIJlJ,'c I
1",11')( 'C'
IIIILJI,Cc
flU /J'J('~~ I"
1l'l'JlICCt
U"')lIC('1
aul/bee
(wJibec
U(flaJ('cl
(I111,1,Cr'
u.;,bbcc
V,.
1-'. awl 1'1 inlCI'IIICdinll'.
ilo.
Ilo.
Ilo.
PllnMroS'.1 illl('rmcdillte.
Du .
PorultlrOSH. do • 1.', nntl 1', intcrlnNliaW. do. ..til /I/)Cc
AI//lber
AIlIJ/iC('
cia IIbCc
Aa/Jbcc
FI and P! Int('rlll~dbl(l~ A I/MI Cc
1', und F, iulrrnwd !;w'. ~ t(~Jlll(·.." 1
.IIlIII'~c
.. lu{'I}CC
HI to Pon(J(lrosa
O~llot)'Jl"
I'lll'notrpo
1'1 al\ll 1,ollntrrnwdiatr • tlo. rlo •. do. do. I JdIHh'nl~l iilt (lrulPdh.t~. Fj ..\-Il.. , p~ tnu·l'm("{li:ill~. do. P(H;(tL'tosa int('rnU'tH..tH-. do. do. POtHlt·roS;.\. I Thtl ftlU art· not 'h~CJ'irniriatory as f{'g.lnlS ,1ftf('t'l;,ut\IS in IR'fWlralll1.' of thj!{ g{'nutYI'(,l (or lhp
rr0'lIl\'nCr .listrlbullor.s.
coUth~nsl·t1
•
GENETIC
,L~ALYSIS
OF TCMA'l'O CROSSES
17
typic designations Ponderosa illterme.-1illte and Pondel·osa. '.the
theoretical percentage of plants of these genotypes in. the 1!"2 popnla­
tion is 10.9375. Then, the tl\()oret~':.aJ p~'l;:cntuge for the 33- to
'r,t.
( 10. 93 ( ;:J) (:J t. ( )
6 3 S'mce p I1eno­
102-d ay c Iass autI ~.lor tlle ..li2
IS
100
,or.·.
•
typic dominance j),net, as shown latcr, genic dominance wel'e each
complete, or nettrly so, the penctrances of the POI'lel', BJ to Porter,
and F\ populations would be expected to a'yCl'lLgo about the samo for
individual classes of the cundc(lsed frequency distributions. That
such is the cnse in, respect to the data obtained has been sho\vn.
The llscl'ages are 73.0, 27.0, and 0.0, !'t'specthTely. Then, the pe1'­
centitgc of the li l to POUdC'I'OSfi popul!1tion having the pcnetrances
73.0,27.0, and 0.0, l.'cspC'cti\'l'ly, for the thece clnsscs of the condensed
freq U('Lwy distribution is 12.5 (Aa.RbCc).
This leflv{>s onl.\' the 1i\ nnd P 2 iutermedifltc plwuotype of Ule B t
to Pond (,l'osn, POPUhltlOIl fOt' which Ule pcnctrnnces h,we. not heen
determined. The penetnulce of any given phenotyp(l of any popu­
lULion fot· any desired class (,fln he determined by lise of the formula.
100x=(a.:bl+a~bd-(t3ba+ . . . +n"b,,), in which x is the percentage
(table 5) of the population in any given clnss, ai, (/2, 03, . • • an are
the pellclrnllC('S of lhe phellotype under consideration for the snme
class, nnd bl , b~, ba, ••• b" tU'C the corresponding theoreticlIl percent­
ages of plftnts of eat'h of these phenotypes in tltc population for which
the detc'rmiIlntiol1s arc being made. Sincc the 1!"1 and P 2 intcrmcdiate
phenotype occurrcd in both tho F2 and the BI to Ponderosa popula­
tion, these two populations w('I'e used to cstimate the penet"ancc of
this phe-l1otype fOI' thc 6-day clnss of the condensed frcquency dis­
tributions. The formula fOl' dctcrmining the penetmllcc of plants of
the 1"2 populfttion fOI' the 6-day class is ([JI=(100x-albl-a~b2(/3b3-CL;b;-(l6bO)-+bJl, in which tho valuc aJl corresponds to (t4, bccallse
the 1i\ and P2 intcl'll1edin.te phenotype. is the fomth phenotype listed
unclel' Hw 1~ population in table 8. Similarly, the formula fol' de­
termining the- ponet.mnccof plants of theE I to Ponderosa population is
a v= (100:c-a,ab:s-a.b,,-:-Clabo)+-bJl, in which the symbols have the con­
notations just given. 1"0(' obtnining an ttvernge of the two penctrances
the formula is v= [( IOOX-Cllbl-(ll)2-a3b3-Cl~b5-a6b6) (100x' -a'3b'3
-eL' sb l ~-lL' ob' 6)]+ (bv+b l JI), ill which bJl is the theoretical percentage of
plttnts of Lhe 1;\ and P 2 int(,l'lll£.'diate phenotype in the }1'2 population
ancl bl JI is the eOlT('sponding value -for the BI to Pondero~~. popula­
tion. In llsing this formula" the pcnetrnllces for individual classes
must be- adjusted so thllt the perccntv.ges total 100. For example,
Rinee pliLllts of the FI ancl P 2 intermediate phenotype fall into the
(1-day null 9- to 3D-day classes only, the Ponderosa intermediate and
Ponderosl1. penetral1ccs for these two clnsscs must be adjusted to total
100. This is most easily clone by expressing them as percentages of
th.:!il' sum. For the u-day dass this is [4.3-+(4.3+38.0)] ]00=10.2.
l . ikewise, the obtnined vlIllleS of the condensed fl'cquency distI·ib1.l­
tions nlust be adj us ted so that the percentage values for these two
clnsses total 100. Substituting the proper vitlues from tables 5 and
8, making the necessary adjustm.ents} and I"NllTanging so that the
plus values fn,1I together and the minus values full together, we havo
av=[(lOO)(46.i) (100)(24.8) - (73.0)(1.5625) - (73.0)(28.1250) ­
•
+
u
•
+
(73.0){12.5000) - (10.2)(9.3750) - (l0.2)(1.5G25) - (73.0)(12,5000)­
8-1:1L60 50--3
18
TECHNICAL BULLETL.~ 998, U. S. DEP'l'. OF AGRICULTURE
T .... RLE S.-Phenotypes and their penetrances for period from first bloom to first fruit
•
set, theoretical ,proportiol!s of each phe1ll1l;/lpe in the F2 andBI to Ponderosa popu­
lations, obtained and theoretical propor!,ft'rls oj these populations i,1 each class of
the cO(lde/tseci frequeTII:Y distributions (table 5), and x 2 lIalues for testing goodness
of fit i
'l'heorel}t,1! propar.
tion of ilullt'ltt'{\
population
clll&~
I II
I
________________=1 ~~~ ~1~~~2~,I(~~I~
Pcnetrnnee In Inlllc:ltcd
l'h~notypc
.
I
Porter...• ".........................................
1'. ami ". illlcrmcdh,te...•.•••• "............... ••.•.
F, .... ",'
' " .... " ......,." ................. 1
F,andP:intermetli:ltc... "." ..................... j
l'ondcroSlIlnlerlll\,dialU, ............. ," ....." •. ".'
l'ot\derosn ........" ....... · ......... · ...........
,i
prrce1It.\ Percwl
73.0
73.0
<:I.()
2ti.51
·1.3
4.3
27.0
27.0
27.0
73.5
38.0
38.0
j'tTcctlt
Percrnl
0
0
0
0
57.7
57.7
I
1.56:!5
2S.12.10
12• .500(l
~U.87001
U.:l7.50'
1.[,02:>1
I Proportion III Indieuted l'in.'lS I
-;:IaYS• II dnrs
9-30 I 3:1.102)
days
PtrCf,nt
0
0
12.5 .50.0 25.0 12.5 '
x'
I~~:[::
1- - - ; - - - -------------------------F,:
I j
I
l'opuhlt!ou
01)1:111"'\1 ................................ '..
'l'heofl'til,,1 .., _..................... .. ......\
D, to POl\d~r()s",
Obtained ............................ ..........
'!'hcorl,t!l111 .......... _••••.. '..................
_ _"
Peru,11'
43.6 i
~3." Ii
19.4·
:H.O;
1
Percellt
lil.S
00.0
5S.S I
(j-1,.1 1,'
Perctllt
~.Il}
6.3
!I
21.S -}
21.0 I
I
1.456
~ SIlS
-. !l I
+
2
(10.2')(25.0000) - (10.2) (l2.5000)] -+- (4G.S750
50,0000). Oomplc\'­
ing the ('a\('uitttions, we find the a vemge penctmncc of the F1 and
P2 intl'rmedintc phcnotyp(1 fOl' the G-dny clnss to be 2G,5, From the
fOI'e~oing examples, derivntion of the nppropI'intc formuln. and it."
apPlicntion 111'1.' app a ['(,.11 t fol' filly CI:1SS and phenotype of I1ny givcn
populntioll. This completes the infol'll1ntioll essentinl to dptcl'min­
ing the ph(,llotY[J('s, their [)('netrances into the condensed frequency
distl'ibu tions, llll' theoretical percentage of eneh phenotype in the
popull1.tioll, and the obtllined and theoretical vldlil'S fo[' the F2 and
BI to PondNosn populations wi th l'l'spe('t to number of dl1Ys from
first bloom to firsL fruit set. Thl' Yit!lleS al'(' gh'cn in table S.
'l'h~ x2 values for t('sting gooclu('ss of fit b(~Lwcen the obtained I1mi
tJU'orctiCILI valucs of the 1·\ Ilnd H\ to Pon(\rl'osll populations nrc 1.456
Ilnd 2,808, respeclh-eIy, and in both eases P>0.20 (Bl, 7). 190),
OUt' other (rst, ill\-olving 111e 01'igilll11 dn.Udol' ('neh plall~, ",us nceded.
The th('or('t ienl IllNLll of lhe 1i':/ wus clllculu.led from the gl'netic hypoth­
esis !Hh-l1l~ccd and the ditllt forthe two buckeross populutions. Below
arc giYcll thc phcl1or:)1)('s (ns showll in tltble S), the symbols for their
pel~cNllnges in the population, and the theoretical means and their
symbols.
•
SU/IIbol!M
JlerceI/IIIge - - - - - - ­
0/1'(1/)//'
III/ioll
J)IIV,'
J>h~notypt.':
Iorter. ,"' ...... , • ______ .• __ .• ____ .•.• _____ _
I~'l intermcciintc _____ "_ ..
'-'_ . ___ • ___ _
P l - " " " . , .. • . .. - • - - • • - - •. - - - . - - - . - - - - - • PI nncl p~ illtcrrncdillte
POItd('rosll intermediate" _. ____ • __ • ______ ._. ___ }
.Pon(h:rQ~a _ '"
""" _.. '" _.. _•• ,. _ • ___ •
j'llllld
"_0"
•• _
.," ••
________ ._
XI
G.!) 8.2 7. (j
]0. S
37.5
•
OE~TETlC .-L~ALYSIS
OF
TO~UTO
19
CROSSES
The mel1n (X2) of PI l1nd 1<"'1 intprmedill.ta Wl1S deteJ'InillCd 115 follows:
.As cun bp 5(,('11 from the nhoyC' tubuhl.tiol1 nnd table 7, the formuiu.
for lh(' nWJUl (:C6) of the HI to Porter is lOOX6=XIXl +X2X2 +xaxa, Sub­
stituting the nppropL'ifitC' ynIues from the abo\'(' tnbnlntioll ilnd t,n,blcs
5 und S gives (S.O){lOO)=(12.5)(6.9)+75x2+(12.5)(7.G), Ot x~=S.2
dll.Y~, The menn (X4) of the 1<\ nnd P2 intel'Lll('dinte phenolype WfiS
detennim'd similarly. TIl(' forlilultL for the I1lMll (Xi) of the ill to
l)ondt'rosn. is lOOx1=:l'3x3+l'4:r4+:l."~X5' Substituting ill this formula
the Ylllnes from the nboye tllbulntion uud titbIt's 5 nnd 8, we hnyo
(20.4)(100)=t12.5l(7.G)+50x4+(37.5)(37.5), or xl=lO.S days. Tho
formula for cltleuhtting the thpo['('ti('ltl mean tXg) of the 1i\ is 100X5=
:c\Xl+J.'2X2+J'3X3+l·4:t1+XsX5. Substituting the propl\r yullll.'s from tho
0.1)0\'(\ labulittion nnd lithIc's 5 und S gh'ps 100x8= (1..5()25)(G.D)
(28,1250)(8,2)";" (12.51 ti ,0) + (4G,SiSO) (10,81 + (i 0,03(5) C:17 .5), or xs=
12.5 dn,ys. This is lllt, ohtnin('([ f;"l('itll of the 11'2. 12,5±0.S47 days,
Sinec the YHrious lUlftlysps of diP dn,tn, support the hypothC'sis thitt
]H'riod fmlll first bloom to first fmit set WitS difrC'1't\ntin\ed by three
mil,joL" gene, pnil's, it (,I\ll justifinbly be concluded thut sueh was the
+
i;US('.
!'\mIOO
FRO~(
r'lRs'r PHt'!1'
SI~T
TO FmST Flt\:LT RIPB
TIl() ll1(1ttll:; and Uld/' s(illldnrd d('\'intiollS, vl11'inl1('es, find condensed
frpqul'I1('Y distdhution:; for ]H'riod from fi.Tst fruit S(~t to first fmit ripe
nrc' gin"/l, in [nblt' 5, A 51 lIdy tlf (lit' /l1t'1111S nnd '?l1ritUl('('s hilS reveuled
•
plil'llo\ypie dominlLl1{'p of It short PI' period.
As n'g:tl'(ls this dHU'lletrr, 19.a pl'l'('etlL of tlH' plants of POIvlerosa
ft'll into tllp Gn- lo Ill-dity ('litss of thp eond('l1s(\d fl'eq uPlley distribu­
tions find tJw prl'('rntngf's, of tJ\(' 1<'1 nnd BI to Pondrrosl~ popull1tiol1s
in tlti:; ('lnss \\'1'1'1' 1.5. find 4.8, rl.'spl'ctin'ly (tahle ::;). HrIlce, 7.S
prJ'Cl"nt of Ihl.' 1"2 population llnd 2·4.9 P(lJ"('l.'ut, of \1](' J3 1 to }>onderosa
popUlation h('\tiW(lt\ t hl' Sltllll' IlS tilp Pondpl'osn. pnrent in respect to
tJH' third {'JI):;~ of UH' cond('J)s('d fr('((lH'n(')~ distributions, This would
1n.<I i('lI tt" lhltt Pol'! ('\' !lnd P0I1(\('r05/\ \\,\"1'(' din'PI'put illted hy I,\\,o gl'ne
pail's ns l't'goal'lls ]wriml from first fruit Sl.'t to first fruit ripe. Theo­
n'lienl g<'llOtyP('S hlHwd OIL this nS:-lumplioll il1'P listed in tnhlp D. The
tl1l'Ol·pticnl nWIUl of thp .:\abb ill\d (laHb genotvj)ps of the 13~ to Pondel'­
0";11 popul/Ltiotl WitS ('il]culnlr(\ ill tlIP Siunr T11nnner ns tIll' llieoretlenl
I1W1U1:-l of lwriod fl"Om first hloom (0 first fruit set. Tlw lllC'nn for the
FI find P2 l11t('l'lll('(lintc' phc'll.otype WftS found to be :15 di1YS. SillCo
n.- 'l'hf()rflic'ol
gPlIolypt's and IJ/tcno/Yllf!t 0/ ciijJl'rclli populations, ImMel on
that Porifr /lIlt! l'oJIIlaosa lire liijrl'ft'utio/ui by .2 major gena pairs
as rcgards period from first /r'til 8l't to Jir,~t fruit ripe
T \1H,f:
UII' h'l1Jl)ilH.~i~
A;,hb
l":;~(;~fJ~'1
H, to
(;1'11,,1, ril:'
l'hl'rmtYP(1
,..1,111/1
POf!<'r
.f\.lll~
AIlRn
.. Iullb
•
l'ond:;~::~1
F,
I'U:(I'r
n"fllll.l'P<'
.I.IH/f
1'•. mt! P,lnu·nllnl!· ,t.lf./.
;\11'
,L.II,,;
lJlt.
.111 1111
}',.
.IIIFI',
_lal,11
<lall[/
1111111,
1/Il1,/,
1'1ll'!lotrpl'
I'''rlt~r.
1'1'lIlllltlhll,·rmedur~.
~'I:ltltll"illt,·rnh.. lul\'.
III to
<I('lI11t;'I'<'
AulllJ
_lu,.ll
Iii/W,
1', anll FtlUll'tllll'.liat(', I/ilb/!
Ph
1-", ,llld p, illl~n[)cdL1tO.
00.
Po •
l'oml'·flJSI.
)0',•
(/.'.)
POntl~ros"
r'/It'!I0(YPC
1-'1<11111 P!illt~rn\(',H3tC.
Do.
Ponderosa •
20
'l'ECfu~ICAL BULLETIN 998, 1:". S. DEPT. OF AGRICUL'l'URE
this lies between the mean of the Fl (3l.3 days) and that of Ponderosa
(44.6 duys) J the effects. of th..- gene pairs must have be(>n cumulative.
Since phenotypic dominance and, us shown lat(>r, genic dominance
were each complete or ncarly so, plants of the F2 populaLion possessing
the genotype ALlbb 01' (lnHB wet'e of the Fl and P 2 intprlllcdiu,tc phcno­
tY1)c. Plnnts of the AAHb and AuBB genotypes were of the 1\ and
]\ illtermNliate phenotype and had the same pcnetrullces for the
different dnsscs of the condellsed frequency distributions as Porter.
The pt'netrallccs of plants of the 11'1 and P 2 illtel'lnediale ph(>notype
CIUl be calculated by the methods nnd fOl'nlUla nll'eiltiy pl·esented.
This (Jomplet£'s the information essentinl to determining the pheno­
types, the penetl'ltnccs of tlH'SC, phenotypes into tIll' condl'nsed {re­
qlH'Il('Y distributiolls, the theorl'lietil IWI'('('lltngc of eneh phellotype
in the srg['egnJing populations, (Itt:' ohtnin.('(land throretical pCl'crnt­
nges of llic ('ondt'llsrcl (['equ(,[H'Y distributions, and the YlllidiLy of the
h.\1)Ollirsis IlS ['('ganls prriod from first fruit seL to fi[·s\, fruit ripe.
The l'csults nre giycn in table 10.
•
r.r.\Ilr.~:
lO.--Phenotypcs (I/lil their ]Jl'lIdrCII/(,('S lor period fro/ll first fruit set 10 first
fruit ripi', th('orrlir(ll proportions of C(ldt pJu.'1101Yfl<' in the I;cgregalillg 7JOpll/aliolls,
obtained LlIII/ t/z('IJrcli('al pro]Jorlioll,~ of thes(' poplll(llioll.~ ';/1 e(l(·1t cl(!s.~ of Ihe ('011­
dwsed frequency distributions (tabie 5), (luri ~x V(lllleS for Il!sling goodll/?ss of fit
--------" --------------------------------------------------­
PcnctrtluC(' In indil.'atcd clnss" :
'l'I11'oret leal proportion of
IndlcatN[ PQllui:ltlou
•
, i'roportIOIl lu lndiultl'd cluss i
t
:
~1~::-~1;'5i
POJlu[.ltlon
I'
____________________
. ____ ~
Prrc(IIl , Ptrun/
D, 10 Portl'r:
Ohhlirwd ................. .
'rtworeticaL. __............. .
F!;
0.2
1).1.3 i
4.2
5.0 W.!>:
t
Obt::.itll'd ............................ 1
!
TltcorNic;II .•_.......................
9~.S
Ob:ainl'd .... "...... "....... "'" .....
Sl.S ;
D, to 1'om]er05.1:
J
UU ~i
.{
13·1
Degrt....s of
(r('edom
x,
flO·lIt
I
days
,_ _ _ _ _ _ _._ _ _ ___
l'ercelll ;
o.}
O·
1.5 '}
1 t):
.71S
2
4.S }
.SS()
2
11.3
4.8 '
; ___
__'[_'h_eO_re_!l~_~I_1__'_-'_'_'_"_H_
.._,_._.__._.!_ _S:t9
_.c...
--!_ _ _ _ _ _ _ _ _ _ _'._ _ _ __
'l'hr X2 ,~11Illl'5 O.:3a4c, 0.718, and 0.S86 (tahlc 10) have P Yfilues bc­
twcen 0.7 and 0.,'), showing thnt the fit bcLwl'l'n thr obtllinl'd lind
throrctienl YiillleS is good. The tllPol'ctieullllrtHl of t1ir Ji'',! population
as enkulilted hy :nrbstitutiw \'itlUl'S from tables 5 and 10 nnt! thC' :Fl
and P2 Il1tl'l'lU(.(lintc llll'lln "'(;35 dIlYB) ill the formula 100x.s=:rl l +
:r.2X2+.r3:c3+J.·~:c~+X5:c1i is 33.2 dilTS, \\'lddtis not significlllltly difl'l'l'cnt
from thc obtllLlWd meall, :32.2±O.904 days. 'l'hus the l11l'ilnS, YllriItrlC'C'S, odgillld (nOll('lllssified) llldi ddulll-plllut diLlll, dC'tnilcd flW[Uency
diBtribuLi'ons l Ilnd conlicll::wd fn'quellt'y distributions confirm the
x
•
21
GENETIC k"\'ALYSIS OF TOMATO CROSSES
hypothesis that as regards period fl'Om first fruit set to first fruit rip~
Porter und Pondero~a are diffel'lmtiuted by two major gene pairs,
•
]'EJUOD FROll SEEDING TO FIRST FRUIT RIPE
The means tl,nd their standard deviations, variances, and condensed
frequency distributions for period from seeding to first fruit ripe are
given in tnhle 5, Phenotypic dominallce was complete or lletlrly so,
Sineo the pal'cnts were found to be differ('utiated by nt least three
mnjol' gene pail's us regards period (rom seeding to first bloom, by three
us r('gal'(ls period from first· bloom to first fruit set, and by t,,·o as
rogtll'(ls period fl'om first fruit set to first fruit ripe, the number of
gene pail's difi'ert'utinting POl'ter and Ponderosn in respect to period
from set'din~ to first fruit Tipe> provides SOlll(' t'vidt'uec IlS to whether
lotlil pl('iot.ropy WI1S involvpd Hnd hence wh('thcl' thl','e gene pairs
explain the l'('suits for all tlu'e(' l'ompoll('nt ('hllrllcU'rs. Of ('OUTse, if
sueh is the ense, onl' of the gem' pilir!) hud no t'n't'et on period from
first fl'uitst't t.o first fruit ripe, TIlt' dl1tU \\"('1'(' examint'd lo sec wheth('r
thl'y fit the hypothesis that the plll'ellts w('rc difrl'r('ntinted by only
three mnjor gene pnirs ns regHl'ds period from s£'('ding to first fruit
rip£'. To fndlitllt(' analysis of the ditta, the tll(~orC'tiCI1I genotypes firc­
list('d in lithI£' 11.
From table; 5 it ('fin be se(,n that the percentng('s of the F2~ BI to.
Ponderosa, find Ponderosa populntions ill the fOlU'th clnss of the con11.-TheoreHcal YCltolypcs and 1Jhe1l0typcs of differ!!lll. 1JQ]JIl/n/iolls, based 011
tlte Ity polhesis that Porter and Ponderosa arc J:1Tercllliatcd by S major ytille pairs
as rey(mls 11Criod frol/l secdillY to iirst, frllit ripe
TARLE
•
l'ort~r (I',l AAIIIlCC
11, to l'()rl~r
Oenolvpe
l'hcnolypi\
A.IUIICC l'orlcr.
AA II IlCe
1', nnd F, inlerme·
dhU!.
AAl!bCC
do,
F,
AuJlbC, G~lIotypc
AAlIl'Ca
AAIWee
AAlme,
AAl'bCc
,do. A.IUbCC
AullPee
AaBI'er
!Iu. do, AARbCc
AaJl"CC
AaUbC,
do. F,. AA flbee
A.'I/JI.CC
,,\. tI~,('c
A.IIJ1iec
AalWee
• lqIH'Cc
.Iu l/ I're
Aa}II,(:('
AaPhC,
.Ial'bce
• laMeC
•1/;''/'('<
•JaMer
aalWe('
aaBlier
aallB~c
0" 11!.('(.'
1IIlBt,Cc:
•
POlUierosn (I'll
lra/Jbc,
TI, to l'onlirrosn
}',
u<,lJhre
url'II.('C
IIQIi/I!',
tlil~J (C
GenolYII(}
J'hclloIYJl6
..taBbe,
F,.
AaB/ice
F, lIlUl 1', intermedi·
nte•
PhenotYP6
Porter.
]', and }', intemlc·
dint",
.} ', lind 1', interme·
(!fait'.
I'. find F, Intcrme·
dIM".
AubbCc
Do.
Aubbcc
Do.
1", IIntl I? lnteflllC-
au l!bcc
aaPb(,e
do.
,[j:lt~.
do.
Ilo.
l'oUlleroS3,
do.
tlo.
I', amI F.
t1bl~.
Do.
Do.
intermc­
do • r', and p, int~rnlC'
(linte.
PI ;uu! Pi intcrnu!..
dUlle.
r'" mul I', intcrme'
F,
dh'tv•
do•
do •
do,
do.
do.
do,
do,
do,
dn.
do.
rln.
)'ol1dero!'ll.
22
'fECFL"'ICAL BULLE'l'IN 99S) U. S. DEP'l'. OF AGRICUL'l'UHE
densed freq neneY' distributions are 1.8, 9.6, and 82.9, respectively.
On t.he basis of three gene pairs diffeTentiating Porter and PonciC'rosa
and the assumption thllt the plnnts repl'escllted by the first two of these
percentages hud the triple rec~'ssive genotype, the expected pel'centngf's
of the F2 and BI to Ponderosa popu1ations in thig clll.ss.urc 1.3 und 10.4.
The x2 values fer testing goodness of fit are 0.29U and 0.206, neitlH'l' of
which has fl, P value less than 0.05. So far, the data support the hy­
pothesis of three pn.irs lIf genes differentiating the parents. From tflO
genotype.. . "sted under BI to Ponderosa, it is appurent that the .i1aBb(,c
<'enotype has the sllme phenotype and peneU'llllreS as the Fl' Simi­
farly, th(l aabbcc genotype hilS the SI1.I11(' ph(lnotY])(l HncI pellI'U'lUlt'eS us
Ponderosa. The six oUH'r g(,llotypcs of the HI to Pond ('l'osa populnlion
11TlI cl(lsignlttcd FI lWei 1'2 inl(,l'l11('(\inJp.
Th(' V(,lletl'iUu'('S of I.he li\
and 1'2 intel'll1Nliate ph('llotyp~ fOL' the foul' ('lass('s of the fl'eql,l('ncy
distributioll, eal('ulai('(l hy tlPplying Pl'o('('(ltl!'es n.nc\ forlllulns nlt'('udy
giv('n to the ill to l)ondl'rosa population, nl'l' PI'('s(lIlted in tahle 12,
Turning to It COI1Si<il'I'lltiOtl of thl' gl'IlOtyp('S of the BI to l>ort(lI'1isted
in table Il, w(' see thnt plimts of Ih(' ~.L1Rn('eg(,1l0Iyp(' had the sn.Jlle
plH'not~rpe nnd P(llwtl'um'('s ns plnnts of l>ortl'1' und thnt; plnnls of the
AnBb('r g<'llOlypl' hurl th(' snn1(' ph(\l1olypp nnd lWtwtrnll('l'S. ns the li'l
plnnts. Th(' phpl10typir t\('signnlion giYl'n to plnnts hnying uny of the
si.~ otllPr g('nolyp('s of Ill(' HI to 'POl'IC'[' population \\'I1S PI und ]"1 inter­
l1l('(liate. Th(' ]H'IH'tl'n.ll('('s of plnnts of this plH'IlOtY]J(' ,'-('I'r e111rlllntNI
from Uw 13 1 to POl't('L' dn.ta in I hc' uSlll11 mnlln('l' nnd U1'(, gin'll in lable
12, Sinc(, ph NI.Otypi(' uncI, ns shown lnt(ll', gl'nie dOlllinnnrr \\-('re hoth
('ompll't(' 01' l1('al'ly so, tlH' plll'llotn)('S fOl' the Fz POPUI!11ion \\-('1'0 ns
list pc\ in tn,hlp 11.
X('x:t (,Ollll'S 111(' test of till' Ylllillity of thl' hypothesis. Sin('1' the BI
to T)ort('r po])ulntioll was llsed to ('stimnt(' lh(' 1)('IWtl'ill1('('S of the PI
and FI intC'I'llll'dintl' phpnotyp(' nnd tllP B t 10 Pon<iN'osn population to
estimntc tho pruelntnc(ls of the PI find P 2 intl'l'll1ediatc phenotype
•
•
TARt.E 12•• ~Phrllot!fpes Dlld
fheir pCMirfJ1ll'es for pl?tiod from serdiJl(I 10 jirSlfruit
riw, theoretic(ll proportion of ('lll:h flh(,llot!lJl~ in th!! F'2 population. ob/allled (llld
Ihcorrlil'ltl pl'Oporliolls of /lwl population in ('(It'll class o/the ('olltil.'llsed jr!!qllellcy
cli.~lrill1llioll ilalile Ii), ami x 2 rulue for lcsli1ty {l(/OdIlCSIi of }it
''''II
l")fI"r
I'. :Iml
1<', 14[H70
Ibn
1731'>5' 191!N2
Ilays
.hys
Parrill
Percrlli
I'((U,,/
Perrent
;n n
.. [.'1
Ha days
45 I
in tl'rmedl1lt· .. i~'.:2
~',
5,0
'lwl 1': inlcrUl('tlHw.
l'flu,jtrosa 0
;~II-U
II
IJ
.;~I
!iI/
43
0
0
~;
·1
;:
~i5
·1 1
3!,t:t
1;10
()
b~.
'l'h~orN
pro·
portion of ~'z pop·
ubtlou
9
J)(\~r(l(~S
17,1·1~~ . WI 242
d:1YS , d,l~'S
Ollt~i!.~'1
Parrr,t
-tn :t
.
I:h'·orl'tl[;.ll. _.
- .... ------.-- --­
..
4) :;
Parmt
1.111
2J 1
of fn't!·
dam
3
•
GENETIC A.."f.-\.LYSIS OF TOMATO CROSSES
23
(whereas the averages of all tlu'ec segregating gcnerations were used
previously), the lesting of the validity of the hypothesis was necessarily
limited to the obtltined and theoretical percenta.ges of the }1"'2 popula­
tion, Thu anlllysis is given in table 12, The x2 \>alue, 45,258, has &
P value considerably less than 0,01. Calculated us previously and on
the basis that the 1>nronts are differentiated by tbree pail'S of genes,
the theoretical luean of the 1;\ is 160.6 dnys, which is considerably
gl'ell.ter than the oblaiue'd value, 155,O± 1.209 dnys, The hypothl"lsis
that Porler and Ponderosa, 115. reglll'ds period from seeding to first fruit
rip(', W('I.'C difr(,l"<:>ntiated by only three lllltjor gene J>nirsis not in con­
formiLy with the datil., If !lOU(' of the lllujor gCIlt) 1>nil'8 difl'el'entill.ting
the component Chal'llcL('rS cxhibit pleiotl'Opy, then th(1 pnrents, IlS re­
gards pt'riod from sel'ding to lirst [wit 1'i1)e, must huvo bccn dilTer­
entillted by at, lellst eight, major gene pairs,
I~TBnAC1'IONS
•
•
OF GENES
In studying the clltta to dl'tcrmine the nntme of the inlel'fidiolls of
the gelll'Sk Pl'l'ioti from seeding to first fruit ripe fiud its component
ChlU'llett'I'S wcre (:on:;ider('(l together.
As hilS been poinlt'd out, the cvidcll{'l' fl'om Il study of the genetic
vllrinlll'('S supports the hypothesis that the genes for a shorter period
from sc'eding to first bloom, a shortN'Pl'riod from first bloom to fu'st
fruit set, nnd n. shol'tcr period from flrst fruit set to first fruit ripe were
completely dominllnt, or nelll'ly so, 'rhe h),])otheses advllnced and
t('SlNl ns to the number of gene pities difTC'l'rlltiat iug the two parents in
l'('sp('ct to all thl'('(~ of lht'sc ('Ompollcnt ehnl'neters involy~ the assump­
tion that til(' genes tending to produce shorter pe['iods were completely
do~ni[uUl.l, or nellrly so, Since tests confirmt'cl the hypotheses, genic
dominance of those genes tending to prodlH.'e the shol'ter periods must
htwe been. eomplet<', 01' nearly so. Hence, lhe intraallelic intc['llcLions
of the g<'Il,es must lllw(' becn such that their en'eels were noL cumulative
IlS 1l1<'Il!;lul'Nl by [he end results (the chll1'Ucte['s studied), Period fl'OIll
se('dhlg to first bloom wns found to be as short for plants of the Aabbcc,
{In Hbcc, or aabbCe g('llotvpe as for pIllllts of the -tL:1BBCO gcnoLype,
Hl'll('(', one of the domilllUlt genes produced almost llS g['ellt, if not as
gl'cttt, nn ('(recl as all si" tloln.inant genes together, 'l'herefol'e, the
mtl'1'I111clic interncLions of the genes W('l'O such that the efrects of (;110
g<'IlC'S were not (:umllhltive, Period from first bloom to first fruit set
wns longer for plllntsof the. Aabbcc, a(lBbcc, Ilnd aabbCc genotypes llmn
for vlnnts of the' A(~BbCc genotype. Period fl'Omfil'st fruit set:. to fll'St
fruit ripe, likewis(\, WIlS IOllgcl' for plauts of the ..labb nn,d annb geno­
types than for plants of lh~~ .ilaRb genotype, 'l'hus the intel'l111elic
int('raNions of the genes di/l'el'cntiltting dtesc t,,'o COmpOIlC'lI!; cllllr­
ilclers W('1'(, sud\ thaL the ('ffeets of the gencs were eumlilative.
The fnets just sttlted lu'e most simply c.."plllined 011 the Ilssmnption
diM fiS l't'gm:ds genic domiuilIlcc the. genes studied were rcsponsi.ble for
the' production of substfillC(,S h!lVlllg n. th1'('shold Il.boye wInch 110
nddilionnl shol'tc'uing of period, or periods, rcsulte(L The saUle is true.
of ille .int<'mllelic intcrn<:tions of those genes difl'(,l't'ntillling period
from se('(\iug to Ill'st bloom, Th('u, as reganls period from seeding to
first bloom !lily OL\t' of the dominllnt gC'ncs wns Cllpnblc of bringing
llbouL production of [he amount of slIch n substallce uecessary for
24
TECHNICAL BULLETIN 998, U, 1::1, DEPT, OF AGRICUVrURE
maximum reaction in a given time, This is not true of the interaUelic
internctions of the genes differentiating period from first bloom to first
fruit set, 01' of those of the genes differentiating period from first fruit
set to first fruit rip,3, I\S mttXimulll reaction wus not reached until at
least one domillnnt gene of euch pail' of alleles WitS p}.'('sent, FOI' the
history of the development of the hypothesis of thl'esholds see
Goldsduuid t (7),
The l1n.ture of the interactions between genes difFerentiating
individuul component chn.rnctcrs is considered latm', in connection with
the nnnlyses of the inlerreliLtiolls of the chal'tlctcrs,
•
'VEIGJlT .I'EH ]'-'HUIT ASf) ITS Com'ONENT CUAluC1'Ens
NU~IUEn
ll,.\G:\I'rliDE
o~'
CllAHAC'1't~lt
0)0' LOCULES
DH't'EltEXCt,S AND DOllIXANCtJ
Porter plnnls I1vernged 2.1 lo(:ules per fruit nnd Ponderosa plants
10.0, or 7.!::l more (ttlbfe 13). The genetic vurinllce fOl' lhe F2 populn­
tion is grca,tcr thnn that fOl' either backcross, 11n<l tho genetic vtlritlnce
fOl' Bl to POI'lpt' is gr('tlter thltn that for Bl to PondeJ'l)sn. The menn
of the. }i\ lies somewhttt closer to the menn of Porter than to that of
Pondorosn, the mean of Bl to Porter lies somewhnt closer to tlmt of
PoriN' lImn to thnt of the F I , nnd the mean of the BI to 1'ondel'OSit lies
somewhnl elOS(\I' to thnt of the FI than to th11t of Pondel'Osa. 'rhese
findings show thnt phenotypic dominnnce was pill'! inl for fewer loculcs
and indicate lhnt genic dominanco wns parlinl nlso,
XCllDtm 01" .'IAJOll Gt"Nl~ I'AlltS 1)IF~'BHt:NTIA1'ING Tilt:
I'A1U1N'fS
Exnminntion of the frequency distributions for number of loculos
(table 13) reveals lhnt 62.8 pcrct'nt of Ponderosa plants fell into
c)nss('s having avernges of .10 or morc locult's per fruit. Of the Bl to
1'onc\prosn populntion, 19.5 percent of the plants fell into these classes.
On the bilsis of two pnrtinlly dominnnt gene pairs for fewer locules
pel' fruit Ilnd one pal'linlly dominnllt g(\ne pair for more locnles per
fruit, Itppl'Oximntely 15.7 p('l'('(\nL of the plnnls of the Bl to Ponderosa
population would be exp('(~led to fnl! inlo cinsses baving nve1'llges of
1001' llll)re locules ])('1' fmit This vnlue is not gl'eatly difl'eren!; from
the Olle obtnin('d. TIl(' dnln are nl1alyzed to determine whet.her they
conform to the hypoillesis thnt the pnrents were difl'erentinted by
thr(\(\ pnil's of genes of which two were pnrtilllly dominnnt for fewer
locul('s per fruit ami one wns pnrtinlly dominant for more locules.
To enl('ulnte til(' theol'('tieal frequellcy dist.1'ibutions it was nec('ssary
to lIn\Te nn estimnt(' of (1) the e{reels of gelle suhstitution and (2) the
stantlnrd d(lyintion of a single determillation.
'1'h(l ll1el'UlS of the pnrenlnl J ]1\, nnd hn('keross populations given in
tnhl(l 1:3 wel'c uSt'e1 to obtnin a rough ('sLimale of the effects of gene
suhstitution in the genotypes of the hackel'oss populations. Tho
difl'cl'ell('cs belwe('n Illeans. of number of .loeules pel' fruiL nrc: POl'ter
nut! 1;\, 2.4; Ii', and Pon(\(>t:Osn., 5..5; l'orter and Ponderosa, 7. !::l. '['he
Ynlul'S 2.4 tlnt! 5,51u'e 30A nnd (i!).(i ])(Ireent, resp<'etively, of 7.9. ,,'jth
tJles(\ l)er('entnge figures IlVlti1nbl(\, (he dr('('t, of the substitution of IL
gl'IlC t('nding to pl'oduec morl' locules }It'l' Jl'ltit eftn be l'oughlyesti­
nmled for the Bl to Porter population. The percentage t'f1'eets aelded
•
•
•
•
•
:E
~
$
I
$
..I
c
I!j
TAIII,I~ l3.-.Means, within-plot variances,grand-total variances and standard deviations of the nonsegregating populations, and frequency
distributio.Tl8 for number of locules
Wlthln·ploL
}'ollUlation
Meau
~n
~
}'requency distrIbution by B,'crage number of locules per frulL
Vllrl·
Oranr!·
total
Oraud· stllud·
totol
ard
de·
Environ· Ocucllc variance' via·
mental
tion'
ancc
.
1
~
2
3
4
6
6
7
8
9
10
11
12
13
11
15
~
CIJ
---- ---- ---- --- ,--- ------ ------ --- --- --- ------ --------- --~
Per- Per- Per- Per- PerPer· Per- Ptr- Per· Per- Per·
Per· Pn"
Per·
Nu,,,ber Number
Po.rOOr........ " .. ~._ ••'" ... ......
JlI Lo l'orler _•••••• _•••
}.,
.........._...........
ill to l'ondcroSB •••••_••
Fl......................
J·onderoSB••••••••••••••
2.1
3.1
4.6
4.7
7.1
10..0
0.0010:1:1
.004\l87
.00II840
.008211
.011407
.013031
Number
Number Number
.... " .......... (J.O:l3i75
0.184
0.011lO36 ...... _............... "' ........... "' ..
.908
.. -_ .......... - .9116300
.026992 _........... _.... ,. ........... .,.
.00II389 ....... "' ............ .............. - ...
----_ ............
6.414375
2. 5:~1
Orlgl11l11lndlvldual'lllant data Wt're tratlsformed to logarithms. , No tmnsformatiotl of originai dato. I
ttf.1
00.6
3tl.6
.9
12.4
.2
0
UII'
3.6
32.2
16.9
20.6
2.1
0
rtf.,
0
18.1
36.6
19.6
6.5
1.1
cenl
0
10.0
30.0
20.8
21.2
2.8
cen!
0
2.2
8.6 8.8
17.8
7.11 cent
0
.6
2.G
8.4
14.5
5.0
unl
0
0
.4
4.0
10.8
10.6
u'll
0
.4
0
2.9
7.4
10.0
unl
0
0
0
1.
9.
20.
UTit
0
0
0
.4
5.6
12.2
cent
0
0
0
.2
3.0
15.6
cent
0
0
0
.2
1."
6.7
mil
0
0
0
.2
.2
2.2
ttrtt
0
0
~ 0
.2
5.6
o
0
~
n
I
CIJ
t.,;)
01
26
'l'ECHNICAL BULLE'fIN 998, U. S. DEPT. OF AGRICUL1'URE
in going from AABBcc, the genotype of Porter, to AaBbOc, the geno­
type of the F I , nre 30.4 (a) +30.4 (b) +69.6 (0), or a total of 130.4.
On the bnsis of 100 percent, a or b adds (3004+130.4) 100 01' 23.3
percent, and 0 adds (69.6+130.4) 100 or 53.4 percent. Then in
the genotypes of the BI to Porter substitution of a or b results in an
inCl'ease of 0.233 X2A or 0.56 10cuIes per fruit and substitution of
o results in an increase of 0.534Y2.4 or 1.28 locules per fruit. In
the genotypes of the BI to Ponderosa, substitution of a or b resulf:;
in a 69.6-perc<lnt gain. and substitution of 0 in a 30A-percent gain.
Therefore the diffCl'ence between plnnts of the FI V.1aBbOc) and
Ponderosa (aabbOO) genotypes is 69.6+69.6+3004 Qt. 169.6 per­
cent, a and b contribute OAI0X5.5 or 2.25Iocules, and 0 contributes
O.180X5.5 Ol' 0.99 locule.
The means of the genotypes of the backcross populations (table 14)
'were calculated from these estimatos of effects of gene substitutions.
'rhe formula y=mx+b (15) was used in estimating the grand-total
variances of genotypes of table 14. '1'he mea.Ill'; (table 13) of POl·tOl·,
Ii\, !Lnd ~?onderosa were designated XI, :/"2, and Xa and the grand-total
variances of these populativns (tn.ble 13) were designated Yl! 112, and
Y3, respectively. The value of 1n1 was obtained by use of the fOl'lllula
and is 0.400677. '1'he value of bl was obtained by usc of
1n1=Y2-'!!J,
X2-~;1
The corresponding
1Ja-Y·
values of 1n2 and b2 were obtained by use of the formulas m2=~3_X;
and b2=Y2-m2~~2' and 11,re 0.985268 and -3.438306, respectively.
The difference between 'lnl and 1n2 and the difference between bl and b2
arc too gl'cat to justify using aVerages for 'In and b. Consequelltly,
lhe values of tnt and bl were used to estimate the grand-total variances
for genotypes of B, to Porter and the values of 1n2 and b2 were used to
estimate the grn.nd-tot,nl vadances for genotypes of BJ to Ponderosa.
The grand-totnl stn.ndr..rd devintions, and hence the grand-total
variances , had to be used in estimating the frequency distributions of
the genotypes because the obtained frequency distributions of the
populations with which the theoretical frequency distributions are
compal'cd inducle difl'erellces between means of blocks, difl'erences
between plants within blocks, and, finally, difl'erences attributnblo to
interactions, which, all togethei', compose grand-total variation.
The methods and procedures used in cl\lculnting the theoretical
frequency distributions of table lt1 are the same as those used in
cnlculating the t heoreticnl frequency distributions of tn.blo 3, except
that n \'el'age nllucs of 1n and b were not used in cstimating the grnnd­
total variances. In the stub of table 14, II total" signifies nIl plants
of the indicated populn lion nnd II balance" signifies all except those of
Lhe F, and parental gcnoLypcs. A comparison between the theoretical
ft'equclley disll'ibutions (table 14) and the obtained frequency dis­
tl'ibutions (lable 13) for the backcross populations shows that there
nrc mol'(\ inclh'idllttls in somo of the lower clnsscs of the lat.t('l· than can
be explained by ('\tn.nee deviation. Also , the theoretical means for
both ba('kcl'oss popllll1.tions nrc higher than the comparable obtained
means. Howey!.'r/ the fils between the obtained frequency distri­
butions and the thcol'otieal frcquency distributions fOl' the two parental
•
the formula bl=YI-1nlxl! and is -0.807647.
•
•
•
TAnLl-~
•
•
14.-Theorelical means, {/rand-lolal variances and slandard devialions, and frequency distributions of the B1 to Porter and B1 to Ponderosa
populatior!s for number of locules
Population and
genotype
Mean
Grand·
total
Yllrianee
Grand·
total
standard
de"iation
I
o
Frequency distribution by a"crage number of locules per rrult
l'!l
3
4
9
11
12
13
14
6
5
7
s
- ____1____1_ _ _ 1_ _
_ 1_ _ _ 1_ _ _ 1_ _ _ 1_ _ _ •_ _ _ •_ _ _ _ _ _ _ _ _ _ _ _, - - - ' - - - 1 - - 1
1
1
"!O
2
15
B, to Porter:
Numbtr
Numbtr
Numw Ptrcent Percent Ptrcent Percent Percent IPerunt Ptrcmt Ptrcent Ptrunt PtrCl':11t Perullt Percent Ptrctnt Pcrct>lt
A ...IRRcc.............
2.1
0.033..5
0.184
98.5
1.5
0
0
0
0
0
0
0
0
0
0
0
0
A ...IRbcc •• _..........
2. 7
.274181
.524
35.2
58.5
6.3
0
0
0
0
0
(!
0
0
0
0
0
AaRRcc.............
2.7
.274181
.524
35.2
{,s.5
6.3
0
0
0
0
0
0
0
0
0
0
0
AaRbcc".............
3.2
.474519
.689
15.4
51.6
30.1
2.9
0
0
0
0
0
0
0
0
0
0
AARBCc•••• _•• _....
3.4
.5541"55
.745
11.3
43.9
37.9
6.7
.2
0
0
0
0
0
0
0
0
0
AABbCc.............
3.9
.754993
.869
5.4
26.9
43.2
21.2
3.2
.1
0
0
0
0
0
0
0
0
AaBBCc.............
3.9
• 754WJ
.869
5.4
26.9
43.2
21.2
3.2
.1
0
0
0
0
0
0
0
0
AaBbCc.............
4.5
.9950100
• fillS
2.3
13.6
34.1
34.1
13.62, 2
.1
0
0
0
(!
U
0"
0
.]'otal•••••••••••••• --3-.-31••••..•••••••••••·.-•• ~-3-5.-2 -25-".1---!0-.-8 -2.-5 - - . 3 - - - 0 - - 0 - - 0 - - 0 - - 0 - - 0 - - 0 - - 0
Bal"nee'.......... •••••••••• •••••••••••• ••••••••••
18.0
44.4
27.8
8.7
1.1
0
0
0
0
0
0
"0
0 -=
0
I
B, to Pondcrosa:
AaRbCc•••••••••••_.
AaBbCC.............
AabbCc••••••••. _....
aaRbCc".............
AabbCC.............
aaRbCC.............
aabbCc...............
aabbCC•••••.•••_....
4.5
5.5
6.S
6.8
7.S
7.8
9.0
10.0
.995400
1.98OGfoS
3.261516
3.261516
4.246784
4.245784
5.429106
6.414374
.998
1.407
I.S06
I.S06
2.061
2.061
2.330
2.53.~
2.3
1.7
.9
.9
.5'
.5
.3
.2
13.6
6.1
2.5
2.5
1.3
1.3
.6
.3
34.1
16.1
6.8
6.8
3.7
3.7
1.8
1.0
34.1
26.1
13.4
13.4
7.6
7.6
4.0
2.3
13.6
20.1
19.7
19.7
13.3
13.3
7.5
4.6
2.2
16.1
21.:'
21.9
17.6
17.6
lUI
7.7
.1
6.1
17.4
17.4
) i). "3
19.:i
15.6
11.7
.9
.8
3.5
2.4
9.2
13.!)
12.0
14.7
16.6
H.G
17.8"
13.4
15.8
0
1.5
10.7
10.7
lr..l
16.1
16.6
J~.3
0
.2
4.7
4.7
11.1
11.1
15.6
15.8
0
0
1.5
1.5
5.9
5.9
11.9
14.3
10.7
12.0
7.9
7.9
5.1
4.5
0
0
.5
.5
2.5
2.5
7.5
11.7
0
0
0
0
.8
.8
4.0
7.7
0
0
0
0
.3
.3
J.S
4.6
1.7
.9
.4
0
0
0
0
0
0
.9
3.8
- - - · 1 - - - - - 1 - -__ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
TotaL............
7.3 ..._ ••••••• _........
Balance'.......... .......... ••••••••••.• •••••••••.
6.5
3.2
2.21
.9
.6
.2 ~
...8
o
E
E;
... Ul
Ul
~
~
~
~
o
0
l:!;j 0
Ul Ul
fi5
, Total less plants of the F, and parental genotypes. Tbe theoretical proportion or each genotype In balanee or population is 16.lfJ67 percent.
J:.:)
-1
28
'f.ECHNICAL BULLETIN 998, U. S. DEPT. OF AGRICULTURE
genotypes and the FI genotype are good, 8S the P values of the x2
values for testing goodness of fit lie between 0.20 and 0.10, between
0.70 and 0.50, and between 0.70 and 0.50, respectively. (The geno­
types having the same theoretical frequency distributions as the
nonsegregating populations are: Porter, AABBccj F I, AaBbOcj
Ponderosa, aabbOO.) These facts indicate that the poor fit for the
backcross populations is probably due to overestimation of the
means of the genotypes. The difficulty could be duo to failure of
ml and blJ and m2 and b2 to give sufficiently accurate estimates of the
grand-total variances from which grand-total standard deviations of
0. single determination were calculated.
A method is needed whereby the frequency distributions obtained
for the segregating populations can be used to estimate the frequency
di.stributions of the genotypes. Such 0. method is developed, and the
procedures are illustrated, in connection with the analysis that
follows.
In this study the BI to Porter and Bl to Ponderosa populations were
used to estimate the frequency distributions and means of the geno­
types. All three segregating populations can be Sl} used if this is
necessary or desirable. Again, the partitioning method was used.
Frequency distributions ob:ained for Porter, FIJ and Ponderosa were
accepted as those of the genotypes AABBcc, AaBbOc, and aabbOO.
Hence, the frequency distribution given (table 14) for the balance of
each of the backcross populations does not include plants of these
three genotypes. The frequency distribution of the balance of Bl to
Porter (table 14) was obtained by multiplying each class percentage
of each genotype from AABbcc to AaBBOc, inclusive, by 0.166667
and summing the results for each class. The corresponding values for
the balance of BI to Ponderosa were obtained similarly from the per­
centages of the genotypes AaBbOO to aabbOc, inclusive. In order
to estimate these frequency distributions, it was necessary to have
obtained frequency distributions for the balance of BI to Porter and
the balance of BI to Ponderosa. These were obtained by deducting
the frequency distribution.:; of the parental and FI genotypes from the
obtained distributions of the backcross populations. The method
of procedure and results for the BI to Porter are given in table i15.
With the exception that the P 2 , not the PIJ frequency distribut on
was used, the procedure followed in calculating the obtained frequency
distribution of the Bl to Ponderosa was the same.
The theoretical proportions of the AABBcc (PI) and AaBbOc (F I)
genotypes of the BI to Porter population were taken for each class of
the frequency distributions (last two lines of table 15). The sums of
the values thus obtained were entered as the second line of table 15,
opposite the entry It AABBcc+AaBbOc." These valu.es were sub­
tracted from the values of line 1, and the remainders (with the minus
value for the It 8 locules" class eliminated by combination with a plus
value) were entered as line 3. Line 4 was obtained by cxpressing the
values of line 3 on the basis of 100 percent.
To determine the proportions that the obtained frequency-distri­
bution values are of the theoretical ones, each value in line 4 of table
15 was divided by the corresponding value of the theoretical frequency
distribution of the balance of BI to Pori,er (table 14). For example,
32.5-;-18.0= 1.805556, the value for class 2. Then the corresponding
•
•
•
29
GENETIC ANALYSTS OF TOMATO CROSSES
TABLE
•
15.-Deducl'ion of the frequency dlstnbutions of the PI and FI genotypes from
the BI to Porler frequency distribution for number of locules
Genotypo or gcnotypcs
of ill to 1'ortor popula·
tlon
·~-requcncy
2
distribution by I!.voruge number of locules pcr fruit
oj
3
5
6
8
7
Theoret·
leal
port on I
rcro.
9
------ - - ------ --- - - - - -
l'trcellt Percellt Percent Percellt Percent Percent Percell! Perun!
All genotypes •••••••••• _••
36.6
32.2
18.1
2.2
0.5
10.0
0
0••
AA RIlcc+Aul1bCc .••••••
12.2
2.4
4.4
4.5
1.1
.3
.1
0
Balance: ,
As U pllrt of ill to
Portcr•••••••••••••••
24.4
29.8
13.7
5.5
1.1
.3
.2
0
As n unIL ••••••••••••
32.5
39.7
18.3
7.3
1.5
.3
0
AAHRcc (1'1) ... __ • __.....
00.5
3.5
0
0
0
0
0
15,9
35.6
.9
2.6
.4
AaRbCc (FI) ..............
8.6
0
3g.0
••
I
percent
100.0
25.0
75.0
100.0
12.5
12.5
I ilnse Is DI to 1'orter except in line 4, in which It Is balance of BI to Porter.
, Llno 3 was ohtained by subtracting lin~ 2 from line 1 and adjusting the resulting values In the "8Iooules"
and "9 loculcs" coiumns to eliminate a minus quantity. Line 4 is valucs of line 3 expressed on basis of
100 pcrcont.
figUl'es of t,he theoretical frequency distributions of the genotypes from
AfiBbcc to AaBBOc of the BI to Porter (table 14) were multiplied
by the appropriate class proportions to obtain the frequency distri­
butions listed in table 16 opposite the portion of the stub headed
"Fil'st operation." For example, (35.2) (1.805556)=63.6.
The second opel'l1,tion involved placing the figures for each frequency
distribution given under the first operation on the basis of 100 percent.
This was done by di viding each figure by the appropriate total percent­
age given in the last column of table 16 and multiplying by 100. For
example, 63.6+120.0=53.0, the figure listed under the second opera­
tion for genotype A.fiBbcc and class 2. The new theoretical frequency
distribution for the balance of the BI to Porter population, given in
the next-to-last line of table 16, was obtained by multiplying the class
values by 0.166667 and summing for each class. The ratio of the
percentage value for each of the classes 2 to 6 of the obtained frequency
•
TABLE
lB.-Calculation oj theoretical frequency distributions of the genotypes of the
balance of the HI to Porier for number of locules
Frcquenc~'
distribution by average numbcr of looules
per fruit
Item
}'Irstopcrntion:
.'1ARbcc.............. __ •__ •
AaRRcc••••• ________• __ ._.•
Aallbcc•.•• ______ •______ • __ .
AA RBCc______•• __ .....____
AABbCc••••. __ .... ____ •• __
Aa BBCc...__ •__ • ____ ••• ____
Second opcratlon:
AAlIbcc• • __ •.. __ .• __ .... __•
AaRRce•• _____.....________
.ria Rbcc. __ • __ •__ •____• __....
AA RIlCe....__ ...........__
A ..t libCc....__ •••• __ ....... .'lull flCc .•.•.•. __ ." • __.....
Balance of population ...____ ....
•
Rntlo of obtained to theoret· iC',}II ..................... __ ...
2
3
4
Perc'll!
63.6
Percent
52.3
52.3
46.1
39.3
24.1
2t.l
Percent
4.1
4.1
19.8
24.9
28.4
28.4
Percent
0
0
2.•
5.6
17.8
17.8
Percent
0
0
0
.4
6.6
6.6
43.6
43.6
3••
3.4
20.6
27.5
32.8
32.8
20.1
0
0
2.5
6.2
20.5
20.5
8.3
0
0
0
.4
7.6
7.6
2.6
6.1.6
27.8
20.4
9.8
9.8
63.0
63.0
28.9
22.5
U.3
11.3
30.0
1. 083333
~8.0
43A
27.8
27.8
39.0
1. 017949
.910448
Total
6
.879518
Percent
120.0
120.0
00.1
00.6
86.7
86.7
100.0
100.0
100.0
100.0 100.0 100.0
100.0
.846154 I Ratio of \'nlue given In line 4 of table 15 to valuo given for same elnss ofCrequency distribution of bahmce
of HI to I'ortcr in Ulble 16.
30
'TECHNICAL BULLETIN 99S, U. S. DEPT. OF AGRICULTURE
distribution (line 4, table 15) to that in this new theoretical fl'eq\lel1cy
distribution Was calculated and appears in the last line of table 16.
]'01' example, 32.5+30.0=1.083338, the first figure in that line.
'fhe two operations given in table 16 were repeated twice. Usually
two repetitions arc sufficient to give a vel'y good fit betw{'en the ob­
titined and the theoretical frequency distributions. The theoretical
frequency distributions for the genotyp{'s of the balance of the Bl
to POl'ter are given in table 17 togethcT with those for the balaTlec of
the BI to Ponderosa and the parental l1tld FI genotypes, TluLL a good
fit was obtained by two repetitions can be seen by comparing th{'
obtained Md theoretical frequeney distributions of these two baek­
cross populations (table 18). Any degree of aCCUnlcy desil'ed can be
had by vitrying the number of repetitions when doing the clllculntions
ptLrtitioning thc backcrosse::j into their component genotyp('s,
The means of the genotypes of table 17 other than A.AbbCc and
the parental and FI genotypes were estimated from the frequeney
distributions by the standard methods, The 27 genotyt)('s of the
F2 population have only 12 different meal1\') and in this respect aro
l'('pl'('sented by Lhe 12 gonotypes given in table 17. The 8 genotypes
of the Bl to Porter have 6 different means, and the same is true of the
R g('notyprs of the Bl to Ponderosa, The two backcross populations
hn,,"c only 1 mean in common, that of the Ifl genotype,
To illustmte the method of detel'lnining what genotypes lllwo the
f·.),Il1C means, the gl'OUp reprcscntcd by AaBbCc is discussed, The other
genotypes of this group al'e AABbCO, AaDBOO, Aabbcc, Itne! (taBbee,
Undel' the hypothesis advanced, the genes tending to produce mOloe
looules pN' fruit have equal effccts; A find Bare paL'lially dominant
fot' fcwer locul('s pel' fruit i and 0 is partially dominant for moro
locules p('r fmit. '1'hon, a substituted in AA to give Aa, b substi­
tuted in BB to give Bb, and 0 substitut('cl in Cc to give CO all hn,ve
('((un,] drects. Likcwis(', a substituted in A(~ to give aa, b substituted
in Hb to give bb, and 0 substituted in ec to give Cc have equal effects,
It follows thn,t aa, bb, and 00 hn,ye equal effects in inCl'on,sing numb('l'
of lo('ules Ot', to put it another wn,y, that .llA, BB, and ec have ('qun.l
cfl't'C'ts in c\('cl'easing number of locules, AaHbCc ane! AAJ1bGO have
1he' samc men,ns, b('cituse 0 added to Cc has tho same efl'ect as (~ added
to ALl, and A added to Aa has the same efrect in deet'casing llllmbC'I'
of locules as c added to 00, Substitution of A for c and C for a gh"es
..:1r.Llib Oc, the li'l genoLyp(', which of courso has the same meall as the
FI populn,tion, 4..5 loculcs per fruit, Identical Tcn.soning shows that
.flaH11 CO, also, has It nlC'n,n of 4.5 locules, Aabbec alld AAHbOO
have lhe sn.m(' mcan, beeaus(' the effects of Aa and Bb am tho sa,mc~
as are the elTc'cts of bb and CC, and those of cc and AA. Substitution
in th(' Aabbcc g('notype of thosc g('ne pairs having the same cffccts
gin's LlclHbC'o. Icl('ntieal rcasoning shows that the aaBbec and
AL1RbC'C genotypes haye the samo mean. 'rho 11 other gl'Oups of
genotypC's ha,-ing the same mC'ans wel'C determined in th(' same
tnUllll('I' and likewise tue repI'cs('n ted by only 1 g(,l1otype in tablc 17,
'I'll(' only gl'nolypps whose freq ucney dislri bu Lions and, hene(', means
""eL'C not dNpI'minrd by partitioning the frequeney disLributiolls of
tbe 13 1 populations into lhos(' of the compon('nt g('not.vpcs n.re AAbbC'c
!tnd (LaBRC'e. The means of thesc genotypes, whieh arc identical,
•
•
•
•
'l'A II I.E ]
•
•
7.-E,~li1'lUtcd tbeoretical lIIcallS a1ll1 frequency distributi01lS of the gCIIO/YIJCS of the blllllnce of BI to Porter, the 1<'2, and the balance of BI
to POllder(!SIl for 1I1ullber of lucllies IIna pro7Jorliolls of BI lind F: populations tha/. are of individual genotypes
]~n'(IUClWY
Oenotypo or populalion
1 Mean 1--;;---\
3
\
4
j'
5
-1-­
I'roportiotl 01-
dlslrlbutlon by Il\'cruge numbcr 01 loculi,,; per lrult
6 --, .. 7_1 __8_1 __9_1_1_0_1_1_1_1-=-.1-_13_1
H
15
1 II,
--------/---1---------AAlmce
A.-llJb.:c'
AuiJlire ' .
... •••••••.•
""""'U"'"
AAIlHCc ,...................
AA IlIiCe , .................. .
AaBbCe , ....................
AAI,IiCr' ...... "..
AulibCC' .....
AubbCc'
. .... ..
.•.•.•
............
Aa/!uCC' .
flUIJl,C}C' .
~ .................... ",
aobliCC' .......... ., .......
Jl, to I'ortcr ...................
F.. .....
................
H, to I'o'uleros'l.. ............ .
l' •
PucUlI
Numlier Porce,1I Percmt Percmt Perunl Ptrunt Ptrcrnt Perunt Percrnl Ptrcent Percrnl PtrcrnJ Percrnt Ptrcent Ptrcrnl Ptrcrnt
1.5625
12.5
(I
1I
o
o
1I
o
o
o
()
o
o
o
uQ.5
:1.5
~.IO
0.2500
2.~.0
o
o
o
., 4R
()
o
0
o
o
o
o
2.0
(J
55.1
41.9
6.2500
12.5
o
(1
o
o
o
1I
o
o
o
18.0
2.1
o
:1I.6
4S 4
~:ui
:1. 121iO
12.5
o
o
o
o
0
o
o
o
o
24. Ii
5.3
.:1
2.~.1
H.8
3.11
17.1875
25.0
o
o
(I
0
o
o
o
6.5
o
o
:n.1
18 [)
13.·j
:10.5
3.74
25.0000
12.
6
o
o
o
o
0
o
o
2.6
.4
8.6
35.6
36,0
4. :;0
.0
15.0
6.2[1IJ()
()
lJ
o
,2
(I
0
1.3
15.6
5.7
2tl. I
Hi. II
2ti. 7
5.46
1.7
0.2
0.2500
o
o
o '''iffi" 17.1875
o
0
.2
.9
l4.n
4.2
5,'0
-la.n :10.1
.2
.3
5.UO
25.0
o
o
o
6,9
4.9
1.7
.2
1:1.1
24.0
21.4
2.7
24.:1
.1
.1
lI.ll7
6.:U.oo
,I
25.0
o
0.8
.8
.3
11.2
12.:1
15.6
18.6
17.8
1.0
H.8
7.Lf;
.1
.1
3.12(10
12.f1
.3
16.1
2,6
1.4
.7 19.0
la.o
12.8
o
(J
1a.8
11.1
.8
8.5
8.55
I. 562.~
12.6
5.6
2.2
tl.7
12.2
15.U
10.5
10.0
20.5
o
()
5.0
1.1
2.8
7.8
Ill. 00
o
o
o
0
o
o
II .1
2.7
.3
:10.4
:12.2
18.:1
10.0
:l.la
.1
.1
1.4
.4
.2
2.5
2.6
7.0
4.5
1S.:1
2'l.3
12.11
16.7
10.4
4.07
.7
.4
5.5
2.5
1.1
9.3
10.8
7.5
17.8
14.5
.2
2.1
6.5
21.1
7.UI
Pet'S"1l1 in Il, to Porter popuilltion. 'J'rC$Cnl In H, to Ponderosa IIOPullltion •
• 'l'h,\ tiu.'oreticlIl Irequenc)' d Slributiou lur tbls geuotype was calculated In the slime IIIllllller n.~ those 01 tablo 3. Tho standard deviation lor this genotype Is 1.393.
I
1
~
~
g
~
~
S
~
~
~
o
(')
=
g
~ rJl
~
.....
~
;3
TAnLE
IS.-Theoretical and obtained frequency di8triblllions, X % values for testing goodness of
number of locules
fit, degrees of freedom, and values of P for
I x,
Frequency distribution by average lIumber oC looules per Cruil
I'Ollulution
2
3
Per·
Perunt
4
5
Per·
Per-
1\
i
S
U
10
11
12
13
H
15
Ptr-
P.runl
Per-
Perunl
P.r·
Ctn!
Per­
unl
0
0
0
0
0
0
0
0
0
0
cent
0
0
Ctll/
0
Percenl
Per..
UIII
Ptr·
cwl
Per·
unl
0
0
0
0
} 2.32i
0
0
0
0
0
0
0
0
I
Degrees
cree':fom
I
til
P lies
betWt'eIl­
-- --- --- --- --- --- --- --- --- --- --- --- --- --- --.Porter:
Obluined _•••• ,w",.w __ ._ ••••••••••••
'J'/!Coretical ••••••• _. _"'" ..........
Dnlnnce oC n I to Porter; •
Obtained ............................
Tbeoretical ••••••••••••••• _•••••.••••
F,:
],,:
Obtnined ........... _................
·)'hcoretical ........ _" ••.••••••• _•••.
Obtllined...........
~J·heorctJcaJ ••• __ .<
ow • • : : : : : : : : : : : : : : :
Hulllnce oC n , to Ponderosu: ,
Obtnilled .........__.................
Theoretical..........................
Ponderosa:
Obtained............................
~·beorctiCIII ..........................
<wi
00.5
(.n!
0
0
ctf.1
0
0
0
0
0
0
0
0
0
0
}.... _.. ,........ ,......•....... f1
0
0
0
0
0
0
0
0
0
0
0
0
} :1.352
I
4
I O.iO IIl1d 0.50.
!'J 0
0
0
0
0
0
0
0
} S.888
I
8
I 0.50 nlld 0.30.
l"J
0
8.8
8.U
C,.6
6, i
0
0
0
0
0
0
0
0
}_ ...... ,........ ,..............
20.5
15.8
12.2
14.3
15.6
11.7
6.7
7.7
2.2
4.6
[,.6
3.8 } 7.789
39.7
30.7
IS.3
18.4
7.3
7.4
2.2
2.2
0
16.S
15.9
:15.6
34.1
36.0
34.1
S.c,
13.6
:1.0
2.3
0
0
0
(l
0
12.4
10.4
206
16. i
10.6
18.:1
8.8
12.11
8.4
i.D
4.0
-4.5
2.0
2.6
2.6
4.7
(I
Z.!.:i
0
0
0
0
2.8
2.8
21.11
21.7
21.1
21.°
18.0
18.0
12.5
12.6
8.3
8.:1
0
0
0
0
0
~.9
i.8
4.6
5.0
i.7
10.•~
11.7
10,0
14.3
.I',
, 'rotal popnilltionlcss plants oC the p, Bnd
genotYl)('"~.
"l'otnl populalionlcss plants of the P,undF. gcnotrll~s.
1
=
=
0
0
32.5
:12.:1
3.8
tol
~
Z
0
D8.5
0
~
0
0
3.5
1.5
~1().8
~
~
I
1
I 0.20 and 0.10
~
\::j
I
10
I 0.70 und 0.50
~
~
>
o
:0
~
d
:0
l":l
GENETIC
A...~ALYSIS
33
OF TOMATO CROSSES
were estimated as follows: In certain combinn,tions aa-Aa equals
bb-Bb equals Cc-cc. These combinations and differences are:
•
aa-~Ia
bb-Bb
Cc-cc
nHcc
Bbcc
bbCe
bbcc
",4Acc
..'lace
aaCe
aace
AARb
AaBb
Clabl,
ClCIBb
Dijftrtllce.
1. 26
1. 51)
1. 88
2. 17
The difrercnce AAbbCc-L1.tlBbCc approximates the average of the
above difret·cnces, which is 1.72. The estimaled. menu of .f1.tlbbGc·
is 1.72+3.74. (menu of L1.tlBbC'c), or 5.46. 'l~he frequeney distribu-·
tion of Lhe AAbbCc nnd aaBBCc genotypes was enicultttcd from thisc
mQiLll and til(' sLnndnrd devin,Lion of a single dptenninaLion givell in
fOCltnole 3, lable 17, lnthe same mltnner as tite frequency distributions
of the genotypes given in lablC' 3.
'I'his (!omplC'tes the esLinH\'lion of the theort'tiral frequeney distri­
butions n.nel m('lUlS of all geIlotypes of the segregating populations.
The values Im~ given in table 17. The theoretical means nud fre­
quency distributions of the three segregating populations were calcu­
lIlted in the sn.me nUlt1ner as those in table 3. A ('omparison of the
melUlS of the sl'gl·cgating POpulMions gin~n in tables 13 and 17 re­
veals that the obtained and theoret.ical means are in close agreement.
The tests to determine whether lim obtilined freqllcll(,)T distributions
arc in ngl·cement with the hypothesis adYllt1ced nrc given in table 18.,
A stud)T of the obtained and theol·cti(·u,1 frequcney distl"ibutions
and the P viLlut'sn'venls that the obtltilwd fn'qneney disl!·ibutions.
are iu clos(' agreement with the hypothl'sis nUll Porter and Ponderosa
nre diftel"('ntiated by three pnirs of major genes as l"l'gards numbet of
locules per fruit. Two of thl'se pairs of ge11(~S nrc partially dominant
for fewt'l" locnles, and one is pat·tinny dominant for rnore loculei'>
per fruit.
•
WEIcnT PER LOCULE
~.AGXl1·UDD m' CHAnACT~:R DIFFERENCES .... ND bO~IlNANCE
Tlw nH'ans for weight per loeulc' arc giyen in table 19. Wcights per
10('\lle for the lwo pnl"l'nts were not matc'rinlly tliffert'nt, I1.vcrn,ging
10.2 gill. for Portt'r llnd 9.S gm. for Ponderosa,. The ml'11.I\ for the. 11'.
is gr(:n.tel· thnn the 1ll('1111 for either parent. The sltmc is true of the
Ill('UllS for lhe B. to Portt'r, lll(' F 2 , and the B. to Ponderosa; but the
m{'ltns for these populations an: smnller thnn that for the Fl. Cleady,
th(' 1;\ ShOWNl heterosis for weight per locn]e.
The genetic ynri/mees fo\· wl'ight per locH1e and weight per fmit
could not be cillculltted, for rl'IlSOllS given latl'l· (in the scction on tho
varimwes) .
~l"~IBER
OF llAJOR GEXE P_URS DIFFEREXTIATIXG TilE PARENTS
Examination of the cond('llsed frequen~y distributions fOt" weight
per 10('\lle (tabl(' 19) 1:eveals that the F2 und B, to Pondc1"(\su popula­
tions ilrtl tIle only om's having any indiyiduals fal1in~ into thl.' 33.5­
to 61.5-gm.-pcr-loclIle ('lass. This sug~('sts that ("ompnrntively few
major !!~ne paiL·s may hil.ye bl.'en responsible. for the h/.'tprosis noted
for weight ppr locule. 'The fMt thn.t only 1.9 percC'nt of the li'~ plnnls
fall into the 33.5- to 61.5-gm. cbss indicates thilt three. major genu­
•
34
TECHNICAL BULLETIN 99S} U. S. DEPT. OF AGRICULTURE
'l'ABLE
19.-llfearls and condensed frequlmcy distributions for we'iglit p"r locule and
weight per fruit
~renn
w~tgh~ per
Popullition
locllle
Porter••••••_._ .................................__..........._...................
"BI to Porter............................................................................................................"...............................
Fl....'" "' ...... """ ................ _............_............. ~ ... ". ............... "" .................._... _. "'......_.._.................. _....................._
~~i~l~g~:~~~:::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
I
l'oplIlaU()(\
I
Crult
Gm.
10.2
•
Gill.
21.5 36.0 6.;.0 r':1.5
01.3
97.1
11,8
J.I.4
13.5
1:1.7
U.8
C'ollll~'lS<!d CrCl(iIency: dIstribution byWeight "cr. loculu III ,,",ms
-
f
~(eun
w~l~ht per
-
1.5-15.5
i.
Wright per Crult III ll"UIIS
t
.
1,17•.5-31.5: 3.1•.5-61.5 i 12•.5-32.5\ :11•.5-02.5 I 07.5-232.5
I
, "
~---------"---·--·~·t--,---·--
l'ort('r ... ~~ ..
~
III to Porter ............... ~ ........... ..
<O. . . . . .
................................... ., .... '
f·, ..................... "............
f
F: ................ "." ................
DI tol'lInt!er<lSlL ................ , ...... .
Ponderosa...............................
l'trc<mt
Ill), 0
it1:g
;·I.G
69. !I
00.0
1
PerUlI1
I
0
J1,:~ I
g
Percent
0.·1
23,5!
29.5 l.
10.0
I
1.9
.6
0
i Pr.rUllt I Perccllt
Perctnt
0
{)\J.(\
O. ,I
f>J.2
li~:g
g
11.5
:1. 1
4.0
ir..O
00.7
50.5
12.5 40. :! 45.5 l)ail's dHfC'rcntillL('(1 wei~hl per locule in this cross. '['he fnct Lhn,t 0.6
percent of the pltlHts of til{' HI to Pont\C'l'os!t populntion fnll into tluLt
(·lass indiC'ltt('s the Sunl(> thing Ilud sugg(lsts that two of tlw gN1C pl1il's
tending to in('l'(~ns(' wcigltt' pel: loculc cnt('I'('d the CI'OSS from tho
l:lolHIC'l'osn p!Ll'eut. The genotypes giY<'11 in titbIt, 20 IU:P those l'xpccted
on the. hypothl'sis tlULl, Ils l'(lgnrds \\'(light pel' lotuk, l'ol'ter nnd
Pont\pros!1 WNl' difl'(lI'(>ulitLll'd by thl'PC mn:jor g(llle pnil's, nnd thnt
two of th(lst· g(lnc pni!'s teuding to lncre:lsc wl·ight P(lI' 10('\110 were
Clll'l'iNl by Pondt'I'O:>ll.
In thl' '13 1 to Pondpl'osn population the POndt'I'osal minus plwnotypc
might b(' l'X(lN'tN[ to lu1\<(\ thl' snllle Pl'lwtl'lllleCS for til(' difl'el'cnt
dnss(ls of tlll' ('01)(1('115('(1 fl'('queuey distributions !IS plnnts of Pon­
clt'rosH.. Plnnts of tho }i\ genotyp(1 would be (lxpect·('(\ to hnvc lhe
snrn(, penetml1(,(,s ns plants of the FI popu\ntion. This le!l,Y('s unde­
t(ll'mined, ns l'l'gn:rds tllt' 13 1 to Pond(,l'osa popu\ntiol1, only (.he lwne­
tmu('ps of tlll' F.1 plus plWllotypC. To p;;;timn.tc thesl' peue[;I'IlJl('cs,
the HI to :Pol1del'Osn, populntiol1 wns used !lnd the snmc fonnulns n.nd
methods ghrPll [l1'('\-iOllSly wel'(~ ilppliNl.
gxumil1alion o( tnble II) l'e\'('nI5 that 0.6 P(')'c('nt of the plllllts of
the HI to Pond('rosn popllln.tion CeLli into the :33.5- to 61.5-gm.-Jwr­
10c\lle cInss, whereas none of tlH' plnnts of the HI to ]>Ol'tl'I' population
do so. It is logical to mmum(' that the plnnts of the HI lo PondCI'OSIL
popllintion fulling into this ('Iuss nl'" of the LluJWGG, Aa.HRCc, and
.A(~BbC(} ~('noLyp('s. In. the HI to Poeter population of 448 plants,
however, If the plants of the AAHbCc genotypc (HI to POI·tl'l') hnd the
same pen(·tntnce for the 38.5.- to G1.5-g111. e!nss ns pllm ts of tiJ{' aboye­
nwntiolled g(,l1otypes ill thl' HI to Ponli('1'05n. population, U)(:ol'cti('ally
orily 1 p!ll,nt [(0.000)(0.12;>)(448)] would [1111 into this dilSS. ITcn('e,
it WOHld b(\ ('xpl'C·tNI thn t, by ehlll1('e, !1 Inrge per(,(,l1 tnge of 13 1 to
POl'tCl' populntiOlls would llllYe no plnllls flll1ing into lhe 33.5- to
•
•
GENETIC
.L~ALYSIS
OF TO}.L-\TO CROSSES 35
20.-Theoretical gello.lype,~ and phenotypes of different populations, based on the hypothesis that Porter alld POlllierosa are differentiated by 3 major gene
palrs as reyard$weight per locule
T.\nI.E
•
Porler (1',)
AA/Jbce
Il, to Porter
Oc,wt}1>e
.-l.-II~Ce
AABbec
AAbbe,
~',
AanlJCc
.I.',
l'henotype
OCllotY(JC
PhcIIOI,'pe
·F, plus.
AA nnC'c
]0', pillS,
~.. 1IIId I', IlIler. ~lA nnc,
DII.
IIlL~I!ute.
Do.
.-lAnBee
A.ibtice
AaUbCe
AaUbec
l'orlcr.
"LA l'b CO
F"
.IAP/Jee
r', IIml 1', llller· A.'ll/bec
.-IIIblle.;
.Aflbbcc
l~ortcr
lII"ll~lIc.
00.
I (miIlIlS),
A.,llJ/Jca
.IAF,bCc
•"I.lhbce
AI/HRCa
,lll[lllCc
AaRBee
AIIUIj('C
,-l ••Ubec
,·lllRbcc
Ponderosa (1',)
aaRRCC
DI to I'olldcrosn
GClIotype
Phenotype
.tlaBRCO },", plus.
AalJBCe
Do,
}', lind 1',llIIcnlledi· AaP.bCO
Do.
tit",
~.. (llus,
.-IalibCc 1-'"
Do,
aa nllco' l'ollderoM.
)-', tlud P, !nlcrmedl· aaHBec ('oUllcros:! I (minlls).
nlli •
Do.
aallbCa
Do,
Do.
aaHbCe
1)0•
Porter"
}'I j)11I~.
Do.
·}',uud 1', iutermcdi·
r" phIS,
:lte.
r't.
.I.', (tlld 1'\ lnlermelli·
:11\',
Aa/Jbea
Aa',IJ('c
• lulJbcc
m.H}lCO
aulUICc
aullRcc
aal'bCO
aaPIJCc
UtI
"'J<C
oa';!.CC
U~MiCC
•
1.l31~CC
Do.
Do,
l'on,'r, (minus) •
j"ondl.l To53..
l'olllll'fOS!1, (wums).
Do.
llo.
Do. POlld('rosn llminus).
l'olld(~roS:l \ I minus). Poml,'roSll, lminus), D\)•
6 L.5-gIll, ('lns5. A:1RbCc gC'notypt' phmts We!'e therefore ('ollsidered
as IIlwi1lg n pellett'nn('C' of (Ui PC'l'('C'llt for this ('lass, nlso. Since 99.6
pen'('l) t of tlll' POl'tC'r plH'[JotypC' plnn ts of tll(' BI to Porl('1' populntion
fall into till' 1.5- to 15.5-glll. ('Inss, nll the ])o1'tel:l minus phellotype
plllllts might bC' expC'ded to fnll into this duss. Examination of table
~o l'('nnls thnt pitll1ls of the POndL'I'OSn2 minus genotypes would be
expl'N('d to fllU into lll(' SUllIi' ('Ins::; of llH' ('oIHll'1Is('(1 fr('quPllty dis­
tributions ns plants of the Aabb('c gl'notypl'. 'rhis wns assu1l1NI to be
the ens('. B}" nsing the TIl to Port('1' populntioll for pmpos('s of esti­
ll1n,tioll, th(' Pt'l\('lt'IU1('PS of tIll' 1.\ und 1\ int('L'J)1N\illte phC'notyp(' Wl'!'O
dl'tl'l·minp(i. TIU' fOl"ll1Ulns nnd mpthods of )H'o(,pdurp were the sUllie
ns for tIlt' nnalysis of lllunlH'r of mnjor gel\(' pairs dill'el'putiflting period
from :fir~t, bloom to firSl fruit set. In 'using tlll'se, formulns, the pene­
tritrl('('S of till' plnn ts of the pll('llotypP beiIlg estimntNl w(,I'e I1dj usted
so thnt thc' pel'ccn[n.g('s lotnlpd HlO, if they did not do so ulrendy.
TIl(' )H'lWtL'illl('l'S, tht'ol"<>[ielll fn'quPllcit,s of the dilfcl'Pllt genotyp('s,
and titl'ort'ticul rH'I'('t'ntn~('s of tIl(' ('olldl'llsed frl'quCl1cy distributions
\\"('1'(' ('ulc'ulatt"d with tll(' n'sults givcll in tnblc 21.
Si!l('p tlt(' X~ vn.lllC' of tllblc 21 hns it P vnJ\H' grcatt'l' than 0,05, the
fit lH'twl'(I/l tIll' obtttilWd and th(,Ol'('li<'ltl vnlu('s is good. To t'llicuinte
the tlil'(ll'pti('alnWHn of lht' )1'2. itWil$ nt'('(':';:'lnry to ('stimnte tIl(' IllPnns
of all th(, phpnotYPt'S of tnb\(> ~l. Th(' JlWilnS of tltP }\, Porlrr,nnd
Pond('I'OSI\ p()pnl!lti()11~ !In' gin'l\ in tn.bl(' Hl. The l1H'nn of plants of
tlit' Pontll'l'OSlll minlls plit'llotypC' would bl' (·xj)p(·tpd to npPl'oximnte
that of the l)on(\l'I'ostl p!u'C'nt. l:3in('p nIl tht, pln.nts of the Porterl
36
~'ECHXICAL BVLLETIX ODS, U. S. DEP1'. OF AGRICULTl'RE
minus Ilnd Pondet'osll2 minus phcllotYPl's fnII into the 1.5- to 15.5-gm.­
per-10culc clnss, tbe Ilvel'nge of this clnss would be expected to npproxi­
mnt!,' the menns for these two phenotypes. It is [(1.5+15.5)+2],.
or 8.5 gill. With these constu,nts itYllilabll'. the menn of plants of the\'
FI plus phenotype wns estilllilted fl'om the Bl to Ponderosa populnlioll
by Ilpplying llu,thods ilnd fO;ll1ulns ilh'~'ildy given, It is 18,7 gIll.
'1'1l(' mean of plnnts of the }i I Itnd PI llltermedin te phenotype WIlS
estimated from the dnlil of the B. to Porter populntion, and is 10.7
gm, The theol'eti('ul n1{'lln of the F2 populntion us eslimn.ied by
methods Ilnd formulus nlretldy given is la.l gill" whieh is ,TeIT ('lose
,to the obtnined 1l1('nn, la.5 gm. Oil the wholt" th(' dntll ('olwineingly
support the. hypothpRis thnt PortPI' Illld ])on(\('1'OSI1 W('I'e difl'erpntintcd
by three mnjor gene. pairs itS I'('glll'ds weigh t per locule.
•
TMU.E.21.-Phello/Y]lt's (llld.their 1!('nrtrcwc~s for we/gilt 1}('r loculI', !h~orelical 1!TO­
1lOrilOn of t'llch phellotype PI lhe h populatlOll, obilltlled lind Iheorel/(:a[ proportWll8
of tlt(lt 1JOpulll/iOII ill !'ach class of tltl' condelllled !rcqucllcy distribution (table 19}
UlItI x 2 va/tICS 101' trsting goodl/fsS of fit
-------------'------~------------------------~-------11'('l1NTau('(' in ImlllOltcd class
1_____ ,
~. _ _ ,_l 'J'ltl'OfI,t\"11I1ro·
i
I)Ortion lit P,
I
· U.- I'.a- 33.5-!
I
--- ._-- -----­
._--------
r', JlluS
.,. -
}\
~"1I1111
PI
!nl,'rnh~lhll~
"
~
~
"
... - ..
~"
.. - -
. .......
' " . - - -. -
.... _.
I'ortrr
I'onl'n .minnsl
POluleros:.t( .mhnlsl
l'Qnd~ros.'11 minus'
..
"
l'OIHll'rosn
. --,
.... "" ...
~"
>
.~- .. -
.. . ..
~
.. ~ . . ~~ ... -
,
... ,
~ ~
. .
>
1 5.5 gill.
31,5\:111.
J'uetlll
PtrcfIIl
5:1. 4
450
H3
113. (\
!l(tG
.,
100.0
\10.0
•• , . , "
~,
...
"
"
~ ... -
'
.
W.O
100 0
..
'~~~• •
Ptrcml
1.6
3.5,;' ,
11.4
W.O
0
P,'rCfIII
!!!),68/.1
12.f{)oo
2S.12f.l(}
0
0
0
,-I
0
100
Jl()llUllltfon
01.51;111. 1
,
,
I.M:.!.;
:1.12;,()
()
0
(I
I, ~r.2.1
H.()025
0
9.3/ro
r·
I
, Proportiou In llltll('lllNl ('!lk"S
1__
I
}'t JlOPlllalloll
~
j D,'grccs
I
~
I Crloc\lolll
•
I .1.5-' i 17.5:- . :1:1.5_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ I~O.51'~; 31.5!!~:~, _ _ _ 1_ __
Obtal",,!
Thl'<lf('lil;l!
., .........................................
,.,.
H' -
..............................
l'uCfll1 ,Per(erIt
:-4 tJ
2;1. 5
;5.S~
23./,
puce,,'!
I 9 '} :ii:
I
4.510
1
2
WEIGHT ..EIt FHUlT
~'AG~I'ITD~~
O~'
('IlAI!Ac'rgn DIn'EREXCfS AXD DO.\IIXAXCE
Thp l11('IU)S for wcight pel' fnlit nrc gin'll in tnbl(, 19. 'rhe difl'er­
el1('e between the 1l1NU1S of the two pl1rellts is 7().2 gm,'1'he menns.
of the plu'('nts u\"("l'ilg(' 59.G gm., and tit(' 11l('lln of the FJ is 65.0 gm.
'1'1\e mcnn ofb\ does not difl'er significnntly from thnt of J!'\, the 111('11.11
of BI to Porler is closet' to the Ill!'flll of Port!,I' than to that of F I, nnd
the lIlt'iUl of 131 to })on<l('rosl1 dol'S not <lill'l'l.' significnntly fl'om the·
menn of Pond('r:o~a. Jt is e,-id('nt, lhllt these "nitH.'s do not fit nnv'
simplt, interpretation of intranll(l\ic and intl'I'nll(,lic illtNactiolls of tl;(~
genl's. Howl'\'I'l", lhe }'\ 5ho\\'('(\ phenotypic dominllllc('. of gren tel'
weight P(,l' fruit. It is inlN'Nning to note thnl [('\\'1.'1' locuks showed
pal'tinJ domillillH'(" g)'pnU'1' wl'igh t P('l' lo('ul{' ::;howed lletC'J"osis. nnd
Uw;e t\Yo eO!ll[HlIll'ot ehnl'lH'tl'rii t'ombinl'(\ Il1tdlipli('ntiydy to produc~
partial plH'llot,rpi(' dominn[lt'C,' of gren t(\[' \nigh L per frni L.
•
GE~ETIC
z.;l:~IIlEn
•
Ot'
~1.-I.Jon
.-L"ALYSIS OF TOMATO CROSSES
37
OEI>E PAIRSDIFFEnEI>TIATll>O THE I'AREWl'S
SinC(I numbel' of locules find weight per locnle "'ere each difr('rellti­
ated by titre(' lIInjol' gene pnirs, w(,ight p<'r fruit wns dHI'(,I'('nlinted
by six mnjol' genc pnil's if pl('iotl'OPY WfiS noL itwoly('(l. The menns
and condcl'sNI fr('quency distdbutions for w(,ight pCI' fnlit, given ill
tnblc 19, w('n' rxnmin('(i to d('lermiuC' wht,til(,I' us Iew fiS thl'N~ mfijor
gene pairs diIT(~l'('ntiut('(ll)orl('I' find Pon<iel'osn itS rrr"llrds this chumc­
tel'. It ('llll be Sl't'll thut 99,G pI'l'e('nt of tht· plnnts 0 the Porter popu­
lation full into the 12,;3- to 32.5-gm,-p('!'-fl'uit clnss of the condensed
frequene)' distl'ibutiolls, und thut 54.2 p('l'('enL of the HI to Porter
plimls u.nd nOlle of the F J plnnts do so. This would indicnte thu.t ono
llHLjOl' g(\I1(' Pllil' difrel'cntiuled the two pal'ents. On the bnsis of all
assumption tiln,t this WI1S t1H' ('l1se, it would bi:' (I:~q)ected thu.t 25 pel'­
('ellt of th(ll;'~ population would fnl! into the first tinss of th(l condensed
frequene)' distt'ibuliolls, [nst('u.ti, only 11,5 pel'('ent do so, ).iore­
o\'e1', within lhe limits of lhe pl'obnble (lITOrS of l'Ilndom sampling the
pel'cC'nlnge of the HI to Poudel'osu. population in uny given dnss of the
cond"'llscd fn'qllC'ltc,Y distributions docs not difl'cr lUntednlly from tho
pCI'Celltng(l of the Ponderosa populntion in tllllt clnss, The menns
und ('ondC'ns('d fl'equPllcy distl'ibutions ('annot be C'xplnined on tho
bnsis thut ns fc,,' as thl'('e pnirs of gC'nes dill'(lrcnti!lted the pnl'cnts.
11 C'11('(' , the yuhws in tnblc 19 do not provide tln~{ evidence of pleio­
tropy,
•
•
Information COl\Cl'rning the nature of th(' intC'l'tlctions of the three
llHtjor pIlil's of g(\l1C's dilfC'rentin ting numbcr of loclIles pCI' fruit is
pt'oYidcd by lIlbll' ] 7. '1'h(\ menns of this tuhlc show that ill gcneral
till' g('IH'S tt'nding to iU('I~Nlse ntunb(ll' of locules pt'r fruit hnNc a greater
(,erN,tin comhinntion with g('ll(IS lpuding to produce mol'c locules
than lht'," do in eOlllbinfitioJl with tItt' 1111('lcs of these g(lncs, The
..:la find Hb gene pitirs sho\\'cd pm'tinl dominnnce fOr fewcl' 10('llIeS per
fruit nnd t~H\ ('(' gen.o pni!' P!lrtilll dOI.\lil~ancc fo~' mOre locules pCI' fmit,
Both the llltt'l'llll('l!(' t1lld llIlnmllcll(' llltl'l'tlctions were found to be
cum uillt i\'~\; !uld tlll'I't' is considt'l'nbk ('vidence thut these types of
inl{\I'I1l'tions UI'(' nol indl'pl'lltipnL, bc('ause the dilterl'llCeS between the
homozygous domil1llut t1mllwtcl'ozygous indiyidunls with respect to
uny gi~'('n gene pn.il' lpnd to inc-rense fiS Humber of genes tending to
produce mort' lo('ulcs increllses,
With rl'spect to weight pl'I'lo('ule, genic dominnueC' isnot complete,
stnec l.L higher pN'ccntngt' of thc plllnts of thll A..:.1HHC(' genotypo
thnn of those of the Aalib('c genotype fnlls into the :33,5- to li1.5-gm.­
pcr-lorule c1nss of the con<i('nsed fr(lquency dislt'ibutions, Since a
hil71ll'L' pel'cC'n~nge of the plnnts of lhc A.:1Hl-fCC genoLype fall~ into
Lills duss than of th" plnnts of llny other gC'llOtypC, both lhe mtcI'­
allelic und intrnnllrlic iiI temelions of the gel\('S must be snch thnt the
efl't'cts of the gt\l1l'S t1rc t'UI11ltilltiyl', Also, the fnct lhat the mefill
(tnbl(' Hl) for (ht' ..:li1bb('(' gl'notypc (Porl('1' populn.tion) is ns Inl'ge ns
thut fOl' the au 81U'(' genotype (POIltIl'l'OSil populotion) shows thnt
the ..:1..:.1 g(\I1l' pnLL' is ns efl't'divein incI'l'lIsing weight pel' locule os tho
BB find CC gene pllil's combined.
.
38
'fECHXICAL Bt:LLETIX OOS, 1:, S, DEP1'.
Q}'
AOHlCUVfURE
I~'r":III1BI~A'rIOl'iS OF CU,\IIAC'rEUS
l'EIUOn ,,'UO",!
SEEI>l~C
1'0 .... ItS'r "'Rl'IT IUI'E A:SD I.TS COJII'OXENT
CIIAIIAC'rERS
To obtl1in inforrntttion on I'I'lnt10ns bl'b"C'(,11 the. UlJ'(.'(' components
of p('riod from s('eding to fil'sl fruit ripe filld the l'l'lntin) illlPOl'tllllCC
of ('nch in ('nusing the Ylll'illbilit." of the (kpend(,llt dllll'ncl('I', the
con'clation ('o('{l1cirnts nnd tin.' 1'1'ln tin' pel'c('nlllg('s of 1Il(' YI1I'inl1(,(,s
nc('otlI1 t('d for b,\' l'C'g['('ssion \\'('1'(, Cl1lcuhltcd, The corl'('\n Lion co('Hi­
cients f()[' IH'I'iod from s('('(ling to first bloom (Xt ), period from first
bloom to (h'st fruit set (X2 ) , I1nd p(,l'iod from first fruit set to fil'SL fruit
rip(\ (X~), log('lhC'l' with lhr l'pll1liy(' lWI'C'('ntnges of the vl1rinnce of
period from sppt\ing to first Cruit rip(' (1·) 11('('olluted COl' by J'('gression,
IlrC' gin'll in table 22,
•
'l'AIII,I~ 22.~·~Corrd(lliM
rocjfidclIls for period from secdill(J 10 first II/IJom (XI),
}Jl'rioli fro/ll first lJ{oom to jiri't fruit Sft eX:,. (lllcl prriuti from first fnti! sci III fiNt
lmit rip,· ();3). tOOf/hl'r u'itll ti,l' rrllllili' perl'(l/l(lfJr,~ of lhe I'ariu/lcc of period .frOIl~
suelillota jirsl fruit ripe (Yl (lCC'owltcd for by rc!}rcssiolt
t'urrclation coeJfi('iNlts
l'Ojllll3(iOIi
}'Ortcr ....................... .
ill t!J Porter
Pl .•..
. ~ .. ~. ~-.
lit tIJ 1'Ulhlrrusa •••..
} ....:.,
~
}'ol1!l\·nls.I
o l;~'l
-1}.:!Hfifj
-O.·li9~
-.I~M»i
-II~W
.JII,\II
-.U;Ob
-.Oti""ti
-.,11(;11
-.I~K"
-.~·HJil,
-.";":;1
-.!!:.~.u
-.1;1>'1
-.NI
-.1I'~~
-.3\1.\1
-.4tkll
! H~lllll.W [lcrccl1tn~\' o( mrl·
!1m',' uec()ulltNl (or by
r\'grrs,lol1
Pert'lli . P,ralll
72. D
11.~1
;03
(ll.n
:t'i, [)
ttl 2
~)(}.S
PeTC(1I1
15.R
l:t t
n~
:1".1)
~:;1. 5
23,2
I
16.13
IS.7
25.1l
29.;1
60.0
The ('oIT(,lfllion ('OC·nil'il'llts (rI2) forpt'I'ioc\ £('om seeding to firs! bloom
nnd pt'riod fl'om first bloom to lil'::;t fl'uit spt nl'l' smflll. This is truc
nlso of thl' ('ol'l'e,hUon ('o(,JIjeil'llts ("'~) for'l)(1I'IOt\ Cl'om seeding to first
bloom Ilnd pl'l'iod from first fruit St't to first fl'uit ripe. For nil practi­
elll PUI'])O::;('S, pC'!'iot\ [nun scpding to llrsl bloom nnd tlw othel' com­
IlOIlPl1t t'hUl'/l('[P['s fin' ('s;:lPlltinll/int\e(lpndpnt. '.I'llI'll, IlS j'('gnl'(ls the
.inll'I'I'l'ln t iOlls of lbl's!' dllll'l1ell'I's thpl'l' js no e"it\pnc(' of pll'iotrop~y Ot'
~('IH'li(' ,linl~!lg(', ,'rhpl'{' is ('\'i(\<'11('(' , h O\\' (,"(II', of n slight, ll('gnti.\'o
1Il1('l'1WtlOll 1Il\'olnng lht' eompOII('nl ('\HlI'netl'I'S and til(l enVII'Onl11l'nt,
'l'h1tt this J'(·lntio!\ is phvsiologiel11 is sho\\"I1 b,T lhe fl1ct tlwL it is
exhibited by both the nOl;sl'gl'pgnling oml thl' segl'pgllting populntions.
B('('nmw til!' c(ll·["(,ln.tioll (,O('fIil'1('nts' n,'p :;111 nll , this l'plntiOIl hfls .littlo
pl'ncti(,!1l siguifi('I1Il('p, In other words linkng(', pl(\ioll'OP~', or tho
int('['n(·tioni irl\'oh'ing thQ eOm[)Ollellt ehnrnC'ters nnd the pll\'ir'onnwnt
ofr('I'litt!(, hindl.'nlH'(, to ('0mbining shorter period from s(,pC\ing to Iirst
bloom with ~llOrll'" Iwl"iod from Lirsl bloom to first fmit set I1ml shorlCl'
period fmm first fruit Sl'l to first fruit ripe.
'1.'h(· ('OIT{·1:1tion ('o(,(ljeiPllts (r~3) for ])l'I'io(\ f['om first bloom to first
fruit sd nllll Pl'I'jOt! from f1r:'lt fruit s('t to first fl'uit l'ipe 11['(, llll'gcl',
Allthosl' fol' the nOllst'g!'('gnting JloJlulutions (Portc!', TIt to ])ortl'l', li'1,
nnd POlldl'l'o~nl fin~ Inl:gPI: tlll1l\ tho;:;c fOl' the S('gTl'gllting POpullltiollS,
fiml fiI'l' Ilegn th·c. tIl (,'1'1.' HI to Porle'l' is c'onsidel'ed fi Jlonsl'gl'l'gn ting
•
•
GENE'l'IC k.'iALYSIS OF 'rOl\lA'l'O CROSSES
39
populntion beCftuSe both the chHl'Ilcters mentioned exhibited almost
e(Jmpk,tc, if not c:oI'npleLe, phenotypic dominance oC tho goncs con­
tl'ibutcd by Porlor,) ::5inco n short('l' pel'iod Crol11 fil'st bloom to fiI'st
fruit seL Hlld It shorter period Crom first Cruit set to first Cruit ripo wero
combincd in the Porter pltl'ellt, lhe CIlet thnt the eOITeintion coeflicienfs
for tho segl'('gnling popuitLtions lire smullel' than thosc COL' tho n011­
scgregating popltln tions cOns li tll les fairly dependablo oddonco that
some of tlw g<.'t1es !:p.llding Lo produce (1 shot'ter pel'iod from first bloom
to first fl'uit set \\"('re linlZ(,d wiLh some or ll~(' I~pnes teuding to produco
Il sborLl'l' pel'iod from first fruit seL to first ft~lit dpe l 01' thnt som~ of
tho g('Ill'S l'xhibited plt'iott~opy, The llPgn,ti,Te correlation 1'01' the
llons('gl'(·gn.ting popultltions shows thnt the physiologicnl I'enct~ons
wert' Sll('1l lhn t on I'til n. \'(~rngc less length of Olll' 01' thest' two Ill'nods
WiLS n('('olllpnni('d by gl'l'IHl'l' knglh of tilt' oUlel',
'.l'ho genetic, inknge
Or pleiotropy, !IS the e!lSl' mIl.\' be, Jncililnt('s eombinillg Lho two elesit'­
aulo e1I1U'uet('1'S, whol'cIIS tile physiQlogknJ rellctions in\'ohTing ~ho
compolll'nt dml'nctrl's nnd lho t'lwil'OIlIllCllt thn,t lend to IH~gntlvo
cOl'I'C'lution eOl'lIieicnts hindu!' cOlllbinntion of such chul'flcLcrs, That
the PhysiOI(,)pi('nl I'l'fletions noted did not pl'ohibit eombinntion of the
two desimblc ('hllt'netC'I's is shown by the Jnet that tho two wero
combined ill the POl'lN' pnrcnt,
TIlt' ['('hlti\'(' pt'L'('('nlngp:; (ttlblp 22) of til(' ytll'in,Jl('(' of p('l'iod fl'om
s('(·diug (0 111,:;t fnllt ripl' 1t<'('OlllltNI rOl' b," the l'l');l'pssion of this
eltnl'llt't l'l' on its ('omIHHH'nl ('huI'nt'l.l'l'S i ndi('n ll' tht' rclnt i"C ('ontribll­
lions of lItt' Inllt'l' to til{' "ttl'inllt'(' of (hp d('pl'ndl'nt ('hU,I'tldt'l', In
inlPl'lll'pting 1I1l':;1' datn" it is !H'('l'SSIU'Y to I\('('P in mind thnt the PCI'­
t't'lllng('s WPI'l' oiJtH,ilH'(1 hy rnullipl~'ing tht' simpl(' ('oITe1ntion co­
('f1it-ipnt:; (ry! by tIll'iI' !'l':;rH'l'ti\'p stnnthll'(l. pn,l'linll'('gl'l'ssioll ('oeflieicnts
(b'yl n,nd Ih(,1t b~' .10(1. By this IH'O('P(JUl.'P, th(' Pl'opol'lionn,lc ('011­
Il'ibutiol1 of Plldl ('otnpolll'1l1 ('hal'n el PI' to til(' YtlrilLll('(1 of the (\ppcnti­
('Ill ('Iml'll\'ll'l' is ('rnlutltl'(lin it:; n,ln,tion to llmt. of till' OllIPI'('OmpOll('lJt
chnl'IH't('I'~, Stud," of tilt' "nlui':' lisled unLil'I' nJ{C'ht(iw 1H'I'('(llIln.gl' ot
vnl'iulll'l' tll'l'OUllll,d 1'01' by I'pgn's::;ioll," in tn,blt' 22 I'l'Vl'a!s thaL 1'01' tho
l l 01'll'l', HI to POI'll'l', nlld 1'\ popll!n,tions till' gl'palt'l' plll'l of the Yfl.l'i­
HIH'P \\"11"; I'Ontrillll{I't! II.,' lwriod frol1l s('l'dill~ to first bloom (l'!hb'?h,23) i
for til(' FJ IIlId HI t() POndl'l'OSn popllln,l ions, bYIH'l'iod fl'Oln first hloom
tu fir:ll f['uil spt (I'!hb'1l~131; nud fo,:' llll' POl1dl'rosu. populn(ion, by
JH'riod from Ilrst i'l'tlil Sl'1 to first fl'\lit. I'ip(', '1'ltis shows that, of tho
t\tl'l'\' ('ompoIH'nl elmr:H'tl'rs, lH'riod from first bloom to .fir::;l fruit set
ha:; lhl' low('sl j'('ln,tirl' P!.'./'('l'lltn~(' ynlLll':; i'OI' thl' nons('gl'(,~l\.lillg pop­
nill,! iOlls !Llld hns t I\(' hi~ht'sl ('ot' tltt' ~wgrP~n.t ing populatiolls, Sin('o
dominill\('(' was nllllosl, if lIot ('Ill irdy, ('0 III plp( l' for nil tllI'pt' ('om~
pOll!'lIl !'htlrnl'll'I's or pel'iod from s(,pdillg (0 iil'st fl'llit ripp, sl'grl'~IILion
or t Ill' ~('ll(,s diI1'I'I'l'lll int i lIg tlll'St' ('Ii n,l'tWt PI'S is pli('llOtypic'nlly d is(,Cl'H­
il>l(' ollly in til!' F2 and. HI to Pondl'I,'OSil populntions, Sill('l' lht' 1'('­
f.,rl'(,:lsion of p('riod from :w('dillg to lir:;t fruit. dpl' On I,W,l'iod from fil'S!;
I}loom to first [I'll it Sl'l tl('('OUlIls for It ~l'('n,t('r n'ln,t i W' P('I'('P11 UI~(' of
till' YII,riIlIH'p of tltis Ilmin ('htll'lH'tC'I' in titp :i(,~l'l'gn,ling populn(io!ls (linn
do its 1'(,~I'(,:isions on till' two otlwl' (!ompoll('nt '('il:U'u('Il'rs, it i:; l'yitil'nt
thlLt (itis sitllllliull is (Iu(' to Sl'gl'l'gnlioll of lill' gl'IH'S difl'C'l'('ntin.ting
pP.l'iod. frolll fit'sl bloom to fil':;l fnlit s('t. This is ('ollfil'llwd b~· the
difrPI'P11{'('S Iwl \\"1'('11 [Il(' ml'uns or POl'tpr nnc! l'ond('l'osn for the' (\II'PC
(,Oll1pUUl'nts of period from sl't'eling to first fruit ripe, The's!' difrl'l'­
•
•
•
·40
TECHNICAL BULLETIN OOS, U. S. DEPT, OF AGRICUL'l'URE
.enCes (table 5) are 12,1, 30,6, and 14.4 days, respectively, Hence,
the intm'l'clations of the chnl'!lctel's were such nsto indicate that,
,other things being equal, the gl'eatest strides townrd combining earli­
ness of mnturity with other dcsirn ble chamcters ill tomatoes can be
made by emphnsizing, in selection, shortness of period from first
bloom to fil'sl; fruit set.
'rhe values listed undel' "Relntivc percentn,ge of vnl'iance accounted
for by regression" in table 22 provide some evidence as to whether
the Pl'Opol'tionate pnrt of the elwil'OnmentnJ vn.dance of the depend­
ent chm'ncter contl'ibuted by onc'h of the component chnrnctcl's, as
determined hy regression, wns inherited, As regards the eadiness­
of-maLtII'ity chal'neters in the nOl1segregn.ting popuintions, oXII.minntion
of tlw table roveals I hnt the reln,tive pel'('(lntage values for the regres­
sions involving period from seeding to first bloom form tt conl,illllously
decre!Lsing series f!'Olll POl'tel' to Pondel'osa, and those for the Togl'es­
sions involving pel'iod from first bloom to first fruit set n,nd period
ftom first fruit S('t tQ first fruit ripe 1'01'111 continuously ineron.sing series
'from Port(lr to Po 11(\ (I1'OSI1 , SincC' the pQpulations I1re listed in Lltbio
22 in Itccordnncc with the closeness of th{'ir gC'netic relations, thosel'in­
tion just noted cunstitutes convincing oyid('nce that the rt'ln,tivepro­
pOl,tiQlll1tC pl1rts of the (lllyironmclltal YnriallCc of the main character
contributed hy (Inch of the eomponent chnrneters, as det,erminccl by
rC'gressioll, were inhC'rited, Tho tendC'tlcy for the regl'ession involving
pC'rioci fl'om seeding to first uloom to account for the gl'ent(lr pttrt, of
the en vil'onm(lntal vtl,rin.nec of period from soeding to first fruit ripe
was PHl't iall,v dominant, and the degl'ce of pnl'tiHl dominance was of
tt mtitC't' high ortlcl', Hel'(I ttgnin, since one of the greatC'st difIlculties
in applied genetics is to select plants that nrc superior hecause of their
genot.ype rut,her thau uN'auso of the environment, the interrelations
of the chal'!lctcl's wel:C' such that selection or tomatoes for a shorter
period from Ul's!, bloom to first fruit sC't mthC'I' than on the basis of
either or tbe other component c'hnrnetel's ofl'ers the gl'eatest promise,
'With this infol'l11f1.tion avnilable conceming tho int(ll'l'elntions of the
compoll('nt ('hHl'l1cters for pC'riod from sC'l'Cling to first fruit Tipe, some
cQnclusions ('nn be dmwn about Lho numbel' of majol' gene pairs
difl'(I['eutiating this chnl'n('lC't' !Lnd tllso the l1n,ture of the internctions
of these genes, At this point it is nppropl'inte to r(lmark thttt in this
study,
in most such studies, the resenl'clt wOI'};:er is not denling
directly with the int(ll'n('tions of genes hut instend is dealing with tho
internetions of substnnc(ls nlld cluu'nctel's differentiated by genes,
For a discussion of this point, see Goldschmidt (7),
Period from s(lcC\ing to Hrst hloom WHS found to bo dW'el'entiated by
thrC'e major gene pn,irs, None of thC'se genes were curried in the same
chromosQmes us the genes diffel'entin,tillg the two other component
chm'!wters, Pleiotropy played no pnl't, and the negative l'eliLtion
betwC'ell period from seeding to first bloom ttnd period from first
fruit set to first fruit !'ipe WitS so smull us to be of little practical
significance, Such being the cnse, the three gene pairs difl'erentiating
period from seeding to first bloom were not the S!Lme as those differ­
entiating eithel' of the otlH'l' componC'nt charncters, Period from first
hloom to first fruit set WfLS found to be difrcrentiated by three major
•
•
ns
•
GENETIC ANALYSIS OF T01IATO CROSSES
41
gene pnil's, and pel'iod from fil'sL fl'uit set to ilrst fl'lliL ripe by two,
This signifies involyemcnt. of genetic linkage 01' pleiotropy or both,
If pleiotropy WitS involved, it wns shown by only olle pail', itS in(li­
viduals eombining the two c1UlI'nctN'S wero obtaincd in both sC!5I'o­
~ating generations, This proves that pel'iod fl'om seeding to first
fruit l'tPO wits dUl'el'entin.t('d by Itt lenst s('.Ye11 mitior gene pairs and
thnt if (ns secms pI'obabll') gcnetic linknge nlolll' WitS inYolved, l'nthel'
thitn pleiotropy 01' both, this clHll'lwter wns difl'cl'enlinted by eight
major genc, Illlil'S,
Sill(,(\ the g(\IH'S diff('I'entin ting period from sceding to fil'St bloom
wpre incleppndent of thos(~ difl'l'I'('l1linting the two othol' component
ChlU'tlctNS ns l'pgnl'([s linkng(', plt'iot ropy, Ilnd-essentinlly-thc
lnLol'!lc'Lions invoh'ing lite eomponont Chnl'ilelcl's nnd tlll' onvil'omnont,
it is Itppitl'Cnt thnt lho l'fl'l'cts of till' (')'el1('5 difl't'I'(,ntiating the first­
mcntiolll'd ehn\'lletl'1' and the' dl'ccts of lhose ditl'el'entitLting the two
othl'l' ehnl'll('tpl'S Wt'I'(\ ndditin', Howl' ,'el', tho efl'eds of lIll' genes
difr(~\'('liliating pPl'iod from first bloom to first fl'uit set and t.hose
difl'cl'Plllln.l.ing' pel'iod fl'om fh'st fl'llit set to fil's!; fnrit ripe Wfll.'t) loss
tlll),n udtlitivc, bccause tht' intel'ttcliolls involving these two ch!u,ttctl'I'S
awl lhe ellvil'onllu'nt produC'l'cl it Ilegttlive rda lion, thn.(; is, !t .,horter
pcriod from first bloom to lirst fruit set t(lncl('(\ to be nccompauiod by
a longN' p(\l'iod fl'om first Tr'uit set to first fl'uit. dpt' ,
Filldillgs on intNllct ions of the g('Ul'S al'e Sllllllllluizcd ns follows:
In nit ens('s PNtnining to the mlttlll'ity ellH.l'ndl'rs, the intmnlll'lic
intc'l'lldions of till' gl'nt'S WNO snch litnt. t\tl' efl'('els W<"l'e not cUl11ulntivc,
ns both phenQtypie nnd gpnic dominnnce were complete, 01' nearly so,
Lihwisp lIl(' inll'l'ullplic intl'I'nc'lions of the gPnt'S diffNcntiatillg pel'iod
from sPl'<iirig to fil'st bloom WNe Stich thn t the l'f1'ects w(lt'e Hot C1Il11uln.­
ti\Te, Howp ,Tl' I', lhe opposite wus Lnll' of the intl'rnUelic illi.(,I'nel.ions
of t\w glllll'S dif1'PI'('ntiating ppriod ft'()m first bloom to first fl'uit set
!lItd lhose ot' tllP g't'IIl'S dUI'l'I'entillling period from first fl'uit set to
first fruit ripl', 'rite l'f1'l'etof intl'l'nl1plic intomelions within a COlll­
pont'nl ('hlu'nl'tPl' w('I'e C'tlllllrintive, The inLl'I'ndions betw('('n tIl(;
g('IH'S difl'l'l'{'llt ial ing ppriocl from s('l'tling' to firsL bloom alld t.hose
<lifl't'l'l'ltlinting (h(' two Ollll'I' component mnlUl'ily ('hn.l'Iletel's w(lre such
thltt till' pn'pet::; WPI'O {'Uluulnti,'e. and additi\'p, The intprlwliollS
betwt'(lll tlH' gPnt'R c1ifl'C'I'putialing pel'ioC\ from first bloom to fil'St fl'Uit
s('l !LlHl thOR(I dirrl'I'pntiHling pPl'iod from first fl'uit S('t to Ill'st fruit
ripe W('\'(' :ilIdt tltnl: till' ('(reels Wl'l'e ('umulnt i\'(\ but l('ss than ndditive,
TIt(' dnltt (\0 not. fUl'ltish l'yidl'lI('(' W\wthl'l' th(' g(,Il('S dilrl'rentillting
period from sl'pding to first. bloom hnd l'Cjunl ('freels, It has been
showu thnt tlt(' gPlU'S difl'el'Plltinling til(' two Ot\1(,I' ('ompoIlNlt mat.l\l'ity
rilltl'nelt'L'$, I'l'sp'petin\y, did not, In l'('speel; to the dl'l)('nc\(lnt ehlll'ae­
t('1', pl'l'iod fL'OTIl s{,pC\ing to first· fruit rip!', on nn n.vel'Hge the gene's
dilf('I'('lltinting pt't'iod from first bloom. to first fruit set lind n, greater
ef[('c·t thnn thosp diffl'l't'lltintillg pc'rioc\ from first fruit sp( to first huit
l'ipp; and. in lul'll, on nn nYl'l'ngl' (hl' In\tPI' hitd. gl'Nlt!'\' pf1'(l(,(.8 thnn the
gl'llt'S tlilrt'\'pntint ing pt'riod from st'pding to fil's!, bloom. 'fhis shows
thnt tl1l' s(,ypn 0\' l'i"hl mnjor {YP1H' pnil's di fl'l'I'l'llt in li no' pt'riod from.
sepding to fll'Rt fl'uit ~ip(1 did
hayc 0<[11111 er1'eels,
'"
•
•
•
not
42
TECHNICAL BULLETIN 998, U. S. DEPT. OF AGRICULTURE
WEIGHT PER FRUIT AND ITS COMPONENT CHARACTERS
The correlation coefficients for number of locules per fruit (Xl)
and weight per locnle (X2 ) are given in table 23. 'fhe correlation
coefficient of the two independent characters is largest for the F l ,
smalles.t for Ponderosa, and next smallest for Porter. Among the
segregating populations, the correlation coefficient for the Bl to
Porter is the largest and those for the F2 and Bl to Ponderosa do not
differ materially. These results are those expected on the assumption
that the covariance of number of locules llnd weight per locule, llS
depicted by the corrolation coefficients, is differentiated by genes
and that the deO'ree of covariance exhibits decided heterosis. Since
the highest and lowest clegl'ees of covariance were found in nonscgre­
gating populations, it is evident that pleiotropY' andlillkage of genes
played little if any part in producing the results noted. It follows
that the rellltions found must have been due to intel'l1ctions between
the populations B,nd the environment.
•
TABLE 23.-Correlation coe.ffrcicTlts for nUlIlber of locules PCI' fruit (XI) and weight
per locule (X2), together 'with relative percentages of variance of weight per fruit (Y)
accoltnteil for by rcgression
Population
I
Correlation
coefficient
Relatlvo percentage I of
vorianeo accounted
for by regression
r"
Porter ••.•••.•••• , •••••••••••.•..•••••••••••••.•••••••• , •••••••••••.
.B I to Porter ••••••••••••••••••.•••.••••.•••••••.•••••••••..••••••.••
Fl ............................................................''''''
F ......................" ".....__........".........................
TIl to Ponderosa ................................................... .
Ponderostl ..........................................................
-0.4015
-.5317
-.8i26
-.4225
-.4329
-.2866
Percent
2.9
58.7
1.7
67.9
34.1
11.9
Percent
94.3
37.6
95.0
31.0
65.7 85.0 •
I The Callure of the reiative percentages for any gh'en popui<ltion to add up to 100 Is duo to tho fncl that
in c!licuilitillg (wemgc number of loctlles per fruit and a\'crago weight per loeuie tho values were expressed
in whole numbers.
The relatlve· percentllges of the variance of weight per fruit (Y)
accounted for by the regression of weight per fruit on number of locules
per fruit (l'y l b'Y1.2) Ilud its regression on weight per locule (l'Y2b'Y2.1) are
given in table 23. In Illl the nonscgl'egating populations weight per
locule had the prepondcrnnt influence on this variance. 'fhe relative
percentage of the vllI'iance accounted for by the regression on weight
per locule is less for the Pondel'Osa popuilltion than it is for the POI'ter
01' the J.;\ popuilltion. 'fhis supports the conclusion, all'cady dl'aWll
regarding p('I'iod from seeding to fil'st fruit ripe n.nd its component
chlll'acters, tllltt in some cases, at lenst, the l'elative propol'tionn.te
P!1.l't of the yarinnce of the dependent ehnrneter accounted for by the
l'cgrcssion of this character on finy given component character wn.8
genetically contl'olled to some extent. Among the segregating
gcncl'ations the relative proportionate part of the variance of weight
pN' fruit accounted for by the regression of this chamcter on number
of locules prl' frllit WIlS eonsidentbly gl'cater. This is due to the
segrcgn,tion of the genes clifICl'entinting the two componrnt characters.
Such bring the ('ase, since for the Bl to Portel' and F2 populatiolls
the relative percentnge valucs are larger for number of locules, it is
•
GENETIC
•
•
•
A...~ALYSIS
OF TOMATO CROSSES
43
evident that in these generations the genes differentiating that charac­
ter had a preponderant influence, The practical interpretation is
that in breedill~ fOl' large size of fruit the most rapid strides can be
made by sclectlllg for large number of locules in the F2 population.
Since number of locules and weight per loculc were each difi'cren­
tiated by three major gene pairs and were found not to cxhibit either
genetic linkuge 01' pleiotropy, it is apparent that weight per fruit
is differentil1ted by six majol' gene pairs.
.
As l'egnrds the genes difi'erentiating number of locules, both the
intl'fiallclic and the interollelic intemctiolls of the Aa" Bb, and Gc
gene pairs were sllch that the efl'ccts were cumulativc. Both the
intmallclic I1nd the intm'allelic inteructions of the genes difl'eren­
tiating weight pel' fruit were found to be cumulative. The inter­
actions between the genes differentiating the two component char­
aCli}I'S, also, were such that the efl'ects were cumulative. It has
becn shown thnt the intemctions between tho populations and the
enviroruncnt were such thnt grel1ter number of locules tended to be
uccompltniod by lesser weight pel' loculc, or yice versn, The end
results of these reactions cllmulated geometrically, us number of
locules pOl' fruit times wl'ight per'locule gives weight per fruit.
Since the Au gene pail' for weight per locule had n preponderant
effect und number of locul{'s had greater influence than weight per
locule in detcnnining weight per fruit, it is apparent that all the
genes diffel'enLiating these t\\'O component chul'Ilcters did not have
equal efl'ects,
PERCENTAGE OF FLOWERS THAT SET FRUIT, PERIOD FU01\[ SEEDING TO
FIIlST FRUIT HIPE, AND WEIGHT l>ER FUUIT
The analysis to determine interrelations of percentage of flowers
that set fruit, jwriocl from seeding to first fruit ripe, and weight per
fruit denJt with the component characters mUler than the dependent
characters. The rcason for this is that any interrelation of component
chal'llcters infLu{'uccd the dependent character unless the effect of
one comporl,{'ut ehal'l1cter exactly offset tli;'; ·.... r another. (The latter
is unlilwly. If it did occur, this could be ascertained by studying
the component clw.l'I1eLers.) 'l'nble 24 presents the data on interrela­
tions of pel'centage of flowers that set fruit, period from seeding to
first fruit ripe, and weight pCI' fruit as determined by comparing per­
centn!?e of popuitttion expected ill the most desi:rable class on the basis
of in<lependent inheritance and percentage obtained in this class.
The char'aet{'rs consider{'(l desimhle nre grel1ter percen tage of flowers
that sct fruit; short{,l' period fl'Olll seeding to first bloom, from first
bloom to fU'st fruit s{'t, ancI from first fmit set to first fruit ripe; more
locull's per fruit; I1nd greatel' w{'ight per locule. Details of the method
used in i1,nulY)ling the data arc given in all earlicr publication (18,
p. 11S). 'With l'ef{'l'ellee to table 24, it should be pointed out: that
pleiotropy of one of a few gene pail'S cannot be distinguished from
genetic liulmge in cases involving multiple gene inheritance. For
cOIlY{'nil'uee, and bectlUse it seems thl1t in most cases genetic linkage
is involycd l'itt1i{'r than pll'iotl'Opy or both phenomena, the term
"gelwlie linknge''' is lIsrd in int{'l'pl'cting the data. It mllst he kept
in mind thnt, unll'ss othcrwisc staled, pleiotropy or l)oth phenomena
could be involved.
44
TEc.FL~ICAL BULLETIN 998, U. S. DEPT, OF AGRICULTURE
24.-Interrelatiolls of COlllponellt.~ of period from seeding to first frllit ripe,
componellts of weight per frllit, and percentage of flowers that set frllit, as deter­
mined by compar-ison of percentage of pop Illation expected in the 1IIOllt desirable
class on the bas';s of illdepelldent inheritance alld correspollding obtaineci percelltage
T.\BLE
•
Proportion olllopulnllon In 1I10St deslrnble. class' both as to chnrncter In stub
nnd lIS toCI
t
I
I3rn~ cr rLn(
populuUulI
Period lrom
seeding to tlrst
bloom
I
I
I
I
.Perlod Irom
first bloom to
first (rult sut
1
I
I
I
Period Iroll1
\
(rllit set to
Ifirst
first Iruit riIlO.
x I' I
• lIn~ Ie: 0
locllles
W.I 'M
e g. !,cr
locllle
I
}~x· I
g".
Ob·
g". lOb. .\'
Ob- \ ],,,.
Oh·
1':x, lOb.
_ _ _ _ _ _ _ , peeted ~l pected !~ peetedj tuIno<l pcetC«( t tnlned ,pcctCd ~
!
I
I
I
;i
I
I
l'erccntngo o( flow·
r
ers thut seL (rulL: I'errwl Perc(JII ; ['rrc<lIt ·l'uce'Il ·l'fTrtllt '.percttlt Percelll '['ercelll Percellt Percellt
['orWr.
••
·1.-1·1
~,60 I 15.73
1.1.00 I 1. ,IO! S. 10 I n
1 0
2.14
I. 2<J
B. ' to ".ort('r .
3,55
2.110 /18. o:!.
21.S' 1 .97, 7.:17 I :I. jI
.00
~. H
2. UO
Pt••. '" .. ....
1.2·1
1.72
:1.19
,172
.27
1.20! 2.21\
2.15
I. no
1.72
F, ...••. .,....
7.75
4.S:I
11.57
18.('~
I.S:!! 5.50
7,0$
.22
0.72
5.50
lh to Pondl·r·
i
osa •.. .... g,Or.
7,,\.11 7.90
1:1.,10
1.3:1
1i.0$ 1 15.57
5.:15
12.H
13,49
Pomlcr()sa
3.2:'!
2.70 I 4. ·12
0.00
.62
2.70 j 0.00
4. l·'
5.50
i.59
Xl1ry,~~[:;fl(IC."Ic:~. 0
H, to I'Mter,..
I.rot
{;~.£o.i>orl;I(.r:.
12.47
7.S1
r', .....
0S"I···· ..
··
1
Wcl:N[l~,~~C\~~llIO:"
I'ort('r
. .•.•
to Porter....
lJ~' ........... _.
11~:to·i·olilfcr:·
]I,
OSIl
.....
l'olllicroSll.....
:'.'8103
O! ()
2.·16
S. t9
11.69: :12.1()
i.flU· Il.Ga
K·.~:31
O! 0 L............................... .+1
:1.57 :,.' •.•. 1........................ 2. tiS , 10.73 '. ............ ,. ...........
1.1H
6.15\, ............................. j........ 2.50
1.·?,Q3-
0.21
v v
3.,15
u
97·.al~
-
2.58
1.79
0.+1
•• 4,
7. 2:1
0.15
21.01
II.OS
8. HI
it·18
21.SIJ
10.55
• !ri
.·19
2.00
1.7.1
5.0l
,I. ,IS
0.51
·I.H
5.R5
O. H
fl. 05
2.04
I.~O
8.84
0
6.70
32, III
0.37
i.59
.9.
.~G
5.58,············ .... ••.. ····1......··
0.1l0 ,.......................\....... . I
3,02 ........ r........................ 3.70 ............................... ~,o7'RI'" •.\'••••••• - ........,........ o.
r.
. . . . . . . . . . . . . . . . . .••• . .
4.0., ..•..• .. 1..······
0.00
·1..·· ..·· ........1'....... I..·....· ................1" ....... , Dug(rIIblll "htlrMtl'rs; llil(her percellllllll' o( IIc)\"I'rs that set (ruit, (ower <111\'5 (rolll sCl'clillg' to first hloOIll,
(aWl'r tillY:; (rOIll flrst hlO()1II to nrst (rult $~t. ruwcr dll)', (rOIll first (rtllt set to 'flrst (rult ripe, higher IIlImber
olloclIles, ntHl grclltl'r weight per loctllc.
};'01' aU pl'l1clieal purposes, p('l'cl'nLltgc of flowers that S(·t fl'uit welS
ind0prndent of pC'riod from sC'eding to firs!. bloom find weigh!; })('('
loculI.'. Inll.'l·df'pf'lldl'llC'e of UI('sr chnmctl.'l's was sligh!; 01' 1100H'xislellt.
HOWl'YI.'I', pl.'rel·nl age of flowers that Sl.'t fl'ui t; wus not il\(lcpl'ncient of
prriod from first bloom to first fruit sel, period from first fl'uit sot to
iiI's!; fruit ripl.' , 0[' rtumlwr of loC'ulps. FOI' ]H'['iod fl'oll1 first hloom to
fil'st; fruit s(·\: nlld lK'[,(,pntage of lIowel's UH1I., s('(, fl'lliL (tnNe 2·~), the
dif\,pl'elH~es l)('lwN'1l thp pxpedcd 0.11<1 ohtn,illC'd l)('reelltnges fOl' the
POI·tN', 1;\, nne!. Ponderosa pOl)ulat ions Ill'e no gl'elttel' than would OCCUI'
hy dUUlte. Ho,,'eYl'[', for the segl'pg'l1,ting pOpUhlt ions the ohtained
vaiues nrc gl'(·at.01· tlllm those ('xlwe(rd 011 the basis of indc'pl'IH\cnt;
inlH'L'itllll('e. SineI.' tho two dt'simble ('hurnclel's ('Iltel'eel the Cl'OSS fl'om
the~ Portel' pfl.l'ent. the~w 11,1'1' thp 1'('Strlts ('xpeelpcl in the (wrntof grnelic
linkngt'. As 1'('gftJ'(ls uumlwl' of 10(,II"'s and PCI'(:(·lltn.gl' of flowl'l's that
Sl't fl'uit, tlw obtn,inC'd vn.ltll's nrC' lrss thull those (·xpC'etcd. Again,
sinc(' gt'll('S dil\'('l'l·nLin.tillg the two dt'sil·n.ble ehn,l'ftetel's clI('['('(1 the
CI'OSS from dif\'l'l'ellt pn.l'l'lIt s, tIlt, 1'('Stt! ts n,I'O those eXIH'cLcd in the
('vent of g<'Helie linkage. PIC'ioll'oPY eOllld be n'SlH)Jlsible fOI' the
results notl'd, hut gl'lll·ti(' linlmgo is lhe mOI'c pl'Ohable en.lIse.
Ycry lilth'. if nn.'·, intC'l'delwlldenet' appl':\J's bl'Lw('('ll !lumbel' of
lO(,lIies PPI' !'1'Ult and IWl'iod 1'1'0111 s(,pding to first, bloom (titbit· 24).
For nUl11bpl' of lo(:ul('s and pl'l'iod from first bloom to first fl'uil set t.he
•
•
GENETIC
•
•
A.,.~ALYSIS
OF T02\lATO CROSSES
45
obtainNl pC'rc('ntllgC's of the s('gregating populations n1"O less tho.n
those expect eel 011 the bnsis of independent inherilllncc, Sinee tho
genes lending to produce more locules pN fruit nnd those tending to
produco short('l' Ill'l'iod from fil'St bloom to first (nlit set <mtCl'ed the
cross from difl'£'l'ent pllrents and siIte(' the obtllineclllnd expl'eted ,ralnes
ar(' pC'rC:l'lItngrs of plntlts ('ombining thrse two d('sirnblc duu'twirrs,
the n'sults nl'l' LhoSt' l'xpected on lhe busis of gelll'tiC' linkllgc, Oenetic
linkage WitS to 1.)(' ('xpl.'eted, sinee pNC'entagl' of flowers thnt sot fruit
was found to bl'linked witlt pPl'iod from first bloom to fil'st fruit set
nnd numlwl' of lo('ulcos [H'r fruit. As regnrds numb('r of locu\l's Il.ud
period frolll first fruit sel to first fruit ripe, in (,,"pry illSliLJlee the ob­
t!Lined pl'l'('cntngl's nrc gn'!Lter titfL[l the exp('c,.t('d, 8in('(' the nULgni­
cudI.' of t;IIP di::H'I'l'PllllelPS does not differ sigllifiellnlly b('lwe('n the
S('gl'C'gftlil1g !l!ld tlH' nonsegn'gating POpullltiOIlS, t1w ['c'lnJiofL is not
due to gt'l1pli(' lilllmgp 01' plpiotl'oPY. 'l'his t'plalion fneilitates mther
lhan hindC'l's (hc.' Iw(,pding pl'ogrnlll, It tHcuns that lhe e[wi!'onrnentul
('on<iitions ('ol1(/\I('i,'o to iIH'l't'lIS{' in llumbC'1' of IO(,llles I)('I~ fmiL iu'e nlso
('onducin' to shol't~'!ling of t1H' pC'riod from fil'sL fruit S('L (0 first fruit
ripl',
TIl{> {'olll.:lusions to Iw dmwll l'C'glll'ding we'.ight 1)('1' loeulp fU'(>. these:
W('i~hl [It'r lo('ult' is (';iSl'llliillly indl'pc.'ndellt of pP!'iod ft'om seeding
to fil'st bloom ilne! pt'l'ioe! [['om first bloom to first fruit Si't. Howe\,{'t',
w(light I}('r 10l'ulL' ILnd Iweioel £i'om first fl'uit sC'l to fil's~ fruit ripe
show il. !'ld !lC'!' sl ['()llg I'('lntioll, dll{' to inlel'l1('tiollsil~volving the two
ChiLl'n('(('l's and til(' ('Iwironment. The internet ions nrc sueh thlLt eHvi­
TOnInI'nlal ('ontlit,iOIl" l(·nding to il1(,I'('I15(' wC'ight pt'l' 10cu1e [Llso tend
to ShOI'tt'll lhl' pl'!'iod fl'om first fruit set to fil'st fruiL ripe,
YAHI,\:-;CES O~' ])EH10D I"RO':II SEEJ)JNG TO FmST I"nulT Rll'E AND ITS
(;0.\11'0"";;:-;1' C",\/lACTEIlS, A~O Y,.\/lI•.\NCES OJ.' '''EIGIIT l'En LOCULE
The Yltl'itl!l('('S of IWriod from sl'pding to first fmit ripe a.nd its
compOIll'nt {'lttll'lH~t{'I'S !lnt! tI\l' \"ill'iu.m'('s of weight Pl'I' 10(,1l1e pl'oyide
It m('allS of It':,lillg till' yulidity of the IllPtliod t'mploYNl to estimate
till' t'll"ironrn!'ltltd !tntl gl'll('lie Yill'inltC'l'S and determining wlll'thel'
till' gl'lwlie Yarit~ltc'(·s fl.S ('slimILIl'd ilU'llld(' the intl'l'IlCtions, The lotnl,
e!lyil'Onnll'lllnl, n,nd gl'nl'lic: Yfll'iuu('ps of pl'rio(l fl'om seeding to first
fruit ripp tllJd its ('OlllPOIlC'llt ChaI'aet0l'S ure gi"cn in tnble 2,5,
For Ill! matmiLv I'IIIU'Il(:tt'l'S tlw lotHI YIll'ianN':; for nil thl't'('. 1I0n­
s('g'n'gnlillg POPUilLlioIlS IlPPI'oximnlc Ih(' eOl'l'espon<iing cm'iron­
llH>nlnl Yill'itll1('t'S within tit(' limits of til(' <!("'iItLions eXlwcte<i owing to
proun.bl(' ('ITOI'S or mut/oIll sampling, COlls('(llll'ntiy, the yulidity of
the lllptho(\ pmploYl'd to ('st.imtltc the (,l1vil'onm('nlil.l vtLl'inJ1('es, !lnd
hPll('P lhe g(,lll'lit "al'ilmel's !llso, is subslantiat('(l fol' period fl'om
sC'('ding t.o fil'st fruit l'i p{' I1nd its eOmpOl1l'l1t eh!lI'ac:tel'S, If there htLd
b(l(\!l no intpl'ndioJls, thl' sums of the vHl'inn('{'s or the component
chtll'!L('ll'l's would IlpprOxinuLll' til!' 1'C'5pN:tin~ vllI'ianel's of p('riod [rom
s('('ding to fl.1'St fruiL rip!', within the limits of tIll' deyifLtions l'xpedl'Cl
owing to pl'obnbll' ('ITOrS of l'Il.ndo[ll sumpling, The llwol'otienl vnri­
fillC!'S (sums of \"!ll'iIUl('C'S of ('ompOllrnt ehn.l'Il.etC'l's) nnd l,11c obtnincd
vllritHH'l'S n!'p l.!:ivc,Jt in lnhIC' 2G, Tn ("'eI'Y ('nRC' the lhl'ol'eticnl variances
ti['L' 1l1rgl' l' thiin till' obtnin('(l.
This pI~oyes lluLt tlwl'e \\'('I'e internc­
tion,;, To dl'tl'l'milll! wlll'th('!' the dtlL!l 1'01' th(~ sl'grC'gnting geucmLions
•
TECHNICAL BULLETI~ 998, U. S. DEPT. OF AGRICULTURE
46
TABLE
25.-Total, environmental, and genetic variances for period from seeding to
first fru.it ripe and ita component characteTi
.
Vllfianco
C bamcter IUld population
Total
Period (rom seeding to first bloom:
Porter _....................... ""'''' _.............. ____
Dt to Porter .............................................. Ft••_••_•••••••••••_•••_••••••••••••••__••_•••_•••••••••••
'01_ .. _ .... __, _ _ ...... _ _ _ ...... _ _ ..... _ _ _
~~.to F~ii~fe~ro:~'::::::::::::::::::::::::::::::::::::::::::
l"onderosn ... __,................ "' ...... "'.. .. ......"'......___ ..... _..___ .. _____ .... .. ~ ~
Period (rolll first bloolll to first (rult wt:
Porter ..........._•••_•••••••••••••__••_••••••••••••••••••
Bt to Porter ••••••••••••••••••••••••••••••••••••••••••••••
Ft .••••••••••__...........................................
],-, .. " " " ' "
.....
'"
..................................... II, to Ponderosa ••••••••••••••••••••••••••••••••••••••••••
l'ollllcros!I. .., ...........................................
Period (romllrst (rult set to 11rst (rult ripe:
['orter ~ ' .......... _.............._.......... _.................. "_"'__ "__ "'_"'.'" ... _.. __...... .. ,~: ,t..D... ~:~~:~r~~:
::::::::::::::~:::::::::::::::::::::::::::::
F•.•. " ................................................... D t to Ponderosa ..........................................
1'0I1deros" .•••••••••••••••.•••••.•••••••••••••••••••••••••
Period (rolll setodi11g to first (ruit ripe:
Porter .... "••••••••••••••••••.•••••, ••••••••••••.•••••••••
TIl to Porter ••••••••••••••••••••••••••••••••••••••••••••••
................... , ............. ....-..........., ..... ]o·t ••••••••••••••••••••••••••••••••••••••••••••••••••••••••
}',
,
B. to Ponderosa ......................................... . Ponderosa........... , ••••••••••••••••••"" "" •••••••••• Dav.
Environ·
lIIental
nav.
Genetic
DaVI
--------------. ---_ _-_ .. _-­
36.5.:1
00.787
41.7i1
61.859
73.202
1211.478
130.680
8.348
19.037
16.873
84.140
J711. :m
270.2118
9. 635
10.005
15.5\18
57.330
124.028
270.286
····-···2ti:084
20.624
2:1.411
009
50.200
112.525
377.354
19.918
20.937
26.0<J7
32.328
83.311
378.501
········2ii:ssi
44.439
85.100
tlti. 119
158.970
2:17.110
380.756
49.804
74.722
00.814
92.107
········iti:474
········ii6:803
172.0i7
-.. ---------.. -­
2'~.
38.056
01.021
38.82'2
35.700
48. tlO8
380.600
•
....
.•••....2ti:iiii9
25. 1114
..... --_........ _---- ..
..---­
----....-.. ----... ----_ .... -.
53.593
-------------.... -......------­
----.. ---_-- .. -­
2'J.214
-. ----------- ...
05.039
and those for the nonsegregating generations differ, the percentages
that the obtained variances arc of the theoretical val'iances were
calculated. 'fhey arc presented in the last column of table 26. In
every case, the percentages for the BI to Porter, F I, !lnd F2 popUlations
arc higher than that fOI' either pal'ent and those for the BI to Pondel'Osa
population are higher than that for Ponderosa. Clearly, the r£'lations
between the different populations arc those expected on the basis of
heterosis. Considered as a whole, the differences clue to heterosis are
statistirally significfLllt. Thus there is no indication of a difl'erence in
response between the segl'egating and nonsegregating populations.
Such bl'ing the cltse, and sincn thNc is no consistent difference among
the total, environmental, and gem\tic percentages for the F2 population
or among those for the B1 to Ponderosa population, the heterosis noted
for the percentl1ges that the obtained variances nre o( the respective
theoretical vnrianccs is due to intern.ctions between the populations
and the environment. One other interaction pertaining to tihe
maturity characters has been demonstrated (see section entitled
"Intel'l'elations of Ohl1racters"), that involving two of the component
charn.cters and the environment. It has been shown that a shorter
period from bloom to fu'St fruit set tended to be accompanied by a
longer period from first fl'llit set to first fruit Tipe. Such a relation
between these chaI'ncters in respect to environmental variability would
tend to cause a decrease in the variance of the depe.ndent character
such as was noted for all the populations. (Sec table 26.) Then, it
is apparent that the interactions arc included in the !!enetic variances
as well as in the total and environmental vl1rinnces. However, in this
study the nature and effects of the interactions were such that the
•
•
GENETIC ANALYSIS OF TQMATO CROSSES •
variances of the dependent character were less than those expected on tlle basis of no interactions. Such being the situation, and since the
component chamcters are undoubtedly the end result of the inter­
actions of substances and other component characters differentiated
by the genes and the elwironment, the variances of period {!'Om seeding
to first fruit ripe and .its component characters are of little vnlue in
estimating number of gene pairs, unless the llatUl'e and effects of all the
interactions arc known Il,nd formulns are dcyeloped and employed that
take into account the effects of these interactions.
TABLE
26.-0btaiTled and theoretical lIariances for period from seeding to first fruit
ripe
PQPu/lltlon
Kind of VlltlllllCO
Porter.............._........ 'rotnl , ••••••••••••••••••_..... .
Il, to Vorter..................... 110._.......................
:F·!__ ~_ .. ~ ____..... _...._._...",... _....
.. .. (IQ .._
...................... "' ..... _ ................ _
Totnl .•••_..._................
}.,_••__................... { Ellvlronmont..I_...............
(1~n~t1c •••••••••••••"
•
47
......... .
'['ntu!. ....................... ..
B, to I'onderoSll............ { EpvlronmCllhtl__............. .
(len~ttc. __ ..................... .
l'onderoSll._._............. Toml ......................_... .
Ohlllined
ThcQretiC:lI. \ - - - - - , - - - . - ­
In dllYs
In temlsot
theoretical
NI11IIbtr
05.515
IO:!. S:!5
Sl.2.'i;!
205. :!08
125,·12~
79, 7S~
3O:J.~8
255. {Hi
108.001
n7.130
Number
H~30
85.100
m.l1o
Perunt
67.8 82.0 81.~ 158.070
92.107
77. r, Ctl.863
8.1.8 &.2 67.2 60.2 49.0 237.116
172.0i7
65.030
350.756
n .• The means and total yariances of weight per locule, obtained f!'Om
the original individuill-plllnt data t.rallsforml~d to logal'ithms, arc given
in table 27. The mean of the logarithms for POl'ter is 1.018253 and
th[tt fol' Pond('l'OSll is 0.954593; thc I'('spective variances al'c 0.005147
and 0.0369ot9. Totn.l Yltl'ittnce is hU'gcl' fol' the Pondel'osa populat.ion
than fol' the }i'2 01' L1l(' BI to Ponderosa population. Also, t.he total
y[tl'iance for tilc BJ to Pondcl'osn popu.l!liion is liugel' than that for
the F'.!I which ('ollstit.ules rathel' ('ol1yin<:ing evidence that the high
yariability of the Pond{'I'OSIL popullLtion wfls'inherited. Ckar}y, therc
is no readily (\etectnble consistent relation between the means and
vILrinn('('s such us wus noted for nil th(' othcl' ehul'itctcrs. From these
results it is evidC'nt tlU1t the gC'Iletic v[lriullC(lS for weight per locule
cnnnOL bt' estimnt.('{1 by USc of the proc('dtll'(ls nnd formulus employed
previously. It. follows that thl.'} g('nclic vlll'innces for weight per h'uit
cannot be esLimntcd.
TABLe
27.-},Jeans 01/11 Jo/al variances oj weight per [oeu/c, obtained from original
individU(I./·p/cLrli data trans/armed to logarithms
Totnl \'nrlnnco
P(lplllnUOll
1'0rt~r._ ........................ " .......................................
D, tol'ort~r .•••••• ,. ............................................" ......
F, .......................................................................
•
F, .. . __ ... ,. ...........................................................
-n, to I'onderoSII ....................................................... ..
PonderOSll............. '" ...............................................
1. OIS2.5:!
1.0i09:1G
1.\fISnU
I. 1:J8.l81
1.1249-11
.054593
0.005147 • 020 iii .0),\822 .023018 .o:m~5 .00GU~~ 48
'l'ECHNICAL BULLETIN 998, U, S, DEPT, OF AGRICULTURE
DISCUSSION
~[atters calling for discussion include the. genetic and statistical
design of the. experiment Ilnd the procedures and methods developed
and employed in analyzing ulld interpreting t.he dllta, the number of
mnjo(' gene pairs difi'erentiatillg tho parents us ('('ganls the chuI'fl('ters
studied, the compllrutivc. effects of these g~'ne plllrs, and the inter­
actions involving the genes and the. environment,
•
DESIGN OF ]~XI'EltUIENT, ANI) PltOCEDCltES AND METHODS USED IN
ANALYZING DATA
Th(' g('l1etie design of the experiment inYolwd determining the
populaliom; to be grown and the ('oIllI>OlI('nt ehllrlL('krs to be studied
(14, 17), The thn'e nOlt.'legr('gnting populations, the PI, li\, and 1~2'
W('I'(' ~'ss('nlilll Lo the genctit d('sign beenuse all were l1('ed('d ill eyulu­
aling ph('llotypic nnd genic, dominnn('(', in ('stimating P('lH'tl'llnCes,
in ('stiml1ting p)WirOll11H'nlnl Yllrhmct's Ilnd 11('11('(' gt'lwtie yurian('('s,
and in cI('LI.'('ling Ull' illtel'llC'liolls involving gt'llolYPt's unci the t'llyiron­
m('Ht Ilnd d(,t('['mining thl'ir nlltoUl'l', All' thl'('e sl'gl'('gating popula­
tions, the B t to :P j , 1,\, and B t to P2, Wl're ('sscntinl in dl't(,l'luining the.
('uLil'(' gem'tie hypoLiwsis, In oth('1: words, the dat,n, fol' t.hese six
POpullltiolls wcre ll('cesSill'Y to dC'nlopnwllt of til(' formulns and
lll(·thods of pro('('(hm' used in tmnlyzing and iJlt('rprcling the dittu in
(his bulletin, Dividing the dl'l)('nd('nl ehnrnet('l's into their respective
eompoll('nt ehul'iIC'ters wns of Nlll!ll imporlnnee to thegcnetie, dc'sign
of the experinwlIt, X ('itlwr Lht' number of mojo!' g(,110 pnirs difl'cl'­
eutiaLing period from s('('(ling to first fl'uit ripe nOl' the nuture of the
int('rnetions of UH'S(\ gNI('S ('ould luwc. been ddermined without study
of the ('ompOIWJl is of Lhis ehnl'ilct('I',
Th(' stnlislieul dC'sign of thl' ('xp('l'imC-llt wns u randomized eomp\('te
bloek (6, 8, 21) ndnpted to usC' in gC'ndie studies (12, lS, 15), The
varinn('es. e01T('lntion eodIiei(·nls. nnd r('gr('ssion ('o('ffieit'nts wCl'e
('nlcullllC'd from th(' dntil withill blo('ks and within r('pli('ittiolls, That
the 10 blocks of plots usrd ""('I't\ suflici('Jlt to provide ndrC[uate I'iIndom­
iZlltion is :;hown by th(' ('on.sist('Jl('Y of lhe' I'('sults ohtuilWd, Since
eitch block in('\lIdl"d two 2-:1:-plnnt 'plots of cn('h of til<' sl'gn'gnting
popuitltiollS nntl on(' of ('neh of tht' non:;pgr('gnting populntions, suHi­
cieut plants of nl1 g('n('rtltiollil \'"Pl'(\ growil to mnk(' the conclusions
drnw11 from the study 1'('lilLble, The' portion of Lh(' genetic. vnl'inllees
confound cd ,,"ith YILI'inl1C(,S nttl'ibutnblc to difrerellces I.)('twl'en Ill('UnS
of bloeks (J 5) t"mounts to less lho.n 3 p(,j'c('nt, Hence, the J'lmdom­
ized cvmplete bloek was wPil ndaptNI to the g('llctic investigations
mudc,
In drt..e.rminiug th(' llUl~'11ihJ(lc of the e1uu'uet('r di£ferenees and in
testing' significnJ1('e, th(' only deviation from stnndnrd IU'oc('(lurc (21)
wnS ('rl1euln.ting within the I'l'spl'ctive populations th(' stnudard ('I'I'OI'S
101' testing the significflnc(' of diiff'I'(,IlC('S (12, IS), This wus ll('CCSsnry
be('ll.1ls(' Ynrillllces W('l'e not h0I110g('1ll'01lS,
III studying the phc'noI11('non of dominanc(' th(' menns, the val'i­
un(~('s, Ilnd n. ('ompnrison of the. ph('llotypes of th(' diff(')'(\nt gellotypes
were used, Phenotypic dominnncc wns d('t('rmined b:r compuring
•
•
GENETIC
A~TALYSIS
49
OF TOMATO CROSSES
the means of tho two Pttl'Puts and the mean of the }.\' Genic domi­
nttnc(} was dctcrnl.inc.d from tt stud,f of thn meallS, YarittllCPS, nUll
phcnotypes of the diffC'l'Put gNl.otypcs, Of the. tlnN.·, It compnl'ison
•
betwcen phCllotypPS of the dift'('l'ent genot.ypes proyid('s
Ul.(\
most
infonnntioll. and h011('e is the most reliable, The infol'mlltion obtnincd
from a complll'ntiyc study
th('. phenotypes and gCll.OLyp(·s needed
Suppll·ml'll.ting h('eitusp of t.hc ['nthl'L' brand grouping of tho original
data into (:01\(1e115('(1 frequelley distributions, Such bl~oll(l grouping
is likl·ly to obse-lIrc somc of the smnll('r dW'PI'C'nces, ilnd ns n, I'esult what
l1.pp~nrs as complC't() ~lomill.t\ncc mIl}" in l'Nllily bo only partinl genic
dom~na1l.('e, ('Oll('luSIOlL.<; dl'nwll from [lilY sll('h study cnn nnd should
be cheekNl by' It study of lhe Ol'igiunl llittn, thC' !l1C'u:Ils of lhl' dHl'er(\nt
popuintions, Imd tn(' Vnl'ilUlc'C'S, If this is done, the dnln. ('nn be
intl'l'pL'pt('(\ e()l'1'l'('tly us to g('nic domimmco,
For dl'i('l'mining lht, ntlmbt'I' of gl'll(' pil,irs difl\'l'l'ntint Lng the two
pnl'Pltis, it Wlif' found llt'c('ssm'y to stlldy litt' ol'iginfll Illllivi<iunl-plnut
or
diltfl, lh(\ ('ondl'I1;'\('([
fl'l'C1UeIH'~·
distributions, llnll lilt' means, and t.o
('nl('u\tllt' the .F~ llll'ttll fr0tn the gl'nolYlWs nnd phenotypes of thl' two
[)I\('kero;,;s gl'l1l'I'tlt iOIL". Study of the dl'blilNl nnd tho condellsecl
frt'que1l('Y disll'ilmlious Iwld the most pL'omi::w,
'l'he pn,rtiLioning llU'tho<.1 WilS dpvploPl'(l rOl' mnking g('netie allttlys('s
of til(' lIntn" ~I'his llwlhod was npplied, find is il.l\lstr!1ted in this
•
buIll'till, for bOlh dl'litill'd lind. ('ondl'Il:;;('d fr('quem:y distributions,
,rith l'('slwet to Pl'I'('('Jltnge of {fowNs thnt Sl't fl'uit, th(l theoreticnl
ft'('ql!(~n('.\~ distributions \\,(lI'C' bttsNI on lhe pnl'('ntnl nnd Ii'I datiL mul
till' l1ll'l111S of til(' two Ilft('hross populntions; with respect, to Iltll11b('I' of
IOC'l1it's, tll(' fn'C[tH'Il('V dislrilmtions of l;l1(' two bnekel'oss('s and the
dilGn, from til(' pnn'llts nnd ll\ wen' uSNl t;o euleuitltl' tIl(' t.1l('o('(·ticnl
il'l'qIH'IH'y di::;Lriilulioll of tl1(·I<\, TIl(' yalidit.y of the hypolht'sl's wn,s
d('/('l'rnint'd by £ for t('sling- goodut':'is of fit !}('hw'('n the' l,h(,OI'('ticnI
tmel oblninpd fl'l'(ll1P\1('Y distL'i!Jlltion:;, Tit t1H' nvpliC'tLtion of this
method. to P('I'('('nLtlg-(' of nO\\'('r's thlli. spt fl'uit, tlwOl,/,ti('nl fl'('flllPtL('Y
disl t'ilnrl ion.., \y('l'l' (':11 ('111 n1('(1 fol' nil Lhrl'f' S('~I'('gn ling gt'JlC'l'Il.LiOllS,
In thl' !lllmbl'l'-of-lo('ules Il.ppli('nlioll, if tll(' g<'lll'lic hypo!'ll(>sis had
1ll)t bl'l'll sllhsln..l\litlll'd by till' X'! ipst 1'01' goodn('ss of fit betw('('ll the
th('o!,(,tjclll nnd obtllinpd [/,('(lllI'IUOY disLl'ibllt ions of tilt' F,!, tilr obLnint'd
fl'('((ll('IWY distl'ihutions of tIl(' Fz ('ould hllY(' b('(l11 1lS('(1 tog(,thl'l' with
tho.:'" of thr 1>11 {'1;:(,1'0:';:;(,8, parents, and F( to ('llI('ulnlt' throl'l'tiefll fl'e­
q\lP)U'Y disil'iiJuliom; for nU thre(' s('gl'l'galiJt~ gP11l'I'nLions, In tluth
CfiSP t,lH' ynlidity of t Itt' hypothpsis would hllV{' ht'I'n df't.f'l'll1inctl by
It'st.ing goo(\nC';-ls of fit \)(It\\'('(>11 the lheoreti(,fl1 un.d obt'llined fl'equl.'l1cy
di:;tribut.ions of the s('gn'p:n.ting gPllel'lltions. ]){'\ njjpd in'queney
diskilJUlioJl~ ufl'ol'(\ fi, sOtlnciPI' bnsis for g(,ll('l,ie nnn1vs('s t.han ('on(\ellsNl
in'qlll'J1(',Y distrihllLions. How('Y('r, both kinds hil.'~c n, place in genetic
nnn.l \'"P;;,
hi COndp11."ing tll(' fl'<'fI\l('Il('Y di;;t!'ibution::;, maXilltllm diITel'Pl1tintion
of tll<' six POpuil1tions wns gou~ht. OIH' IH'O('('(lul'l' tlw.t nid(·d in
Ilttaining thi:; ohjl'cti\-(' wn::; to ll1al,(' lht' gtoupings SUd1 (W}H'U
po,;sibLt'! thill fo!' 1'!H'h of the' nonsl'gn'gttting populnJions nil pln.nts
£(111 into e\nsse's ('()ntllinin~ no plants of allY {)tht'I.' sueh populntion,
'VhpIWY('!' this ('nnnnl h(\ d01lC', lhe C'ond('\1sing should be sHeh t.hn,t
a miJlimum or oY{'l'illj)ping o('eUl':; , 01\('(' a pnrti('ulnl' grouping is
•
50
'f.ECH...VICAL BULLETIN 998, U. S.DEPT. OF AGRICULTURE
decided upon, of course, it must be applied uniformly to all six of the
populations. The purpose of grouping is to discern major differences
that are obscured by minor variations in the detailed frequency
distributions and to provide a method of analysis for those cases in
which the detailed theoretical frequency distributions cannot be
determined for genotype!;> that have u11ferent but somewhat similar
frequency distributions. Inevitably, the grouping obscures much of
the variation attributable to minor causes. In analyzing and inter­
preting condensed frequency distributions, these facts must be kept
in mind nud the detailed frequencv distributions must be studied also.
All constants (means, va,·iances, coefticients, etc.) should be calculnted
from the individual-pll1nt data.
It should be noted that the means of t.he diiferentpopuJations
providtl the most infol"mntioll as to the number· of gene pnirs differen­
tiating the parents when phenotypic Ilnd genic dominance Ilnd epista..'lis
are eomplete-that is, when one dominant gene produces as grent, or
almost as great, an ('ffeeL as all the dominnnt genes together. Such
was the case in respect to the genes differentiating the pnnmts as
regllrds period from seeding to first bloom.
Comp8l·isons were made involving the phellotypes and respective
gcnotypcs of thn diffc,·ent populations; yltrinnces, cOITelntion and
}'egrcssion (~oefficients, nnd relntive percentages of the vlt,·innee
Ilccountl'd (0'· by l"('g,·ession were ealctllnte<l; nnd the frequency of
oC'CUrl"l'l1ee of individuals in the, mOl·o desimble dnss ns regni"<Is two
chnmcLcrs wns ·dl'termincd. D('tnils of thc methods used in this
determumtion nppenn·d in nn enrlil.'l" publicntion (18). These stntisti­
('nl ('onstllnts nnd methods of lLunlysis were npplied to a study of the
popullLtion!; nnd of the dl.'p('ndent nnd eomponelltehnmcters. Agnill,
the C'ompnrisons involving the phenotyp('s n!1<l genotvpes of the
Tespeetiye. pop\llntiOlls provided the most inforIllntion. Iloweyer, the
constnnls cnkulnted and oth('l· Ill('thods of proC'edure contributed
much to the Ilnnlysis Ilnd nidl'd mn.terially in the finn] interpretation
of the dlltn. H('rc it should be pointed out that rclntive percentn,ges
of Lhc YllrinIlC'e of th(' dependent chnl"llcter at"countcd for by regression
somctimes n'·c ne~nth'e in sign.
'fhe methods nlld procedmes outlined do not provide for: n progeny
t('st. ]1"0'· prog('ny t('sts of sel('C't.ions mnde nt. rnndom 0'· otherwise,
the m(·tho<ls !llld proC'edUl"es involving pcn('t,·nnc<'s \\'('r(' deYclop('d 11ud
illustrllt('d by the senior nuthor prl.'viollsly (11). Progl.'nies obtniued
by sdf-fe,·Lilizing plnnts of the seg'·('gnting poplIlnt,ions should be
inelud('{l. Progenies obtnined by s(,lf-fel·tilizing plnnts of the F2 and
the two bn<'k(Toss generations could be grown eith('r in nIl inelusive
study with nll the geuerntions used in this study or in nn expe,·iment
the following yent· with the P., F., Ilnd P 2 genl.'rntions. In either event
the pllrtitiouillg ml.'thod of gNletic anlllysis should be used.
Thus fnr in this bulletin, gene pnu·s hayc been designated by symbols
that differcntink· the genes \\;thin chal·ncters but not between cha1"l1c­
ters. This pro('edme simplified the analyses; but it is inappropriate
for general use, owing to the confusion thnt might result. Therefore,
different symbols 11I"C now assigned to those genes found to have dif­
(erentintcci the pnrents. The ne\\r symbols, in which the subnumcrnls
•
•
.' GENETIC
•
D, respectively, of the former Character:
Perccntagc of flowers that set fruit ________________ _
Period from seeding to first blooltl. _______________ _
Period from firi;t bloom to first fruit set,. __________ _
"et Lo first. fruitripe _________ __
Period
first, fruit
Numberfrom
of loctllCil
______________________________
Weight per loctllc _________ ". ____________________ _
M ..\JOR
OeM ."nbol. FJ.F2hfl'!/3 Pd.,
B.b.B2b2B31'3,
S.3.S2S283 SJ'
R.,.
tc.ic. tC'jic'jLc3ic3'
/(2'2,
W.ttl.1J'2W2 W 1W3,
GENE PAIRS Dln'ERENTU,TING CUARACTERS
Pf'riod from seeding lo first. fruit ripe is differentiated by eight. major
gene Pilil's, It Sel'ms highly prohn bl~\ tim\' Iinknge inst.ead of pleiotroRY
produced t,hc r('\lllions noLed betw('(IJl the foul' s('l'i(,s of genes ii, Ss,
Rr, uud Ide with the exc{lpLion of lht' Pi nnd Ss I'('lntion, hncause aU
the Ilssoeinlions Ilot(·d IU'O (,hose ('xpeet(ld on the bllsis of linkage, If
pl('ioll'Opy W(>1'(' lIn·oln'd, sudl n'llltion5 would bt' coineidentnl, which
for nil thNle g('m' s('I'il's is highly impl'obllble. Howl'ver, ns pointed
ou(, bdor(', SOIll(> of tht' gl'nes of the Pi nnd Ss s('ries mllst be identical,
us peJ'('l'nlng(\ of f1ow('l's lhnt S(\t fl'uit hilS nil dfect on pcriod from fit'St
bloom to fil'St frui(' set. '1'hl' Lclc nud W1V scri(~s of g('lIes, difl'CI'('ntint­
ing Humin'l' of 10(,IIIl's Ilnd ,,'eil!ht l)pr locule, I'espect,in,ly, W('l'e inde­
p{,lldt'nt 115 l'l'gllrds Iinkllg(' 1111(\ pleiotropy, Thus, sin('(' nU (). of the
ciml'llcl('I'S 11ffect yit'ltl of ripe frui(' p('r plnnt, at lenst 15 mn,jor gene
pnil's pitlyed 1\ pllrt ill the differl'ntilltion of this chlll'neL('I', Thnt only
15 Ilnd not IS hlw(' b(,rn definikly ili('ntifiNI is nttributed to the fact
t.lInt the PJ und Ss series hn\'e SOI)lC gene pnirs in common,
INTEllACTIONS
TI\(~ infonllntion on dominance for the dopendl'nt nnd independent
chlll't1ct(>rs is summnrized in tnble 28, All the eigh t characters listed
in the tnble nffl'et yield of ripe fruit pCI' plnnt; therefore, any of the
gell(>s listed in the tnblc were instrumental in differrntinting yield of
ripe fruil p('r plnnt, With these fucts in mind, it is interesting to
callsid('I' Lht' dOminllllce relatiolls, .For percen luge of flowers thn(, set
fruit phl'110typic Ilnd genic dominance were intcrme<iillte, Both
ph('notypic 11IHI gcnic (lominIUlc(> werc complete for period from seed­
ing to first fruit ripe unci its component chal'llcters, Both were pm'tial
for fewl'r locules pCI' fruit, "'eight per locule showed heterosis, and
T ,\.£11.,; '2S.-Summary of illformail'on on ciominance for dependent.
churucicrs
.
---,-..
I
(l1IIi
-".~"' -~.~------:-------;-------
('hamctcr
•
51
OF TOMATO CROSSES 1, 2, 3, a1\d 4 stand for A, B, 0, and
designations, follow: NUliBER OF
•
A.~.-\LYSIS
Perr~nta~\' 01 flowers that setlrult .. ....
l'cri(ldlrOln S<:Nlln~ to first lrult ripe.....
S['"dlll>: to tlrSl bloom . ." •..• "••• _.
~'Irst bloom to first fruit set.... ••••••.
~'irst Irult S('t to liNt fruit ripe........
\\'el~ht \lcr fruit ..... ..................
Xumber or locules •..,
......
~~.~~:~~UIC .. , eo e.' .••••.••••
}'. gCIIOtytlQ
I
independent
------
Domlnnllco
1'lwllot)'plc
Oenlc
f',f,F,J,f'./aF./I ••• Intcrmcdilltll. ••• Illtcrmc(lintc,
. ...... COlllplete ....... COllllllctc,
B,h,B,b,B.b •.• ., .. ••••• do .•••••••••
Do,
do....... •••• Do,
R,r,R.r•.••••••••• : .... •do ••••••••••
Do,
..... ....... .•.• l'nrthll.......... IntcrmctllntcorJmrtlnl,
1-c1/c.Lc.lc,r.clk•..• .... do . .•••••••. Partial.
11"./1.', W.le..
!letl!rOsls.••••••. Intermedillteor pllrtlnl,
s,.,S,·,.S•••....••.......
I'hW'
!
!
52
'l'1~CrIXlCAL Bt:LLETIX OOS, U, S, DEPT'. Ol-~ AGRICUL'l'URE
genic dominnnce fOl' this Chill'fictm' WilS intermediate or pill'tial. The
genes Ide IlndW1D combined to produc0 ptlrtinl phenotypic dominllnce
lor weig~1 t per fmit; henee the genes dilfen:mtinting \\'eigh t pm' fruit
showed pnl'tiiLl dominiln~'e ilnd pl'Obnbly in some instllnccs intel'lllO­
diato dorninilUetl , '1'11(.'11 the eOmpOlll'llt chlll'l1cters of yield of ripe
frui t (Jl'I' plant showed thc following degre('s of phenotypk dominance:
Compl(lte dominlUlee of the lesser contl'l1sted eharach'I', parlinl domi­
lHU1CO of Lhe lesser contrasted chlll'neter, intCl'mcdilttll domiunnce,
pnl'tild domina.ncc of the gl'cl1ler (,Olltmsted ehftmctct', Ilnd heterosis
of the greate!' eontmstl'd Chllt'ftctt'l', 'l'lt(l· dif\'l'!'ent gl'lll'S afi'ccting
yi\:k~ of ripe frui L pCt' plnn ~ sho\\'('(1 the following cl~gl'('l'S of' genic
dOmlIlIiIWC': Complele dOmtnfUl('O of the gl'lles telldlllg to produce
the smlLlll'r YlLitH.'i', pl~I,tilll don,linn,ll('l' of th~ genes tending to produce
the 51111\ lit'1' VllltH'S, lllte!'I1lNlmte dOll111laurC', nnd. pel'lmps, pnrtial
dOmLllItIH'{, of the g('ll('$l tending to pl'oduce til(' 1!u'gel' '~nl\leS, Clendv.
tl\('r(' wns Il wide runge ill tlH~ C'xpreMion of both phl'llOLypic ilml gNlic
dornintUlc'c ns I'('gllnls yield of ripe fruit pet' plant,
'
The tel'lniuology mwd and. the conCt'pt of tht' plH~llom{,llOll of domi­
nlW('e {'XPl'l'sst'd tIl lhis bulletin WC'I't\ set COl'tlt in ItIl C'arliN' publication
by thl' sellior' ILlllhol' (10), and thC' literntu('l' deillillg with heterosis
WIL'; r('\'iew{'d by \\""hnl('v (;ddL Thnt g(,llic domillnllC'c is dept'ndC'ut
upon tht' gCllotypie rnili'eu wns poillted out by Fisht't, (4) and mltny
ot\tl'I'S (1). This would incli('nte thnt the inteml\('lie lind intmnlll'lic
inll'l'It<:Lions 1l1'O not sepllrllble. strielly spenkinfF' The dittli presented
0(1'(,1' sonH' ('\'id('nee in support of this contentIon,
'rhe intcl'l'C'lntions of the chnl'll.ders nS regards linkngc, plciotl'OPY,
and t'lldl'onml'nt are sllmmlUi7.ecl in tnble '29, Linkages nl'O shown
fol' SOIn{' of til(' g('nQ.'l difi'{'ren tinting pl'reen tngo of f\O\\'('I'S thn..t set
fruit, pl'riod fl'OIll firslIJloolll to first f(,lIit s('t, 'period from first fruit
set to fil'st fruit ript', nnd numb('r of locules per fmit, 'l'he nssocinLion
bl'tW('('1l IH'ITl'ntng<' of f1o\\,l'rR lbnt set fmit llnd pel'iod from first
bloom to {il'st fntil S{'ti i~ tllll,t t'xpeclC'd on the basis of pleiotl'oPY,
HOWe\<el'j thel'!.' is 80111(' qUN;tion wheth('l' this should be considered
'1'.\111.1':
20,- SUlllllwry of
ilt/crrcl(Ia()n,~ 0/ l'IlIlr(lc/crs (IS regards lillkllflf, 1J1rto/ro7JY,
and Clll'ironlll(,llt
Illtt'rrrJ~tlous l
Churocter 1
lib SJ
Pfr<'Ntt:IRP
fmiL!f[,
or
Oowers th,'t
..
S.!t
I'Pflod (emu 5<'1.'.1101( to III't
blooll\ .m);
PI'cil.l from /lr~t hloo[[\ to Jir'L
-;<'1. ; S,"
I'!'rio\l lrmu fif'\t frUIL $('[
!rua. r1pl~ i Ur I .. ~
(rlllt
to /lest
~!lmi"'r of 1()(,1l1~s 'l.rle'
""lght t"'r lor'ul" (11'11' ..
0
I?r Mlc IItf IJb S4
7
0
0
0
0
+
0
0
0
.,.
0
0
0
_.,,-
0
0
0
0
I)
0
0
0
O·
.~-~---
R, Lclc II"w IJ/J SJ If' Ule W!D
-.. ,
0:
0
0, '"
0,
0
0
0
0,
+
-
0
0
0'
0
0
0
,- +,
.-,i +
.,'.-c:
•
•
GENETIC
•
•
•
A-~ALYSIS
OF
TO~rATO
CROSSES
53
an nctunl case of plciolt'opy, The en\'ironmentnl effects wcro such
that. a dccrcnsc in period from fil'St fruit SOl, to first fruit ripe tended
to be n.ccompnnied by IUl inel'cnse in cllch of th(} othel' mntUl'ity chnr­
acters. Also, dCCl'cnSC in number of locules tendcd to be nccompnllied
by incrcnsc in weight per locule,
N cxt Iinkngc, pll'ioll'OPY, nnd thl' (Ill yironnl('ntlli l'l,ltttiOllS noled
tHe c'oll."itlN'l'd in n'I2:I\1'd lo thl' int('I'Il('~i01\S, Lillkngl' is I'L Ilw('\umienl
inlN'u('tioll, ItS lilt' 'l'l'IntiolU; I1nd lu:;sol'illLlons OblnilH'd nre (hie to the
fllc,t lhnL till' gl'nt'S in \"01\'('(\ HI'l' \o{'ull'lL in till' l:in·IIl(~ ehl'OInOSOllle,
PI('iolropy is !In intNI\.{'\ ion dClwndl'llt upon phYl'liologil'ld gf'l1etic
n'fI('tlons, in ~h!\t L1w gt'nl's tin' l'('spoJ).'iihll' fOt, l,he pl'odu('l,ion of sttb­
SLIHWl'S LlmL 1Il{[UP1Wl' till' t!(','plopllwlIl o( morl'· thun Olll' {'/HH'll{'tcr,
glwll'onml'tllui inll'l'twlions im'ol "l' till' ~t'IH'S ItS \\'l'lI liS till' ('lI\'irOll­
llWHt, Fol' ~'XII,nlpll', tnli:.l' intl'I'tH'tions bt,.t,\\'('('ll ppl'l'pntng(' of tlO\\'PI'S
L1mL ~il'l fruit (i"f) Ilnd tJtlriml from firsl fruiL sl'l to lirgL fruit I'ipl' (Rr).
As ll1l'u~llI'l'd b)< LIH' PHd products, this IS It Sl't'O]1<I-ordpl' illLPI'lt('tioll,
bJ gl'll(' s('ri('s X HI' ~('lH' ~(\I'il'H X Pit dr(Hlm(lnl. It follows lhM from,
lIll" HLnnd[lOl11L of (lUlUltit,ntiw inlwritnu('(' til(' illl!'I'II('ciolls fll'('. It
Ht~tti..;ti('nl-g:('J\l'ti(' ('olll'ppl, Intl'l'IIdions (Jbtninl'd by ptw\,ilioning
xJ iJltl) il-; ('omporH'lIts \\'('1'(' lls('d b\" Fislll'r (al IIml In' Pm\'('l's I\lld
lIiJll'::i (JEJI to t(lst fol' linkll~('1 nIHI :;t~\listies Wl'r(' used I)y 1'ow('rs (13)
to <l(,(,l'rnirl(' till' Jlut,tII'l' of t!t(l ill(,pnl('~ioll.'; of P;('Il('S eflt't'i('t! in difl'l'I'('nt
l'('gions or till' eht'o!llosOIlWS Lhlll, nfl'l'ell'd Hlllnl)l'L' of locull's nnd size of
.fl'lti t.
..:\.:n~' of Ill(' inlpl'twtl(1)S of ~('lI(,s notNlns 1I1l'{'('lillg finy of Ul(~ ('om­
pOJlt'nt clwl'ft('(,I'S dp/tIL with in this study \\'('\'(' illU'rildiolls of g('ll('s
difrl'l'(,Jltilltin~ yh,ld or dpl' fl:lIit Pl'I' plllnl. Wit.h thi;; fiw!. in mind, it
is int('t'p,;ting t.o noll' th{' illt('l'IlCLion,; 0f L1lf' grJl(,s difl'C'I'l'l1Liatillg l,he
('OmIH)I\('nl ('hn 1'IH'lt'I'", 'I'Ill' int I'llfilh,]je and inLpI'lllh'lk inl(,I'lt('tions
of tilt' .Ff P;I'J\!' .'{I'I'i(\.; \\"('1"(' SU!'l1 thut gl'ni(' clominmH'(, wns iIlLC'I'Jlwdint(l.
'I'll(' inll'ut\lll'lie llllll intp['III1"lil' intt'I'i\('tioll:; or til{' Rb sC'rics of gClH'S
W('I'(, SI1('11 thM OIl!' of t.lt£' six dominnnt. gC'J)('S shol't;('Jlf'Cl tho 1H'J'iod
fl'OIH ,,(,pding to fit"'l bl.ool1l n:; mll('h ns nil six, \\"hi('ll show:; 1,llfI.t hoth
domiJlllll!'1' lind I'pi:-:tn.;j.; \\'1']'(' ('omplPl;l', For LJw Ss S('l'it'S II.nd R1'
8('l'il':' or gl'IW'i, gP1tie dominnm'p wn::; ('ompl(,t(" Also, l;h(' ('{rects of
111l' gl'lll' pllll'''' \\';'I'l' l'unllllnl iq', (ll'nie domillll1l('(' WIlS partinl 1'01' the
gI'JH'S r/,(,) f'/'2 \ l('ntlin~ lo pl'Oclu('I' fl'Wl'I' 10('11\('8 P('I' fruit nnd fOl' tho
gt'HI' {LC}l tl'll(ling to Pl'Otlll('P 11101'(, locul(,s 1)('1' fruit.
'rhl'inlNnllelic
intl'l'iwt\on'i or th('sl' gl'll('S \\"('t'(' slI('h thilt. \ h(' 1'1l't,\'Ls of the g(']1(\ puits
w('n' c'um Ii In l i \'l', Finn.ll,'" fol' lll<' \ \ '11' s('rif'S of gl'lH'8 Ir('nil' dominllll('e
wn'i lit IN\sl ('\08(' lo inll'rnw(\itlt(' hut WflS pl'obn,hly pflltinl, nne! the
C'r!,p(,ts of thl' l.!I'IW ]luir;; W('I'P ('11 111111 nliql,
~ ('xC Ihl' inll'l'ulll'lir inl ('I'ill't iOlls of {hp g('IU's fiS dcmollsll'fi led by
tlll' int('I,,'(,hllions of tlte' ('ompotH'n( ('hI1l'I1('t('rs fll'(' ('onsit\('I'NI. The
(·11'1'(:1,; of till' Bb st-I'il's of gf'IU'S, thc S,'? sPI'ips, lind lile Rr 8PI'i('s, re­
sp(,<'th-('Iy, WPI'P found to lw ('utlllliatiy(', On nil ft"('I'I1~e llH' S gcnes
would bl' l'xlwl'l('(l to s!tol'l('n till' Iwl'iod from firsl bloolll to first fruit
~wl II'S":; in Ih(1 pI'pSl'n('p of tit!' H gt'lll'S than in I lip PI'('spn('(' of the l'
g!'ltP,;, if tlH' ph~'siolop;i(,111 1'('n('\ionR nll'pdinp; {he's(' l\\"0 ('OmpOIWllt
('1IIlI'll('«'I'S lhnt Wl'l'P insti~l\I('d hy th(' (,lIyil'onmpnt \\'('1'(' llH' snmc ns
thos!' insli!!:illpd by till' ,)';~'und HI"g(,IlP iWl'i('s, Thnt ~lII('h WflS lhl' ('nsc
8('('1115 IlI'()Il!lhlP 1\011) tit(' l'pslIllR of (;olds!'ltll1idl's wOl'k (7) with
ph('llo('opil's, In file( it s(I('ms uhnos{ Ilxiomntie l.hflt this wns tho
54
TECHNICAL BULLETIN 998, U. S. DEPT, OF AGRICULTURE
case, because the second-order interaction (88 gene series X Rr gene
series X environment) was such thnt, on an avernge, when the 8s series
responded to a given environment by shortening the period from fit'St
bloom to fil'St fruit set the Rr series in the same plant tended to pro­
duce a lonO'er pet'iod ft'om fh'St ft'uit set to fit'St fruit ripo, Then the
effects of these two series of genes were less thnn additive as regards
the dependent chnractm' period from seeding to fil'St fl'uit ripe, About
the same situation existed in respect to the Lclc series nnd the Ww
sel'ies oC genes, in that gl'eatet' number of locules, Oil nn aVCl'nge, was
aecomplUlied by less weight per locule, Since nlllnbel' of locules
times weight pel' loculI.' gives wt'ight per fruit, the ell'ects ft'om such n
second-order internctioll lue lllultiplicntiYe ns l'('gnnls the dependent
cbal'actor',
From this discussion of the illtel'!1clions of the genes, it is clenr that
the natul'e of tilC'se internctions vnl'ied accol'ding to which genes Were
involved, 'rhls is equnIly true of the i1lteractions between the genes
and th<' cnVil'Oml1(\nt, Study of int('I'ltctioIlS of g('nes nnd of genes
and ('nvil'onnumt occurl'illg ill respect to difi'cl'cntinLion of yield of
rip<, fruit p('r plnnt l'cvenled thnt the etl'ccts of the genes Ilnd environ­
ment w(,I'e less them ndditiye, additive, 01' somewhnt less thltn multi­
plielltive, In nil studi(\s il~volving such llltcrllctions, it should be kept
in mind thnt in all probnbility the intc1'Ilctions I1l'e between substances
and bt'Lwoen chlu,/tcters produced by the genes and the euyil'onments.
•
SUMMARY
In CI'OSS('S bdweI.'Il the PortCl' and Ponderosa varieties of tomato
(Lyco]ler8'icon esc~tlentu.Jn Mill.), each of the following characters was
found to bo difl'('I't'ntin,ted by tlm\('. major gl'lle pairs: Period from
seNling to first bloom, pel'iod from fil'st bloom to first fruit set, num­
ber of locul('s P('l' fl'lIit, and w('ight pel' locule. Pcr'ccntage of llowCl's
that sct ft:uit wn!'; difl'cl'('.ntiltted by four mnjol' gene pairs; period from
first fruit set to fh'st fruit ripe, by two; period from seeding to first
f!'llit ripe, by ('ight; nnd weight prl' fruit, by six, Altogether, mnjor
gene pail'S do!1nit.ely identified as nfl'ectillg yield oC ripe fruit per plant
Humbel'Ni 15,
For percentagt' of flOWCl'S that set fruit both phenotypic and genic
dominancc W(~I'(' intermedin,te,
FOI' the pt'J'iod from seeding to first bloom, both phenotypic and
genic dominance wel'e complet(\, With such iIltI'flIlllelic aI~d intet'­
nll(·lic in/;el'llctions, tho efl'ects of the genes for this charnctm' wore not
cumulative.
Both olH'notypic nnd grIlic dominance were complete for period
from fit1·;t bloom to first f{'uit set and for pcriod ft'om first fruit srt to
first f!'llit ripe, However, epistasis was not complete for the genes
difl'crentiating either of these charltcters; consequently the intemllelic
interilctions of till'se genes wero such tilltt the effects of the gene pairs
were algebmically cumulntive, whereas the intrnltllclic interactions
were such that the effects of the genes within any given pair of alleles
were not cUlllulative,
Both phenotypic and genic dominance were partial for the genes
difl'erentin,ting number of locul('s PCI' fruit. The intrallllelic and
intel'llllelic interactions of these genes were such that the effects of the
•
•
I
GENETIC A.l~ALYSIS OF TOMATO CROSSES
55
genes were algebraically cumulative within and between pairs of
alleles. Genic dominance was partial for the genes (LcILc2) tending
to produce fewer Iocules per fruit aud for the gene (LC3) t,ending to
produce more locules per fruit..
'rhe contrasted Chal'llcter greater weight per Iocule showed heterosis.
The datil. al'e not. discriminatory as to whether genic dominance WllS
intermediate 01' whether the genes tending to produce greater weight
pel' locnlo exhibited a slllall degree of partial dominance. The intra­
a.llelic nnd iuternllelic interactions of the genes were such that the
etl'eels of the gen('s wero nlgebraically cumulllLive. The data show
conclusively that dominance audhetel'osis depend upon the same
physiologicnI-gNletic phenomelUt.
The nltlul'c of the intc-l'lIctions betwel'11the genes differentiating the
component chul'Ilcters of weight per fruit was studied. All these genes
played It purL in difl't'l'enlinting the yield of ripe fruit pel' plnut. The
nnturc of LIle intcl'tlcliolls vuried according to the pnrticulnr genes in­
volyed. 'l'his is ('qunlly true of the intel'llctions between these genes
and the Nw1!'cnmcnt. Study of intel'llctions of genes and of genes
and envil'onnll'nt in respcct to diff('rel1tit'ttion of yield of ripe fruit pel'
plnnt l'cYl'nled thllt the en'eels of the interllctions vlll'ied, being less
than addit;ive, nddilin" or somewhl1t less than multiplicative accord­
ing to l!w component chl1rncters und tIll' genes difi'erentiating them.
Not all the gl'lH'S hnd equltl effects, either within or between com­
ponent chal'l1cters.
'rhl' gellelic variances ns estimated included the interactions. In
all cnSl'S, the gcnetic vl1l'iunccs for period from seeding to first fruit ripe
were .kss tluU1 would he expect('d on the basis of the assumption that
the intel'ttctions between genes and between genes ftnd environment
weJ'e sueh thilt the vllril1!lc('s of th(' component characters were additive.
The term "l'(\lu,tive percenlage" is applied to the relative proportion­
ate Plllt of the variance of n. dependent chamcter accounted for by the
variance of any given individual COmPOll('ut character.
RNlent'ch proel'dur('s and ml't:hods, including genetic and statistical
expl'l'imcntnl design, IU'C developed und illustrated that should mate­
riltlly I'ltcilitllte physiobgicnl-gelll'Lk and de\rclopmental-genctie stud­
ies. 'l'lH' method of gelleLic nnnlysis developed hns been termed the
"partitioning method."
•
•
LITERATURE CITED
(1) DOIlZll..l.NSKY, T.
10-11. (1E~ETICS AND 'l'HE OIUGlN Ot' SPECIES.
New York.
(2) EAST, 1'.:. :\l.
10a(). IIETEHOSIS.
Ed. 2, rev., 446 pp., illus.
Genetics 21: 375,...307.
(3) FlsHEH, R. A.
H)30. STA'rISTIC.U, ~IETIIOUS FOR Rt}SEARCH WOUKEHS.
iIlus.
•
Ed. 3, 283 pp.,
Edinburgh and Londou.
(,1) - ­
1031. 'I'm: }}VOI,l'TION OF umIlN."NCE. Cambridge Phil. Soc. BioI. Rev.
0: [345]-3()S.
(5) - ­
1034. STATISTICAl, ~n:THoDS I'on lU}SEARCIl WOUKJo]US. Ed. 5, 310 pp.,
ilills. Edinburgh and Loudon.
(6) - ­
1037. Till:: DESIGN Ot' EXI'EHl~IJo]N'I'S. Ed. 2, 260 pp., illus. Edinburgh
alit! London.
.56
'lECHNICAL BULLETIN 998, U. S. DEPT.• OF AGRICULTURE
(7) GOLDSCHMIDT, R.
1938.
375 pp.,
PllYSIOT,OOICAL GENE'l'ICS.
illus.
New York and London.
(8) HAYES, H. K., and bL\lER, F. R. 1942.
MB'I'HODS 0.' PLANT BREEDING.
London. 432 pp.,
illus.
New York and (9) JON}cS, D. F. 1917. DO~IINANCE
(10)
(11)
(12)
OF LINKED FACTORS AS A )IEANS OF ACCOUNTING Foa HETEROSIS.
Genetics 2: 466-479, illus. P:..lARSON, K. 1930. 'l'ABLES FOR STATIS'rICIANS AND BIOlIETRTCIANS. Pt. 1, cd. 3, 143 pp., illus. L-:mdon. POWERS, J,. 1934. THE NATUR}) AND IN'I'rJRAC'l'ION OF GENES DII'FERENTIA'I'ING HABTT OF GUOWTII IN A CROSS BETWEEN VARIETIES 01' 'l'RITICUAl VUL­ GAHE. Jour. Agr. Hes. 49: 573-005, illus. 1930.
'I'IIE NATl'HE 0.' 'l'IlE INTERAC'I'ION OF GENES AFFEC'I'ING 1'OUR Ql'AN'rl'I'A'I'IVE CHAUAC'I'EllS IX A CROSS BB'I'WEI~N HORDEUM m:.'ICIENS AND HORDEU:'! VULGAHE.
Genetics 21: 308-420. 1930.
S'l'UDIES ON TilE NA'l'URE OF 'l'ITE INTEUAC'I'IONS OF TilE GENES ])H'nmml'J'IA'I'ING Ql:AN'I'I'I'ATIVE CHARACTERS IN A CROSS BE­ TWI~EN r,Y(,OI'EIISICON .:SCULENTUM AND I,. l'HIl'INEI,LU'OLIUAI. Jour. Gellet. 39: [139]-170. 1041.
IXHEHI'l'ANCE OP QUANTIT,\'1'IVE CHARACTERS IN CROSSES INVOLVING '1',,"0 Sl'BCIES OF li'{COl'ERSICOX. Jour. Agr. Hes. 03: 149-174. 19·12.
TilE NA'lTHE OF TilE SERms 0.' EXYmON~IENTAL VARIANCES AND 'l'IfE ESTL\L\TION OF TilE GENE'J'IC VARIANCES AND THE GEOMETRIC ~IEANS 1:-;' CHOSSt]S INVOLVING SPECIES 0.' LYCOPERSICON.
Gen­ etics 27: [501J-575, illus. 1!J.l4.
AN l~XI'ANSION OF JONJ~S' THEOHY FOR TlfE EXl'T,ANATION OF HETER­ OSIS.
ArneI'. N:tt. 7S: 275-2S0, iIIus. (13)
(1,1)
(15)
(16)
(17)
(IS)
1045. mH...\'rIVE YTFlI,DS O~' INBRED
Bot. Gaz. 100: 247-20S. 19,15.
(10)
(20)
(21)
(22)
(23)
•
r,tNES
.um 1'1 HYBRIDS OF TOlIATO. •
STHA WBERRY RREEDING S'rUDIES INYOLYING CROSSES BETWEEN THE CLrr,TIYA'l'ED YARIE'rIES
FHAGAIUA ANANASSA) AND THE NATIVE ROCKY lIOUN'r.UX STRAWBERRY (F. OVALIS). Jour. Agr. Res. ex
70: 05-122.
- - - :tnd H INI>S, L.
1033. IXIHlHl'J'ANCE OF REACTION TO STEll RlrST AND RARRING OF AWNS IN
BAHI,EY CROSSES. Jour. Agr. Hes. 40: 1121-1120, illus.
- - - and Lyox, O. B.
HJ4L IN1!ERl'rANCI~ STl'DIES ON DURA1'ION OF DEYET,Ol'MENTAL STAGES IN CllOSS~JS W!'l'HIN 'l'IJE GEXUS LYCOI'EHSICON.
Jour. Agr. Hes. 63: 120-1'18.
SXEDECOH, G. W.
1040. STATISTICAL l!E'rrrOIlS AI'PI,lED T{' EXI'ERLIIEN'I'S IN AGRICUUL'URE
AND ·RIOI.OGY.
Ed .•1, 'lSi') pp., ill us. Ames, Iowa.
'rnloFEEFF-lh;ssOVSKY, N.
1931. GEHICII'J'ETES VARllSHEX IN DEll 1'IlAXOTYI'ISCHEN MANI1'ESTIERUNG EI::-;rr:I~R m,NOYAHfA'I'IONEX YON DROSOPHILA FUNEBRIS.
Natur­ wissenschaften 19: 493-497, illus. "THALEY, 'V. G.
104.4. HETEROSIS. Bot. Hey. 10: 461-40S.
'V.
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•