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-- 1.1 I 111111.25 111111.4 111111.6 MICROCOPY RES')LUTION TEST CHART NATIONAL BUREAU Of SiANOAROS-196l-A MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU or STANDARDS-1963-A { , <:'.' ",- ... !.i tS . ~. t"' , / 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 0)" ..... I 2 • S - ~ .-Submitted fc,;;.,pubO!:RUon9\farrh 1, 1949. FOI'IJlC'r1y StU~lIt ~ista~ U. S. Southern Great Plains Field Station. Unpublished ¢,-ta'a:J C£) S·13160-50-1~ lL.J ~ 1 ~ ~ u.. ~ Zf ~ C£) o .....:l 2 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 • • 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. 'U, S. 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