Download Alan Robertson

Copyright 0 1990 bv the Genetics Societyof America
Alan Robertson
(1920-1989)
ALANROBERTSON
was born on February 2 1, 1920,
in Preston, England, and died in Edinburgh on April
25, 1989, after a longillness. His early education was
at the Liverpool Institute, and he then went on to
Gonville and Caius College, Cambridge University,
from which he graduated with a B.A. in Chemistry in
194 1. He commenced postgraduate research in physical chemistry at Cambridge but his studies were interrupted by the outbreak of World War 11; he published several papers on physical chemistry but did
notcomplete his Ph.D. ALANworked with C. H.
WADDINGTONOperational
in
Research during thewar
and subsequently was invited to joinWADDINGTON
in
the Agricultural Research Council Animal Breeding
and Genetics Research Organization (ABGRO), initially at Hendon and later in Edinburgh. He studied
with SEWALL
WRIGHTin Chicago and JAY LUSH in
Ames in 1947, then returned to ABGRO in Edinburgh. He remained in Edinburgh for the rest of his
career in what became the ARC Unit of Animal
Genetics, directed initially by WADDINGTON
and later
by DOUGLAS
FALCONER,
and was promoted to Deputy
Chief Scientific Officer in 1966. ALANreceived a
D.Sc. from the University of Edinburgh in 1951 for
his work in genetics and was appointed an Honorary
Professor in 1967. He was appointed OBE (Order of
the British Empire) in 1965 and received many other
honors for his contributions to science, notably election as a Fellow of the Royal Society of London in
Generics 125: 1-7 (Mav. 1990)
1964 and of Edinburgh in 1966, a Foreign Associate
of the National Academy of Sciences of the USA in
1979, a Foreign Honorary Member of the Genetics
Society of Japan, and a Member of the Spanish Real
Academia de Ciencias Veterinarias. He was also
awarded honorary doctorates from the University of
Stuttgart-Hohenheim, the Agricultural University of
Norway, the State University of Liiige and the Danish
Agricultural University. ALANis survived by his wife
MEG, whom he married in 1947; his three children,
MARK, HILARY andMICHAEL;and three grandchildren.
ALANROBERTSON'S
early contributions to genetics
were in the field of animal breeding and primarily
focused on breeding dairy cattle for increased milk
production (although one of his first papers, with M.
LERNER,
was an analysis of the heritability of a threshold trait, viability, in poultry). In the mid-1940s to
1950s animal breeding theory was in its infancy. Together with J. M. RENDEL,
and prompted by the ideas
and HAZEL(1944),
of LUSH(1947) and DICKERSON
ROBERTSON
showed how the genetic gain per year
resulting from mass selection for milk yield depended
on the relative selection differentials and generation
intervals in the four pathways for breeding replacement bulls and cows each generation: cows to breed
bulls, cows to breed cows, bulls to breed bulls, and
(1950)
bulls to breed cows. RENDELand ROBERTSON
showed that, with no progeny testingof bulls, progress
2
T. F. C. Mackay
depended on selecting cows on their own performance, and that the
maximum rate of progress that
could be expected was an increase of 1% of the
average yield per year in a small herd. ROBERTSON
and RENDEL(1950)demonstratedthat,although
progeny testing ofbulls resulted inonly a modest
increase in genetic gain to 1.1% per year in a small
herd (because the increase in generation interval necessary to evaluate the bull’s breeding value offsets the
gain in selection differential), with artificial insemination the herd size could be increased 20-fold, so
that progeny testing of bulls together with performance testing of cows could give a theoretical rate of
progress of 1.7% per year.
Having demonstrated quantitatively the theoretical
merits of progeny testing,ALANROBERTSON
set about
considering the practical problems of implementing a
progeny testing scheme on a national level. In a breeding program using progeny testing,most selection can
be placed on the “bull to breed bull” pathway. ROBERTSON showed with A. A. ASKER(195 1) thatselection
decisions made in a few herds greatly dominate the
genetic improvement of the breed as a whole. Herds
of British Friesian cattle (and of eight other breeds;
ROBERTSON1953) can be grouped into three
tiers.
The top tier, composed of a few herds, breeds superior bulls, which are sold or used by multiplier herds
in the second tier; sons of these bulls are then sold to
the third groupcomprising the bulk of the herds. The
problem then reduces to one of finding methods to
evaluate bullsin the top tier and
using them most
efficiently to breed future sires. Progeny testing, of
course, involves estimating bulls’ breeding values on
the basis of theperformance (milk yield) of their
daughters. If the daughtersof the various bulls under
test are unevenly distributed among herds, variation
in management practices leading to different production levels between herds and between years will seriously confound the estimation of the bulls’ breeding
values. This led ROBERTSON
and RENDEL(1954) to
suggest the“contemporarycomparison”method
of
evaluating bulls, whereby the average yield of a bull’s
daughters in a given herd andyear is compared to the
average yieldof other cowsin that herd and year,
taking into account the number of animals in each
group. The tested bulls can then be ranked and the
best chosen to breed young sires. This method works
best if the rank order of breeding values is the same
regardless of the overall level of production of the
differentherds,and
if the accuracy in estimating
breeding values does not differ for different production levels (that is, if there is no genotype by environmentinteraction between milkyield and plane of
nutrition). The absence of such genotype by environment interaction was shown to be true generally (MASON and ROBERTSON
1956), and in 1954 the contem-
porary comparison method of progeny test evaluation
was adopted by the Milk Marketing Board of England
and Wales. It has been used extensively in the dairy
cattle industry in Great Britain, and only recently has
theadvent of schemes formultiple ovulation and
embryotransfer(MOET)promisedtochangethe
basic structure of the industry-as had been foreseen
by RENDELand ROBERTSON
(1950) as a method for
increasing the contribution to genetic gain from the
“COW to breed cow” pathway.
ALANROBERTSON
was concerned with the family
structure of the breeding population for three reasons. First, it is important for optimizing progress per
year because of the conflict between testing few bulls
with manydaughters, thus obtaining
reliable estimates
of breedingvalue, or many bulls withfewer daughters,
thus giving greater selection differential. ROBERTSON
(195’7) showed quantitatively how best this balance
might be achieved. Second, the efficiency of a breeding program depends on the
accuracy of the estimates
of the heritablilities and genetic correlations of the
selected traits. Suchestimates are notoriously variable,
and ROBERTSON(1959a,b; 1962) and LATTER and
ROBERTSON
(1960) showed how the accuracy could
be improved with the use of efficient experimental
design. Third, selection causes inbreeding both because the selected parents area restrictedsample from
the population and because selection increases the
proportion of genes in common in the selected group
(ROBERTSON
196l), leading to inbreeding depression
and loss of genetic variation in selection lines.
The mid-1950s marked the beginning of the flood
of information that was to become available on biochemical polymorphisms in populations, and animal
breeders were quick to question what use this information might bein improving productionin domestic
livestock. There was initial excitement about associations between blood group polymorphisms and traits
of commercial importance in dairy cattle and poultry
raised the
as an aid to selection, but ALANROBERTSON
following important caveats to searching for associations between marker loci and quantitative trait loci
(QTLs) that remain equally relevant today (NEIMANNand ROBERTSON
1961). (1) If the association
SBRENSEN
is caused by linkage, there will notbean
overall
association between the markers and QTLs in a population at linkage equilibrium, although a transient
association may occur following a cross of two populations or if the marker locus and Q T L are closely
linked. (2) Statistical problems arise because multiple
simultaneous tests of association are made between
the marker loci and production traits, causing spurious false positive associations if care is not taken to
set the overall significance level to compensate for the
number of tests and to remove sets of quantitative
traits that are highly correlated genetically. Even so,
Alan Robertson ( 1 920-1 989)
different associations may prove significant in different samples. (3) Real associations between marker loci
and QTLsmay be different in different genetic backgrounds, so that the same correlations will not necessarily be found in different populations. (4) The practical value of taking accountof an association between
a marker locus and a QTL in selecting animals depends on whether the proportion of the genetic variance of the traitexplained by the association approaches the heritability of the trait. The proportion
of genetic variance attributable to significant blood
group associations is generally very small.
These problems, coupled with his growing conviction that the number of loci responsible for most of
the variation for quantitative traits is small compared
to the potentially large number of biochemical polymorphisms, led ALANto doubt theutility of searching
for associations between the two categories of traits.
By 1966 he was convinced that the future of animal
breeding wasin understanding the biochemical and
physiological correlates of response to selection. Several research projects measuring
such correlates of
response to selection for growth rate in mice were
laterinitiated by his colleagues in Edinburgh (e.g.,
BRIENet al. 1984; SHARPet el. 1984).
ALAN ROBERTSON
recognized from the beginning
the greatvalue of molecular polymorphisms in tracing
the history of populations, and thought the most interesting question to be addressed waswhy so much
variation was maintained at theseloci.Finding
no
evidence that heterozygotes forblood group loci were
superior to homozygotes with regard to production
characteristics in dairy cattle, he suggested that such
polymorphisms were neutral (NEIMANN-SORENSEN
and ROBERTSON
1961) before the formalproposal of
the neutral mutation, random drift theory of molecular evolution (KIMURA1968). ALANretained his interest in the growing field of molecular evolution,
following the unfolding globin gene-family story with
particular interest, and was often asked to speak to
animal breeders on the application of molecular biology to animal improvement.
Dairy cows are not themost tractable of experimental animals, and early in his career ALANROBERTSON
turned his attention to Drosophila melanogaster as a
model system with which to examine the validity of
existing theory, to determine in what way the theory
neededtobeextended
to cope with discrepancies
between observed and predicted results, and to investigatethe nature of quantitativegenetic variation.
This interaction between experimental and theoretical research can be traced from the now classic series
of papers on an experimental check of quantitative
genetic theory with his colleagues G . A. CLAYTON,
J.
A . MORRISand G . R. KNIGHT. Selecting for increased
and decreased numbers of abdominal bristles from a
3
randomlybredpopulation,
CLAYTON,MORRISand
ROBERTSON
(1957) showed that the short-term average response of replicate populations agreed well with
that predicted from
estimates of heritability in the
base population, and thatgenes controlling abdominal
bristle numberact additively and are neutral
with
respect to fitness. However, the long-term response
was unpredictable (CLAYTONand ROBERTSON
1957),
often reaching a plateau at which genetic variability
was still present due to the maintenance of homozygous lethal or sterile genes with heterozygous effects
on bristle number, so that artificial selection was balanced by natural selection. In lines selected for low
bristle number, a sudden rapid response in females
was accompanied by an increase in variance; this was
later inferred to be caused by mutations at the bobbed
locus (FRANKHAM
1980). Correlated response of sternopleural bristle number could not be well predicted
from the correlations in the base population (CLAYTON et a l . 1957). The primary questions to emerge
from these experiments were how to predict limits to
selection for given population sizes and selection intensities, what determines the response of a character
not directly selected in a line selected for another
trait, and what are the relationships among quantitative traits and fitness and its components. ALANROBERTSON and his colleagues addressed these problems
theoretically and by further experimentation.
Fora simple additivemodel, ROBERTSON(1960)
showed that the expectedlimit to artificial selection is
equal to the expected response in the first generation
multiplied by twice the effective population size, with
a half-life of 1.4 times the effective population size.
The theoretical limit is the same if two populations of
size N are selected independently and then crossed
and reselected, or if a single population of size 2N is
selected. These predictions were found to hold gen(JONES,
erally true for
experimental
populations
FRANKHAM
and BARKER1968; MADALENA
and ROBERTSON 1975). The theory of limits to artificial selection was later extended to include the effects of linkage (HILLand ROBERTSON1966; ROBERTSON1970,
1977). The effect of linkage on thefinal limit depends
on population size, the problem being whether the
negative associations between linked loci withopposite
effects on the trait caused by selection can be broken
by recombination before they are fixed by chance.
The general consensus is that linkage will not substantially reduce the limit to selection expected with free
recombination for most combinations of parameters
relevant to selected populations. This was confirmed
experimentally by MCPHEEand ROBERTSON
(1970).
Drosophila selection lines, in whichrecombination was
suppressed over 80% of the genome, reached limits
to selection for sternopleuralbristle number that were
reduced 25% from limits achieved with free recom-
4
T. F. C. Mackay
bination. NICHOLASand ROBERTSON
(1980) further
extended the theory of limits to artificial selection to
the case where thelimit is caused by a balance between
natural and artificial selection, showing a reduction in
the final limit and maintenance of genetic variation at
the limit, as observed experimentally. Natural selection must be very strong before this sort of plateau is
achieved.
The problem of unpredictable correlated responses
to selection raised by the early Drosophila experiments was investigated using computer simulation by
BOHREN,HILLand ROBERTSON(1966). The asymmetrical correlated responses to selection often observed in practice couldbeexplained
because the
genetic covariance between two characters is very
sensitive to changes in gene frequency caused by selection or drift, so that the predictive value of the
genetic covariance estimated in the base populations
does not hold for many generations.
ALANROBERTSON
saw selection experiments with
laboratory animals as most useful in determining the
nature of quantitative genetic variation in terms of
the forces creating and maintaining variation for
quantitativetraits, andthenumbers,
effects, gene
frequencies and interactions of loci controlling them.
The extent to which spontaneous and X-ray-induced
mutation causes genetic variation for bristle traits was
and ROBERTSON
(1955, 1964)
examined by CLAYTON
by response to selection of populations of different
genetic origin (highly inbred, plateaued, and genetically variable base populations). The concept of mutational variance (the input of new additive genetic
variance pergeneration) was introduced,and was
estimated from thevarious experiments to be roughly
times the environmental variance (VJ for spontaneousmutations and 0.003 V, for X-ray-induced
and ROBERTSON
(1955) emphamutations. CLAYTON
sized that this mutation rate was large in an evolutionary context, and that levels of variation observed in
natural populations could easily be obtained by mutation-drift balance for a neutral character in a small
population. Genes of large effect oftenappear in
selection lines, for example recessive lethal chromosomes (e.g., CLAYTON and ROBERTSON 1957) or visible
recessive genes (e.g., MADELENAand ROBERTSON
1975) with heterozygous effects in the direction of
selection. With a view to distinguishing whether these
genes of large effect were initially present in the base
population or had arisen de novo during selection by
and NARAIN
mutation or recombination, ROBERTSON
(1 97 1) determined
theoretically the average age and
average time to elimination of recessive lethals in small
populations, and ROBERTSON
(1978) derived the distribution of time before a single copy of a recessive
gene appears as a homozygote in a later generation.
ROBERTSON
(1 955) proposed that the maintenance
of genetic variation for quantitative traits could be
understood in terms of their relationships with fitness,
and thatquantitative traits could be
divided into three
broad categories: traitsperipheralto
fitness, traits
with an intermediate optimum, and major
fitness components. For the first category, neutral traits, variation in thetrait is not associated with variation in
fitness, populations harbor a large amount of mostly
additivegeneticvariation,
there is no inbreeding
depression, and variation islikely maintained by a
balance of mutation and drift. At the other extreme
are major componentsof fitness for which populations
display small amounts of mostly nonadditive genetic
variation, possibly maintained by a balance between
mutation and selection against deleterious recessives
at mostloci and overdominance at some loci. Such
traits characteristically exhibit
severe
inbreeding
depression, and are expected to be negatively genetically correlated with other major components of fitness. ALANROBERTSON
was intrigued by the fact that
the population means of quantitative traits were stable. He evaluated the hypothesis that this stability was
a consequence of an intermediate optimum with respect to fitness. Individuals with extreme values of the
traits are more fit either because stabilizing selection
acts directly on the trait or because extreme individuals are more homozygous and heterozygotes are less
fit. For both models there are problems explaining
the maintenance of variation for these traits.ROBERTSON (1956) showed that stabilizing selection leads to
fixation at loci affecting the selected trait and decreases genetic variation for the trait. ALAN was in
any case not happy with the stabilizing selection model
because of its implicit assumption that selection acts
on genes only through their effects on a single character, which is perhaps why hedidnotconsidera
balance between mutation and stabilizing selection as
a model for maintaining variation. However, neither
can heterozygote advantage be
generally true, because
of the genetic load incurred.
Having conceived the above theoretical framework,
ROBERTSON
then proposed several experiments to test
the strengthof natural selection acting on quantitative
traits, many of which he and his colleagues applied to
Drosophila bristle number. One test of the strength
of stabilizing natural selection is to perturb thepopulation mean of a trait by a few generations of artificial
selection, then relax artificial selection (to determine
if stabilizing natural selection will change the mean
toward its initial value) and apply artificial selection
in the opposite direction (to determine the amountof
remaining genetic variation for the trait).If the mean
of the trait does not alter under relaxed
selection but
responds to reverse selection, then strong stabilizing
selection does not operate on the trait. Several published (CLAYTON,
MORRISand ROBERTSON
1957) and
(1920-1989)
Robertson
Alan
unpublished experiments of this sort were conducted
laboratory to determine the strength
in ROBERTSON’S
of stabilizing selection for Drosophila bristle traits. In
all cases the means of the selected lines responded
little to relaxed selection, despite considerable residual genetic variation at the time selection was suspended. Another approach is to manipulate chromosomes from lines selected forhigh and low bristle
score so that one chromosome is heterozygousfor
chromosomes from the high and low selection lines,
and the others arehomozygous for either the low or
high bristle background. Because the optimum model
involves fitness interactions between loci, if stabilizing
natural selection acts on the trait, the mean bristle
score will increase when the segregating chromosomes
are in a low background and decrease when they are
in a high background. ALAN ROBERTSON
personally
performed several several such experimentsand
found no tendency forthe mean scores of his synthetic
populations to change (ROBERTSON
1967). These observations led ROBERTSONto conclude that, at the
majority of loci controlling variation for bristle traits,
the segregating alleles are neutral with respect to
fitness. LATTERand ROBERTSON
(1962) directly measured the fitness of lines selected for several generations for two bristle characters and wing length, using
a methodof fitness estimation devised by KNIGHTand
ROBERTSON
(1957). After five generations of selection, the mean fitness of abdominal bristle lines declined 28% relative to unselected controls, and the
wing length lines by 7%, with evidence of low lines in
all cases being less fit than high selection lines. This
was again interpreted to argueagainst strong stabilizing selection for those traits in the base population.
ALAN’Sfinal Drosophila experiment was also concerned with this question. He proposed to measure
directly relative fitness of homozygous chromosomes
with different bristle numbers by competition with a
marked balancer, and to determine whether fitness
changes on changing the genetic background.
The description of quantitative variation in terms
of the gene frequencies, numbers,and effects and the
interactions of the individual loci controlling the traits
is necessary if quantitative genetics is to evolve beyond
statistical descriptions. ALANROBERTSON
spoke often
of these problems inhis reviews (e.g., ROBERTSON
1967, 1968) andwas actively involved in experiments
to address these questions. The theory of limits to
artificial selection (ROBERTSON
1960) in fact suggests
an experimental approach to inferring gene frequencies at loci involved in selection response. I f the initial
population size is restricted by inbreeding, the limit
to selection from the bottlenecked lines will be reduced over that obtained fromselection from a large
base population by an amount that depends on how
important are initially rare genes (eliminated from the
5
bottlenecked lines) in determining selection limits. J.
M. P. DA SILVA(1961), a Ph.D. student of ALAN’S,
showed that selection from a single pair resulted in a
reduction of the limitby 30%, suggesting that the
majority of alleles fixed by selection were not initially
rare.
The ultimate goal is to identify the individual loci
responsible for quantitative variation, and in this context ALAN ROBERTSON
was encouraged by the work
of THODAY
and his colleagues (reviewed in THODAY
1979) in mappingQTLs. ROBERTSON
was quick to
point out that the question being addressed by these
studies was not how many loci affect the variation for
a quantitative traitbut, rather,how many loci account
for the bulk of the difference between selected lines
(e.g., ROBERTSON
1967, 1968). ALANviewed the distribution of gene effects on quantitative traitsas being
such that most loci have small effects, but a few have
large effects and cause mostof the variation. MCMILLANand ROBERTSON
(1974) showed that the results of Q T L mapping experiments using recombination of an extreme-scoring chromosome with a multiply marked tester chromosome to identify regions
with significant effects on the trait will always overestimate the effect of detected loci and underestimate
their number (because several linked loci affecting the
trait may occur in a segment) and can even identify
loci that donot exist if the assumption that all loci on
the tested chromosomes carry “higher” alleles than
loci on the tester chromosome is violated. A practical
suggestion for partially alleviating the latter problem
is to ensure that tester and tested chromosomes are
selected in opposite directions from the same base
population, with subsequent backcrossing of the
markergenesintothetesterchromosome.
Such a
third chromosome was synthesized in ALANROBERTSON’S laboratory and used by his Ph.D. students L. R.
to partition the effect of
PIPERand A. E. SHRIMPTON
a high sternopleural bristle number chromosome into
segments bounded by recessive visible markers. The
and ROBERTSON1988a, b) supresults (SHRIMPTON
port themodel of distribution of gene effects outlined
above despite the methodological problems.
This review of ALAN ROBERTSON’S
work isin no
sense comprehensive but I hope, forthose not familiar
with this subject, that it has conveyed a sense of the
breadth of his contribution to quantitative genetics
from its most practical application in animal breeding,
through statistical methodology, theoretical underpinnings and tests of the theory, evolutionary implications and, finally, to the Mendelian genetics of quantitativetrait loci. For those who actively workin
quantitativegenetics,perhaps
it will serve as areminder that muchof the accepted folklorein this field
can be traced back to ideas of ALANROBERTSON,
and
areas in which these have been extended subsequently
6
T. F. C . Mackay
and formalized by others will be recognized.[For
more comprehensive reviews of the contributions of
ALANROBERTSON,
see HILL and MACKAY(1989).]
Although his scientific publications reveal an astonishing range of interests, ALAN’S influence
through personal contact was undoubtedly his most lasting contribution. For those who studied atthe Institute of
Animal Genetics in Edinburgh, ALAN’S
daily informal
coffee sessions were an invaluable opportunity to exchange ideas and meet other workers in the field who
were attracted to Edinburghby the presence of ALAN
and his colleagues. ALANwas invariably generous with
his time and ideas, and could always be approached
for advice by studentsand colleagues alike. Many
scientists currently working on quantitative genetics
can trace their roots either
directly or indirectly to
ALANROBERTSON
at the Institute of Animal Genetics
of the University of Edinburgh; more than anything
this must be a tribute tohis influence.
HILL, W. G., and T . F. C. MACKAY, 1989 EvolutionandAnimal
Breeding. C.A.B. International, Wallingford.
HILL,W. G., and A. ROBERTSON,
1 9 6 6 T h e effects of linkage on
limits to artificial selection. Genet. Res. 8: 269-294.
JONES,L. P., R. FRANKHAM andS .J.F. BARKER, 1968 Theeffects
of population size and selectionintensity in selection for a
quantitative character inDrosophila. 11. Long-term response to
selection. Genet. Res. 12: 249-266.
KIMURA,M., 1968 Evolutionary rate at the molecular
level. Nature 217: 624-626.
KNIGHT,G. R., and A. ROBERTSON,
1957 Fitness as a measurable
character in Drosophila. Genetics 42: 524-530.
LATTER,B. D. H., and A . ROBERTSON,
1960 Experimental design
in the estimation of heritability
by regression methods. Biometrics 16: 348-353.
LATTER, B. D. H.,andA.
ROBERTSON,1962 T h e effectsof
inbreeding and artificial selection on reproductive fitness. Genet. Res. 3: 110-138.
LUSH,J. L., 1947 Family merit and individual merit as bases for
selection. Am. Nat. 81: 241-261; 362-379.
MADALENA,
F. E., and A. ROBERTSON,1975 Population structure
in artificial selection: studies with Drosophila melanogaster. Genet. Res. 24: 113-126.
MASON,I . L., and A. ROBERTSON,1956 The progeny testing of
I wish to thank M. ROBERTSON,
W. G. HILL, R. C.ROBERTSand
dairy bulls at different levels of production. J. Agric. Sci. 47:
B. S. WEIR for comments on the manuscript. This work was sup367-375.
ported by National Institutes of Health Quantitative Genetics ProMCMILLAN,
I . , and A. ROBERTSON,
1 9 7 4 T h e power of methods
gram grant GMI 1546 and a NATO award for collaborative refor the detection of major genes affecting quantitative characsearch. This is Paper No. 12532 of the Journal Series of the North
ters. Heredity 32: 349-356.
Carolina Agricultural Research Service.
MCPHEE, C. P., and A. ROBERTSON, 1970
T h e effect of suppressingcrossing-over on the response to selection
in Drosophila
TRUDY
F. C. MACKAY
melanogaster. Genet. Res. 16: 1-16.
NEIMANN-SBRENSEN, A , , and A . ROBERTSON, 1961
T h e association
Department of Genetics
between
blood
groups
and
several
production
characteristics
North Carolina State University
in three Danish cattle breeds. Acta Agric. Scand. 11: 163-196.
Raleigh, North Carolina 27695-7614
NICHOLAS,
F. W., and A. ROBERTSON,
1980 The conflict between
naturalandartificialselection
in finitepopulations. Theor.
Appl. Genet. 5 6 57-64.
LITERATURE CITED
RENDEL,
J. M.,and A. ROBERTSON,1950 Estimationofgenetic
gain in milk yield by selection in a closed herd of dairy cattle.
BOHREN,B. B., W. G. HILLandA.
ROBERTSON,1966Some
J. Genet. 50: 1-8.
observations on asymmetrical correlated responses to selection.
ROBERTSON, A,, 1953 A numerical description of breed structure.
Genet. Res. 7: 44-57.
J. Agric. Sci. 43: 334-336.
SHARP, W. G. HILLand A. ROBERTSON,
BRIEN, F. D.,G.L.
ROBERTSON,
A,, 1955 Selection in animals: synthesis. Cold Spring
1984 Effects of selection on growth, body composition, and
Harbor Symp. Quant. Biol. 20: 225-229.
food intake in mice. 11. Correlated responses in reproduction.
ROBERTSON,A,,1956Theeffectof
selectionagainst extreme
Genet. Res. 44: 73-85.
deviants based on deviation or on homozygosis. J. Genet. 54:
CLAYTON,G.A,, J. A. MORRISand A. ROBERTSON,1957An
236-248.
experimental check on quantitative genetical theory. I. ShortROBERTSON,
A,, 1957 Optimum group size in progeny testing and
term responses to selection. J. Genet. 55: 131-151.
family selection. Biometrics 13: 442-450.
CLAYTON,
G. A,, and A. ROBERTSON,
1955 Mutation and quantiROBERTSON,
A., 1959a Experimental design in the evaluation of
tative variation. Am. Nat. 89: 151-158.
genetic parameters. Biometrics 15: 219-226.
CLAYTON,
G. A,,andA.
ROBERTSON,1957 Anexperimental
ROBERTSON,A,,1959bThesamplingvariance
of thegenetic
check on quantitative genetical theory. 11. T h e long-term efcorrelation coefficient. Biometrics 15: 469-485.
fects of selection.J. Genet. 55: 152-170.
ROBERTSON,A,,1960
Atheoryoflimits
in artificialselection.
CLAYTON,
G. A,, and A. ROBERTSON, 1964T h e effects of X-rays
Proc. R. SOC. Lond. B153: 234-249.
on quantitative characters. Genet. Res. 5: 410-422.
ROBERTSON,A,,
1961
Inbreeding
in artificial
selection
proCLAYTON,
G. A,, G. R. KNIGHT,
J. A. MORRISand A. ROBERTSON,
grammes. Genet. Res. 2: 189-194.
1957AnexperimentalcheckonquantitativegeneticaltheROBERTSON,A,,1962Weighting
in theestimationofvariance
ory. 111. Correlated responses. J. Genet. 55: 171-180.
components in the unbalanced single classification. Biometrics
DA SILVA,
J. M. P.,1961Limitsofresponsetoselection.Ph.D.
18: 413-417.
thesis, University of Edinburgh.
ROBERTSON,
A., 1967 The nature of quantitativegeneticvariaDICKERSON, G.
E., and L. N. HAZEL, 1944 Effectiveness of selection, pp. 265-280 in Heritage From Mendel, edited by A. BRINK.
a supplementtoearliercullingof
tiononperformanceas
University of Wisconsin Press, Madison.
livestock. J. Agric. Res. 69: 459-476.
ROBERTSON,
A,, 1968 The spectrum of genetic variation, pp. 5R., 1980 Origin of genetic variation in selection lines,
FRANKHAM,
16 in Population Biology and Evolution, edited by R. C. LEWONpp. 56-68 in Selection Experiments in Laboratory and Domestic
TIN. Syracuse University Press, Syracuse, N.Y.
Animals, edited by A . ROBERTSON.CommonwealthAgriculROBERTSON,
A,, I970 A theory of limits in artificial selection with
tural Bureaux, Slough.
Alan Robertson (1920-1 989)
many linked loci, pp. 246-288 in Mathematical Topics in Population Genetics, edited by K. KOJIMA.Springer, Berlin.
ROBERTSON,
A., 1977 Artificial selection with a large number of
linked loci, pp. 307-322 in Proceedings of theInternational
Conference on QuantitativeGenetics, edited by E. POLLAK,0.
KEMPTHORNE
and T. B. BAILY.Iowa State University Press,
Ames.
ROBERTSON,
A,, 1978 T h e time of detection of recessive visible
genes in small populations. Genet. Res. 31: 255-264.
ROBERTSON,
A., and A . A. ASKER,1951 The genetic history and
breed-structure of British Friesian cattle. Emp. J. Exp. Agric.
19: 113-130.
ROBERTSON,
A,, and P. NARAIN,1971 The survival of recessive
lethals in finite populations. Theor. Popul. Biol. 2: 24-50.
ROBERTSON,
A,, and J. M. RENDEL,1950 T h e use of progeny
testing with artificial insemination in dairy cattle.J. Genet. 5 0
21-31.
7
ROBERTSON,
A., and J. M. RENDEL,1954 T h e performanceof
heifers got by artificial insemination. J. Agric. Sci. 44: 184192.
SHARP,G. L., W. G. HILL and A. ROBERTSON,1984 Effects of
selection ongrowth, bodycomposition, andfoodintake
in
mice. I. Response in selected traits. Genet. Res. 43: 75-92.
SHRIMPTON,A.E., and A. ROBERTSON,1988a The isolation of
polygenic factors controlling bristle score in Drosophila melanogaster. 1. Allocation of third chromosome sternopleural bristle effects to chromosome sections. Genetics 118: 437-443.
SHRIMPTON,A. E., and A. ROBERTSON,1988b The isolation of
polygenic factors controlling bristle score in Drosophila melanogaster. 11. Distribution of third chromosome bristle effects
within chromosome sections. Genetics 118: 445-459.
THODAY,
J. M., 1979 Polygene mapping: uses and limitations, pp.
219-233 in QuantitativeGeneticVariation,
edited by J. N.
THOMPSON,
JR., and J. M . THODAY.AcademicPress,
New
York.