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
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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
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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-
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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)
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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
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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
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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.
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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.
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
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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
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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-
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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)
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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
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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
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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.
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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.
