Alan Robertson (1920-1989).

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ALAN ROBERTSON was born on February 2 1, 1920,

in Preston, England, and died in Edinburgh on April

25, 1989, after a long illness. 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 in- terrupted by the outbreak of World War 11; he pub- lished several papers on physical chemistry but did not complete his Ph.D. ALAN worked with C. H. WADDINGTON in Operational Research during the war and subsequently was invited to join WADDINGTON in the Agricultural Research Council Animal Breeding and Genetics Research Organization (ABGRO), initially at Hendon and later in Edinburgh. He studied with SEWALL WRIGHT in Chicago and JAY LUSH in Ames in 1947, then returned to ABGRO in Edin- burgh. 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. ALAN received 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 elec- tion as a Fellow of the Royal Society of London in

Generics 125: 1-7 (Mav. 1990)

Alan Robertson

(1920-1989)

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. ALAN is survived by his wife

MEG, whom he married in 1947; his three children, MARK, HILARY and MICHAEL; and three grandchil- dren.

ALAN ROBERTSON'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 thresh- old trait, viability, in poultry). In the mid-1940s to

1950s animal breeding theory was in its infancy. To-

gether with J. M. RENDEL, and prompted by the ideas of LUSH (1947) and DICKERSON and HAZEL (1944),

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 replace- ment bulls and cows each generation: cows to breed bulls, cows to breed cows, bulls to breed bulls, and bulls to breed cows. RENDEL and ROBERTSON (1950)

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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) demonstrated that, although

progeny testing of bulls resulted in only 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, ALAN ROBERTSON 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. ROB-

ERTSON showed with A. A. ASKER (1 95 1) that selection

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; ROBERTSON 1953) can be grouped into three tiers. T h e 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 group comprising the bulk of the herds. T h e problem then reduces to one of finding methods to evaluate bulls in 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 the performance (milk yield) of their daughters. If the daughters of 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 se- riously confound the estimation of the bulls’ breeding values. This led ROBERTSON and RENDEL (1954) to suggest the “contemporary comparison” method of evaluating bulls, whereby the average yield of a bull’s daughters in a given herd and year is compared to the average yield of other cows in that herd and year, taking into account the number of animals in each group. T h e 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 different herds, and if the accuracy in estimating breeding values does not differ for different production levels (that is, if there is no genotype by environ- ment interaction between milk yield and plane of nutrition). T h e absence of such genotype by environ- ment interaction was shown to be true generally (MA-

SON 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 the advent of schemes for multiple ovulation and embryo transfer (MOET) promised to change the

basic structure of the industry-as had been foreseen by RENDEL and ROBERTSON (1950) as a method for increasing the contribution to genetic gain from the

“COW to breed cow” pathway.

ALAN ROBERTSON was concerned with the family structure of the breeding population for three rea- sons. First, it is important for optimizing progress per year because of the conflict between testing few bulls with many daughters, thus obtaining reliable estimates of breeding value, or many bulls with fewer 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. Such estimates are notoriously variable, and ROBERTSON (1 959a,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 are a restricted sample from the population and because selection increases the proportion of genes in common in the selected group (ROBERTSON 196 l ) , leading to inbreeding depression and loss of genetic variation in selection lines.

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different associations may prove significant in different samples. (3) Real associations between marker loci and QTLs may be different in different genetic back- grounds, so that the same correlations will not neces- sarily be found in different populations. (4) T h e practical value of taking account of an association between a marker locus and a Q T L in selecting animals depends on whether the proportion of the genetic variance of the trait explained by the association ap- proaches the heritability of the trait. T h e proportion of genetic variance attributable to significant blood group associations is generally very small.

These problems, coupled with his growing convic- tion 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 ALAN to doubt the utility of searching for associations between the two categories of traits. By 1966 he was convinced that the future of animal breeding was in understanding the biochemical and physiological correlates of response to selection. Sev- eral research projects measuring such correlates of response to selection for growth rate in mice were later initiated by his colleagues in Edinburgh (e.g., BRIEN et al. 1984; SHARP et e l . 1984).

ALAN ROBERTSON recognized from the beginning

the great value of molecular polymorphisms in tracing the history of populations, and thought the most in- teresting question to be addressed was why so much variation was maintained at these loci. Finding no evidence that heterozygotes for blood group loci were superior to homozygotes with regard to production characteristics in dairy cattle, he suggested that such

and ROBERTSON 196 1) before the formal proposal of the neutral mutation, random drift theory of molecular evolution (KIMURA 1968). ALAN retained 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 the most tractable of experimental animals, and early in his career ALAN ROBERTSON 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 needed to be extended to cope with discrepancies between observed and predicted results, and to inves- tigate the nature of quantitative genetic 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

.

MORRIS and G . R. KNIGHT. Selecting for increased and decreased numbers of abdominal bristles from a polymorphisms were neutral (NEIMANN-SORENSEN

randomly bred population, CLAYTON, MORRIS and 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 that genes controlling abdominal bristle number act additively and are neutral with respect to fitness. However, the long-term response was unpredictable (CLAYTON and 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 bal- anced 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 (CLAY-

TON et a l . 1957). T h e primary questions to emerge

from these experiments were how to predict limits to selection for given population sizes and selection in- tensities, 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. ALAN ROB-

ERTSON and his colleagues addressed these problems theoretically and by further experimentation.

For a simple additive model, ROBERTSON (1960) showed that the expected limit 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. T h e 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 generally true for experimental populations (JONES,

FRANKHAM and BARKER 1968; MADALENA and ROB-

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4 T. F. C. Mackay

bination. NICHOLAS and ROBERTSON (1 980) further extended the theory of limits to artificial selection to the case where the limit 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, HILL and ROBERTSON (1966). T h e asymmetrical correlated responses to selection often observed in practice could be explained 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.

ALAN ROBERTSON 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 quantitative traits, and the numbers, effects, gene frequencies and interactions of loci controlling them. T h e extent to which spontaneous and X-ray-induced mutation causes genetic variation for bristle traits was examined by CLAYTON and ROBERTSON (1955, 1964) by response to selection of populations of different genetic origin (highly inbred, plateaued, and geneti- cally variable base populations). T h e concept of mu- tational variance (the input of new additive genetic variance per generation) was introduced, and was estimated from the various experiments to be roughly

times the environmental variance (VJ for spontaneous mutations and 0.003 V , for X-ray-induced mutations. CLAYTON and ROBERTSON (1955) empha- 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 often appear in selection lines, for example recessive lethal chromosomes (e.g., CLAYTON and ROBERTSON 1957) or visible recessive genes (e.g., MADELENA and 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 mutation or recombination, ROBERTSON and NARAIN (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 that quantitative traits could be divided into three broad categories: traits peripheral to fitness, traits with an intermediate optimum, and major fitness components. For the first category, neutral traits, variation in the trait is not associated with variation in fitness, populations harbor a large amount of mostly additive genetic variation, there is no inbreeding depression, and variation is likely maintained by a balance of mutation and drift. At the other extreme are major components of 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 most loci and overdominance at some loci. Such traits characteristically exhibit severe inbreeding

depression, and are expected to be negatively geneti- cally correlated with other major components of fit-

ness. ALAN ROBERTSON was intrigued by the fact that the population means of quantitative traits were sta- ble. 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. ROBERT-

SON (1956) showed that stabilizing selection leads to

fixation at loci affecting the selected trait and de- creases 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 he did not consider a 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.

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unpublished experiments of this sort were conducted in ROBERTSON’S laboratory to determine the strength of stabilizing selection for Drosophila bristle traits. In all cases the means of the selected lines responded little to relaxed selection, despite considerable resid- ual genetic variation at the time selection was sus- pended. Another approach is to manipulate chromosomes from lines selected for high and low bristle score so that one chromosome is heterozygous for chromosomes from the high and low selection lines, and the others are homozygous 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 experiments and found n o tendency for the mean scores of his synthetic populations to change (ROBERTSON 1967). These observations led ROBERTSON to conclude that, at the majority of loci controlling variation for bristle traits, the segregating alleles are neutral with respect to fitness. LATTER and ROBERTSON (1962) directly meas- ured the fitness of lines selected for several generations for two bristle characters and wing length, using a method of fitness estimation devised by KNIGHT and ROBERTSON (1957). After five generations of selection, the mean fitness of abdominal bristle lines de- clined 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 argue against strong stabilizing selection for those traits in the base population. ALAN’S final 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.

T h e 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. ALAN ROBERTSON spoke often of these problems in his reviews ( e . g . , ROBERTSON

1967, 1968) and was 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 re- duced over that obtained from selection from a large base population by an amount that depends on how important are initially rare genes (eliminated from the

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 limit by 30%, suggesting that the majority of alleles fixed by selection were not initially rare.

T h e 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 mapping QTLs. 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 trait but, rather, how many loci account for the bulk of the difference between selected lines

(e.g., ROBERTSON 1967, 1968). ALAN viewed the dis-

tribution of gene effects on quantitative traits as being such that most loci have small effects, but a few have large effects and cause most of the variation. MC- MILLAN and ROBERTSON (1974) showed that the results of Q T L mapping experiments using recombination of an extreme-scoring chromosome with a mul- tiply marked tester chromosome to identify regions with significant effects on the trait will always over- estimate 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 do not 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 marker genes into the tester chromosome. Such a third chromosome was synthesized in ALAN ROBERT-

SON’S laboratory and used by his Ph.D. students L. R. PIPER and A . E. SHRIMPTON to partition the effect of a high sternopleural bristle number chromosome into segments bounded by recessive visible markers. T h e results (SHRIMPTON and ROBERTSON 1988a, b) sup- port the model of distribution of gene effects outlined above despite the methodological problems.

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6 T. F. C . Mackay

and formalized by others will be recognized. [For more comprehensive reviews of the contributions of ALAN ROBERTSON, see HILL and MACKAY (1989).] Although his scientific publications reveal an astonish- ing range of interests, ALAN’S influence through per- sonal contact was undoubtedly his most lasting contribution. For those who studied at the Institute of Animal Genetics in Edinburgh, ALAN’S daily informal coffee sessions were an invaluable opportunity to ex- change ideas and meet other workers in the field who were attracted to Edinburgh by the presence of ALAN and his colleagues. ALAN was invariably generous with his time and ideas, and could always be approached for advice by students and colleagues alike. Many scientists currently working on quantitative genetics can trace their roots either directly or indirectly to ALAN ROBERTSON at the Institute of Animal Genetics of the University of Edinburgh; more than anything this must be a tribute to his influence.

I wish to thank M. ROBERTSON, W. G. HILL, R. C. ROBERTS and B. S. WEIR for comments on the manuscript. This work was sup- ported by National Institutes of Health Quantitative Genetics Pro- gram grant GMI 1546 and a NATO award for collaborative research. This is Paper No. 12532 of the Journal Series of the North Carolina Agricultural Research Service.

TRUDY F. C. MACKAY

Department of Genetics

North Carolina State University Raleigh, North Carolina 27695-7614

LITERATURE CITED

BOHREN, B. B., W. G. HILL and A. ROBERTSON, 1966 Some observations on asymmetrical correlated responses to selection. Genet. Res. 7: 44-57.

BRIEN, F. D., G. L. SHARP, W. G. HILL and A. ROBERTSON, 1984 Effects of selection on growth, body composition, and food intake in mice. 11. Correlated responses in reproduction. Genet. Res. 44: 73-85.

CLAYTON, G. A,, J. A. MORRIS and A. ROBERTSON, 1957 An experimental check on quantitative genetical theory. I. Short- term responses to selection. J. Genet. 55: 131-151.

CLAYTON, G. A,, and A. ROBERTSON, 1955 Mutation and quantitative variation. Am. Nat. 89: 151-158.

CLAYTON, G. A,, and A. ROBERTSON, 1957 An experimental check on quantitative genetical theory. 11. T h e long-term effects of selection. J. Genet. 55: 152-170.

CLAYTON, G. A,, and A. ROBERTSON, 1964 T h e effects of X-rays on quantitative characters. Genet. Res. 5: 410-422.

CLAYTON, G. A,, G. R. KNIGHT, J. A. MORRIS and A. ROBERTSON, 1957 An experimental check on quantitative genetical the-

ory. 111. Correlated responses. J. Genet. 55: 171-180. DA SILVA, J. M. P., 1961 Limits of response to selection. Ph.D.

thesis, University of Edinburgh.

DICKERSON, G. E., and L. N. HAZEL, 1944 Effectiveness of selection on performance as a supplement to earlier culling of livestock. J. Agric. Res. 69: 459-476.

FRANKHAM, R., 1980 Origin of genetic variation in selection lines, pp. 56-68 in Selection Experiments i n Laboratory and Domestic Animals, edited by A . ROBERTSON. Commonwealth Agricul- tural Bureaux, Slough.

HILL, W. G., and T . F. C. MACKAY, 1989 Evolution and Animal 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 and J. S . F. BARKER, 1968 The effects of population size and selection intensity in selection for a quantitative character in Drosophila. 11. Long-term response to selection. Genet. Res. 12: 249-266.

KIMURA, M., 1968 Evolutionary rate at the molecular level. Na- ture 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. Bio- metrics 16: 348-353.

LATTER, B. D. H., and A. ROBERTSON, 1962 T h e effects of inbreeding and artificial selection on reproductive fitness. Ge- net. 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. Ge- net. Res. 24: 113-126.

MASON, I . L., and A. ROBERTSON, 1956 The progeny testing of dairy bulls at different levels of production. J. Agric. Sci. 47: 367-375.

MCMILLAN, I . , and A. ROBERTSON, 1 9 7 4 T h e power of methods for the detection of major genes affecting quantitative characters. Heredity 32: 349-356.

MCPHEE, C. P., and A. ROBERTSON, 1970 T h e effect of suppress- ing crossing-over on the response to selection in Drosophila melanogaster. Genet. Res. 16: 1-16.

NEIMANN-SBRENSEN, A , , and A . ROBERTSON, 1961 T h e association between blood groups and several production characteristics in three Danish cattle breeds. Acta Agric. Scand. 11: 163-196. NICHOLAS, F. W., and A. ROBERTSON, 1 9 8 0 T h e conflict between natural and artificial selection in finite populations. T h e o r . Appl. Genet. 5 6 57-64.

RENDEL, J. M., and A. ROBERTSON, 1950 Estimation of genetic gain in milk yield by selection in a closed herd of dairy cattle. J. Genet. 50: 1-8.

ROBERTSON, A,, 1953 A numerical description of breed structure. J. Agric. Sci. 43: 334-336.

ROBERTSON, A,, 1955 Selection in animals: synthesis. Cold Spring Harbor Symp. Quant. Biol. 20: 225-229.

ROBERTSON, A,, 1956 The effect of selection against extreme deviants based on deviation or on homozygosis. J. Genet. 54:

ROBERTSON, A,, 1957 Optimum group size in progeny testing and

ROBERTSON, A., 1959a Experimental design in the evaluation of

ROBERTSON, A,, 1959b The sampling variance of the genetic

ROBERTSON, A,, 1960 A theory of limits in artificial selection.

ROBERTSON, A,, 1961 Inbreeding in artificial selection pro- grammes. Genet. Res. 2: 189-194.

ROBERTSON, A,, 1962 Weighting in the estimation of variance components in the unbalanced single classification. Biometrics 18: 413-417.

ROBERTSON, A., 1967 The nature of quantitative genetic variation, pp. 265-280 in Heritage From Mendel, edited by A. BRINK. University of Wisconsin Press, Madison.

ROBERTSON, A,, 1968 The spectrum of genetic variation, pp. 5- 16 in Population Biology and Evolution, edited by R. C. LEWON- TIN. Syracuse University Press, Syracuse, N.Y.

ROBERTSON, A,, I970 A theory of limits in artificial selection with 236-248.

family selection. Biometrics 13: 442-450.

genetic parameters. Biometrics 15: 219-226.

correlation coefficient. Biometrics 15: 469-485.

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many linked loci, pp. 246-288 in Mathematical Topics in Popu- lation 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 the International Conference on Quantitative Genetics, 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 T h e genetic history and breed-structure of British Friesian cattle. Emp. J. Exp. Agric.

19: 113-130.

ROBERTSON, A,, and P. NARAIN, 1971 T h e 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.

ROBERTSON, A., and J. M. RENDEL, 1954 T h e performance of heifers got by artificial insemination. J. Agric. Sci. 44: 184-

192.

SHARP, G. L., W. G. HILL and A. ROBERTSON, 1984 Effects of

selection on growth, body composition, and food intake in mice. I. Response in selected traits. Genet. Res. 43: 75-92.

SHRIMPTON, A. E., and A. ROBERTSON, 1988a T h e isolation of polygenic factors controlling bristle score in Drosophila mela- nogaster. 1. Allocation of third chromosome sternopleural bristle effects to chromosome sections. Genetics 118: 437-443.

SHRIMPTON, A. E., and A. ROBERTSON, 1988b T h e isolation of polygenic factors controlling bristle score in Drosophila mela- nogaster. 11. Distribution of third chromosome bristle effects within chromosome sections. Genetics 118: 445-459.

THODAY, J. M . , 1979 Polygene mapping: uses and limitations, pp.