Copyright 0 1995 by the Genetics Society of America Perspectives Anecdotal, Historical And Critical Commentaries on Genetics Edited 4 James F. Crow and William F. Dove

SEWALL WRIGHT’S “Systems of Mating”

William G. Hill

Institute of Cell, Animal and Population Biology, University of Edinburgh, Edinburgh EH9 3JT, Scotland

INETEEN ninety-six marksthe 75th anniversary of widely accepted for discrete characters, but controversy N the publication in this journal of the series of five remained as to the basis of variation in continuous traits papers by SEWALL WRIGHT(1921a-e) on “Systems of (PROVINE 1971). WEINBERG (1910),FISHER (1918), and Mating.” The definitions, methods, and results he pre- WRIGHT(ignorant of the work of the other two) set sented in these and two other papers published at about what became the accepted framework. WRIGHTalso suc- the same time (WRIGHT 1920,1922) have had a major cessfully addressed the problem of how genotype fre- and lasting effect on the theory and application of pop- quencies change in populations as a result of nonran- ulation genetics. My aim in this paper is to review the dom mating based on relationship or performance. work in these papers and to consider their influence Previous analysis of, for example, full-sib mating had mostly, but not exclusively, on animal improvement, involved the laborious evaluation of genotype probabili- but without being comprehensive in either topics or ties, whereas WRIGHT’Smethods were computationally references. Indeed, were I to cite only WRIGHT’Sworks simple and general. They were then and are still not that developed ideas from his 1921 papers, there would easy to understand, partly because of his use of path be a long bibliography, and it is easy to see why the coefficients with analysis in terms of continuous vari- reference lists in WRIGHT’S ownpapers looked so ego- ables rather than genotypes and partly because critical centric. PROVINE’S(1986) excellent biography provides points were dealt with very tersely. a full review ofWRIGHT’S role in genetics and evolution- WRIGHThad invented and used path coefficients be- ary biology, while WRIGHT’S(1968- 1978) four-volume fore the 1921 papers. The initial steps in their develop- treatise describes much of his work and views. ment, to describe general and specific size factors in- Background: WRIGHThad a broad training in biol- fluencing bone size of rabbits, had been taken while he ogy and came into genetics as a graduate student of was a graduate student. He had computed all partial Castle at the Bussey Institute of Harvard University. He correlations, but found that such an analysis provided worked mainly on coat color patterns in guinea pigs no understanding of causation. By computing the path for his Ph.D., which stimulated among other things his coefficients, which in statistical terms are standardized interest in multilocus inheritance and interactions. His partial regression coefficients, he aimed to describe the firstjob, from 1915, was as Senior Animal Husbandman effect of causalcomponents. In1918 WRIGHTpublished at the U.S. Department of Agriculture in Washington, his first version of the method of path coefficients (al- with a particular remit to analyze extensivedata on traits though notcalling them such), partitioning variation in such as color and body weight collected by ROMMELon length of an individual bone to independent hereditary inbred lines of guinea pigs to test the value, or other- causes including general size, length of leg bones, wise, of using inbreeding in animal improvement pro- length of hind limbs, and an independent term. grams. WRIGHT alsoundertook a substantial amount of In the first paper in which he undertook a genetic biometrical work and a widespread correspondence on analysis of a quantitative trait, WRIGHT(1920) used path animal breeding. It was, therefore, important that he coefficients to analyze data on the proportion of white could interpret data on quantitative traits from both color in spotted guinea pigs, and attributed variation inbred lines and livestock populations. These and other to three principal causes: heredity (h),environment problems he tackled in the “Systems of Mating” series common to litter mates (e), and other factors, largely while still with the U.S. Department of Agriculture. “ontogenic irregularity” or developmental noise (d). The Mendelian theory of inheritance had become The quantity h is the path coefficient from genotype to phenotype and equals the correlation between them. Address for cmrespondence: William G. Hill, Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Rd., WRIGHTshows that h2 is the proportion of variance at- Edinburgh EH9 3JT, Scotland. E-mail: [email protected] tributable to heredity; this is, of course, the heritability,

Genetics 143: 1499-1506 (August, 1996) 1500 W. G. Hill

\d C. D.

FIGURE 1.-WRIGHT’S famous diagramfrom his 1921 papers. The original legend is included.

/ Dam 3‘ FIG- 2.-A diagram illustrating the relations between two mated individuals and their progeny. E, H’,H” and If”’ arc the genetic constitutions of the four individaaab. G, C’, G“ and C”’ are four genn~elb. E and D ~p-t tangible external conditions and chance imgu- laritia as facton in development. C rcprcscntscbmce at segregation as a factor in determining the composition of the germ-cells. Path coefficients are represented by small letters. a term that he did not coin (see BELL 1977 for a discus- thereby setting the basic framework for the analysis of sion). In his partition of variation, WRIGHT had a term the effects of inbreeding and assortative mating on the for common environment of sibs but not dominance, correlation among relatives. In particular,WRIGHT com- whereas FISHER (1918) hadone for dominance but not putes how, for a locus with two equallyfrequent alleles, common environment. WEINBERG(1910) had already the frequency with which A alleles unite with A, a with included both (see translationby MEYER in HILL1984), a, and A with a depends on the correlation f and shows but had been ignored! that the percentage of heterozygosis is p = (1 - f)/2. The “Systems of Mating” series: Although the path The result is then used to show how h2 depends on diagram for coat color in guinea pigs first appears in heterozygosity and thus f: WRIGHT thereby made the the 1920 paper, it returns in part I of the better known critical transitions from a correlation f of continuous “Systems of Mating” the following year with one sig- variables to a functionp of frequencies of discrete geno- nificant change, which took WRIGHT beyond the work types and back to another quantitative measure h2. of WEINBERGand FISHER,the addition of a term (m) Subsequently (p. 121), WRIGHTdefines m more ex- describing the correlation of the parents, which en- plicitly as “the correlation betweenthe genetic constitu- abled him to analyzethe effects of nonrandom mating. tions of the parents” and provides many formulas, in- The figure fromWRIGHT (1921a), surelyone of the best cluding that for the correlation between full sibs when known diagrams in biological science, is reproduced there is nonrandom mating, i.e., m f 0. [Unfortunately, here (Figure 1).Important definitions in the 1921 pa- his results for dominance were incorrect and were cor- per are indeed obscure. He introduced and defined f rected subsequently (WRIGHT1931 and by hand on the (called the inbreeding coefficient in a later paper) as reprinted copy of the 1921 papers issuedby Iowa State follows (p. 118): College Press). FISHER (1918) had given the right for- If there is assortative mating fromany cause, there will mulas for the dominance contribution to the sib corre- be some correlation between the gametes which unite. lation.] WRIGHT alsopoints out that if an expression Represent this correlation by f: can be provided form, the correlations and path coeffi- Later (p. 119) he introduces m: cients in eachgeneration can be expressed in termsof those in the previous generation. The correlation between the egg and the sperm de- pends on that between the parental formulae which we This he does in the second paper (WRIGHT1921b), will represent by m . . . The correlation between the par- initially deriving resultsfor repeated brother-sister mat- ents is greater or less than that between their genetic ings: “As the reader may feel some doubt as to the constitutions, depending on whether the assortative mat- validity of the method of analysis used here, it will be ing is based on somatic resemblance or consanguinity. well to begin with a case in which the results have al- For these two cases he gives formulas relating f to m, ready been determined by direct methods. . . . In this Perspectives 1501 case the correlation between mates is simply that be- cient of relationship of two individuals as the correla- tween a brother and sister, produced by the preceding tion between them. He is not explicit as to what mea- generation.” He gives arecurrence formula for m, sure on the individuals is being taken, but the formulas which he shows can be written in terms off in preceding imply it is the sum of values of the gametes, regarded generations (f and f ‘I) as the now familiar result f = as quantitative traits, of an individual. Hence the rela- (1 + 2f + f ”)/4. WRIGHTprovided such recurrence tionship is referred to by LUSH(1948) as the correlation formulas for a range of repeated mating systems and of genic values. The relationship rsd between sire (S) thereby essentially solved the problem of computing and dam (D)in terms of their own and their offspring’s the consequences on genotype frequencies for mating (0)inbreeding coefficient is given by systems based on consanguinity. The third paper deals with assortative mating based TYd 2f/J(1 + J)(1 fd) on phenotype, in which WRIGHT(1921~) showed that, and the numerator of the expression (to which we shall in contrast to mating of relatives, the consequences de- return) is the covariance of genic values.WRIGHT pend on the numberof lociaffecting the trait. Although (1922) showed how to compute the inbreeding coeffi- there may be little increase in homozygosity when the cient of 0 from a general pedigree by the now famous nonrandom mating is continued, the variance in the formula

population can increase greatly with verystrong positive + assortative mating. The fourth paper is on selection; fo = C(1/2)”+ ”’ (1 +f,) although the mathematical results have had less influ- ence than those in the first three papers, significant where summation is over all paths, of length n and nf conclusions are drawn. For example, he introduces the from the parents of 0 to the common ancestor A with idea of selecting for an intermediate fixed phenotype inbreeding coefficientf,[Subsequently, WRIGHT (1951) and shows this does not lead to a substantial reduction changed the algorithm but not the result by simply in variability of the trait, just as for perfect negative counting the total number, n + nr + 1, of zygotes in the assortative mating, even if the trait is completely herita- path, aform that can also beapplied to sex-linked loci.] ble (WRIGHT1921d). The final paper comprises a re- These formulas are sufficient to enable inbreeding and view and a summary (WRIGHT1921e, pp. 177-178) of relationship to be computed for all pedigrees, and in the series: the 1922 paper WRIGHTused them to compute the in- breeding coefficients for animals of theShorthorn It will be seen that all of the systems of mating have breed, finding one bull, Comet, with an inbreeding their advantages and disadvantages. Closeinbreeding au- tomatically brings about fixation of type and prepotency. coefficient of 0.47. The impact that high values such as Intermediate types are fixed as readily as extremes. It is this had on WRIGHT’Sideas on both animal breeding the only method of bringing to light hereditary differ- and evolution is discussed later. WRIGHTsubsequently ences in characters which are determined largely by fac- contributed further both to methods of calculating the tors other than heredity. On the other hand, close in- inbreeding coefficient, showing how it could be esti- breeding is likely to lead toward reduced fertility, size and vigor. mated by sampling rather than taking all paths back in Matings between relativesmore remote than first cous- the pedigree (WRIGHTand MCPHEE1925), which was ins have little significance as inbreeding, except in so far useful in analysis of livestock breeds, and to its predic- as there is continued breeding within a population of tion for specified mating systems. small size. In the “Systems of Mating” and associated papers, Assortative mating and selection can lead to fixation of extreme types only and are not very efficient in this WRIGHThad made major advances: he had introduced respect. Selection, however, is the only means of perma- the ideas of path coefficients and of the inbreeding nently changing the relative proportions of the various coefficient, given a formal definition to relationship, genes present in the original stock. It is an essential ad- shown how to compute changes in inbreeding and het- junct of the other systems as means of improvement. erozygosity, quantified the effects of assortative mating, Assortative mating leads to the greatest diversification of the population as a whole, and thus is practically and more. These are fundamentalto anymodern popu- always accompanied by selection either in nature or in lation genetics course and were a great achievement. live-stock breeding. Under conditionssuch that all prog- WRIGHT’Sinbreeding coefficient, both as a conceptand, eny are to be saved for breeding, this diversification of as he showed, an easily computed quantity, is arguably the population is a disadvantage. Disassortative mating his mostimportant, widely used, and lasting single tech- is the method which best holds the whole population together, pending the fixation of the average type by nical contribution to population genetics, even though close inbreeding. alternative definitions and derivations were obtained subsequently and FISHER (1949) wrote a whole book on Inbreeding and relationship: In the following year, The Theory of Inbreedingwithout citing WRIGHT.Further, WRIGHT(1922) formally definedthe correlation of the inbreedingcoefficient was noncontroversial, in con- uniting gametes, as theinbreeding coefficient and trast to some of WRIGHT’S later ideas such as the shifting extended the ideas to relationship, defining the coeffi- balance theory. 1502 W. G. Hill

Influences on animal breeding: I now take up some threads from the papers. I shall deal mainly with impli- cations for animal improvement, where his ideas and methods had ready application, and in some circum- stances WRIGHT’Sdefinitions led to more naturalappli- cation than others. Further, his work on animal breed- ing also had an impact on his views on evolutionary biology, on which he concentrated after his appoint- ment to theUniversity of Chicago in 1926. The photo- graph of WRIGHT(Figure 2) was taken in 1928, shortly after his move. Although WRIGHTnever had a significant research group, he greatly influenced JAY L. LUSH of IowaState College (later University) who became the leading fig- ure in the genetics of livestock improvement and per- haps WRIGHT’Smost important disciple. LUSHhad pre- viously corresponded with WRIGHTand then attended his classesin Chicago immediately after moving to Iowa in1930. LUSH established a major school at Ames, where he and colleagues trained many who were to become influential in animal breeding in the United States and abroad. LUSH’Sbook Animal Breeding Plans (1937 and later editions) was nontechnical but had a big impact on thinking. He prefaced it, “The ideas in this book have been drawn freely from the published works of many persons, I wish to acknowledge especially my indebtedness to Sewall Wright for many published and unpublished ideas upon which I have drawn, and for his friendly counsel.” LUSH’S(1948) mimeograph The Genetics of Populations, which was widely read but FIGURE 2.”SEWAl.L. WRIGHTin 1928, shortly after moving unpublished until recently (1994), included a formal to the University of Chicago. exposition of m;ch of WRIGHT’S work, particularly that relating to animal improvement. “Systems of Mating” damental genetic statistics by KEMPTHORNE,both of and otherimportant papers were reprinted in 1949 and whom were verymuch committed to use of the analysis 1958 by Iowa State College Press witha preface by LUSH of variance.KEMPTHORNE (1957) included, however, an and some handwritten corrections by WRIGHT. expository chapter on path coefficients in An Introduc- The quantitative genetics and animal breeding group tion to Genetic Statistics. Path coefficient methods did in Edinburgh were also influenced directly by WRIGHT not feature significantly in the 1940s to 1960s in other (see FALCONER1993). ALANROBERTSON spent some centers of quantitative genetics and animal breeding time with him in 1947 while converting from chemist research and teaching: Berkeley (LERNER,DEMPSTER) , to geneticist. Subsequently WRIGHT visitedEdinburgh Birmingham (MATHER,JINKS), Edinburgh (ROBERT- for a year (1949-1950) and taught a course, much of SON, FALCONER,REEVE), Ithaca (HENDERSON),Raleigh it summarized in a review paper (WRIGHT1952) that (COMSTOCK, ROBINSON,COCKERHAM). In what is proba- was a forerunner to his treatise published later. bly the most widely used text on quantitative genetics, The method of path coefficients was used almost ex- FALCONER(1960 etseq. ) makes no use of path coeffi- clusively by LUSH,but now is little used in animal breed- cients. ing research. It was developed at almost the same time Dehitions of inbreeding and relationship: WRIGHT’S as FISHER(1918) invented the analysis of variance to definition of inbreeding coefficient (variouslyf or F) in partition variability betweenhereditary and nonheredi- terms of a correlation is obscure to population geneticists tary causes. The path diagram provides a nice picture not used to thinking in terms of quantitative traits. What of the model and many quantitative problems can be he did was to attach implicit valuesto each gamete, which solved withthe method,and it is featured in LI’S(1955) are sums of the effects of the genes on some arbitrary text on population genetics. Unless people were trait, essentially assuming what has become known as schooled in path coefficients to the exclusion of vari- the infinitesimal model (BULMER1980) or, alternatively, ance/covariance methods, however,they generally attaching to an arbitrary locus assigned allelic valuesof used the latter. Indeed, at Ames, applied statistics was 1 and 0. For this reason, MAL~COT’S(1948) definition taught by SNEDECORfrom his book, and the more fun- of inbreeding as probability of identityby descent is less Perspectives 1503 opaque to population geneticists or students. Both alter- ern procedures are due to HENDERSON,initially in his natives have specific useful features, however: WRIGHT’S 1949 Ph.D. thesis while a student of LUSH at Ames, can naturally take negative values, for example, when where he saw how to simultaneously estimate fixed ef- parents are less related than random, which leads on to fects (e.g., environmental groups) and predict random his partition of the correlation of uniting gametes using effects (e.g.,breeding values); he elaborated later in the his F statistics (WRIGHT1951). MALECOT’S butnot context of dairy cattle (HENDERSON1974). The method, WRIGHT’Sis readily extended to include mutation, for which he called best linear unbiased prediction example, to compute heterozygosity for infinite alleles (BLUP), became applied to dairy sire evaluation in the (KIMURA and CROW1964), andto more than one locus, 1970s, but with computing kept to a minimum by pre- for example, the probability that alleles are identical by dicting breeding values only of siresand ignoring other descent at both of a pair of loci. This is important in relationships. computing covariances among relatives in which contri- The additive genetic contribution to the variances butions from epistasis (see KEMPTHORNE 1957) are in- and covariance of all animals in a population can be cluded. Similarly, such higher-order terms are essential described by the numerator term in WRIGHT’Sdefini- when computing probabilities of identity and correla- tion of relationship. This could be readily evaluated in tions among inbred relatives (COCKERHAMand WEIR a sequential manner to construct a table or matrix. (In 1972). 1963 I attended LUSH’Scourse at Ames based on The Predictionof breeding value: Thereare various Genetics of Populations, in which he illustrates the compu- threads to developments in animal breeding that date tation of the genic covariance. He described the con- back to or rely heavily on the “Systems of Matings” struction of a “covariance chart,” which he used exten- papers. Perhaps that of greatest current utilization is in sively, for one is so labeled in my handwritten notes breeding value prediction, to which WRIGHT’Sdefini- and there is a separate mention that it is a covariance tions of inbreeding and relationship in terms of covari- matrix.) It is more commonly described, to follow HEN- ances and correlations transfer directly. In livestock im- DERSON’S usage, as the numerator relationship matrix. For provement, the objective is to select animals expected example, the covariance of records of a pair of half sibs, to have the highest performing offspring, so that accu- otherwise unrelated, is vA/4, and thevariance of inbred rate prediction of breeding value is of fundamental im- individuals is (1 + f) V,, where VA is the additive genetic portance. The problem is, however, that selection may (or genic) variance. In general, using, as is the animal have to be practiced among animals that are notdirectly breeding custom, A to denote the matrix and a,i its comparable on performance either in space or time elements, the (co)variance of the performance of two and have different amountsof information available on individuals is ailVA.[The numeratorrelationship is twice them or their relatives. In dairy cattle, bulls are used in the coeficient de parent6 of MALBcoT (1948).] HENDER- artificial insemination unequally over many herds, and SON showed how this covariance matrix featured in a cows to rear the next generation of bulls have to be simple way in generalizations of his mixed model or chosen among herds. Furthermore, it is necessary to BLUP equations. Evaluation of the equations requires combine information on several traits of different eco- the inverse of the numerator relationship matrix, which nomic importance. Theseproblems were seen by LUSH needs major computation to get from A if many animals (see 1937, 1948 for details) among others. He showed are being evaluated. HENDERSON(1976) found, how- how records from different individuals, e.g., the animal ever, that the elements of A” could be evaluated by itself, its sibsand progeny, differed in their information simple steps directly from the pedigree. This enabled content and how a progeny mean should be regressed the computationsfor the so-called animal model, which to allow for different numbersof records. His colleague includes an equationfor each animal, to be undertaken HAZEL (1943) showedhow information on multiple with all the data, even for dairy populations of millions traits should be combined into aselection index, basing of animals. The methodology is widespread and stan- his arguments on a path coefficient approach to multi- dard for breeding programs of most species of livestock ple traits. and has spreadinto improvement of trees. Thus, The problem of comparisons of dairy sires having WRIGHT’Sconcept of relationship and inbreeding in daughters distributed unequally over many herds re- quantitative genetic terms corresponds directly to the quired both statistical and computational input. This animal model BLUP framework, and the pedigree of was first provided through the contemporary compari- the method was undoubtedly from WRIGHTto LUSHto son (ROBERTSON1953), in which environmental effects HENDERSON. were eliminated in a crossclassified structure by assum- Current methods of estimating genetic variance com- ing that sires of contemporaries were randomly sam- ponents, heritabilities and correlations are based on max- pled. The problem of simultaneously estimating the imum likelihood, specifically on restricted maximum like- breeding value of all animals to take account of nonran- lihood (REML) developed primarilyby THOMPSON (1973 dom usage became more important as progeny test re- et seq.) for quantitative genetic application, although sults became used by breeders. The principles of mod- there is increasing use of Bayesian ideas. In these meth- 1504 W. G. Hill ods, general data structures including information on working for the Department of Agriculture had a very animals of different generations are handled by using the significant influence on his views not only on animal numerator relationship matrix to specify the covariance improvement but also on the evolutionary process, for between all observations. Critically, as for the develop the shifting balance theory was developed before he ment of BLUP,increased computing power has facilitated moved to Chicagoand published “Evolution in Mende- the utilization of theoretical developments. lian Populations” (WRIGHT1931). Many years later, Population size: WRIGHThad a great interest in the WRIGHT(1978) recalled that he was impressed by four importance of the size and mating structure within pop- observations: the large responses obtained by CASTLE ulations on the opportunities for and rates of genetic to high and low selection for extent of color in the improvement by artificial selection and the beneficial coats of hooded rats, which showed the power of mass and harmful effects inbreeding might have. In the “Sys- selection but also revealed unfavorable correlated re- tems of Mating” series (1921b), he computed rates of sponses in mortality and fecundity; the results of his inbreeding for different fixed mating structures in Ph.D. thesis on the interaction among genes for color closed populations and subsequently used his methods and pattern in the coat of guinea pigs, which indicated to estimate levels and rates of inbreeding in livestock that an organism must be viewed as a vast network of populations, an activity that persists to this day. The interacting systems; the great variation found for many schemes hecomputed, such as quadruple second traits amonginbred strains of guinea pigs,which cousin matings, are what have become known as maxi- showed the effectiveness of simple genetic sampling in mum avoidance schemes, in that inbreeding is delayed creating diversity; and thehigh levels of inbreeding and for as many generations as possible but at the expense high relationship to particular animals found in the of higher long-term rates of loss of heterozygosity when Shorthorn breed of cattle, which “yielded the proper family sizes are equal (=MUM and CROW1963; CABAL- balance between the extreme plasticity of the original LERO 1994). heterogeneous Shorthornstock and the more complete WRIGHTlater (1931 et seq. ) developed the idea of fixation of the characters which would have resulted effective population size (Ne)and showed how to com- from closer inbreeding.” These observations led him pute it for a range of breeding structures. WRIGHT’SNe to suggest both the shifting balance theory of adaptive has, like hisf(or F), become a standardfor comparison evolution and the way to improve livestock breeds. Im- among breeding programs. While WRIGHTfound very provement would occur most rapidly in small popula- high levelsof inbreeding in some of the breeds he tions, where favorablenew epistatic combinations of studied, there was concern among breedersin the 1950s genes would arise, and these would spread by migration and subsequently that the concentrationof genes possi- or between-line selection. For further discussion, see ble with theintroduction ofartificial insemination HILL (1989) and CROW(1990). would lead to an increase in rates. This did not happen In animal improvement programs, there are many initially because a wider pool of breeding stock was cases in which a subset of a population has improved tested in artificial insemination than in traditional pedi- rapidly and others have caught upby introgression. For gree programs; but as selection has become more in- example, North American Holstein cattle originated tense and international movement of livestock more from Europe 100 years or so ago, but underwent more common, rates of increase in average relationship are rapid improvement for milk production than theEuro- rising in the world’s major breeds of dairy cattle, with pean populations and have, over the last two decades, inbreeding lagging by avoidance of mating relatives. In largely replaced the latter. There is little or no evidence particular, the high weight given to family information that this or any other example is conferring benefits in modern breeding programs through the use of selec- through epistatic interactions; what is striking is the tion indices or BLUP means that rates of inbreeding almost complete lack of detectable interactions among, are likely to be much higher than with selection on for example, sire families when tested in the United individual phenotype. ROBERTSON(1961) initially iden- States or abroad in different populations and environ- tified the effects of selection on rates of inbreeding, ments, so that there is a major international trade in and formulas have been developed recently by WRAY, dairy cattle semen. THOMPSON,WOOLLIAMS, and colleagues to give more There have been a numberof laboratory experiments precise answers and to allow for selection using combi- to evaluate improvement programs by use of WRIGHT’S nations of individual and relatives’ performance (see ideas on population structure. These have not usually CABALLERO1994 for a review). There is a conflict in been effective, in that simple mass selection in a large that maximizing rates of short-term response leads to population hastypically outperformed a program of increasing rates of inbreeding and loss of heterozygos- selection in small lines with subsequent between-line ity, thereby reducing long-term improvement from selection, at least partly because the experiments have within population selection. used mainly additive traits (see HILLand CABALLERO Breeding structure and shifting balance: The analy- 1992 for review). Direct experimental evaluation of the ses of breeding structure thatWRIGHT conducted while shifting balance theory by interdemic selection and mi- Perspectives 1505 gration has, however, revealed some response indicative COCKERHAM,C. C., and B. S. WEIR,1972 Descent measures for two loci with some applications. Theor. Popul. Biol. 4 300-330. of nonadditive effects (WADE and GOODNIGHT1991). CROW,J. F., 1990 Sewall Wright’s place in twentieth century biology. There was much interest in the 1940s and 1950s in J. Hist. Biol. 23 57-89. inbreeding and crossbreeding programs in animals to FALCONER,D. S., 1960 Introduction to Quantitative Genetics. Oliver and Boyd, Edinburgh. utilize heterosis following their success in hybrid maize, FALCONER,D. S., 1993 Quantitativegenetics in Edinburgh: 1947- with the most obvious potential application being in 1980. Genetics 133: 137-142. poultry breeding for table egg production. The low re- FISHER,R. A., 1918 The correlation between relatives on the suppo- sition of Mendelian inheritance. Trans. R. SOC.Edinb. 52: 399- productive rate ofeven this species compared with 433. maize and the long numberof generations required to FISHER,R. A,, 1949 The Themy of Inbreeding. Oliver and Boyd, Edin- obtain high levelsof inbreeding implied that each burgh. HAVENSTEIN,G. B., P. R. FERKERT,S. E. SCHEIDLERand B. T. LARSON, round of selection was slow and expensive, and selec- 1994 Growth, livability, and feed conversion of 1957 vs. 1991 tion intensities were low. While there is extensive use broilers when fed ‘typical’ 1957 and 1991 broiler diets. Poult. of crossbreeding to utilize heterosis and different prop- Sci. 73: 1785-1794. HAZEL,L. N., 1943 The geneticbasis for constructing selection indi- erties of breeds, e.g., specialized sire and dam lines with ces. Genetics 28: 476-490. high performance for traits of growth and reproduc- HENDERSON,C. R., 1974 General flexibility of linearmodel tech- tion, respectively, there is not much use of inbreeding niques for sire evaluation. J. Dairy Sci. 57: 963-972. HENDERSON, C. R.,1976 A simple method for computing theinverse and between-line selection in animal improvement pro- of a numerator relationship matrix used in prediction of breed- grams. ing values. Biometrics 32 69-83. Thus, it is the case that, for one reason or another, HILL,W. G., 1984 Benchmark Papers inQuantitative Genetics. Part. I. Explanation and Analysis of Quantitative Variation. Van Nostrand animal improvement has been in recent decades and Rheinhold, New York. still isvery much based on additive genetic change. HILL,W. G., 1989 Sewall Wright and quantitative genetics. Genome Consider, for example, broiler chickens, where intense 31: 190-195. HILL, W. G., and A. CABALLERO,1992 Artificial selection experi- selection on juvenile growth has been practiced for ments. Annu. Rev. Syst. Ecol. 23: 287-310. many decades. In a recentcomparison of “1957” broil- KEMPTHORNE,O., 1957 An Introduction to Genetic Statistics. John Wi- ers, available as an unselected control stock, and 1992 ley, New York. KIMURA,M., and J. F. CROW,1963 On the maximum avoidance of broilers, HAVENSTEIN et al. (1994) found that at8 weeks inbreeding. Genet. Res. 4: 399-415. of age the modern strain was almost four times heavier. KIMURA,M., and J. F. CROW,1964 The number of alleles that can Nor is there evidence that levels of heritability are de- be maintained in a finite population. Genetics 49: 725-738. LI, C. C., 1955 Population Genetics. University of Chicago Press, Chi- clining appreciably because of selection and inbreed- cago. ing. Therefore, the ideas of WRIGHT’Sshifting balance LUSH,J. L., 1937 Animal Breeding Plans. Iowa State College Press, theory, which he elucidated at least in part to explain Ames, Iowa. (3rd ed., 1945). LUSH,J. L., 1948 The Genetics of Populations. Mimeograph. the apparentsuccess ofbreeding programs, have, asfar LUSH,J. L., 1994 The Genetics ofpopulations, edited by A. B. CHAPMAN as I know, had little impact on livestock improvement as and R. R. SHRODE,with an addendum by J. F. CROW. IowaState practiced by professional geneticists and the companies Univ. Press, Ames. MAL~COT,G., 1948 Les Mat-tiques de l’H&t?ditt?.Masson et Cie., they advise (but, of course, details of programs in com- Paris. mercial companies are not public). Furthermore,I have PROVINE,W. B., 1971 The origins of Theoretical Population Genetics. surmised (HILL1989) that had WRIGHTknown of the University of Chicago Press, Chicago. PROVINE,W. B., 1986 Small Wright and Evolutionaly Biology. Univer- effectiveness of direct selection in large populations of sity of Chicago Press, Chicago. livestock, he would not have arrived at and championed ROBERTSON,A,, 1953 The use and interpretation of progeny tests the shifting balance theory. in livestock improvement. Proc. Br. SOC.him. Prod. pp. 3-16. ROBERTSON,A,, 1961 Inbreeding in artificial selection programmes. Concluding remarks: Evenif WRIGHT haddone Genet. Res. 2: 189-194. nothing else in his long research career, his standing THOMPSON,R., 1973 The estimation of variance and covariance would be recognized for the major technical impact he components with an applicationwhen records are subjectto culling. Biometrics 29 527-550. made in his series on “Systems ofMating.” Who cannot WADE, M. J., and C. J. GOODNIGHT, 1991 Wright’s shifting balance havewished to invent something so simple and im- theory: an experimental study. Science 253 1015-1018. portant as the inbreeding coefficient? No doubt some- WEINBERG,W., 1910 Further contributions to the theory of inheri- tance. Arch. Rassen. Ges. Biol. 7: 35-49. one else would havedeveloped it later, but he was first. WRIGHT,S., 1918 On the nature of size factors. Genetics 3: 367- 374. I thank NICKBARTON, ARMANDO CABALLERO,DOUGLAS FALCONER, WRIGHT,S., 1920 The relative importance of heredity and environ- GENEFREEMAN, PETER KEIGHTLEY, WILL PROVINE,and particularlyJIM ment in determining the piebald pattern of guinea pigs. Proc. CROW for helpful comments. The errors that remain are mine. Natl. Acad. Sci. USA 6: 320-332. WRIGHT, S., 1921a Systems of mating. I. The biometricrelations between offspring and parent. Genetics 6: 111-123. LITERATURECITED WRIGHT,S., 1921b Systems of mating. 11. The effects of inbreeding on the genetic composition of a population. Genetics 6 124- BELL,A. E., 1977 Heritability in retrospect. J. Hered. 68: 297-300. 143. BULMER,M. G., 1980 The Mathematical Themy of Quantitative Genetics. WRIGHT,S., 1921c Systems of mating. 111. Assortative mating based Clarendon Press, Oxford. on somatic resemblance. Genetics 6: 144-161. CABALLERO,A., 1994 Developments inthe predictionof effective WRIGHT,S., 1921d Systems of mating. IV. The effects of selection. population size. Heredity 73 657-679. Genetics 6: 162-166. 1506 W. G. Hill

WRIGHT,S., 1921e Systems of mating. V. General considerations. in Quantitative Inheritance, edited by E. C. R. REEVE and C. H. Genetics 6: 167-178. WADDINGTON.Her Majesty’s Stationary Office, London. WRIGHT,S., 1922 Coefficients of inbreeding and relationship. Am. WRIGHT,S., 1968, 1969, 1977, 1978 Evolution and the Genetics ofPopu- Nat. 56: 330-338. htions, Volumes 1-4. University of Chicago Press, Chicago. WRIGHT,S., 1931 Evolution in Mendelian populations. Genetics 16: WRIGHT,S., 1978 The relation of livestock breeding to theories of 97-159. evolution. J. him. Sci. 46: 1192-1200. WRIGHT,S., 1951 The genetical structure of populations. Ann. Eu- WRIGHT,S., and H. C. MCPHEE,1925 An approximate method of gen. 15: 323-354. calculating coefficients of inbreeding and relationship from live- WRIGHT,S., 1952 The genetics of quantitative variability, pp. 5-41 stock pedigrees. J. Agric. Res. 31: 377-383.