Sewall Wright

The Interpretation of Population Structure by F-Statistics with Special Regard to Systems of Mating

Kimura and Crow (1963b) have recently made an interesting comparison between two classes of systems of mating within populations of constant size: ones in which there is maximum avoidance of consanguine mating and ones in which all matings are between close relatives around an unbroken circle. These are illustrated in Figs. 1 and 2 in populations of eight. The rate of decrease of heterozygosis in the former class had, as they note, been found long before to approach 1/(4N) asymptotically with increasing size of population, N (Wright, 1921, 1933a). Two cases with patterns of mating similar to those of Kimura and Crows second class, except that the matings were between neighbors along infinitely extended lines instead of around a circle, had also been considered in these papers. These systems consisted of exclusive mating of half-sibs or of first cousins, otherwise with a minimum of relationship. It was found that there is no equilibrium in either case short of complete fixation locally, in spite of the linear increase in number of different ancestors with increasing number of ancestral generations. This was in contrast to systems (half first cousin or second cousin) in which this increase is more than linear and a steady state is rapidly attained with respect to heterozygosis. Kimura and Crow were surprised to find that the limiting rates of decrease of heterozygosis in their circular systems are much less than under maximum avoidance approaching [v/(2N + 4)]2 in the case of half-sib matings and [7/ (N + 12)]2 under first-cousin matings with large N. Maxi-

Breeding Structure of Populations in Relation to Speciation

THE problem of speciation involves both the processes by which populations split into non-interbreedingl roups and those by which single populations change their characteristics in time, thus leading to divergence of previously isolated groups. The first step in applying genetics to the problem is undoubtedly the discovery of the actual nature of the genetic differences aniong allied subspecies, species and genera in a large number of representative cases.. Differences which tend to prevent cross-breeding are obviously especially likely to throw light on the process of speciation, but all differences are important. Our information here is still very fragmentary. We know enough, however, to be able to say that there is no one rule either with respect to cross-sterility or to other characters. In some cases the most significant differences seem to be in chromosome number and organization. At the other extrem-ie are groups of species among which gross chromosome differences Iand even major Mendelian differences are lacking, both cross-sterility and character differentiation depending on a multiplicity of minor gene effects. IIn general, there are differences at all levels (cf. Dobzhansky, 1937). But even if we had a complete account of the genetic differences within a group of allied species, we would not necessarily have much understanding of the process by which the situation had been arrived at. A single mutation is not a new species, except perhaps in the case of polyploidy. The symmetry of the Mendelian mechanism

Path Coefficients and Path Regressions: Alternative or Complementary Concepts?

(1) The authors concur with Tukey in treating the standardized and concrete forms of correlational statistics as if they were alternative conceptions between which it is necessary to make a choice. It has always seemed to me that these should be looked upon as two aspects of a single theory corresponding to different modes of interpretation which, taken together, often give a deeper understanding of a situation than either can give by itself. (2) E1ven when the sole objectives of analysis are the concrete coefficients, actual path analysis takes a simpler and more homogeneous form in terms of the standardized ones. The application of the method to data usually requires algebraic manipulation of coefficients pertaining to unmeasured variables on the same basis as measured ones. As the former can only be dealt with in standardized form, homogeneity requires that all be so dealt with in the course of the algebra. It is such a simple matter to pass from either form to the other (in the cases in which standard deviations are available to all) that the economy of effort in using the concrete coefficients as far as possible, where these are the objectives, is usually outweighed by the loss of economy in other respects. (3) It is of first importance in path analysis to make use of all of the available data. This is not done by Turner and Stevens in most of their examples. The use of standardized coefficients leads naturally

Physiological and Evolutionary Theories of Dominance

INTRODUCTION MENDEL found that one member of each of his seven pairs of alternative characters of the pea reappeared in the first cross-bred generation to the complete or nearly complete exclusion of the other. Although lie attributed 1o great importance to this himself, there was some tendency, following the rediscovery in 1900, to consider a law of dominance as oiie of thle fundamental principles of heredity. It has long fallen from this estate and it has beeii questioned whether careful measurements would not show complete dominance to be the exception rather than the rule. An approach to complete dominance is common enough, however, to present a number of interesting problems. In the first place, it is clear that dominance has to do Wvith the physiology of the organism and has nothing to do with the mechanism of transmission, i.e., \with eredity in the narrow sense. Studies of dominance bear oii two different groups of problems. The accurate measurement of degree of dominance of particular genes under varying conditions furnishes one of the most available tools for carrying physiological analysis back to the ultimate controlling factors. On tile other hand, statistical generalizations in regard to dominance may rest not only on the average consequences of physiological principles but also on general evolutionary treiids and thus may throw light on the evolutionary process.

On the roles of directed and random changes in gene frequency in the genetics of populations.

Science has largely advanced by the analytic procedure of isolating the effects of single factors in carefully controlled experiments. The task of science is not complete, however, without synthesis: the attempt to interpret natural phenomena in which numerous factors are varying simultaneously. Studies of the genetics of populations, including their evolution, present problems of this sort of the greatest complexity. AMany writers on evolution have been inclined to ignore this and discuss the subject as if it were merely a matter of choosing between single factors. Mly own studies on population genetics have been guided primarily by the belief that a mathematical muodel must be sought which permits siinultaneous consideration of all possible factors. Such a model must be sufficiently simple to permit a rough grasp of the system of interactions as a whole and sufficiently flexible to permit elaboration of aspects of which a more complete account is desired. On attempting to make such a formnulation (\Vright, 1931) it was at once apparent that any one of the factors

On the Probability of Fixation of Reciprocal Translocations

The chance of fixation of a reciprocal translocation in a population of plants, with exclusive sexual reproduction, is of the order 10-3 if the effective population number (N) is 10. It is of the order of 2 x 10-6 in groups of 20 individuals and of the order 3 x 10-14 in groups of 50 individuals. It is assumed that the heterozygotes are semisterile, and that there is no compensating advantage in semisterility by reduction of competition among the progeny and that the translocation has no advantage per se. These figures may be compared with 1/2N, the chance of fixation of an indifferent mutation. Reciprocal translocations in animals have a slightly better chance of fixation than in plants in populations of the same effective size, even if only the balanced types are viable and fertile. Cases in which the heterozygous unbalanced type are at no disadvantage in viability and in number of gametes produced, only the homozygous deficiencies being eliminated, have considerably better chances of fixation than in the cases above. The chance is roughly 3 x 10-3 in populations of 20, 4 x 10-6 in populations of 50, 3 x 10-10 in populations of 100 and 5 x 10-18 in populations of 200. In all the cases given here, there is an element of uncertainty as a result of which the true chance may be smaller or greater by a small factor (less than 4). A statement in a previous paper gave a somewhat exaggerated impression of the difficulty of fixation of reciprocal translocations. It remains true, nevertheless, that such fixation can hardly occur under exclusive sexual reproduction except in a species in which there are numerous isolated populations that pass through phases of extreme reduction of numbers. The most favorable case would seem to be that in which there is frequent extinction of the populations of small isolated localities, with restoration from the progeny of occasional stray migrants from other localities. If one of the unbalanced homozygotes is viable and fertile (unlikely in a reciprocal translocation but not unlikely in the case of a small insertional translocation), the chance of fixation of the nondeficient modified chromosome may be much greater than in the cases considered above and would even be slightly greater than that of an indifferent mutation if the unbalanced homozygote and the heterozygotes that include it are at no disadvantage compared with the balanced homozygotes.

Statistical genetics and evolution

Introduction. When Darwin developed the theory of evolution by natural selection, practically nothing was known of hereditary differences beyond their existence. Since 1900, a body of knowledge on the mechanism of heredity and on mutation has been built up by experiment that challenges any field in the biological sciences in the extent and precision of its results. The implications for evolution are not, however, immediately obvious. I t is necessary to work out the statistical consequences. Studies in the field of statistical genetics began shortly after the rediscovery of Mendelian heredity in 1900. Those of J. B. S. Haldane [7] and R. A. Fisher [4] have been especially important with respect to the application to evolution. My own approach to the subject came through experimental studies conducted in the U. S. Bureau of Animal Industry on the effects of inbreeding, crossbreeding and selection on populations of guinea pigs [21, 22, 23, 37] and through the attempt to formulate principles applicable to livestock breeding [19, 20, 24, 25, 13, 34]. On moving into the more academic atmosphere of the University of Chicago, I have become more directly concerned with the problem of evolution. I should note that the deductive approach, to which I shall confine myself here, involves many questions that can only be settled by observation and experimental work on natural populations and that a remarkable resurgence of interest in such work is in progress [2, 9] .

The analysis of variance and the correlations between relatives with respect to deviations from an optimum

SummaryThe formulae for the mean and variance of squared deviations from an optimum are given for the cases of no dominance and of complete dominance, first assuming no environmental complications but later removing this restriction. The variance in each case is analysed into contributions due to (1) additive gene effects, (2) dominance deviations, (3) epistatic deviations, (4) environmental effects and (5) nonadditive joint effects of heredity and environment. In the case of complete dominance, formulae are developed which apply to epistatic relations in general. These lead to formulae for the correlations between parent and offspring and between two offspring.It appears that in a population in which the mean of some measurable character is at the optimum, the parent-offspring and fraternal correlations in adaptive value are approximately the squares of the corresponding correlations with respect to the character itself, whatever environmental complications there may be. Where the mean is not at the optimum, there is less difference between the correlations in adaptive value and the corresponding ones with respect to the character itself.

Modes of Selection

At the lowest level is selection among genes in mere capacity to persist and in mechanism of exact duplication. It seems probable, as suggested by Darwin (cf. Hardin 1950) and developed by Haldane (1933) and Oparin (1938), that life originated in an organic soup that could only have accumulated in the prior absence of life and that was one that provided all necessary metabolites. It is hardly probable that the chemical basis for gene persistence and duplication appeared full fledged. We may conclude with Blum (1951) that evolution took the form at first of decreasing mutability. Along with this may have occurred the evolution of stable genic association in cells, and mechanisms of exact duplication of the entire system by mitosis. *Address of the President, Society for the Study of Evolution, delivered at the

Random Drift and the Shifting Balance Theory of Evolution

The word “drift” has been used rather frequently in population genetics, but not always in the same sense. The author is probably responsible for its introduction by using it in papers in 1929, though with no intention of giving it a technical meaning. It has, however, come to be so used and thus is in need of careful definition.