Sewall Wright (1889-1988)

The genetic contributions of Sewall Wright is briefly reviewed with special reference to J.B.S. Haldane's work. These include his work in population genetics, statistics, and animal breeding.     

R.A. Fisher's contributions to genetical statistics

R. A. Fisher (1890-1962) was a professor of genetics, and many of his statistical innovations found expression in the development of methodology in statistical genetics. However, whereas his contributions in mathematical statistics are easily identified, in population genetics he shares his preeminence with Sewall Wright (1889-1988) and J. B. S. Haldane (1892-1965). This paper traces some of Fisher's major contributions to the foundations of statistical genetics, and his interactions with Wright and with Haldane which contributed to the development of the subject. With modern technology, both statistical methodology and genetic data are changing. Nonetheless much of Fisher's work remains relevant, and may even serve as a foundation for future research in the statistical analysis of DNA data. For Fisher's work reflects his view of the role of statistics in scientific inference, expressed in 1949: There is no wide or urgent demand for people who will define methods of proof in set theory in the name of improving mathematical statistics. There is a widespread and urgent demand for mathematicians who understand that branch of mathematics known as theoretical statistics, but who are capable also of recognising situations in the real world to which such mathematics is applicable. In recognising features of the real world to which his models and analyses should be applicable, Fisher laid a lasting foundation for statistical inference in genetic analyses.     

From Hopeful Monsters to Homeotic Effects: Richard Goldschmidt's Integration of Development, Evolution, and Genetics

Richard Goldschmidt's research on homeotic mutants from 1940until his death in 1958 represents one of the first seriousefforts to integrate genetics, development, and evolution. Usingtwo different models, Goldschmidt tried to show how differentviews of genetic structure and gene action could provide a mechanismfor rapid speciation. Developmental systems were emphasizedin one model and a hierarchy of genetic structures in the other.While Goldschmidt tried to find a balance between developmentand genetics, critics, such as Sewall Wright, urged him andeventually helped him incorporate population dynamics into hismodels as well. As such, the history of Goldschmidt's researchon homeotic mutants highlights the continuing challenge of producinga balanced and integrated developmental evolutionary genetics.     

THE EVOLUTION OF LANDSCAPE GENETICS

The main objective of this special section is not to review the broad field of landscape genetics, but to provide a glimpse of how the developing landscape genetics perspective has the potential to change the way we study evolution. Evolutionary landscape genetics is the study of how migration and population structure affects evolutionary processes. As a field it dates back to Sewall Wright and the origin of theoretical population genetics, but empirical tests of adaptive processes of evolution in natural landscapes have been rare. Now, with recent developments in technology, methodology, and modeling tools, we are poised to trace adaptive genetic variation across space and through time. Not only will we see more empirical tests of classical theory, we can expect to see new phenomena emerging, as we reveal complex interactions among evolutionary processes as they unfold in natural landscapes.     

Panpsychic Organicism: Sewall Wright’s Philosophy for Understanding Complex Genetic Systems

Sewall Wright first encountered the complex systems characteristic of gene combinations while a graduate student at Harvard’s Bussey Institute from 1912 to 1915. In Mendelian breeding experiments, Wright observed a hierarchical dependence of the organism’s phenotype on dynamic networks of genetic interaction and organization. An animal’s physical traits, and thus its autonomy from surrounding environmental constraints, depended greatly on how genes behaved in certain combinations. Wright recognized that while genes are the material determinants of the animal phenotype, operating with great regularity, the special nature of genetic systems contributes to the animal phenotype a degree of spontaneity and novelty, creating unpredictable trait variations by virtue of gene interactions. As a result of his experimentation, as well as his keen interest in the philosophical literature of his day, Wright was inspired to see genetic systems as conscious, living organisms in their own right. Moreover, he decided that since genetic systems maintain ordered stability and cause unpredictable novelty in their organic wholes (the animal phenotype), it would be necessary for biologists to integrate techniques for studying causally ordered phenomena (experimental method) and chance phenomena (correlation method). From 1914 to 1921 Wright developed his “method of path coefficient” (or “path analysis”), a new procedure drawing from both laboratory experimentation and statistical correlation in order to analyze the relative influence of specific genetic interactions on phenotype variation. In this paper I aim to show how Wright’s philosophy for understanding complex genetic systems (panpsychic organicism) logically motivated his 1914–1921 design of path analysis.     

“The Theory was Beautiful Indeed”: Rise,Fall and Circulation of Maximizing Methods in Population Genetics (1930–1980)

Describing the theoretical population geneticists of the 1960s, Joseph Felsenstein reminisced: “our central obsession was finding out what function evolution would try to maximize. Population geneticists used to think, following Sewall Wright, that mean relative fitness, W, would be maximized by natural selection” (Felsenstein 2000). The present paper describes the genesis, diffusion and fall of this “obsession”, by giving a biography of the mean fitness function in population genetics. This modeling method devised by Sewall Wright in the 1930s found its heyday in the late 1950s and early 1960s, in the wake of Motoo Kimura’s and Richard Lewontin’s works. It seemed a reliable guide in the mathematical study of deterministic effects (the study of natural selection in populations of infinite size, with no drift), leading to powerful generalizations presenting law-like properties. Progress in population genetics theory, it then seemed, would come from the application of this method to the study of systems with several genes. This ambition came to a halt in the context of the influential objections made by the Australian mathematician Patrick Moran in 1963. These objections triggered a controversy between mathematically- and biologically-inclined geneticists, with affected both the formal standards and the aims of population genetics as a science. Over the course of the 1960s, the mean fitness method withered with the ambition of developing the deterministic theory. The mathematical theory became increasingly complex. Kimura re-focused his modeling work on the theory of random processes; as a result of his computer simulations, Lewontin became the staunchest critic of maximizing principles in evolutionary biology. The mean fitness method then migrated to other research areas, being refashioned and used in evolutionary quantitative genetics and behavioral ecology.     

The fate of balanced,phenotypic polymorphisms in fragmented metapopulations

In large populations, genetically distinct phenotypic morphs can be maintained in equilibrium (at a 1 : 1 ratio in the simplest case) by frequency‐dependent selection, as shown by Sewall Wright. The consequences of population fragmentation on this equilibrium are not widely appreciated. Here, I use a simple computational model to emphasize that severe fragmentation biases the morph ratio towards the homozygous recessive genotype through drift in very small populations favouring the more common recessive allele. This model generalizes those developed elsewhere for heterostylous plants and major histocompatibility complex alleles, emphasizes one particular outcome and avoids the restricting assumptions of more analytical models. There are important implications for both fundamental evolutionary biology and conservation genetics. I illustrate this with a range of examples but refer particularly to shell polymorphism in snails. These examples show how habitat fragmentation could have a direct and often unappreciated effect on species at the level of their population genetics.     

Applications of Population Genetics to Animal Breeding,from Wright,Fisher and Lush to Genomic Prediction

Although animal breeding was practiced long before the science of genetics and the relevant disciplines of population and quantitative genetics were known, breeding programs have mainly relied on simply selecting and mating the best individuals on their own or relatives’ performance. This is based on sound quantitative genetic principles, developed and expounded by Lush, who attributed much of his understanding to Wright, and formalized in Fisher’s infinitesimal model. Analysis at the level of individual loci and gene frequency distributions has had relatively little impact. Now with access to genomic data, a revolution in which molecular information is being used to enhance response with “genomic selection” is occurring. The predictions of breeding value still utilize multiple loci throughout the genome and, indeed, are largely compatible with additive and specifically infinitesimal model assumptions. I discuss some of the history and genetic issues as applied to the science of livestock improvement, which has had and continues to have major spin-offs into ideas and applications in other areas.THE success of breeders in effecting immense changes in domesticated animals and plants greatly influenced Darwin’s insight into the power of selection and implications to evolution by natural selection. Following the Mendelian rediscovery, attempts were soon made to accommodate within the particulate Mendelian framework the continuous nature of many traits and the observation by Galton (1889) of a linear regression of an individual’s height on that of a relative, with the slope dependent on degree of relationship. A polygenic Mendelian model was first proposed by Yule (1902) (see Provine 1971; Hill 1984). After input from Pearson, Yule again, and Weinberg (who developed the theory a long way but whose work was ignored), its first full exposition in modern terms was by Ronald A. Fisher (1918) (biography by Box 1978). His analysis of variance partitioned the genotypic variance into additive, dominance and epistatic components. Sewall Wright (biography by Provine 1986) had by then developed the path coefficient method and subsequently (Wright 1921) showed how to compute inbreeding and relationship coefficients and their consequent effects on genetic variation of additive traits. His approach to relationship in terms of the correlation of uniting gametes may be less intuitive at the individual locus level than Malécot’s (1948) subsequent treatment in terms of identity by descent, but it transfers directly to the correlation of relatives for quantitative traits with additive effects.From these basic findings, the science of animal breeding was largely developed and expounded by Jay L. Lush (1896–1982) (see also commentaries by Chapman 1987 and Ollivier 2008). He was from a farming family and became interested in genetics as an undergraduate at Kansas State. Although his master’s degree was in genetics, his subsequent Ph.D. at the University of Wisconsin was in animal reproductive physiology. Following 8 years working in animal breeding at the University of Texas he went to Iowa State College (now University) in Ames in 1930. Wright was Lush’s hero: ‘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 1945, in the preface to his book Animal Breeding Plans). Lush commuted in 1931 to the University of Chicago to audit Sewall Wright’s course in statistical genetics and consult him. Speaking at the Poultry Breeders Roundtable in 1969: he said, “Those were by far the most fruitful 10 weeks I ever had.” (Chapman 1987, quoting A. E. Freeman). Lush was also exposed to and assimilated the work and ideas of R. A. Fisher, who lectured at Iowa State through the summers of 1931 and 1936 at the behest of G. W. Snedecor.Here I review Lush’s contributions and then discuss how animal breeding theory and methods have subsequently evolved. They have been based mainly on statistical methodology, supported to some extent by experiment and population genetic theory. Recently, the development of genomic methods and their integration into classical breeding theory has opened up ways to greatly enhance rates of genetic improvement. Lush focused on livestock improvement and spin-off into other areas was coincidental; but he had contact with corn breeders in Ames and beyond and made contributions to evolutionary biology and human genetics mainly through his developments in theory (e.g., Falconer 1965; Robertson 1966; Lande 1976, 1979; see also Hill and Kirkpatrick 2010). I make no attempt to be comprehensive, not least in choice of citations.     

群体遗传学研究中STR数据的统计方法应用

STR作为遗传多态性较高的标记, 被广泛地运用于群体遗传学的研究。对于STR分型产生的基因型频率及等位基因频率数据, 文章总结了各种参数指标的计算及分析方法。其中参数指标包括杂合度、多态信息量、连锁不平衡系数、近交系数、遗传距离以及固定指数等; 分析方法包括主成分分析、系统发生树、分子方差分析、R矩阵、地理信息系统以及空间自相关分析。通过这些参数指标及分析方法的使用, 可以既直观又科学地揭示群体遗传结构、群体间遗传分化以及人类起源与进化等群体遗传学中研究的关键问题。     

Dynamics of Fst for the island model

F(st) is a measure of genetic differentiation in a subdivided population. Sewall Wright observed that F(st)=1/1+2Nm in a haploid diallelic infinite island model, where N is the effective population size of each deme and m is the migration rate. In demonstrating this result, Wright relied on the infinite size of the population. Natural populations are not infinite and therefore they change over time due to genetic drift. In a finite population, F(st) becomes a random variable that evolves over time. In this work we ask, given an initial population state, what are the dynamics of the mean and variance of F(st) under the finite island model? In application both of these quantities are critical in the evaluation of F(st) data. We show that after a time of order N generations the mean of F(st) is slightly biased below 1/1+2Nm. Further we show that the variance of F(st) is of order 1/d where d is the number of demes in the population. We introduce several new mathematical techniques to analyze coalescent genealogies in a dynamic setting.     

The rank ordering of genotypic fitness values predicts genetic constraint on natural selection on landscapes lacking sign epistasis

Sewall Wright's genotypic fitness landscape makes explicit one mechanism by which epistasis for fitness can constrain evolution by natural selection. Wright distinguished between landscapes possessing multiple fitness peaks and those with only a single peak and emphasized that the former class imposes substantially greater constraint on natural selection. Here I present novel formalism that more finely partitions the universe of possible fitness landscapes on the basis of the rank ordering of their genotypic fitness values. In this report I focus on fitness landscapes lacking sign epistasis (i.e., landscapes that lack mutations the sign of whose fitness effect varies epistatically), which constitute a subset of Wright's single peaked landscapes. More than one fitness rank ordering lacking sign epistasis exists for L > 2 (where L is the number of interacting loci), and I find that a highly statistically significant effect exists between landscape membership in fitness rank-ordering partition and two different proxies for genetic constraint, even within this subset of landscapes. This statistical association is robust to population size, permitting general inferences about some of the characteristics of fitness rank orderings responsible for genetic constraint on natural selection.     

The free energy method and the Wright–Fisher model with 2 alleles

We systematically investigate the Wright–Fisher model of population genetics with the free energy functional formalism of statistical mechanics and in the light of recent mathematical work on the connection between Fokker–Planck equations and free energy functionals. In statistical physics, entropy increases, or equivalently, free energy decreases, and the asymptotic state is given by a Gibbs-type distribution. This also works for the Wright–Fisher model when rewritten in divergence to identify the correct free energy functional. We not only recover the known results about the stationary distribution, that is, the asymptotic equilibrium state of the model, in the presence of positive mutation rates and possibly also selection, but can also provide detailed formulae for the rate of convergence towards that stationary distribution. In the present paper, the method is illustrated for the simplest case only, that of two alleles.     

Studying populations without molecular biology: Aster Models and a new argument against reductionism

During the past few decades, philosophers of biology have debated the issue of reductionism versus anti-reductionism, with both sides often claiming a 'pluralist' position. However, both sides also tend to focus on a single research paradigm, which analyzes living things in terms of certain macromolecular components. I offer a case study where biologists pursue other analytic pathways, in a tradition of quantitative genetics that originates with the initially purely mathematical theories of R. A. Fisher, J. B. S. Haldane, and Sewall Wright in the 1930s. Aster Models (developed by Ruth Shaw and Charles Geyer) offers a class of statistical models designed for studying the fitness of plant and animal populations, by integrating the measurements of separate, sequential, non-normally distributed fitness components in novel ways. Their work generates important theoretical and practical results that do not require elaboration by molecular biology, and thus serves as a counterexample to the claims of philosophers whose 'pluralism' still harbors reductionist assumptions.     

The effect of selection on genetic balance when the population size is varying

It is known that a reformulation for variable population size of the classical Sewall Wright model for balance between two genotypes can lead, under some circumstances, to a situation of balanced polymorphism when there is no selection present. In this note it is shown that the presence of selection prohibits the possibility of balance and assures ultimate homozygosity with probability one.     

The Allelic Correlation Structure of Gainj- and Kalam-Speaking People. II. the Genetic Distance between Population Subdivisions

The patterning of allele frequency variability among 18 local groups of Gainj and Kalam speakers of highland Papua New Guinea is investigated using new genetic distance methods. The genetic distances proposed here are obtained by decomposing Sewall Wright's coefficient FST into a set of coefficients corresponding to all pairs of population subdivisions. Two statistical methods are given to estimate these quantities. One method provides estimates weighted by sample sizes, while the other method does not use sample size weighting. Both methods correct for the within-individual and between-individual-within-groups sums of squares. Genetic distances among the Gainj and Kalam subdivisions are analyzed with respect to demographic, geographic, and linguistic variables. We find that a demographic feature, group size, has the greatest demonstrable association with the patterning of genetic distances. The pattern of geographic distances among groups displays a weak congruence with the pattern of genetic distances, and the association of genetic and linguistic diversity is very low. An effect of differences in group size on genetic distances is not surprising, from basic theoretical considerations, but genetic distances have not often been analyzed with respect to these variables in the past. The lack of correspondence between genetic distances and linguistic and geographic differences is an unusual feature that distinguishes the Gainj and Kalam from most other tribal populations.     

Population genetics and sociobiology: conflicting views of evolution

This article explores the tension between the population genetics and sociobiological approaches to the study of evolution. Whereas population geneticists, like Stanford's Marc Feldman, insist that the genetic complexities of organisms cannot be overlooked, sociobiologists (many of whom now prefer to call themselves "behavioral ecologists") rely on optimization models that are based on the simplest possible genetics.These optimization approaches have their roots in the classical result known as the fundamental theorem of natural selection, formulated by R. A. Fisher in 1930. From the start there was great uncertainty over the proper interpretation of Fisher's theorem, which became confused with Sewall Wright's immensely influential adaptive landscape concept. In the 1960s, a new generation of mathematical biologists proved that Fisher's theorem did not hold when fitness depended on more than one locus. Similar reasoning was used to attack W. D. Hamilton's inclusive fitness theory. A new theory, known as the theory of long-term evolution, attempts to reconcile the rigorous population genetics approach with the long-standing sociobiological view that natural selection acts to increase the fitness of organisms.     

Rate of adaptive peak shifts with partial genetic robustness

How adaptive evolution occurs with individually deleterious but jointly beneficial mutations has been one of the major problems in population genetics theory. Adaptation in this case is commonly described as a population's escape from a local peak to a higher peak on Sewall Wright's fitness landscape. Recent molecular genetic and computational studies have suggested that genetic robustness can facilitate such peak shifts. If phenotypic expressions of new mutations are suppressed under genetic robustness, mutations that are otherwise deleterious can accumulate in the population as neutral variants. When the robustness is perturbed by an environmental change or a major mutation, these variants become exposed to natural selection. It is argued that this process promotes adaptation because allelic combinations enriched under genetic robustness can then be positively selected. Here, I propose simple two- and three-locus models of adaptation with partial genetic robustness as suggested by recent studies. The waiting time until the fixation of an adaptive haplotype was observed in stochastic simulations and compared to the expectation without robustness. It is shown that peak shifts can be delayed or accelerated depending on the conditions of genetic robustness. The evolutionary significance of these processes is discussed.     

Pluralism in evolutionary controversies: styles and averaging strategies in hierarchical selection theories

Two controversies exist regarding the appropriate characterization of hierarchical and adaptive evolution in natural populations. In biology, there is the Wright–Fisher controversy over the relative roles of random genetic drift, natural selection, population structure, and interdemic selection in adaptive evolution begun by Sewall Wright and Ronald Aylmer Fisher. There is also the Units of Selection debate, spanning both the biological and the philosophical literature and including the impassioned group-selection debate. Why do these two discourses exist separately, and interact relatively little? We postulate that the reason for this schism can be found in the differing focus of each controversy, a deep difference itself determined by distinct general styles of scientific research guiding each discourse. That is, the Wright–Fisher debate focuses on adaptive process, and tends to be instructed by the mathematical modeling style, while the focus of the Units of Selection controversy is adaptive product, and is typically guided by the function style. The differences between the two discourses can be usefully tracked by examining their interpretations of two contested strategies for theorizing hierarchical selection: horizontal and vertical averaging.     

SPATIAL DIFFERENTIATION FOR FLOWER COLOR IN THE DESERT ANNUAL LINANTHUS PARRYAE: WAS WRIGHT RIGHT?

Understanding the evolutionary mechanisms that contribute to the local genetic differentiation of populations is a major goal of evolutionary biology, and debate continues regarding the relative importance of natural selection and random genetic drift to population differentiation. The desert plant Linanthus parryae has played a prominent role in these debates, with nearly six decades of empirical and theoretical work into the causes of spatial differentiation for flower color. Plants produce either blue or white flowers, and local populations often differ greatly in the frequencies of the two color morphs. Sewall Wright first applied his model of "isolation by distance" to investigate spatial patterns of flower color in Linanthus. He concluded that the distribution of flower color morphs was due to random genetic drift, and that Linanthus provided an example of his shifting balance theory of evolution. Our results from comprehensive field studies do not support this view. We studied an area in which flower color changed abruptly from all-blue to all-white across a shallow ravine. Allozyme markers sampled across these regions showed no evidence of spatial differentiation, reciprocal transplant experiments revealed natural selection favoring the resident morph, and soils and the dominant members of the plant community differed between regions. These results support the hypothesis that local differences in flower color are due to natural selection, not due to genetic drift.