“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.     

Cytogenetics of the grasshopper Moraba scurra

Summary The cytology of a male individual of the grasshopper Moraba scurra which was heterozygous for a complex translocation involving breaks in four different, non-homologous, chromosomes, is described. Chains of up to eight chromosomes occur at first metaphase. Certain chromosomes which never normally show more than a single chiasma form two chiasmata with a fairly high frequency in this individual.Supported by Public Health Service Grant No. RG7212-Cl, from the Division of General Medical Sciences, U.S. National Institutes of Health.     

Genetics and the evolutionary process

Population genetics was put forward as a mathematical theory between 1918 and 1932 and played a leading part in the rediscovery of the concept of natural selection. As an autonomous science developing Mendel's laws at the population scale and a key element of the Darwinian theory of evolution, its dual status led its practioners to initially overlook some consequences of Mendelism not accounted for by the Darwinian theory, including random drift and the cost of selection. The latter were put forward on purely theoretical grounds in the 1950s, but their importance was acknowledged only when empirical data on protein evolution and enzyme polymorphism (since 1965) and on DNA variation (since 1983) were obtained. The neutralist/selectionist debate that ensued involved disagreement over the scientific method as well as over the mechanisms of molecular evolution. Population genetics has long assumed the existence of natural selection a priori. It has since recentred around the null hypothesis that molecular evolution is neutral. This new approach, applied to sequence comparison and to the study of linkage disequilibrium, is logically more justified, yet empirical observations derived from it paradoxically show the overwhelming importance of selective effects within genomes.     

Genetic Variance–covariance Matrices: A Critique of the Evolutionary Quantitative Genetics Research Program

This paper outlines a critique of the use of the genetic variance–covariance matrix (G), one of the central concepts in the modern study of natural selection and evolution. Specifically, I argue that for both conceptual and empirical reasons, studies of G cannot be used to elucidate so-called constraints on natural selection, nor can they be employed to detect or to measure past selection in natural populations – contrary to what assumed by most practicing biologists. I suggest that the search for a general solution to the difficult problem of identifying causal structures given observed correlation’s has led evolutionary quantitative geneticists to substitute statistical modeling for the more difficult, but much more valuable, job of teasing apart the many possible causes underlying the action of natural selection. Hence, the entire evolutionary quantitative genetics research program may be in need of a fundamental reconsideration of its goals and how they correspond to the array of mathematical and experimental techniques normally employed by its practitioners.     

An endangered flightless grasshopper with strong genetic structure maintains population genetic variation despite extensive habitat loss

Conservation research is dominated by vertebrate examples but the shorter generation times and high local population sizes of invertebrates may lead to very different management strategies, particularly for species with low movement rates. Here we investigate the genetic structure of an endangered flightless grasshopper, Keyacris scurra, which was used in classical evolutionary studies in the 1960s. It had a wide distribution across New South Wales (NSW) and Victoria in pre‐European times but has now become threatened because of land clearing for agriculture and other activities. We revisited remnant sites of K. scurra, with populations now restricted to only one area in Victoria and a few small patches in NSW and the Australian Capital Territory (ACT). Using DArtseq to generate SNP markers as well as mtDNA sequence data, we show that the remaining Victorian populations in an isolated valley are genetically distinct from the NSW populations and that all populations tend to be genetically unique, with large F _ST values up to 0.8 being detected for the SNP datasets. We also find that, with one notable exception, the NSW/ACT populations separate genetically into previously described chromosomal races (2n = 15 vs. 2n = 17). Isolation by distance was detected across both the SNP and mtDNA datasets, and there was substantial differentiation within chromosomal races. Genetic diversity as measured by heterozygosity was not correlated with the size of remaining habitat where the populations were found, with high variation present in some remnant cemetery sites. However, inbreeding correlated negatively with estimated habitat size at 25–500 m patch radius. These findings emphasize the importance of small habitat areas in conserving genetic variation in such species with low mobility, and they highlight populations suitable for future translocation efforts.     

Natural selection and population dynamics

To what extent, and under which circumstances, are population dynamics influenced by concurrent natural selection? Density dependence and environmental stochasticity are generally expected to subsume any selective modulation of population growth rate, but theoretical considerations point to conditions under which selection can have an appreciable impact on population dynamics. By contrast, empirical research has barely scratched the surface of this fundamental question in population biology. Here, we present a diverse body of mostly empirical evidence that demonstrates how selection can influence population dynamics, including studies of small populations, metapopulations, cyclical populations and host-pathogen interactions. We also discuss the utility, in this context, of inferences from molecular genetic data, placing them within the broader framework of quantitative genetics and life-history evolution.     

Molecular population genetics and the search for adaptive evolution in plants

The first papers on plant molecular population genetics were published approximately 10 years ago. Since that time, well over 50 additional studies of plant nucleotide polymorphism have been published, and many of these studies focused on detecting the signature of balancing or positive selection at a locus. In this review, we discuss some of the theoretical and statistical issues surrounding the detection of selection, with focus on plant populations, and we also summarize the empirical plant molecular population genetics literature. At face value, the literature suggests that a history of balancing or positive selection in plant genes is rampant. In two well-studied taxa (maize and Arabidopsis) over 20% of studied genes have been interpreted as containing the signature of selection. We argue that this is probably an overstatement of the prevalence of natural selection in plant genomes, for two reasons. First, demographic effects are difficult to incorporate and have generally not been well integrated into the plant population genetics literature. Second, the genes studied to date are not a random sample, so selected genes may be overrepresented. The next generation of studies in plant molecular population genetics requires additional sampling of local populations, explicit comparisons among loci, and improved theoretical methods to control for demography. Eventually, candidate loci should be confirmed by explicit consideration of phenotypic effects.     

Theodosius Dobzhansky and the genetic race concept

The use of ‘race’ as a proxy for population structure in the genetic mapping of complex traits has provoked controversy about its legitimacy as a category for biomedical research, given its social and political connotations. The controversy has reignited debates among scientists and philosophers of science about whether there is a legitimate biological concept of race. This paper examines the genetic race concept as it developed historically in the work of Theodosius Dobzhansky from the 1930s to 1950s. Dobzhansky’s definitions of race changed over this time from races as ‘arrays of forms’ or ‘clusters’ in 1933–1939, to races as genetically distinct geographical populations in 1940–1946, to races as genetically distinct ‘Mendelian populations’ in 1947–1955. Dobzhansky responded to nominalist challenges by appealing to the biological reality of race as a process. This response came into tension with the object ontology of race that was implied by Dobzhansky’s increasingly holistic treatment of Mendelian populations, a tension, the paper argues, he failed to appreciate or resolve.     

DNA水平自然选择作用的检测

上个世纪60年代,Kimura提出的“中性进化”假说使经典的达尔文自然选择学说遭遇了前所未有的挑战。但新近的研究表明：在DNA水平,越来越多的证据支持“自然选择”的进化理论。这些研究成果得益于近年来大量群体和基因组DNA数据的积累,以及理论群体遗传学的发展。在DNA水平检测选择作用是否存在的方法包括两大类：种内多态性检验和种间差异度检验。前者以Tajima(1989)提出的D检验为代表,后者大都基于“中性条件下,种内与种间进化速率一致”的原理。这些方法以中性假说作为零假设,结合统计检验方法分析DNA数据,被称为“中性检验”。这些方法对于解决一些有关进化的基础理论问题和人类遗传学及生物信息学的深入研究都具有重要意义。本文介绍几个应用广泛的检测方法,以使国内的读者了解它们的基本思路和操作方法。     

A population-based age-period-cohort study of colorectal cancer incidence comparing Asia against the West

BackgroundColorectal cancer (CRC) is the third most common cancer worldwide but incidence varied widely. Despite the role of genetics, CRC is also sensitive to macro-environmental factors. Few studies have ever compared across different countries/regions to suggest possible macro-environmental risk factors of CRC. We estimated the effects of age, period and cohort on the changes of incidence of colorectal cancer across different countries/regions.MethodsPoisson regression age-period-cohort (APC) models were conducted to estimate the age, period and cohorts effects on CRC incidence across the West (i.e., the UK, the US and Australia) and Asia (i.e. Japan, Hong Kong, Shanghai, Singapore and India). We maximized the length of the study period according to each country’s data availability.ResultsWestern populations show upward inflections for their 1950s–1960s cohorts, while Asian populations (except India) show downward inflections for their 1950s cohorts. Japanese population also shows upward inflections for its 1960s cohorts, similar to the Western populations. There are apparent upward inflections towards the more recent cohorts for Hong Kong, Shanghai and Singapore; nevertheless, the confidence intervals are wider towards the more recent cohorts.ConclusionOur findings imply an increasing risk of CRC in both Western and Asian populations as their younger cohorts reach older ages. These findings are consistent with the life course argument that macro-environmental changes associated with socio-economic development have specific effects that extend over the life course. Actions that pertain to altering lifestyle-related exposures over the life course are of great importance in combating young CRC risks in the future.     

One selectionist's perspective

Following introductory comments expressing doubts about the validity of genetic load and Haldane's "cost of natural selection," the role of selection (expressed as the average number of adult daughters per female) on gene frequencies in populations has been partitioned into population and time arenas. The population arena (a geometric plane) deals with the fitnesses of different genotypes under the many situations encountered by individual members of the population in a single generation; average fitnesses of carriers of various genotypes are obtained by calculating across these many situations. The population arena includes the point signifying that, on the average, each mother leaves one daughter as her replacement within the population. It is the plane within which evolutionarily significant norms of reaction exist. The time arena is also a (geometric) plane, one that is composed of the edge-on limit (average fitness) of each successive population arena. It does not include the effects of individual situations on relative fitnesses within each population arena; it encompasses only the temporal sequence of average relative fitnesses. Amino acid substitutions in proteins and base-pair substitutions in DNA are events of concern in the time arena; within the population arena, however, gene action (not merely gene structure) is a matter of considerable concern. Thus, the discussions of the 1950s and 1960s regarding genetic variation which were reasonable within the population arena seem less so within the time arena where structural, rather than functional, variation is stressed. The function-structure dichotomy is entangled with the neutralist-selectionist controversy.     

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.     

Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and regressions. Population genetic equations depend on genetic variances. How can we read those statistical expressions with respect to the meaning of natural selection? One possibility is to relate the statistical expressions to the amount of information that populations accumulate by selection. However, the connection between selection and information theory has never been compelling. Here, I show the correct relations between statistical expressions for selection and information theory expressions for selection. Those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics and communication. We can now read the equations of selection in terms of their natural meaning. Selection causes populations to accumulate information about the environment.     

Approaches for identifying targets of positive selection

Despite significant advancements in both empirical and theoretical population genetics throughout the past century, fundamental questions about the evolutionary forces that shape genomic diversity remain unresolved. Perhaps foremost among these are the strength and frequency of adaptive evolution. To quantify these parameters, statistical tools are needed that are capable of effectively identifying targets of positive selection throughout the genome in an unbiased manner, and functional approaches are needed that are capable of connecting these identified genotypes with the resulting adaptively significant phenotypes. Here we review recent advancements in both statistical and empirical methodology, and discuss important challenges and opportunities that remain as researchers continue to uncouple the relative importance of stochastic and deterministic factors in the evolution of natural populations.     

Sexually antagonistic selection in human male homosexuality

Several lines of evidence indicate the existence of genetic factors influencing male homosexuality and bisexuality. In spite of its relatively low frequency, the stable permanence in all human populations of this apparently detrimental trait constitutes a puzzling 'Darwinian paradox'. Furthermore, several studies have pointed out relevant asymmetries in the distribution of both male homosexuality and of female fecundity in the parental lines of homosexual vs. heterosexual males. A number of hypotheses have attempted to give an evolutionary explanation for the long-standing persistence of this trait, and for its asymmetric distribution in family lines; however a satisfactory understanding of the population genetics of male homosexuality is lacking at present. We perform a systematic mathematical analysis of the propagation and equilibrium of the putative genetic factors for male homosexuality in the population, based on the selection equation for one or two diallelic loci and Bayesian statistics for pedigree investigation. We show that only the two-locus genetic model with at least one locus on the X chromosome, and in which gene expression is sexually antagonistic (increasing female fitness but decreasing male fitness), accounts for all known empirical data. Our results help clarify the basic evolutionary dynamics of male homosexuality, establishing this as a clearly ascertained sexually antagonistic human trait.     

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.     

SNP genotypes reveal breed substructure,selection signatures and highly inbred regions in Piétrain pigs

The Piétrain pig originates from the Belgian village Piétrain some time between 1920 and 1950. Owing to its superior conformation, the Piétrain has spread worldwide since the 1960s. As initial population sizes were limited and close inbreeding was commonplace, the breed’s genetic diversity has been questioned. Therefore, this study examines Piétrain breed substructure, diversity and selection signatures using SNP data in comparison with Duroc, Landrace and Large White populations. Principal component analysis indicated three subpopulations, and F_ST analysis showed that US Piétrains differ most from European Piétrains. Average inbreeding based on runs of homozygosity (ROH) segments larger than 4 Mb ranged between 16.7 and 20.9%. The highest chromosomal inbreeding levels were found on SSC8 (42.7%). ROH islands were found on SSC8, SSC15 and SSC18 in all Piétrain populations, but numerous population-specific ROH islands were also detected. Moreover, a large ROH island on SSC8 (34–126 Mb) appears nearly fixed in all Piétrain populations, with a unique genotype. Chromosomal ROH patterns were similar between Piétrain populations. This study shows that Piétrain populations are genetically diverging, with at least three genetically distinct populations worldwide. Increasing genetic diversity in local Piétrain populations by introgression from other Piétrain populations seems to be only limited. Moreover, a unique 90 Mb region on SSC8 appeared largely fixed in the Piétrain breed, indicating that fixation was already present before the 1960s. We believe that strong selection and inbreeding during breed formation fixed these genomic regions in Piétrains. Finally, we hypothesize that independent coat color selection may have led to large ROH pattern similarities on SSC8 between unrelated pig breeds.     

Styles of scientific reasoning: Adolf Remane (1898–1976) and the German evolutionary synthesis

Adolf Remane is widely considered to have been one of the most influential German zoologists of the 20th Century, yet Ernst Mayr persistently characterized him as an idealistic morphologist, that is, a typologist unable to understand population genetics or indeed Darwinian theory. This stands in sharp contrast to Mayr's praise for Bernhard Rensch as one of the most important German contributors to the Modern Synthesis of evolutionary theory. Remane's style of scientific reasoning is analysed in his writings on microsystematics, ecology, comparative morphology and phylogenetics and found to be highly consistent throughout these varied fields of research, while differing fundamentally from the eminently statistical foundations of both population genetics and natural selection theory that were embraced by Mayr. A comparative analysis of Rensch's understanding of science in general, and biology in particular, shows him to share core values with Remane, both authors rooted in the Mandarin tradition of the German professoriate. Biographical and socio‐political factors appear to have influenced Mayr's contrasting perception of Remane and Rensch, one that would influence later biologists and historians of science.     

Investigating the Interactions of Yeast Prions: [SWI+], [PSI+], and [PIN+]

The relationship between quantitative genetics and population genetics has been studied for nearly a century, almost since the existence of these two disciplines. Here we ask to what extent quantitative genetic models in which selection is assumed to operate on a polygenic trait predict adaptive fixations that may lead to footprints in the genome (selective sweeps). We study two-locus models of stabilizing selection (with and without genetic drift) by simulations and analytically. For symmetric viability selection we find that ∼16% of the trajectories may lead to fixation if the initial allele frequencies are sampled from the neutral site-frequency spectrum and the effect sizes are uniformly distributed. However, if the population is preadapted when it undergoes an environmental change (i.e., sits in one of the equilibria of the model), the fixation probability decreases dramatically. In other two-locus models with general viabilities or an optimum shift, the proportion of adaptive fixations may increase to >24%. Similarly, genetic drift leads to a higher probability of fixation. The predictions of alternative quantitative genetics models, initial conditions, and effect-size distributions are also discussed.     

Genome and population dynamics under selection and neutrality: an example of S-allele diversity in wild cherry (Prunus avium L.)

Self-incompatibility, a common attribute of plant development, forms a classical paradigm of balancing selection in natural populations, in particular negative frequency-dependent selection. Under negative frequency-dependent selection population genetics theory predicts that the S-locus, being in command of self-incompatibility, keeps numerous alleles in equal frequencies demonstrating a wide allelic range. Moreover, while natural populations exhibit a higher within population genetic diversity, a reduction of population differentiation and increase of effective migration rate is expected in comparison to neutral loci. Allelic frequencies were investigated in terms of distribution and genetic structure at the gametophytic self-incompatibility locus in five wild cherry (Prunus avium L.) populations. Comparisons were also made between the differentiation at the S-locus and at the SSR loci. Theoretical expectations under balancing selection were congruent to the results observed. The S-locus showed broad multiplicity (16 S-alleles), high genetic diversity, and allelic isoplethy. Genetic structure at the self-incompatibility locus was almost four times lower than at 11 nSSR loci. Analysis of molecular variance revealed that only 5?% of the total genetic variation concerns differentiation among populations. In conclusion, the wealth of S-allelic diversity found in natural wild cherry populations in Greece is useful not only in advancing basic population genetics research of self-incompatibility systems in wild cherry but also in the development of breeding programs.