ON THE EFFECT OF FOUNDER EVENTS ON EPISTATIC GENETIC VARIANCE

Mayr (1963) proposed that small isolated propagules from a large panmictic population would occasionally undergo a genetic revolution due to loss of genetic variability. More recently Templeton (1980a) has suggested that founder events may be much more important in systems that have strong epistasis. Because of the work of these and other authors it becomes an interesting theoretical problem to study the distribution of epistatic variance in a population following a founder event. In the model presented here measures of coancestry (Cockerham, 1967, 1984; Cockerham and Weir, 1973; Weir and Cockerham, 1973, 1977; Tachida and Cockerham, unpubl.) are used to examine the effect of founder events on additive-by-additive epistasis. Using this approach, the coancestries, or intraclass correlations, within individuals and within demes, together with the genetic variance components in the ancestral population are used to obtain the variance within and among demes following a founder event. Examples are analyzed for single founder events of 1–25 individuals and multiple founder events of two individuals. Following a single founder event, the contribution of the additive variance to the variance within demes relative to the additive variance in the ancestral population is always less than one. However, the contribution of epistatic variance to the variance within demes relative to the epistatic variance in the ancestral population is always greater than one. Thus, while a founder event decreases the contribution of additive variance to the variance within demes, it increases the contribution of epistatic variance to the variance within demes. The contribution of epistatic variance to the variance among demes following a single founder event is not qualitatively different from the contribution of additive variance to the variance among demes. These results indicate that epistatic variance is less likely than additive variance to cause a genetic revolution following a single founder event. When populations undergo multiple founder events the situation changes considerably. Epistatic variance may contribute as much as four times its original value to the variance among demes, while additive variance can contribute maximally twice its original value to the variance among demes. Thus, epistasis, which is relatively unimportant following a single founder event, may have major evolutionary implications if drift is allowed to continue for several generations.     

EPISTASIS AND THE INCREASE IN ADDITIVE GENETIC VARIANCE: IMPLICATIONS FOR PHASE 1 OF WRIGHT'S SHIFTING-BALANCE PROCESS

Central to Wright's shifting-balance theory is the idea that genetic drift and selection in systems with gene interaction can lead to the formation of “adaptive gene complexes.” The theory of genetic drift has been well developed over the last 60 years; however, nearly all of this theory is based on the assumption that only additive gene effects are acting. Wright's theory was developed recognizing that there was a “universality of interaction effects,” which implies that additive theory may not be adequate to describe the process of differentiation that Wright was considering. The concept of an adaptive gene complex implies that an allele that is favored by individual selection in one deme may be removed by selection in another deme. In quantitative genetic terms, the average effects of an allele relative to other alleles changes from deme to deme. The model presented here examines the variance in local breeding values (LBVs) of a single individual and the covariance in the LBVs of a pair of individuals mated in the same deme relative to when they are mated in different demes. Local breeding value is a measure of the average effects of the alleles that make up that individual in a particular deme. I show that when there are only additive effects the covariance between the LBVs of individuals equals the variance in the LBV of an individual. As the amount of epistasis in the ancestral population increases, the variance in the LBV of an individual increases and the covariance between the LBVs of a pair of individuals decreases. The divergence in these two values is a measure of the extent to which the LBV of an individual varies independently of the LBVs of other individuals. When this value is large, it means that the relative ordering of the average effects of alleles will change from deme to deme. These results confirm an important component of Wright's shifting-balance theory: When there is gene interaction, genetic drift can lead to the reordering of the average effects of alleles and when coupled with selection this will lead to the formation of the adaptive gene complexes.     

EPISTASIS AND THE EFFECT OF FOUNDER EVENTS ON THE ADDITIVE GENETIC VARIANCE

Models of founder events have focused on the reduction in the genetic variation following a founder event. However, recent work (Bryant et al., 1986; Goodnight, 1987) suggests that when there is epistatic genetic variance in a population, the total genetic variance within demes may actually increase following a founder event. Since the additive genetic variance is a statistical property of a population and can change with the level of inbreeding, some of the epistatic genetic variance may be converted to additive genetic variance during a founder event. The model presented here demonstrates that some of the additive-by-additive epistatic genetic variance is converted to additive genetic variance following a founder event. Furthermore, the amount of epistasis converted to additive genetic variance is a function of the recombination rate and the propagule size. For a single founder event of two individuals, as much as 75% of the epistatic variance in the ancestral population may become additive genetic variance following the founder event. For founder events involving two individuals with free recombination, the relative contribution of epistasis to the additive genetic variance following a founder event is equal to its proportion of the total genetic variance prior to the founder event. Traits closely related to fitness are expected to have relatively little additive genetic variance but may have substantial nonadditive genetic variance. Founder events may be important in the evolution of fitness traits, not because they lead to a reduction in the genetic variance, but rather because they lead to an increase in the additive genetic variance.     

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.     

Anecdotal,Historical and Critical Commentaries on Genetics: Wright and Fisher on Inbreeding and Random Drift

Sewall Wright and R. A. Fisher often differed, including on the meaning of inbreeding and random gene frequency drift. Fisher regarded them as quite distinct processes, whereas Wright thought that because his inbreeding coefficient measured both they should be regarded as the same. Since the effective population numbers for inbreeding and random drift are different, this would argue for the Fisher view.SEWALL Wright and R. A. Fisher were central figures in mathematical population genetics; along with J. B. S. Haldane they effectively invented the field and dominated it for many years. On most issues the three were in agreement. In particular, all favored a neo-Darwinian gradualist approach and believed in the importance of a mathematical theory for understanding the evolutionary process. Yet on a few questions Fisher and Wright differed profoundly and argued vehemently. Fisher was contentious and was often involved in controversy, frequently attacking his opponents mercilessly. Wright, in contrast, was very gentle to most people. But there were a few exceptions and Fisher was one. Haldane mostly stayed out of the arguments between them.One question on which the two disagreed was the importance of random gene frequency drift and its role in Wright''s shifting-balance theory of evolution. Wright thought that a structured population with many partially isolated subpopulations, within which there was random drift and among which there was an appropriate amount of migration, offered the greatest chance for evolutionary novelty and could greatly increase the speed of evolution. Fisher thought that a large panmictic population offered the best chance for advantageous genes and gene combinations to spread through the population, unimpeded by random processes. They also disagreed on dominance, Fisher believing that it evolved by selection of dominance modifiers and Wright that it was a consequence of the nature of gene action. These differences were widely argued by population geneticists in the middle third of the twentieth century, and the interested community divided into two camps. Although the issues are not settled, Wright''s shifting-balance theory has less support than it formerly had. As for dominance, there is general quantitative disagreement with Fisher''s explanation of modifiers, but other mechanisms (e.g., selection for more active alleles) have to some extent replaced it. Wright''s theory remains popular and has been generalized and extended (Kacser and Burns 1973).     

Generalized population models and the nature of genetic drift

The Wright–Fisher model of allele dynamics forms the basis for most theoretical and applied research in population genetics. Our understanding of genetic drift, and its role in suppressing the deterministic forces of Darwinian selection has relied on the specific form of sampling inherent to the Wright–Fisher model and its diffusion limit. Here we introduce and analyze a broad class of forward-time population models that share the same mean and variance as the Wright–Fisher model, but may otherwise differ. The proposed class unifies and further generalizes a number of population-genetic processes of recent interest, including the Λ and Cannings processes. Even though these models all have the same variance effective population size, they encode a rich diversity of alternative forms of genetic drift, with significant consequences for allele dynamics. We characterize in detail the behavior of standard population-genetic quantities across this family of generalized models. Some quantities, such as heterozygosity, remain unchanged; but others, such as neutral absorption times and fixation probabilities under selection, deviate by orders of magnitude from the Wright–Fisher model. We show that generalized population models can produce startling phenomena that differ qualitatively from classical behavior — such as assured fixation of a new mutant despite the presence of genetic drift. We derive the forward-time continuum limits of the generalized processes, analogous to Kimura’s diffusion limit of the Wright–Fisher process, and we discuss their relationships to the Kingman and non-Kingman coalescents. Finally, we demonstrate that some non-diffusive, generalized models are more likely, in certain respects, than the Wright–Fisher model itself, given empirical data from Drosophila populations.     

PERSPECTIVE: A CRITIQUE OF SEWALL WRIGHT'S SHIFTING BALANCE THEORY OF EVOLUTION

We evaluate Sewall Wright's three-phase “shifting balance” theory of evolution, examining both the theoretical issues and the relevant data from nature and the laboratory. We conclude that while phases I and II of Wright's theory (the movement of populations from one “adaptive peak” to another via drift and selection) can occur under some conditions, genetic drift is often unnecessary for movement between peaks. Phase III of the shifting balance, in which adaptations spread from particular populations to the entire species, faces two major theoretical obstacles: (1) unlike adaptations favored by simple directional selection, adaptations whose fixation requires some genetic drift are often prevented from spreading by barriers to gene flow; and (2) it is difficult to assemble complex adaptations whose constituent parts arise via peak shifts in different demes. Our review of the data from nature shows that although there is some evidence for individual phases of the shifting balance process, there are few empirical observations explained better by Wright's three-phase mechanism than by simple mass selection. Similarly, artificial selection experiments fail to show that selection in subdivided populations produces greater response than does mass selection in large populations. The complexity of the shifting balance process and the difficulty of establishing that adaptive valleys have been crossed by genetic drift make it impossible to test Wright's claim that adaptations commonly originate by this process. In view of these problems, it seems unreasonable to consider the shifting balance process as an important explanation for the evolution of adaptations.     

PHASE III OF WRIGHT'S SHIFTING BALANCE PROCESS AND THE VARIANCE AMONG DEMES IN MIGRATION RATE

Interdemic selection by the differential migration of individuals out from demes of high fitness and into demes of low fitness (Phase III) is one of the most controversial aspects of Wright's Shifting Balance Theory. I derive a relationship between Phase III migration and the interdemic selection differential, S, and show its potential effect on F_ST. The relationship reveals a diversifying effect of interdemic selection by Phase III migration on the genetic structure of a metapopulation. Using experimental metapopulations, I explored the effect of Phase III migration on F_ST by comparing the genetic variance among demes for two different patterns of migration: (1) island model migration and (2) Wright's Phase III migration. Although mean migration rates were the same, I found that the variance among demes in migration rate was significantly higher with Phase III than with island model migration. As a result, F_ST for the frequency of a neutral marker locus was higher with Phase III than it was with island model migration. By increasing F_ST, Phase III enhanced the genetic differentiation among demes for traits not subject to interdemic selection. This feature makes Wright's process different from individual selection which, by reducing effective population size, decreases the genetic variance within demes for all other traits. I discussed this finding in relation to the efficacy of Phase III and random migration for effecting peak shifts, and the contribution of genes with indirect effects to among‐deme variation.     

EPISTASIS AND THE EVOLUTION OF ADDITIVE GENETIC VARIANCE IN POPULATIONS THAT PASS THROUGH A BOTTLENECK

Traditional models of genetic drift predict a linear decrease in additive genetic variance for populations passing through a bottleneck. This perceived lack of heritable variance limits the scope of founder-effect models of speciation. We produced 55 replicate bottleneck populations maintained at two male-female pairs through four generations of inbreeding (average F = 0.39). These populations were formed from an F₂ intercross of the LG/J and SM/J inbred mouse strains. Two contemporaneous control strains maintained with more than 60 mating pairs per generation were formed from this same source population. The average level of within-strain additive genetic variance for adult body weight was compared between the control and experimental lines. Additive genetic variance for adult body weight within experimental bottleneck strains was significantly higher than expected under an additive genetic model This enhancement of additive genetic variance under inbreeding is likely to be due to epistasis, which retards or reverses the loss of additive genetic variance under inbreeding for adult body weight in this population. Therefore, founder-effect speciation processes may not be constrained by a loss of heritable variance due to population bottlenecks.     

Did natural selection or genetic drift produce the cranial diversification of neotropical monkeys?

A central controversy among biologists is the relative importance of natural selection and genetic drift as creative forces shaping biological diversification (Fisher 1930; Wright 1931). Historically, this controversy has been an effective engine powering several evolutionary research programs during the last century (Provine 1989). While all biologists agree that both processes operate in nature to produce evolutionary change, there is a diversity of opinion about which process dominates at any particular organizational level (from DNA and proteins to complex morphologies). To address this last level, we did a broadscale analysis of cranial diversification among all living New World monkeys. Quantitative genetic models yield specific predictions about the relationship between variation patterns within and between populations that may be used to test the hypothesis that genetic drift is a sufficient explanation for morphological diversification. Diversity at several levels in a hierarchy of taxonomic/phylogenetics relationship was examined from species within genera to families within superfamilies. The major conclusion is that genetic drift can be ruled out as the primary source of evolutionary diversification in cranial morphology among taxa at the level of the genus and above as well as for diversification of most genera. However, drift may account for diversification among species within some Neotropical primate genera, implying that morphological diversification associated with speciation need not be adaptive in some radiations.     

Migration and recovery of the genetic diversity during the increasing density phase in cyclic vole populations

In cyclic populations, high genetic diversity is currently reported despite the periodic low numbers experienced by the populations during the low phases. Here, we report spatio-temporal monitoring at a very fine scale of cyclic populations of the fossorial water vole (Arvicola terrestris) during the increasing density phase. This phase marks the transition from a patchy structure (demes) during low density to a continuous population in high density. We found that the genetic diversity was effectively high but also that it displayed a local increase within demes over the increasing phase. The genetic diversity remained relatively constant when considering all demes together. The increase in vole abundance was also correlated with a decrease of genetic differentiation among demes. Such results suggest that at the end of the low phase, demes are affected by genetic drift as the result of being small and geographically isolated. This leads to a loss of local genetic diversity and a spatial differentiation among demes. This situation is counterbalanced during the increasing phase by the spatial expansion of demes and the increase of the effective migration among differentiated demes. We provide evidences that in cyclic populations of the fossorial water voles, the relative influence of drift operating during low density populations and migration occurring principally while population size increases interacts closely to maintain high genetic diversity.     

Neutral additive genetic variance in a metapopulation

For neutral, additive quantitative characters, the amount of additive genetic variance within and among populations is predictable from Wright's FST, the effective population size and the mutational variance. The structure of quantitative genetic variance in a subdivided metapopulation can be predicted from results from coalescent theory, thereby allowing single-locus results to predict quantitative genetic processes. The expected total amount of additive genetic variance in a metapopulation of diploid individual is given by 2Ne sigma m2 (1 + FST), where FST is Wright's among-population fixation index, Ne is the eigenvalue effective size of the metapopulation, and sigma m2 is the mutational variance. The expected additive genetic variance within populations is given by 2Ne sigma e2(1-FST), and the variance among demes is given by 4FSTNe sigma m2. These results are general with respect to the types of population structure involved. Furthermore, the dimensionless measure of the quantitative genetic variance among populations, QST, is shown to be generally equal to FST for the neutral additive model. Thus, for all population structures, a value of QST greater than FST for neutral loci is evidence for spatially divergent evolution by natural selection.     

Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

Population genetics theory has laid the foundations for genomic analyses including the recent burst in genome scans for selection and statistical inference of past demographic events in many prokaryote, animal and plant species. Identifying SNPs under natural selection and underpinning species adaptation relies on disentangling the respective contribution of random processes (mutation, drift, migration) from that of selection on nucleotide variability. Most theory and statistical tests have been developed using the Kingman coalescent theory based on the Wright‐Fisher population model. However, these theoretical models rely on biological and life history assumptions which may be violated in many prokaryote, fungal, animal or plant species. Recent theoretical developments of the so‐called multiple merger coalescent models are reviewed here (Λ‐coalescent, beta‐coalescent, Bolthausen‐Sznitman, Ξ‐coalescent). We explain how these new models take into account various pervasive ecological and biological characteristics, life history traits or life cycles which were not accounted in previous theories such as (i) the skew in offspring production typical of marine species, (ii) fast adapting microparasites (virus, bacteria and fungi) exhibiting large variation in population sizes during epidemics, (iii) the peculiar life cycles of fungi and bacteria alternating sexual and asexual cycles and (iv) the high rates of extinction‐recolonization in spatially structured populations. We finally discuss the relevance of multiple merger models for the detection of SNPs under selection in these species, for population genomics of very large sample size and advocate to potentially examine the conclusion of previous population genetics studies.     

THE EFFECT OF HOST PLANT PATCH SIZE VARIATION ON THE POPULATION STRUCTURE OF A SPECIALIST HERBIVORE INSECT,TETRAOPES TETRAOPHTHALMUS

The patchy local distribution of the common milkweed, Asclepias syriaca, organizes populations of a beetle that feeds on it, Tetraopes tetraophthalmus, into numerous local demes. Genetic and ecological characteristics of demes of adult milkweed beetles occupying two naturally occurring size classes of patches, defined as large and small, were studied in order to describe the effect of patch size variation on local population structure. Allele frequency variance in two of three protein polymorphisms was significantly greater in collections of beetles from an array of 13 small patches when compared to collections from an array of 11 large populations. A multivariate measure of variance using information from all 3 genetic markers confirmed that the small patches displayed greater overall genetic differentiation. This was further quantified by computing an F_st value, combined across loci, of 0.018 for the small patches and 0.004 for the large patches. No significant difference between patch size classes in mean allele frequency was detected. Mark and recapture studies of the adults found in five small and four large patches showed the residence times of adults in small patches to be less than half of those found in large patches. This was interpreted as resulting from higher emigration rates from small patches. It is proposed that greater genetic differentiation is found among demes from smaller patches because smaller patches support smaller population sizes and further because smaller patches act as net exporters of migrants while larger patches act as net migrant importers.     

HIERARCHICAL ORGANIZATION OF GENETIC VARIATION IN THE SAILFIN MOLLY,POECILIA LATIPINNA (PISCES: POECILIIDAE)

Twenty-two percent of all allozyme variation documented in the sailfin molly (Poecilia latipinna) was attributable to regional differences, while only 3% was attributable to differences among demes within regions. Of the variation documented in a given region, 6–12% was attributable to variation among demes. Cluster analyses supported these conclusions quantitatively. Spatial-autocorrelation analyses offered more explicit support: demes separated by increasingly greater distances were increasingly dissimilar. Analyses using F statistics and rare alleles suggest “effective gene flow rates” (the product of effective population size and gene flow rate) of approximately 4, a level more than sufficient to prevent local independence of gene-frequency dynamics. These results, taken together, suggest that mollies do not have a population structure conducive to the operation of Wright's shifting-balance process and make the striking patterns of interdemic variation in body size and sexual behavior observed in this species all the more interesting.     

Metapopulation structure and fine-scaled genetic structuring in crop-wild hybrid weed beets

This study explores the microspatial and temporal genetic variation in crop-wild hybrid weed beets that emerged from the seed bank in a cultivated field surveyed over two successive years. We demonstrate the occurrence of demes highly genetically differentiated, kin-structured, characterized by moderate effective population sizes, differing in propensity for selfing, and arising from nonrandom genetic subsets of the seed bank. Only one deme identified in the first survey year significantly contributed to the weed beets that emerged in the second year. Spatial structuring appears to be primarily due to gravity seed dispersal and limited pollen flow among weed beet demes. Within each genetic cluster identified by Bayesian assignments and multivariate analyses, F(IS) estimates and level of biparental inbreeding--revealed by progeny analyses--dropped to non-significant values. This suggests that random mating occurs at the scale of genetically distinct demes over a very short scale. Our results highlight the need to carefully depict genetic discontinuities in weed species, when attempting to describe their local genetic neighborhoods within which genetic drift and selective processes occur.     

SPATIAL POPULATION STRUCTURE IN THE WHIRLIGIG BEETLE DINEUTUS ASSIMILIS: EVOLUTIONARY INFERENCES BASED ON MITOCHONDRIAL DNA AND FIELD DATA

The spatial population structure of the pond-living water beetle Dineutus assimilis (Coleoptera: Gyrinidae) was investigated through a field study of population dynamics and dispersal, with a concurrent assessment of the spatial distribution of mitochondrial DNA (mtDNA) restriction-fragment-length polymorphism (RFLP). A comprehensive 2-yr survey within a 60-km² study area revealed pronounced fluctuations in local abundances, including extinctions and colonizations. The recapture of marked individuals showed that dispersal among ponds is frequent in both males and females and connects populations on a large geographic scale (maximum observed flight distance: 20 km). The population structure of D. assimilis is thus characterized by both pronounced genetic drift and frequent gene flow. Together, these two forces generate a pattern of very local and transient genetic differentiation. Mitochondrial DNA samples collected within a few kilometers indicate highly significant spatial structure, if newly founded demes or those that experienced recent bottlenecks are included. These results based on four demes within the study area were placed into a regional context by further samples collected at distances of 100 km and 200 km. F_st estimates computed on increasing spatial scales were variable but showed no increasing trend. Thus, gene flow exerts a strong homogenizing force over a wide geographic range but is counteracted locally by genetic drift. These findings highlight the need to supplement estimates of F_st with additional data to arrive at valid interpretations of the genetic information. More generally, this study raises questions about how to capture the relevant features of dynamic, subdivided populations to understand their evolutionary dynamics.     

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.     

TEMPORAL VARIATION IN POPULATIONS OF THE MARINE ISOPOD EXCIROLANA: HOW STABLE ARE GENE FREQUENCIES AND MORPHOLOGY?

Excirolana braziliensis is a dioecious marine isopod that lives in the high intertidal zone on both sides of tropical America. It lacks a dispersal phase and displays a remarkable degree of genetic divergence even between localities less than 1 km apart. Nine populations of this nominal species from both sides of the Isthmus of Panama and one population of the closely allied species, Excirolana chamensis, from the eastern Pacific were studied for 2 yr for allozymic temporal variation in 13 loci and for 3 to 4 yr for morphological variation in nine characters. The genetic and morphological constitution of 9 out of 10 populations remained stable. Allele frequencies at two loci and overall morphology in a tenth beach occupied by E. braziliensis changed drastically and significantly between 1986 and 1988. The change in gene frequency is too great to explain by genetic drift occurring during a maximum of 14 generations regardless of assumed effective population size; drift is also unlikely to have caused observed changes in morphology. Selective survival of a previously rare genotype is more plausible but still not probable. The most credible explanation is that the resident population at this locality became extinct and that the beach was recolonized by immigrants from another locality. Such infrequent episodes of extinction and recolonization from a single source may account for the large amount of genetic divergence between local populations of E. braziliensis. However, the low probability of large temporal genetic change even in a species such as this, in which gene flow between local demes is limited and generation time is short, suggests that a single sample through time is usually adequate for reconstructing the genetic history of populations.