Fixation of advantageous alleles in partially self-fertilizing populations. The effect of different selection modes

The expected fixation probability of an advantageous allele was examined in a partially self-fertilizing hermaphroditic plant species using the diffusion approximation. The selective advantage of the advantageous allele was assumed to be increased viability, increased fecundity, or an increase in male fitness. The mode of selection, as well as the selfing rate, the population size, and the dominance of the advantageous allele, affect the fixation probability of the allele. In general it was found that increases in selfing rate decrease the fixation probability under male sexual selection, increase fixation probability under fecundity selection, and increase when recessive and decrease when dominant under viability selection. In some cases the highest fixation probability of advantageous alleles under fecundity or under male sexual selection occurred at an intermediary selfing rate. The expected mean fixation times of the advantageous allele were also examined using the diffusion approximation.     

The Genealogical Consequences of Fecundity Variance Polymorphism

The genealogical consequences of within-generation fecundity variance polymorphism are studied using coalescent processes structured by genetic backgrounds. I show that these processes have three distinctive features. The first is that the coalescent rates within backgrounds are not jointly proportional to the infinitesimal variance, but instead depend only on the frequencies and traits of genotypes containing each allele. Second, the coalescent processes at unlinked loci are correlated with the genealogy at the selected locus; i.e., fecundity variance polymorphism has a genomewide impact on genealogies. Third, in diploid models, there are infinitely many combinations of fecundity distributions that have the same diffusion approximation but distinct coalescent processes; i.e., in this class of models, ancestral processes and allele frequency dynamics are not in one-to-one correspondence. Similar properties are expected to hold in models that allow for heritable variation in other traits that affect the coalescent effective population size, such as sex ratio or fecundity and survival schedules.THE population genetics of within-generation fecundity variance has been studied from two perspectives. Beginning with Wright (1938), several authors have investigated the relationship between the effective size of a panmictic population with seasonal reproduction and the variance of the number of offspring born to each adult within a season (Crow and Denniston 1988; Nunney 1993, 1996; Waples 2002; Hedrick 2005; Engen et al. 2007). Although the precise form of this relationship depends on other biological factors such as the mating system and the manner in which population regulation operates, each of these studies shows that the effective population size is a decreasing function of fecundity variance. Furthermore, provided that the variance and the coalescent effective population sizes coincide (Ewens 1982; Nordborg and Krone 2002; Sjodin et al. 2005), these results imply that both the rate at which neutral allele frequencies fluctuate from generation to generation and the rate at which lineages coalesce will be positively correlated with within-generation fecundity variance. For example, it has been suggested that the shallow genealogies that have been documented in many marine organisms are a consequence of the high variance of reproductive success in the recruitment sweepstakes operating in these species (Hedgecock 1994; Árnason 2004; Eldon and Wakeley 2006).These results hold in models in which all individuals have the same within-generation (or within-season) fecundity variance. However, the evolutionary genetics of populations that are polymorphic for alleles that influence demographic traits have also been investigated. The first results of this kind were derived by Gillespie (1974, 1975, 1977), who used diffusion theory to show that natural selection can act directly on within-generation fecundity variance in a haploid population with nonoverlapping generations. By studying a simple model of a population composed of two genotypes, say A₁ and A₂, Gillespie (1974) showed that the fluctuations in the frequency of allele A₁ can be approximated by a diffusion process with the following drift and variance coefficients,where p is the frequency of A₁, N is the number of adults, and 1 + μ_i and are the mean and the variance, respectively, of the number of offspring produced by an individual of type A_i. Most discussions of this class of models have focused on the fitness consequences of differences in fecundity variance, which are summarized by the drift coefficient, m(p), of the diffusion approximation. There are two main conclusions. The first is that because m(p) is an increasing function of the difference − , selection can favor alleles that reduce within-generation fecundity variance even if these have lower mean fecundity. Such variance–mean trade-offs can be interpreted as a kind of bet hedging and could explain the evolution of certain risk-spreading traits such as insect oviposition onto multiple host plants (Root and Kareiva 1986) or multiple mating by females (Sarhan and Kokko 2007). On the other hand, because the strength of selection on fecundity variance is inversely proportional to population size, selection for mean–variance trade-offs will usually be dominated by changes in mean fecundity. For this reason, it has been suggested that within-generation bet hedging will be favored only in very small populations (Seger and Brockman 1987; Hopper et al. 2003), although recent theoretical studies have shown that bet hedging can evolve under less restrictive conditions in subdivided populations (Shpak 2005; Lehmann and Balloux 2007; Shpak and Proulx 2007).Less consideration has been given to the diffusion coefficient, v(p), which differs from the familiar quadratic term, p(1 − p), of the Wright–Fisher diffusion. Because the variance effective population size of a monomorphic population depends on the fecundity variance, it is not surprising that v(p) has an additional dependence on the frequency of A₁ whenever the two alleles have different offspring variances. However, as noted by Gillespie (1974), the relationship between allele frequency fluctuations and the allelic composition of the population is counterintuitive. For example, when p is close to 1, so that the population is composed mainly of A₁-type individuals, the rate of allele frequency fluctuations is dominated by the variance of the A₂ genotype. In particular, if we define the variance effective population size by the expression Np(1 − p)/v(p) (Ewens 1982), then not only is this quantity frequency dependent, but also it depends on the life history traits of the missing genotype whenever the population is fixed for one of the two alleles. In contrast, the coalescent effective population size of a monomorphic population depends only on the offspring distribution of the fixed allele. The discrepancy between these two quantities raises the following question: namely, How does fecundity variance polymorphism affect the statistical properties of the genealogy of a random sample of individuals?The answer to this question is of interest for several reasons. First, although the effects of selection on genealogies have received considerable attention (Przeworski et al. 1999; Williamson and Orive 2002; Barton and Etheridge 2004), little is known about the genealogical consequences of variation in traits that alter the coalescent rate. Extrapolating from models in which the effective population size varies under the control of external factors, we might expect the coalescent process in a model with fecundity variance polymorphism to be a stochastic time change of Kingman''s coalescent. However, the results derived in the next section show that this intuition is usually wrong. The second motivation is more practical. Even if changes in fecundity variance are usually controlled by selection on other traits, the existence of interspecific differences in fecundity variance suggests that there must be periods when populations are polymorphic for alleles that alter the fecundity variance. In these instances, it might be possible to use sequence data to identify the loci responsible for these changes, but to do so will require the development of methods that exploit patterns that are unique to models in which the effective population size depends on the genetic composition of the population. For example, whereas the effects of genetic hitchhiking are usually restricted to linked sites (Maynard Smith and Haigh 1974; Kim and Stephan 2002; Przeworski 2002; Przeworski et al. 2005), we will see later that selective sweeps by mutations that affect fecundity variance would have a genomewide impact on polymorphism.Kingman (1982a,b) showed that the genealogy of a sample of individuals from a panmictic, neutrally evolving population of constant size can be described by a simple stochastic process known as the coalescent (or Kingman''s coalescent). One of the most important properties of Kingman''s coalescent is that it is a Markov process, a fact that is heavily exploited in mathematical analyses and that also allows for efficient simulations of genealogies. Unfortunately, this property generally does not hold in populations composed of nonexchangeable individuals. For example, if there are selective differences between individuals, then although the genealogy of a sample of individuals can still be regarded as a stochastic process, selective interactions between individuals cause this process to also depend on the history of nonancestral lineages. The key to overcoming this difficulty is to embed the genealogical process in a larger process that does satisfy the Markov property. This can be done in two ways. One approach is to embed the coalescent tree within a graphical process called the ancestral selection graph (Krone and Neuhauser 1997; Neuhauser and Krone 1997; Donnelly and Kurtz 1999) in which lineages can either branch, giving rise to pairs of potential ancestors, or coalesce. The intuition behind this construction is that the effects of selection on the genealogy can be accounted for by keeping track of a pool of potential ancestors that includes lineages that have failed to persist due to being outcompeted by individuals of higher fitness. Because the branching rates are linear in the number of lineages, while the coalescence rates are quadratic, this process is certain to reach an ultimate ancestor in finite time. The process can be stopped at this time, and both the ancestral and the genotypic status of individual branches can be resolved by assigning random mutations to the graph and then traversing it from the root to the leaves.The second approach is due to Kaplan et al. (1988), who showed that the genealogical history of a sample of genes under selection can be represented by a structured coalescent process. Here we think of the population as being subdivided into several demes, or genetic backgrounds, consisting of individuals that share the same genotype at the selected locus. Because individuals with the same genotype are exchangeable, the rate of coalescence within a background depends only on the size of the background and the number of ancestral lineages sharing that genotype. In addition, mutations at the selected site will move lineages between backgrounds. To obtain a Markov process, we need to keep track of two kinds of information: (i) the types of the ancestral lineages and (ii) the frequencies of the alleles segregating at the selected locus. Fortunately, because one-dimensional diffusion processes are reversible with respect to their stationary distributions (i.e., the detailed balance conditions are satisfied), the ancestral process of allele frequencies at a locus segregating two alleles has the same law as the forward process. Subsequently, Hudson and Kaplan (1988) showed that the genealogy at a linked neutral locus can be described by a structured coalescent defined in terms of the genetic backgrounds at the selected locus; in this case, recombination between the selected and neutral loci can also move lineages between backgrounds.The objective of this article is to extend the structured coalescent to population genetic models in which within-generation fecundity variance is genotype dependent. (The genealogical consequences of polymorphism affecting between-generation fecundity variance will be described in a separate article.) In these models, exchangeability is violated not only by selective differences between individuals, but also by differences in life history traits that affect coalescent rates and allele frequency fluctuations. Nonetheless, because lineages are exchangeable within backgrounds, the coalescence and substitution rates can still be calculated conditional on the types of the lineages and the genetic composition of the population. In the next two sections, I derive structured coalescent processes that describe the genealogy at a neutral marker locus that is linked to a second locus (the “selected locus”) that affects fecundity variance. This is first done for a haploid model and then extended to a diploid model in which there may be both sex- and genotype-specific differences in fecundity variance. Results for both models are summarized in

Controlling for P‐value inflation in allele frequency change in experimental evolution and artificial selection experiments

Experimental evolution studies can be used to explore genomic response to artificial and natural selection. In such studies, loci that display larger allele frequency change than expected by genetic drift alone are assumed to be directly or indirectly associated with traits under selection. However, such studies report surprisingly many loci under selection, suggesting that current tests for allele frequency change may be subject to P‐value inflation and hence be anticonservative. One factor known from genomewide association (GWA) studies to cause P‐value inflation is population stratification, such as relatedness among individuals. Here, we suggest that by treating presence of an individual in a population after selection as a binary response variable, existing GWA methods can be used to account for relatedness when estimating allele frequency change. We show that accounting for relatedness like this effectively reduces false‐positives in tests for allele frequency change in simulated data with varying levels of population structure. However, once relatedness has been accounted for, the power to detect causal loci under selection is low. Finally, we demonstrate the presence of P‐value inflation in allele frequency change in empirical data spanning multiple generations from an artificial selection experiment on tarsus length in two free‐living populations of house sparrow and correct for this using genomic control. Our results indicate that since allele frequencies in large parts of the genome may change when selection acts on a heritable trait, such selection is likely to have considerable and immediate consequences for the eco‐evolutionary dynamics of the affected populations.     

A Monte Carlo simulation model for studying evolution in age-structured populations

This model provides for any number of genotypes defined by age-specific survival and fecundity rates in a population with completely overlapping generations and growing under the control of density-governing functions affecting survival or fecundity. It is tested in situations involving two alleles at one locus. Nonselection populations at Hardy–Weinberg equilibrium obey the ecogenetic law; i.e., each genotype follows Lotka's law regarding rate of increase and stable age distribution as if it were an independent true-breeding population. Populations experiencing age- and density-independent selection approximate this situation, and the changes in gene frequency are predicted by relative fitnesses bases on λ, the finite rate of increase of the genotypes. Polymorphic gene equilibria occurring at steady-state population sizes are determined by fitnesses based on R, the net reproductive rate. In examples involving differences in generation time produced by age-dependent differences in fecundity, the allele associated with longer generation time may be favored or opposed by selection, depending on whether the density-governing factor controlling population size affects survival or fecundity. If such genotypes have similar R's, a genetic equilibrium may be established if the population is governed by a density function acting upon fecundity. Received: August 23, 1999 / Accepted: July 13, 2000     

Fixation probabilities in evolutionary game dynamics with a two-strategy game in finite diploid populations

Fixation processes in evolutionary game dynamics in finite diploid populations are investigated. Traditionally, frequency dependent evolutionary dynamics is modeled as deterministic replicator dynamics. This implies that the infinite size of the population is assumed implicitly. In nature, however, population sizes are finite. Recently, stochastic processes in finite populations have been introduced in order to study finite size effects in evolutionary game dynamics. One of the most significant studies on evolutionary dynamics in finite populations was carried out by Nowak et al. which describes “one-third law” [Nowak, et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646-650]. It states that under weak selection, if the fitness of strategy α is greater than that of strategy β when α has a frequency , strategy α fixates in a β-population with selective advantage. In their study, it is assumed that the inheritance of strategies is asexual, i.e. the population is haploid. In this study, we apply their framework to a diploid population that plays a two-strategy game with two ESSs (a bistable game). The fixation probability of a mutant allele in this diploid population is derived. A “three-tenth law” for a completely recessive mutant allele and a “two-fifth law” for a completely dominant mutant allele are found; other cases are also discussed.     

Consequences of population structure on genes under balancing selection

This paper describes a new approach to modeling population structure for genes under strong balancing selection of the type seen in plant self-incompatibility systems and the major histocompatibility complex (MHC) system of vertebrates. Simple analytic solutions for the number of alleles maintained at equilibrium and the expected proportion of alleles shared between demes at various levels are derived and checked against simulation results. The theory accurately captures the dynamics of allele number in a subdivided population and identifies important values of m (migration rate) at which allele number and distribution change qualitatively. Starting from a panmictic population, as migration among demes decreases a qualitative change in dynamics is seen at approximately m(crit) approximately equal to the square root of(s/4piNT) where NT is the total population size and s is a measure of the strength of selection. At this point, demes can no longer maintain their panmictic allele number, due to increasing isolation from the total population. Another qualitative change occurs at a migration rate on the same order of magnitude as the mutation rate, mu. At this point, the demes are highly differentiated for allele complement, and the total number of alleles in the population is increased. Because in general u < m<(crit) at intermediate migration rates slightly fewer alleles may be maintained in the total population than are maintained at panmixia. Within this range, total allele number may not be the best indicator of whether a population is effectively panmictic, and some caution should be used when interpreting samples from such populations. The theory presented here can help to analyze data from genes under balancing selection in subdivided populations.     

EVOLUTION OF INCOMPATIBILITY-INDUCING MICROBES IN SUBDIVIDED HOST POPULATIONS

Many insects, other arthropods, and nematodes harbor maternally inherited bacteria inducing "cytoplasmic incompatibility" (CI), reduced egg hatch when infected males mate with uninfected females. Although CI drives the spread of these microbes, selection on alternative, mutually compatible strains in panmictic host populations does not act directly on CI intensity but favors higher "effective fecundity," the number of infected progeny an infected female produces. We analyze the consequences of host population subdivision using deterministic and stochastic models. In subdivided populations, effective fecundity remains the primary target of selection. For strains of equal effective fecundity, if population density is regulated locally (i.e., "soft selection"), variation among patches in infection frequencies may induce change in the relative frequencies of the strains. However, whether this change favors stronger incompatibility depends on initial frequencies. Demographic fluctuations maintain frequency variation that tends to favor stronger incompatibility. However, this effect is weak; even with small patches, minute increases in effective fecundity can offset substantial decreases in CI intensity. These results are insensitive to many details of host life cycle and migration and to systematic outbreeding or inbreeding within patches. Selection acting through transfer between host species may be required to explain the prevalence of CI.     

Empirical Distributions of F ST from Large-Scale Human Polymorphism Data

Studies of the apportionment of human genetic variation have long established that most human variation is within population groups and that the additional variation between population groups is small but greatest when comparing different continental populations. These studies often used Wright’s F _ST that apportions the standardized variance in allele frequencies within and between population groups. Because local adaptations increase population differentiation, high-F _ST may be found at closely linked loci under selection and used to identify genes undergoing directional or heterotic selection. We re-examined these processes using HapMap data. We analyzed 3 million SNPs on 602 samples from eight worldwide populations and a consensus subset of 1 million SNPs found in all populations. We identified four major features of the data: First, a hierarchically F _ST analysis showed that only a paucity (12%) of the total genetic variation is distributed between continental populations and even a lesser genetic variation (1%) is found between intra-continental populations. Second, the global F _ST distribution closely follows an exponential distribution. Third, although the overall F _ST distribution is similarly shaped (inverse J), F _ST distributions varies markedly by allele frequency when divided into non-overlapping groups by allele frequency range. Because the mean allele frequency is a crude indicator of allele age, these distributions mark the time-dependent change in genetic differentiation. Finally, the change in mean-F _ST of these groups is linear in allele frequency. These results suggest that investigating the extremes of the F _ST distribution for each allele frequency group is more efficient for detecting selection. Consequently, we demonstrate that such extreme SNPs are more clustered along the chromosomes than expected from linkage disequilibrium for each allele frequency group. These genomic regions are therefore likely candidates for natural selection.     

An experimental test of the effects of resources and sex ratio on maternal fitness and phenotypic selection in gynodioecious Fragaria virginiana

Resources, sex ratio, and seed production by hermaphrodites covary among natural populations of many gynodioecious plant species, such that they are functionally "more dioecious" as resources become more limiting. Strong correlations among these three factors confound our understanding of their relative roles in maintaining polymorphic sexual systems. We manipulated resource availability and sex ratio and measured their effects on relative fertility and phenotypic selection through the maternal fitness of females and hermaphrodites of Fragaria virginiana. Two results were particularly surprising. First, hermaphrodites showed little variability in fecundity across resource treatments and showed strong positive and context-dependent selection for fruit set. This suggests that variation in hermaphrodite seed production along resource gradients in nature may result from adaptation rather than plasticity. Second, although females increased their fecundity with higher resources, their fertility was unaffected by sex ratio, which is predicted to mediate pollen limitation of females in natural populations where they are common. Selection on petal size of females was also weak, indicating a minimal effect of pollinator attraction on variation in the fertility of female plants. Hence, we found no mechanistic explanation for the complete absence of high-resource high female populations in nature. Despite strong selection for increased fruit set of hermaphrodites, both the strength of selection and its contribution to the maintenance of gynodioecy are severely reduced under conditions where females have high relative fecundity (i.e., low resources and high-female sex ratios). High relative fertility plus high female frequency means that the evolution of phenotypic traits in hermaphrodites (i.e., response to selection via seed function) should be manifested through females because most hermaphrodites will have female mothers. Fruit set was never under strong selection in females; hence, selection to increase fruit set hermaphrodites will be less effective in maintaining their fruiting ability in natural populations with low resources and high female frequency. In sum, both sex ratio and resource availability influence trait evolution indirectly-through their effects on relative fertility of the sexes and patterns of selection. Sex ratio did not impose strong pollen limitation on females but did directly moderate the outcome of natural selection by biasing the maternal sex of the next generation. This direct effect of sex ratio on the manifestation of natural selection is expected to have far greater impact on the evolution of traits, such as seed-producing ability in hermaphrodites and the maintenance of sexual polymorphisms in nature, compared to indirect effects of sex ratio on relative fertility of the sexes.     

Analyzing Gene-Frequency Data When the Effective Population Size Is Finite

The statistical methods used by Schaffer, Yardley and Anderson (1977) and by Gibson et al. (1979) to analyze the variation in allele frequencies in two common types of experimental procedure, where the effective population size is finite, are extended to a more general situation involving a greater range of experiments. The analysis developed is more sensitive in detecting changes in allele frequency due to both fluctuating and balancing selection, as well as to directional selection. The error involved in many studies due to ignoring the effective population size structure would appear to be large. The range of hypotheses that can be considered may be increased as well. Finally, the method of determining bounds for the effective population size, when a particular genetic model is known to hold for a data set, is also outlined.     

The genetical theory of social behaviour

We survey the population genetic basis of social evolution, using a logically consistent set of arguments to cover a wide range of biological scenarios. We start by reconsidering Hamilton''s (Hamilton 1964 J. Theoret. Biol. 7, 1–16 (doi:10.1016/0022-5193(64)90038-4)) results for selection on a social trait under the assumptions of additive gene action, weak selection and constant environment and demography. This yields a prediction for the direction of allele frequency change in terms of phenotypic costs and benefits and genealogical concepts of relatedness, which holds for any frequency of the trait in the population, and provides the foundation for further developments and extensions. We then allow for any type of gene interaction within and between individuals, strong selection and fluctuating environments and demography, which may depend on the evolving trait itself. We reach three conclusions pertaining to selection on social behaviours under broad conditions. (i) Selection can be understood by focusing on a one-generation change in mean allele frequency, a computation which underpins the utility of reproductive value weights; (ii) in large populations under the assumptions of additive gene action and weak selection, this change is of constant sign for any allele frequency and is predicted by a phenotypic selection gradient; (iii) under the assumptions of trait substitution sequences, such phenotypic selection gradients suffice to characterize long-term multi-dimensional stochastic evolution, with almost no knowledge about the genetic details underlying the coevolving traits. Having such simple results about the effect of selection regardless of population structure and type of social interactions can help to delineate the common features of distinct biological processes. Finally, we clarify some persistent divergences within social evolution theory, with respect to exactness, synergies, maximization, dynamic sufficiency and the role of genetic arguments.     

The joint allele frequency spectrum of multiple populations: a coalescent theory approach

The allele frequency spectrum is a series of statistics that describe genetic polymorphism, and is commonly used for inferring population genetic parameters and detecting natural selection. Population genetic theory on the allele frequency spectrum for a single population has been well studied using both coalescent theory and diffusion equations. Recently, the theory was extended to the joint allele frequency spectrum (JAFS) for three populations using diffusion equations and was shown to be very useful in inferring human demographic history. In this paper, I show that the JAFS can be analytically derived with coalescent theory for a basic model of two isolated populations and then extended to multiple populations and various complex scenarios, such as those involving population growth and bottleneck, migration, and positive selection. Simulation study is used to demonstrate the accuracy and applicability of the theoretical model. The coalescent theory-based approach for the JAFS can characterize the demographic history with comprehensive statistical models as the diffusion approach does, and in addition gains several novel advantages: the computational complexity of calculating the JAFS with coalescent theory is reduced, and thus it is feasible to analytically obtain the JAFS for multiple populations; the hitchhiking effect can be efficiently modeled in coalescent theory, enabling the development of methodologies for detecting selection via multi-population polymorphism data. As an alternative to the diffusion approximation approach, the coalescent theory for the JAFS also provides a foundation for population genetic inference with the advent of large-scale genomic polymorphism data.     

Fluctuations in numbers in box populations of Drosophila and selective genetic mechanism of their regulation

Box populations of Drosophila melanogaster are characterized by two types of periodical fluctuations of numbers: with low and high frequency. High frequency fluctuations are determined by existence of preimago and imago stages and subsequent delay in density-dependent limitation of imago reproduction, duration of which is determined by time of preimago stage. The period of these fluctuations should be limited within two generation, that is confirmed by experimental data. Low frequency fluctuations with the period of 13-15 generations are the result of ecological density-dependent effect. In this case during pick density one can observe continuous degradation of population (i.e. decrease in fecundity and life time of imago) and following decrease in numbers. Temporary changes in fecundity of females and their offspring of the second generation are positively correlated with low frequency fluctuations in numbers. Such relationships show the possibility of density-dependent, cyclic, genetic changes in fecundity connected with fluctuations in numbers. It means that at the phase of growth in numbers when the density is still low, the selection is directed to the individuals with high fecundity sensible to overpopulation. The phase of decline in numbers is connected with high density and selection directed to the individuals with low fecundity in low density populations. The changes in genetic structure of fluctuating population lead to the weakening of this fluctuations and to the maintaining of population under such conditions.     

Worldwide population differentiation at disease-associated SNPs

Background

Recent genome-wide association (GWA) studies have provided compelling evidence of association between genetic variants and common complex diseases. These studies have made use of cases and controls almost exclusively from populations of European ancestry and little is known about the frequency of risk alleles in other populations. The present study addresses the transferability of disease associations across human populations by examining levels of population differentiation at disease-associated single nucleotide polymorphisms (SNPs).

Methods

We genotyped ~1000 individuals from 53 populations worldwide at 25 SNPs which show robust association with 6 complex human diseases (Crohn's disease, type 1 diabetes, type 2 diabetes, rheumatoid arthritis, coronary artery disease and obesity). Allele frequency differences between populations for these SNPs were measured using Fst. The Fst values for the disease-associated SNPs were compared to Fst values from 2750 random SNPs typed in the same set of individuals.

Results

On average, disease SNPs are not significantly more differentiated between populations than random SNPs in the genome. Risk allele frequencies, however, do show substantial variation across human populations and may contribute to differences in disease prevalence between populations. We demonstrate that, in some cases, risk allele frequency differences are unusually high compared to random SNPs and may be due to the action of local (i.e. geographically-restricted) positive natural selection. Moreover, some risk alleles were absent or fixed in a population, which implies that risk alleles identified in one population do not necessarily account for disease prevalence in all human populations.

Conclusion

Although differences in risk allele frequencies between human populations are not unusually large and are thus likely not due to positive local selection, there is substantial variation in risk allele frequencies between populations which may account for differences in disease prevalence between human populations.     

Evolution of a length polymorphism in the human PER3 gene, a component of the circadian system

Period homologue 3 (PER3) is a component of the mammalian circa-dian system, although its precise role is unknown. A biallelic variable number tandem repeat (VNTR) polymorphism exists in human PER3, consisting of 4 or 5 repeats of a 54-bp sequence in a region encoding a putative phosphorylation domain. This polymorphism has previously been reported to associate with diurnal preference ("morningness" and "eveningness") and delayed sleep-phase syndrome. We have investigated the global allele frequencies of this variant in ethnically distinct indigenous populations. All populations were polymorphic, with the shorter (4-repeat) allele ranging in frequency from 0.19 (Papua New Guinea) to 0.89 (Mongolia). To investigate if allele frequency has been influenced by natural selection, the authors 1) tested for a correlation with latitude and mean annual insolation (incident sunlight energy), using classical markers to correct for historical population differentiation; and they 2) compared allele-frequency difference between European American, African American, and East Asian populations, as measured using F(ST), to an empirical null distribution of F(ST)values based on a genome-wide dataset of single nucleotide polymorphisms (SNPs) of presumed neutral loci that were previously typed by The SNP Consortium. The variation in allele frequencies between indigenous populations did not show a pattern that would indicate selective pressure on PER3resulting from day-length variation or mean annual insolation, and the allele-frequency difference between European Americans, African Americans, and East Asians was not an outlier when compared to the distribution for presumed neutral SNPs. We therefore find no evidence for differential or balancing selection in the contemporary pattern of global PER3allele frequencies.     

Microevolution of S-allele frequencies in wild cherry populations: respective impacts of negative frequency dependent selection and genetic drift

Negative frequency dependent selection (NFDS) is supposed to be the main force controlling allele evolution at the gametophytic self-incompatibility locus (S-locus) in strictly outcrossing species. Genetic drift also influences S-allele evolution. In perennial sessile organisms, evolution of allelic frequencies over two generations is mainly shaped by individual fecundities and spatial processes. Using wild cherry populations between two successive generations, we tested whether S-alleles evolved following NFDS qualitative and quantitative predictions. We showed that allelic variation was negatively correlated with parental allelic frequency as expected under NFDS. However, NFDS predictions in finite population failed to predict more than half S-allele quantitative evolution. We developed a spatially explicit mating model that included the S-locus. We studied the effects of self-incompatibility and local drift within populations due to pollen dispersal in spatially distributed individuals, and variation in male fecundity on male mating success and allelic frequency evolution. Male mating success was negatively related to male allelic frequency as expected under NFDS. Spatial genetic structure combined with self-incompatibility resulted in higher effective pollen dispersal. Limited pollen dispersal in structured distributions of individuals and genotypes and unequal pollen production significantly contributed to S-allele frequency evolution by creating local drift effects strong enough to counteract the NFDS effect on some alleles.     

Balancing selection and heterozygote advantage in major histocompatibility complex loci of the bottlenecked Finnish wolf population

Maintaining effective immune response is an essential factor in the survival of small populations. One of the most important immune gene regions is the highly polymorphic major histocompatibility complex (MHC). We investigated how a population bottleneck and recovery have influenced the diversity and selection in three MHC class II loci, DLA‐DRB1, DLA‐DQA1 and DLA‐DQB1, in the Finnish wolf population. We studied the larger Russian Karelian wolf population for comparison and used 17 microsatellite markers as reference loci. The Finnish and Karelian wolf populations did not differ substantially in their MHC diversities ( = 0.047, P = 0.377), but differed in neutral microsatellite diversities ( = 0.148, P = 0.008). MHC allele frequency distributions in the Finnish population were more even than expected under neutrality, implying balancing selection. In addition, an excess of nonsynonymous compared to synonymous polymorphisms indicated historical balancing selection. We also studied association between helminth (Trichinella spp. and Echinococcus canadensis) prevalence and MHC diversity at allele and SNP level. MHC‐heterozygous wolves were less often infected by Trichinella spp. and carriers of specific MHC alleles, SNP haplotypes and SNP alleles had less helminth infections. The associated SNP haplotypes and alleles were shared by different MHC alleles, which emphasizes the necessity of single‐nucleotide‐level association studies also in MHC. Here, we show that strong balancing selection has had similar effect on MHC diversities in the Finnish and Russian Karelian wolf populations despite significant genetic differentiation at neutral markers and small population size in the Finnish population.     

Selection against demographic stochasticity in age-structured populations

It has been shown that differences in fecundity variance can influence the probability of invasion of a genotype in a population; i.e., a genotype with lower variance in offspring number can be favored in finite populations even if it has a somewhat lower mean fitness than a competitor. In this article, Gillespie's results are extended to population genetic systems with explicit age structure, where the demographic variance (variance in growth rate) calculated in the work of Engen and colleagues is used as a generalization of "variance in offspring number" to predict the interaction between deterministic and random forces driving change in allele frequency. By calculating the variance from the life-history parameters, it is shown that selection against variance in the growth rate will favor a genotypes with lower stochasticity in age-specific survival and fertility rates. A diffusion approximation for selection and drift in a population with two genotypes with different life-history matrices (and therefore different mean growth rates and demographic variances) is derived and shown to be consistent with individual-based simulations. It is also argued that for finite populations, perturbation analyses of both the mean and the variance in growth rate may be necessary to determine the sensitivity of fitness to changes in the life-history parameters.     

Rapidly evolving adaptations to host ecology and nutrition in the soapberry bug

With reciprocal rearing experiments, we tested the hypothesis that adaptive differences in host-use traits among soapberry bug populations have a genetic basis. These experiments were conducted with two host races from Florida, an ancestral-type one on a native host plant species and a derived one on a recently introduced plant species (colonized mainly post-1950), on whose seed crops this insect depends for growth and reproduction. Compared to the native host species, the introduced host produces larger seed crops over a much briefer annual period. Its seeds are also significantly higher in lipids and lower in nitrogen. The bug populations exhibit greater juvenile survivorship on their home hosts; that is, the derived population survives better on seeds of the introduced host than does its ancestral-type counterpart, and vice versa. Regardless of the rearing host, populations from the introduced host lay much smaller eggs, and fecundity measures show a more complex pattern than does survivorship: the ancestral-type population produces eggs at the same rate on each host, while the derived population is less fecund on the native host and exhibits enhanced fecundity on the introduced host. These results indicate that the population differences are evolved rather than host-induced. They appear to be adaptive responses to host differences in the spatial and temporal distribution of seed availability and nutritional quality, and show that increased performance on the alien host has evolved with surprising speed and magnitude, with concomitant reductions in performance on the original host.     

Serial founder effects during range expansion: a spatial analog of genetic drift

Range expansions cause a series of founder events. We show that, in a one-dimensional habitat, these founder events are the spatial analog of genetic drift in a randomly mating population. The spatial series of allele frequencies created by successive founder events is equivalent to the time series of allele frequencies in a population of effective size ke, the effective number of founders. We derive an expression for ke in a discrete-population model that allows for local population growth and migration among established populations. If there is selection, the net effect is determined approximately by the product of the selection coefficients and the number of generations between successive founding events. We use the model of a single population to compute analytically several quantities for an allele present in the source population: (i) the probability that it survives the series of colonization events, (ii) the probability that it reaches a specified threshold frequency in the last population, and (iii) the mean and variance of the frequencies in each population. We show that the analytic theory provides a good approximation to simulation results. A consequence of our approximation is that the average heterozygosity of neutral alleles decreases by a factor of 1-1/(2ke) in each new population. Therefore, the population genetic consequences of surfing can be predicted approximately by the effective number of founders and the effective selection coefficients, even in the presence of migration among populations. We also show that our analytic results are applicable to a model of range expansion in a continuously distributed population.