Dynamics of neutral and selected alleles when the offspring distribution is skewed

We analyze the dynamics of two alternative alleles in a simple model of a population that allows for large family sizes in the distribution of offspring number. This population model was first introduced by Eldon and Wakeley, who described the backward-time genealogical relationships among sampled individuals, assuming neutrality. We study the corresponding forward-time dynamics of allele frequencies, with or without selection. We derive a continuum approximation, analogous to Kimura's diffusion approximation, and we describe three distinct regimes of behavior that correspond to distinct regimes in the coalescent processes of Eldon and Wakeley. We demonstrate that the effect of selection is strongly amplified in the Eldon-Wakeley model, compared to the Wright-Fisher model with the same variance effective population size. Remarkably, an advantageous allele can even be guaranteed to fix in the Eldon-Wakeley model, despite the presence of genetic drift. We compute the selection coefficient required for such behavior in populations of Pacific oysters, based on estimates of their family sizes. Our analysis underscores that populations with the same effective population size may nevertheless experience radically different forms of genetic drift, depending on the reproductive mechanism, with significant consequences for the resulting allele dynamics.     

Analytical results on the neutral non-equilibrium allele frequency spectrum based on diffusion theory

The allele frequency spectrum has attracted considerable interest for the simultaneous inference of the demographic and adaptive history of populations. In a recent study, Evans et al. (2007) developed a forward diffusion equation describing the allele frequency spectrum, when the population is subject to size changes, selection and mutation. From the diffusion equation, the authors derived a system of ordinary differential equations (ODEs) for the moments in a Wright–Fisher diffusion with varying population size and constant selection. Here, we present an explicit solution for this system of ODEs with variable population size, but without selection, and apply this result to derive the expected spectrum of a sample for time-varying population size. We use this forward-in-time-solution of the allele frequency spectrum to obtain the backward-in-time-solution previously derived via coalescent theory by Griffiths and Tavaré (1998). Finally, we discuss the applicability of the theoretical results to the analysis of nucleotide polymorphism data.     

Climatic and temporal effects on the expression of secondary sexual characters: genetic and environmental components

Despite great interest in sexual selection, relatively little is known in detail about the genetic and environmental determinants of secondary sexual characters in natural populations. Such information is important for determining the way in which populations may respond to sexual selection. We report analyses of genetic and large-scale environmental components of phenotypic variation of two secondary sexual plumage characters (forehead and wing patch size) in the collared flycatcher Ficedula albicollis over a 22-year period. We found significant heritability for both characters but little genetic covariance between the two. We found a positive association between forehead patch size and a large-scale climatic index, the North Atlantic Oscillation (NAO) index, but not for wing patch. This pattern was observed in both cross-sectional and longitudinal data suggesting that the population response to NAO index can be explained as the result of phenotypic plasticity. Heritability of forehead patch size for old males, calculated under favorable conditions (NAO index > or = median), was greater than that under unfavorable conditions (NAO index < median). These changes occurred because there were opposing changes in additive genetic variance (VA) and residual variance (VR) under favorable and unfavorable conditions, with VA increasing and VR decreasing in good environments. However, no such effect was detected for young birds, or for wing patch size in either age class. In addition to these environmental effects on both phenotypic and genetic variances, we found evidence for a significant decrease of forehead patch size over time in older birds. This change appears to be caused by a change in the sign of viability selection on forehead patch size, which is associated with a decline in the breeding value of multiple breeders. Our data thus reveal complex patterns of environmental influence on the expression of secondary sexual characters, which may have important implications for understanding selection and evolution of these characters.     

POPULATION DIVERGENCE IN SEXUAL ORNAMENTS: THE WHITE FOREHEAD PATCH OF NORWEGIAN PIED FLYCATCHERS IS SMALL AND UNSEXY

Models of sexual selection suggest that populations may easily diverge in male secondary sexual characters. Studies of a Spanish population of the pied flycatcher, Ficedula hypoleuca, and a Swedish population of the closely related collared flycatcher, F. albicollis, have indicated that the white forehead patch of males is a sexually selected trait. We studied the white forehead patch of male pied flycatchers (n = 487) in a Norwegian population over seven years. Males with large forehead patches were in general more brightly colored, but patch height was not correlated to body mass, body size, or parasite loads. Conditions during the nestling period did not seem to influence patch height as an adult. Patch height increased slightly from the first to the second year as adults, but then remained relatively constant at higher ages. Patch height was not related to survival. Year-to-year changes showed that males who increased in patch height also increased in body mass, suggesting that expression of the forehead patch may be partly condition dependent. However, changes in body mass explained only a small proportion of the variance in patch height between males. Thus, patch height would not be a good indicator of male quality. Furthermore, patch size was also not related to male ability to feed nestlings, indicating that females would not obtain direct benefits by choosing males with large patches. However, patch height could be a Fisher trait, but this requires heritability and there was no significant father-son resemblance in patch height. Comparisons of the males visited by each female during the mate sampling period indicated that chosen males did not have larger forehead patches than rejected males. Experimental manipulation of patch height did not affect male mating success. These results indicate that females do not use patch size as a mate choice cue. Finally, patch height did not predict the outcome of male contests for nestboxes, suggesting that the forehead patch is not an intrasexually selected cue of status. Norwegian pied flycatchers have smaller forehead patches than both Spanish pied flycatchers and Swedish collared flycatchers. We suggest that this pattern may be explained by the lack of sexual selection on the forehead patch in the Norwegian population as compared to the other populations, where the patch is apparently sexually selected. We discuss possible reasons for these population divergences, such as female choice on an alternative secondary sexual character (general plumage color) and speciation among Ficedula flycatchers.     

Demographic Genetics of Brown Trout (Salmo Trutta) and Estimation of Effective Population Size from Temporal Change of Allele Frequencies

We studied temporal allele frequency shifts over 15 years and estimated the genetically effective size of four natural populations of brown trout (Salmo trutta L.) on the basis of the variation at 14 polymorphic allozyme loci. The allele frequency differences between consecutive cohorts were significant in all four populations. There were no indications of natural selection, and we conclude that random genetic drift is the most likely cause of temporal allele frequency shifts at the loci examined. Effective population sizes were estimated from observed allele frequency shifts among cohorts, taking into consideration the demographic characteristics of each population. The estimated effective sizes of the four populations range from 52 to 480 individuals, and we conclude that the effective size of natural brown trout populations may differ considerably among lakes that are similar in size and other apparent characteristics. In spite of their different effective sizes all four populations have similar levels of genetic variation (average heterozygosity) indicating that excessive loss of genetic variability has been retarded, most likely because of gene flow among neighboring populations.     

Anthropogenic fragmentation increases risk of genetic decline in the threatened orchid Platanthera leucophaea

Protecting biodiversity requires an understanding of how anthropogenic changes impact the genetic processes associated with extinction risk. Studies of the genetic changes due to anthropogenic fragmentation have revealed conflicting results. This is likely due to the difficulty in isolating habitat loss and fragmentation, which can have opposing impacts on genetic parameters. The well‐studied orchid, Platanthera leucophaea, provides a rich dataset to address this issue, allowing us to examine range‐wide genetic changes. Midwestern and Northeastern United States. We sampled 35 populations of P. leucophaea that spanned the species’ range and varied in patch composition, degree of patch isolation, and population size. From these populations we measured genetic parameters associated with increased extinction risk. Using this combined dataset, we modeled landscape variables and population metrics against genetic parameters to determine the best predictors of increased extinction risk. All genetic parameters were strongly associated with population size, while development and patch isolation showed an association with genetic diversity and genetic structure. Genetic diversity was lowest in populations with small census sizes, greater urbanization pressures (habitat loss), and small patch area. All populations showed moderate levels of inbreeding, regardless of size. Contrary to expectation, we found that critically small populations had negative inbreeding values, indicating non‐random mating not typically observed in wild populations, which we attribute to selection for less inbred individuals. The once widespread orchid, Platanthera leucophaea, has suffered drastic declines and extant populations show changes in the genetic parameters associated with increased extinction risk, especially smaller populations. Due to the important correlation with risk and habitat loss, we advocate continued monitoring of population sizes by resource managers, while the critically small populations may need additional management to reverse genetic declines.     

DOES MATE LIMITATION IN SELF‐INCOMPATIBLE SPECIES PROMOTE THE EVOLUTION OF SELFING? THE CASE OF LEAVENWORTHIA ALABAMICA

Genetic diversity at the S‐locus controlling self‐incompatibility (SI) is often high because of negative frequency‐dependent selection. In species with highly patchy spatial distributions, genetic drift can overwhelm balancing selection and cause stochastic loss of S‐alleles. Natural selection may favor the breakdown of SI in populations with few S‐alleles because low S‐allele diversity constrains the seed production of self‐incompatible plants. We estimated S‐allele diversity, effective population sizes, and migration rates in Leavenworthia alabamica, a self‐incompatible mustard species restricted to discrete habitat patches in rocky glades. Patterns of polymorphism were investigated at the S‐locus and 15 neutral microsatellites in three large and three small populations with 100‐fold variation in glade size. Populations on larger glades maintained more S‐alleles, but all populations were estimated to harbor at least 20 S‐alleles, and mate availabilities typically exceeded 0.80, which is consistent with little mate limitation in nature. Estimates of the effective size (N_e) in each population ranged from 600 to 1600, and estimated rates of migration (m) ranged from 3 × 10⁻⁴ to nearly 1 × 10⁻³. According to theoretical models, there is limited opportunity for genetic drift to reduce S‐allele diversity in populations with these attributes. Although pollinators or resources limit seed production in small glades, limited S‐allele diversity does not appear to be a factor promoting the incipient breakdown of SI in populations of this species that were studied.     

Enzyme gene heterozygosity in small island populations of Philaenus spumarius (L.) (Homoptera)

Genetic polymorphism at about twenty enzyme loci in one mainland and in six differentially isolated island populations of Philaenus spumarius (L.) was studied by starch gel electrophoresis. The populations have different average degrees of heterozygosity, so that the most isolated population is the least polymorphic. The differences in heterozygosity seem to be correlated to the size of the population and the degree of isolation from other populations. With a single exception, the most common allele in each locus is the most common one everywhere. The results are compared with the differences observed in the color polymorphism of Philaenus island populations. The allele frequencies of enzyme loci are maintained by selection; the fact that the prevalent allele is the same in all populations may be due to selection and founder principle.Report no. 485 from the Tvärminne Zoological Station, University of Helsinki.     

Genetic variability, population size and isolation of distinct populations in the freshwater fish Cottus gobio L.

Analysis of allozyme data of the European freshwater fish Cottus gobio showed marked genetic differentiation across drainage basins in northeastern Bavaria, which points to the existence of at least two cryptic taxa. Genetic variability within populations differed significantly between these two taxa, which could be due to historical (bottlenecks) or ecological reasons (population size). To distinguish between these two hypotheses we sampled 12 distinct populations from Rhine, Elbe and Danube drainages. Using allozyme data we examined the influence of population size and isolation on genetic variability within populations. We used spatial extent of populations (patch size) as a measure for population size. To estimate isolation we calculated a compound measure which took into account patch size and distance to all neighbouring populations. Both patch size and isolation were highly correlated with genetic variability, explaining ≈95% of the variance of genetic variability within populations. Furthermore, analysis of covariance suggests that the difference in genetic variability between taxa may be explained by differences in population size.     

Modelling single nucleotide effects in phosphoglucose isomerase on dispersal in the Glanville fritillary butterfly: coupling of ecological and evolutionary dynamics

Dispersal comprises a complex life-history syndrome that influences the demographic dynamics of especially those species that live in fragmented landscapes, the structure of which may in turn be expected to impose selection on dispersal. We have constructed an individual-based evolutionary sexual model of dispersal for species occurring as metapopulations in habitat patch networks. The model assumes correlated random walk dispersal with edge-mediated behaviour (habitat selection) and spatially correlated stochastic local dynamics. The model is parametrized with extensive data for the Glanville fritillary butterfly. Based on empirical results for a single nucleotide polymorphism (SNP) in the phosphoglucose isomerase (Pgi) gene, we assume that dispersal rate in the landscape matrix, fecundity and survival are affected by a locus with two alleles, A and C, individuals with the C allele being more mobile. The model was successfully tested with two independent empirical datasets on spatial variation in Pgi allele frequency. First, at the level of local populations, the frequency of the C allele is the highest in newly established isolated populations and the lowest in old isolated populations. Second, at the level of sub-networks with dissimilar numbers and connectivities of patches, the frequency of C increases with decreasing network size and hence with decreasing average metapopulation size. The frequency of C is the highest in landscapes where local extinction risk is high and where there are abundant opportunities to establish new populations. Our results indicate that the strength of the coupling of the ecological and evolutionary dynamics depends on the spatial scale and is asymmetric, demographic dynamics having a greater immediate impact on genetic dynamics than vice versa.     

The origin of selection signatures on bovine chromosome 6

The extent and pattern of linkage disequilibrium (LD) between closely spaced markers contain information about population history, including past population size and selection history. Selection signatures can be identified by comparing the LD surrounding a putative selected allele at a locus to the putative non-selected allele. In livestock populations, locations of selection signatures identified in this way should be correlated with QTL affecting production traits, as the populations have been under strong artificial selection for these traits. We used a dense SNP map of bovine chromosome 6 to characterize the pattern of LD on this chromosome in Norwegian Red cattle, a breed which has been strongly selected for milk production. The pattern of LD was generally consistent with strong selection in regions containing QTL affecting milk production traits, including a strong selection signature in a region containing a mutation known to affect milk production. The results demonstrate that in livestock populations, the origin of selection signatures will often be QTL for livestock production traits, and illustrate the value of selection signatures in uncovering new mutations with potential effects on quantitative traits.     

Some genetic consequences of skewed fecundity distributions in plants

Summary Most plant populations show a skewedrd distribution of fecundity amongst their members, in contrast to the poisson distribution assumed by most population genetical theory. We examine by simulation the consequences of skewed fecundity for plant evolution when combined with sieve selection. In comparison with poisson-based theory, plant populations are likely to show a faster response to selection, especially when the favoured allele is at a low frequency. Selection against a deleterious immigrant allele will also be more effective, reducing its equilibrium frequency in a population. In the special case of heterozygote disadvantage traits will evolve that could not under poisson theory. However, random variation is also higher, giving a 10-plant population an effective population size of about 6.4 under poisson theory. The conclusions are not qualitatively changed by different assumptions on the exact shape of the fecundity distribution, or on heritability, or on reproduction by the smallest plants of the population.     

The Strength of Selection against Neanderthal Introgression

Hybridization between humans and Neanderthals has resulted in a low level of Neanderthal ancestry scattered across the genomes of many modern-day humans. After hybridization, on average, selection appears to have removed Neanderthal alleles from the human population. Quantifying the strength and causes of this selection against Neanderthal ancestry is key to understanding our relationship to Neanderthals and, more broadly, how populations remain distinct after secondary contact. Here, we develop a novel method for estimating the genome-wide average strength of selection and the density of selected sites using estimates of Neanderthal allele frequency along the genomes of modern-day humans. We confirm that East Asians had somewhat higher initial levels of Neanderthal ancestry than Europeans even after accounting for selection. We find that the bulk of purifying selection against Neanderthal ancestry is best understood as acting on many weakly deleterious alleles. We propose that the majority of these alleles were effectively neutral—and segregating at high frequency—in Neanderthals, but became selected against after entering human populations of much larger effective size. While individually of small effect, these alleles potentially imposed a heavy genetic load on the early-generation human–Neanderthal hybrids. This work suggests that differences in effective population size may play a far more important role in shaping levels of introgression than previously thought.     

Landscape structure and the genetic effects of a population collapse

Both landscape structure and population size fluctuations influence population genetics. While independent effects of these factors on genetic patterns and processes are well studied, a key challenge is to understand their interaction, as populations are simultaneously exposed to habitat fragmentation and climatic changes that increase variability in population size. In a population network of an alpine butterfly, abundance declined 60–100% in 2003 because of low over-winter survival. Across the network, mean microsatellite genetic diversity did not change. However, patch connectivity and local severity of the collapse interacted to determine allelic richness change within populations, indicating that patch connectivity can mediate genetic response to a demographic collapse. The collapse strongly affected spatial genetic structure, leading to a breakdown of isolation-by-distance and loss of landscape genetic pattern. Our study reveals important interactions between landscape structure and temporal demographic variability on the genetic diversity and genetic differentiation of populations. Projected future changes to both landscape and climate may lead to loss of genetic variability from the studied populations, and selection acting on adaptive variation will likely occur within the context of an increasing influence of genetic drift.     

Parallel selection on TRPV6 in human populations

We identified and examined a candidate gene for local directional selection in Europeans, TRPV6, and conclude that selection has acted on standing genetic variation at this locus, creating parallel soft sweep events in humans. A novel modification of the extended haplotype homozygosity (EHH) test was utilized, which compares EHH for a single allele across populations, to investigate the signature of selection at TRPV6 and neighboring linked loci in published data sets for Europeans, Asians and African-Americans, as well as in newly-obtained sequence data for additional populations. We find that all non-African populations carry a signature of selection on the same haplotype at the TRPV6 locus. The selective footprints, however, are significantly differentiated between non-African populations and estimated to be younger than an ancestral population of non-Africans. The possibility of a single selection event occurring in an ancestral population of non-Africans was tested by simulations and rejected. The putatively-selected TRPV6 haplotype contains three candidate sites for functional differences, namely derived non-synonymous substitutions C157R, M378V and M681T. Potential functional differences between the ancestral and derived TRPV6 proteins were investigated by cloning the ancestral and derived forms, transfecting cell lines, and carrying out electrophysiology experiments via patch clamp analysis. No statistically-significant differences in biophysical channel function were found, although one property of the protein, namely Ca(2+) dependent inactivation, may show functionally relevant differences between the ancestral and derived forms. Although the reason for selection on this locus remains elusive, this is the first demonstration of a widespread parallel selection event acting on standing genetic variation in humans, and highlights the utility of between population EHH statistics.     

Effective population size and evolutionary dynamics in outbred laboratory populations of Drosophila

Census population size, sex-ratio and female reproductive success were monitored in 10 laboratory populations of Drosophila melanogaster selected for different ages of reproduction. With this demographic information, we estimated eigenvalue, variance and probability of allele loss effective population sizes. We conclude that estimates of effective size based on gene-frequency change at a few loci are biased downwards. We analysed the relative roles of selection and genetic drift in maintaining genetic variation in laboratory populations of Drosophila. We suggest that rare, favourable genetic variants in our laboratory populations have a high chance of being lost if their fitness effect is weak, e.g. 1% or less. However, if the fitness effect of this variation is 10% or greater, these rare variants are likely to increase to high frequency. The demographic information developed in this study suggests that some of our laboratory populations harbour more genetic variation than expected. One explanation for this finding is that part of the genetic variation in these outbred laboratory Drosophila populations may be maintained by some form of balancing selection. We suggest that, unlike bacteria, medium-term adaptation of laboratory populations of fruit flies is not primarily driven by new mutations, but rather by changes in the frequency of preexisting alleles.     

Directional evolution for microsatellite size in maize

Directional evolution in microsatellites is the tendency for microsatellites either to increase or to decrease in size over time between populations. We analyzed 99 microsatellite loci in a sample of 193 maize plants representing the entire pre-Columbian range of this crop for evidence of directional evolution. We took advantage of the known phylogeographic history of maize with the independent movement of maize from its ancestral location in Mexico to North and South America. We show that there is an increase in the average allele size of microsatellites in the geographically derived North and South American groups relative to the ancestral Mexican group. We also show that there is a negative correlation between average allele size and altitude in all three groups. Directional evolution in maize microsatellites can be explained by changes in the mutation rate over time and space, changes in the degree of mutational bias to a larger allele, demographic differences between the ancestral and geographically derived populations, and/or scenarios involving selection on microsatellite size. The occurrence of directional evolution for microsatellite size indicates that the estimation of population parameters with microsatellite data in maize should be done with caution.     

Characterization of ten microsatellite marker loci in the Komodo Monitor (<Emphasis Type="Italic">Varanus komodoensis</Emphasis>)

The Komodo monitor (Varanus komodoensis) is a classic example of a species that has been fragmented into small isolated populations over a limited range. This species, classified as endangered under Appendix I of the Convention on the International Trade of Endangered Species. We describe 10 novel species-specific microsatellite loci characterized in representatives from three of the endemic island populations. One locus, 12HDZ820 appears to be fixed in one population at an allele size not found in the other two. This microsatellite suite should be helpful in augmenting the marker selection currently available for Komodo Monitor population studies.     

Gene flow and melanism in garter snakes revisited: a comparison of molecular markers and island vs. coalescent models

Within populations, the stochastic effect of genetic drift and deterministic effect of natural selection are potentially weakened or altered by gene flow among populations. The influence of gene flow on Lake Erie populations of the common garter snake has been of particular interest because of a discontinuous colour pattern polymorphism (striped vs. melanistic) that is a target of natural selection. We reassessed the relative contributions of gene flow and genetic drift using genetic data and population size estimates. We compared all combinations of two marker systems and two analytical approaches to the estimation of gene flow rates: allozymes (data previously published), microsatellite DNA (new data), the island model ( F _ST-based approach), and a coalescence-based approach. For the coalescence approach, mutation rates and sampling effects were also investigated. While the two markers produced similar results, gene flow based on F _ST was considerably higher (Nm > 4) than that from the coalescence-based method (Nm < 1). Estimates of gene flow are likely to be inflated by lack of migration-drift equilibrium and changing population size. Potentially low rates of gene flow (Nm < 1), small population size at some sites, and positive correlations of number of microsatellite DNA alleles and island size and between M , mean ratio of number of alleles to range in allele size, and island size suggest that in addition to selection, random genetic drift may influence colour pattern frequencies. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 79, 389–399.     

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.