The best of both worlds: Combining population genetic and quantitative genetic models.

Numerous traits under migration-selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be investigated, because studying the influence of a large number of small allelic effects on the maintenance of spatial polymorphism is mathematically challenging, due to the high complexity of the systems that arise. In particular, in the most simple case of a haploid population in a two-patch environment, while it is known from population genetics that polymorphism at a single major-effect locus is stable in the symmetric case, there exist no analytical predictions on how this polymorphism holds when a polygenic background also contributes to the trait. Here we propose to answer this question by introducing a new eco-evo methodology that allows us to take into account the combined contributions of a major-effect locus and of a quantitative background resulting from small-effect loci, where inheritance is encoded according to an extension to the infinitesimal model. In a regime of small variance contributed by the quantitative loci, we justify that traits are concentrated around the major alleles, according to a normal distribution, using new convex analysis arguments. This allows a reduction in the complexity of the system using a separation of time scales approach. We predict an undocumented phenomenon of loss of polymorphism at the major-effect locus despite strong selection for local adaptation, because the quantitative background slowly disrupts the rapidly established polymorphism at the major-effect locus, which is confirmed by individual-based simulations. Our study highlights how segregation of a quantitative background can greatly impact the dynamics of major-effect loci by provoking migrational meltdowns. We also provide a comprehensive toolbox designed to describe how to apply our method to more complex population genetic models.

Liking the good guys: amplifying local adaptation via the evolution of condition-dependent mate choice.

Local adaptation can be strengthened through a diversity of mechanisms that reduce gene flow between contrasting environments. Recent work revealed that mate choice could enhance local adaptation when females preferentially mate with locally adapted males and that such female preferences readily evolve, but the opposing effects of recombination, migration and costs of female preferences remain relatively unexplored. To investigate these effects, we develop a two-patch model with two genes, one influencing an ecological trait and one influencing female preferences, where both male signals and female preferences are allowed to depend on the match between an individual's ecological trait and the local environment (condition). Because trait variation is limited when migration is rare and the benefits of preferential mating are short-lived when migration is frequent, we find that female preferences for males in high condition spread most rapidly with intermediate levels of migration. Surprisingly, we find that preferences for locally adapted males spread fastest with higher recombination rates, which contrasts with earlier studies. This is because a stronger preference allele for locally adapted males can only get uncoupled from maladapted ecological alleles following migration through recombination. The effects of migration and recombination depend strongly on the condition of the males being chosen by females, but only weakly on the condition of the females doing the choosing, except when it comes to the costs of preference. Although costs always impede the spread of female preferences for locally adapted males, the impact is substantially lessened if costs are borne primarily by females in poor condition. The abundance of empirical examples of condition-dependent mate choice combined with our theoretical results suggests that the evolution of mate choice could commonly facilitate local adaptation in nature.

Why wait? Three mechanisms selecting for environment-dependent developmental delays.

Many species delay development unless particular environments or rare disturbance events occur. How can such a strategy be favoured over continued development? Typically, it is assumed that continued development (e.g. germination) is not advantageous in environments that have low juvenile/seedling survival (mechanism 1), either due to abiotic or competitive effects. However, it has not previously been shown how low early survival must be in order to favour environment-specific developmental delays for long-lived species. Using seed dormancy as an example of developmental delays, we identify a threshold level of seedling survival in 'bad' environments below which selection can favour germination that is limited to 'good' environments. This can be used to evaluate whether observed differences in seedling survival are sufficient to favour conditional germination. We also present mathematical models that demonstrate two other, often overlooked, mechanisms that can favour conditional germination in the absence of differences in seedling survival. Specifically, physiological trade-offs can make it difficult to have germination rates that are equally high in all environments (mechanism 2). We show that such trade-offs can either favour conditional germination or intermediate (mixed) strategies, depending on the trade-off shape. Finally, germination in every year increases the likelihood that some individuals are killed in population-scale disturbances before reproducing; it can thus be favourable to only germinate immediately after a disturbance (mechanism 3). We demonstrate how demographic data can be used to evaluate these selection pressures. By presenting these three mechanisms and the conditions that favour conditional germination in each case, we provide three hypotheses that can be tested as explanations for the evolution of environment-dependent developmental delays.

Loss-of-heterozygosity facilitates passage through Haldane's sieve for Saccharomyces cerevisiae undergoing adaptation.

Haldane's sieve posits that the majority of beneficial mutations that contribute to adaptation should be dominant, as these are the mutations most likely to establish and spread when rare. It has been argued, however, that if the dominance of mutations in their current and previous environments are correlated, Haldane's sieve could be eliminated. We constructed heterozygous lines of Saccharomyces cerevisiae containing single adaptive mutations obtained during exposure to the fungicide nystatin. Here we show that no clear dominance relationship exists across environments: mutations exhibited a range of dominance levels in a rich medium, yet were exclusively recessive under nystatin stress. Surprisingly, heterozygous replicates exhibited variable-onset rapid growth when exposed to nystatin. Targeted Sanger sequencing demonstrated that loss-of-heterozygosity (LOH) accounted for these growth patterns. Our experiments demonstrate that recessive beneficial mutations can avoid Haldane's sieve in clonal organisms through rapid LOH and thus contribute to rapid evolutionary adaptation.

Selective maintenance of recombination between the sex chromosomes.

A hallmark of many sex chromosomes is the dramatically reduced rate of recombination between them in the heterogametic sex (e.g. between the X and Y). Sexually antagonistic selection is thought to be the main selective driver of this reduced recombination, with tighter linkage strengthening the association between alleles favourable to females and the X, as well as alleles favourable to males and the Y. Nevertheless, many sex chromosomes retain substantial levels of recombination over millions of years, and some old sex chromosomes remain homomorphic with few signs of recombination suppression and the chromosomal degradation expected to follow. This paper explores the selective factors that can maintain recombination between the sex chromosomes. Specifically, by analysing the dynamics of genes that modify the rate of recombination, I present results demonstrating that certain forms of selection - all involving overdominance in males - can positively maintain recombination in the pseudo-autosomal region. To understand these cases, one has to revise our standard view of sexual antagonistic selection as involving two partners (males and females) to three partners (the X in females, the X in males and the Y).

Comparative analysis reveals that polyploidy does not decelerate diversification in fish.

While the proliferation of the species-rich teleost fish has been ascribed to an ancient genome duplication event at the base of this group, the broader impact of polyploidy on fish evolution and diversification remains poorly understood. Here, we investigate the association between polyploidy and diversification in several fish lineages: the sturgeons (Acipenseridae: Acipenseriformes), the botiid loaches (Botiidae: Cypriniformes), Cyprininae fishes (Cyprinidae: Cypriniformes) and the salmonids (Salmonidae: Salmoniformes). Using likelihood-based evolutionary methodologies, we co-estimate speciation and extinction rates associated with polyploid vs. diploid fish lineages. Family-level analysis of Acipenseridae and Botiidae revealed no significant difference in diversification rates between polyploid and diploid relatives, while analysis of the subfamily Cyprininae revealed higher polyploid diversification. Additionally, order-level analysis of the polyploid Salmoniformes and its diploid sister clade, the Esociformes, did not support a significantly different net diversification rate between the two groups. Taken together, our results suggest that polyploidy is generally not associated with decreased diversification in fish - a pattern that stands in contrast to that previously observed in plants. While there are notable differences in the time frame examined in the two studies, our results suggest that polyploidy is associated with different diversification patterns in these two major branches of the eukaryote tree of life.

The red queen coupled with directional selection favours the evolution of sex.

Why sexual reproduction has evolved to be such a widespread mode of reproduction remains a major question in evolutionary biology. Although previous studies have shown that increased sex and recombination can evolve in the presence of host-parasite interactions (the 'Red Queen hypothesis' for sex), many of these studies have assumed that multiple loci mediate infection vs. resistance. Data suggest, however, that a major locus is typically involved in antigen presentation and recognition. Here, we explore a model where only one locus mediates host-parasite interactions, but a second locus is subject to directional selection. Even though the effects of these genes on fitness are independent, we show that increased rates of sex and recombination are favoured at a modifier gene that alters the rate of genetic mixing. This result occurs because of selective interference in finite populations (the 'Hill-Robertson effect'), which also favours sex. These results suggest that the Red Queen hypothesis may help to explain the evolution of sex by contributing a form of persistent selection, which interferes with directional selection at other loci and thereby favours sex and recombination.

Haploids adapt faster than diploids across a range of environments.

Despite a great deal of theoretical attention, we have limited empirical data about how ploidy influences the rate of adaptation. We evolved isogenic haploid and diploid populations of Saccharomyces cerevisiae for 200 generations in seven different environments. We measured the competitive fitness of all ancestral and evolved lines against a common competitor and find that in all seven environments, haploid lines adapted faster than diploids, significantly so in three environments. We apply theory that relates the rates of adaptation and measured effective population sizes to the properties of beneficial mutations. We obtained rough estimates of the average selection coefficients in haploids between 2% and 10% for these first selected mutations. Results were consistent with semi-dominant to dominant mutations in four environments and recessive to additive mutations in two other environments. These results are consistent with theory that predicts haploids should evolve faster than diploids at large population sizes.

Mutating away from your enemies: the evolution of mutation rate in a host-parasite system.

The rate at which mutations occur in nature is itself under natural selection. While a general reduction of mutation rates is advantageous for species inhabiting constant environments, higher mutation rates can be advantageous for those inhabiting fluctuating environments that impose on-going directional selection. Analogously, species involved in antagonistic co-evolutionary arms races, such as hosts and parasites, can also benefit from higher mutation rates. We use modifier theory, combined with simulations, to investigate the evolution of mutation rate in such a host-parasite system. We derive an expression for the evolutionary stable mutation rate between two alleles, each of whose fitness depends on the current genetic composition of the other species. Recombination has been shown to weaken the strength of selection acting on mutation modifiers, and accordingly, we find that the evolutionarily attracting mutation rate is lower when recombination between the selected and the modifier locus is high. Cyclical dynamics are potentially commonplace for loci governing antagonistic species interactions. We characterize the parameter space where such cyclical dynamics occur and show that the evolution of large mutation rates tends to inhibit cycling and thus eliminates further selection on modifiers of the mutation rate. We then find using computer simulations that stochastic fluctuations in finite populations can increase the size of the region where cycles occur, creating selection for higher mutation rates. We finally use simulations to investigate the model behaviour when there are more than two alleles, finding that the region where cycling occurs becomes smaller and the evolutionarily attracting mutation rate lower when there are more alleles.

Can clone size serve as a proxy for clone age? An exploration using microsatellite divergence in Populus tremuloides.

In long-lived clonal plants, the overall size of a clone is often used to estimate clone age. The size of a clone, however, might be largely determined by physical or biotic interactions, obscuring the relationship between clone size and age. Here, we use the accumulation of mutations at 14 microsatellite loci to estimate clone age in trembling aspen (Populus tremuloides) from southwestern Canada. We show that the observed patterns of genetic divergence are consistent with a model of increasing ramet population size, allowing us to use pairwise genetic divergence as an estimator of clone age. In the populations studied, clone size did not exhibit a significant relationship with microsatellite divergence, indicating that clone size is not a good proxy for clone age. In P. tremuloides, the per-locus per-year neutral somatic mutation rate across 14 microsatellite loci was estimated to lie between 6 x 10(-7) (lower bound) and 4 x 10(-5) (upper bound).

Why have sex? The population genetics of sex and recombination.

One of the greatest puzzles in evolutionary biology is the high frequency of sexual reproduction and recombination. Given that individuals surviving to reproductive age have genomes that function in their current environment, why should they risk shuffling their genes with those of another individual? Mathematical models are especially important in developing predictions about when sex and recombination can evolve, because it is difficult to intuit the outcome of evolution with several interacting genes. Interestingly, theoretical analyses have shown that it is often quite difficult to identify conditions that favour the evolution of high rates of sex and recombination. For example, fitness interactions among genes (epistasis) can favour sex and recombination but only if such interactions are negative, relatively weak and not highly variable. One reason why an answer to the paradox of sex has been so elusive is that our models have focused unduly on populations that are infinite in size, unstructured and isolated from other species. Yet most verbal theories for sex and recombination consider a finite number of genotypes evolving in a biologically and/or physically complex world. Here, we review various hypotheses for why sex and recombination are so prevalent and discuss theoretical results indicating which of these hypotheses is most promising.

Phylogenetic analysis of the ecological correlates of dioecy in angiosperms.

We report on a phylogenetic analysis of correlations between the occurrence of dioecy and several ecological and life-history attributes: tropical distribution, woody growth form, abiotic pollination, small inconspicuous flowers and inflorescences, many-flowered inflorescences and fleshy fruits. Various hypotheses have been proposed to explain why associations occur between dioecy and several of these attributes, yet most assume that dioecy originates more often in clades with these traits than in clades with alternative character states. To investigate correlations between dioecy and these attributes, and to provide insights into the potential evolutionary pathways that have led to these associations, we assigned states of these traits to genera on a large-scale molecular phylogeny of the angiosperms; we then used maximum-likelihood analysis to analyse the presence of correlations and the sequence of acquisition of traits. Phylogenetic analysis revealed correlations between dioecy and six of the seven attributes; only many-flowered inflorescences exhibiting no association with the dioecious condition. The particular correlations that were revealed and the strength of the association differed among the three main monophyletic groups of angiosperms (Rosids, Asterids, and Eumagnoliids). Our analysis provided no general support for the hypothesis that dioecy is more likely to evolve in lineages already possessing the seven attributes we considered. Further analysis of the intercorrelations of the seven attributes provided evidence for non-independence between some of the traits, implying that functional associations among these traits have influenced the ecology and evolution of dioecious species.

The consequences of dioecy for seed dispersal: modeling the seed-shadow handicap.

Recent evidence has suggested that clades of dioecious angiosperms have fewer extant species on average than those of cosexual (hermaphroditic and monoecious) relatives. Reasons for the decrease in speciation rates and/or increase in extinction rates are only beginning to be investigated. One possibility is that dioecious species suffer a competitive disadvantage with cosexuals because only half of the individuals in a dioecious population are seed bearing. When only females produce seed, offspring will be more spatially clumped and will experience more local resource competition than when every individual produces seed. We examine two spatially explicit models to determine the effect of a reduction in seed dispersers on the invasibility and persistence of dioecious populations. Even though dioecious females were allowed to produce twice as many seeds as cosexuals, our results show that a reduction in the number of seed dispersers causes a decrease in the ability of dioecious progeny to find uninhabited sites, thus reducing persistence times. These results suggest that the maintenance of dioecy in the presence of hermaphroditic competitors requires a substantial increase in relative fitness and/or a large dispersal advantage of dioecious seeds.

Masking and purging mutations following EMS treatment in haploid, diploid and tetraploid yeast (Saccharomyces cerevisiae).

The yeast, Saccharomyces cerevisiae, was used as a model to investigate theories of ploidy evolution. Mutagenesis experiments using the alkylating agent EMS (ethane methyl sulphonate) were conducted to assess the relative importance that masking of deleterious mutations has on response to and recovery from DNA damage. In particular, we tested whether cells with higher ploidy levels have relatively higher fitnesses after mutagenesis, whether the advantages of masking are more pronounced in tetraploids than in diploids, and whether purging of mutations allows more rapid recovery of haploid cells than cells with higher ploidy levels. Separate experiments were performed on asexually propagating stationary phase cells using (1) prototrophic haploid (MAT alpha) and diploid (MATa/alpha) strains and (2) isogenic haploid, diploid and tetraploid strains lacking a functional mating type locus. In both sets of experiments, haploids showed a more pronounced decrease in apparent growth rate than diploids, but both haploids and diploids appeared to recover very rapidly. Tetraploids did not show increased benefits of masking compared with diploids but volume measurements and FACScan analyses on the auxotrophic strains indicated that all treated tetraploid strains decreased in ploidy level and that some of the treated haploid lines increased in ploidy level. Results from these experiments confirm that while masking deleterious mutations provides an immediate advantage to higher ploidy levels in the presence of mutagens, selection is extremely efficient at removing induced mutations, leading growth rates to increase rapidly over time at all ploidy levels. Furthermore, ploidy level is itself a mutable trait in the presence of EMS, with both haploids and tetraploids often evolving towards diploidy (the ancestral state of S. cerevisiae) during the course of the experiment.

Selection for recombination in small populations.

The reasons that sex and recombination are so widespread remain elusive. One popular hypothesis is that sex and recombination promote adaptation to a changing environment. The strongest evidence that increased recombination may evolve because recombination promotes adaptation comes from artificially selected populations. Recombination rates have been found to increase as a correlated response to selection on traits unrelated to recombination in several artificial selection experiments and in a comparison of domesticated and nondomesticated mammals. There are, however, several alternative explanations for the increase in recombination in such populations, including two different evolutionary explanations. The first is that the form of selection is epistatic, generating linkage disequilibria among selected loci, which can indirectly favor modifier alleles that increase recombination. The second is that random genetic drift in selected populations tends to generate disequilibria such that beneficial alleles are often found in different individuals; modifier alleles that increase recombination can bring together such favorable alleles and thus may be found in individuals with greater fitness. In this paper, we compare the evolutionary forces acting on recombination in finite populations subject to strong selection. To our surprise, we found that drift accounted for the majority of selection for increased recombination observed in simulations of small to moderately large populations, suggesting that, unless selected populations are large, epistasis plays a secondary role in the evolution of recombination.

Detecting the undetected: estimating the total number of loci underlying a quantitative trait.

Recent studies have begun to reveal the genes underlying quantitative trait differences between closely related populations. Not all quantitative trait loci (QTL) are, however, equally likely to be detected. QTL studies involve a limited number of crosses, individuals, and genetic markers and, as a result, often have little power to detect genetic factors of small to moderate effects. In this article, we develop an estimator for the total number of fixed genetic differences between two parental lines. Like the Castle-Wright estimator, which is based on the observed segregation variance in classical crossbreeding experiments, our QTL-based estimator requires that a distribution be specified for the expected effect sizes of the underlying loci. We use this expected distribution and the observed mean and minimum effect size of the detected QTL in a likelihood model to estimate the total number of loci underlying the trait difference. We then test the QTL-based estimator and the Castle-Wright estimator in Monte Carlo simulations. When the assumptions of the simulations match those of the model, both estimators perform well on average. The 95% confidence limits of the Castle-Wright estimator, however, often excluded the true number of underlying loci, while the confidence limits for the QTL-based estimator typically included the true value approximately 95% of the time. Furthermore, we found that the QTL-based estimator was less sensitive to dominance and to allelic effects of opposite sign than the Castle-Wright estimator. We therefore suggest that the QTL-based estimator be used to assess how many loci may have been missed in QTL studies.

Detecting the form of selection from DNA sequence data.

Clues to our evolutionary history lie hidden within DNA sequence data. One of the great challenges facing population geneticists is to identify and accurately interpret these clues. This task is made especially difficult by the fact that many different evolutionary processes can lead to similar observations. For example, low levels of polymorphism within a region can be explained by a low local mutation rate, by selection having eliminated deleterious mutations, or by the recent spread to fixation of a beneficial allele. Theoretical advances improve our ability to distinguish signals left by different evolutionary processes. In particular, a new test might better detect the footprint of selection having favored the spread of a beneficial allele.

Compensating for our load of mutations: freezing the meltdown of small populations.

We have investigated the reduction of fitness caused by the fixation of new deleterious mutations in small populations within the framework of Fisher's geometrical model of adaptation. In Fisher's model, a population evolves in an n-dimensional character space with an adaptive optimum at the origin. The model allows us to investigate compensatory mutations, which restore fitness losses incurred by other mutations, in a context-dependent manner. We have conducted a moment analysis of the model, supplemented by the numerical results of computer simulations. The mean reduction of fitness (i.e., expected load) scaled to one is approximately n/(n+2Ne), where Ne is the effective population size. The reciprocal relationship between the load and Ne implies that the fixation of deleterious mutations is unlikely to cause extinction when there is a broad scope for compensatory mutations, except in very small populations. Furthermore, the dependence of load on n implies that pleiotropy plays a large role in determining the extinction risk of small populations. Differences and similarities between our results and those of a previous study on the effects of Ne and n are explored. That the predictions of this model are qualitatively different from studies ignoring compensatory mutations implies that we must be cautious in predicting the evolutionary fate of small populations and that additional data on the nature of mutations is of critical importance.

Polyploid incidence and evolution.

Changes in ploidy occurred early in the diversification of some animal and plant lineages and represent an ongoing phenomenon in others. While the prevalence of polyploid lineages indicates that this phenomenon is a common and successful evolutionary transition, whether polyploidization itself has a significant effect on patterns and rates of diversification remains an open question. Here we review evidence for the creative role of polyploidy in evolution. We present new estimates for the incidence of polyploidy in ferns and flowering plants based on a simple model describing transitions between odd and even base chromosome numbers. These new estimates indicate that ploidy changes may represent from 2 to 4% of speciation events in flowering plants and 7% in ferns. Speciation via polyploidy is likely to be one of the more predominant modes of sympatric speciation in plants, owing to its potentially broad-scale effects on gene regulation and developmental processes, effects that can produce immediate shifts in morphology, breeding system, and ecological tolerances. Theoretical models support the potential for increased adaptability in polyploid lineages. The evidence suggests that polyploidization can produce shifts in genetic systems and phenotypes that have the potential to result in increased evolutionary diversification, yet conclusive evidence that polyploidy has changed rates and patterns of diversification remains elusive.