Fixation probability and time in subdivided populations

Limits to the rate of adaptive substitution in sexual populations

In large populations, many beneficial mutations may be simultaneously available and may compete with one another, slowing adaptation. By finding the probability of fixation of a favorable allele in a simple model of a haploid sexual population, we find limits to the rate of adaptive substitution, Λ, that depend on simple parameter combinations. When variance in fitness is low and linkage is loose, the baseline rate of substitution is Λ₀ = 2NU , where N is the population size, U is the rate of beneficial mutations per genome, and is their mean selective advantage. Heritable variance v in log fitness due to unlinked loci reduces Λ by e⁻⁴(v) under polygamy and e⁻⁸ (v) under monogamy. With a linear genetic map of length R Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on s, N, U, and R only through the baseline density: Λ/R = F (Λ₀/R). Under the approximation that the interference due to different sweeps adds up, we show that Λ/R ~(Λ₀/R) / (1 +2Λ₉/R) , implying that interference prevents the rate of adaptive substitution from exceeding one per centimorgan per 200 generations. Simulations and numerical calculations confirm the scaling argument and confirm the additive approximation for Λ₀/R ~ 1; for higher Λ₀/R , the rate of adaptation grows above R/2, but only very slowly. We also consider the effect of sweeps on neutral diversity and show that, while even occasional sweeps can greatly reduce neutral diversity, this effect saturates as sweeps become more common-diversity can be maintained even in populations experiencing very strong interference. Our results indicate that for some organisms the rate of adaptive substitution may be primarily recombination-limited, depending only weakly on the mutation supply and the strength of selection.

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Detecting the molecular signature of social conflict: theory and a test with bacterial quorum sensing genes

Extending social evolution theory to the molecular level opens the door to an unparalleled abundance of data and statistical tools for testing alternative hypotheses about the long-term evolutionary dynamics of cooperation and conflict. To this end, we take a collection of known sociality genes (bacterial quorum sensing [QS] genes), model their evolution in terms of patterns that are detectable using gene sequence data, and then test model predictions using available genetic data sets. Specifically, we test two alternative hypotheses of social conflict: (1) the "adaptive" hypothesis that cheaters are maintained in natural populations by frequency-dependent balancing selection as an evolutionarily stable strategy and (2) the "evolutionary null" hypothesis that cheaters are opposed by purifying kin selection yet exist transiently because of their recurrent introduction into populations by mutation (i.e., kin selection-mutation balance). We find that QS genes have elevated within- and among-species sequence variation, nonsignificant signatures of natural selection, and putatively small effect sizes of mutant alleles, all patterns predicted by our evolutionary null model but not by the stable cheater hypothesis. These empirical findings support our theoretical prediction that QS genes experience relaxed selection due to nonclonality of social groups, conditional expression, and the individual-level advantage enjoyed by cheaters. Furthermore, cheaters are evolutionarily transient, persisting in populations because of their recurrent introduction by mutation and not because they enjoy a frequency-dependent fitness advantage.

Population subdivision and adaptation in asexual populations of Saccharomyces cerevisiae

Population subdivision limits competition between individuals, which can have a profound effect on adaptation. Subdivided populations maintain more genetic diversity at any given time compared to well-mixed populations, and thus "explore" larger parts of the genotype space. At the same time, beneficial mutations take longer to spread in such populations, and thus subdivided populations do not "exploit" discovered mutations as efficiently as well-mixed populations. Whether subdivision inhibits or promotes adaptation in a given environment depends on the relative importance of exploration versus exploitation, which in turn depends on the structure of epistasis among beneficial mutations. Here we investigate the relative importance of exploration versus exploitation for adaptation by evolving 976 independent asexual populations of budding yeast with several degrees of geographic subdivision. We find that subdivision systematically inhibits adaptation: even the luckiest demes in subdivided populations on average fail to discover genotypes that are fitter than those discovered by well-mixed populations. Thus, exploitation of discovered mutations is more important for adaptation in our system than a thorough exploration of the mutational neighborhood, and increasing subdivision slows adaptation.

Slow but not low: genomic comparisons reveal slower evolutionary rate and higher dN/dS in conifers compared to angiosperms

BACKGROUND

Comparative genomics can inform us about the processes of mutation and selection across diverse taxa. Among seed plants, gymnosperms have been lacking in genomic comparisons. Recent EST and full-length cDNA collections for two conifers, Sitka spruce (Picea sitchensis) and loblolly pine (Pinus taeda), together with full genome sequences for two angiosperms, Arabidopsis thaliana and poplar (Populus trichocarpa), offer an opportunity to infer the evolutionary processes underlying thousands of orthologous protein-coding genes in gymnosperms compared with an angiosperm orthologue set.

RESULTS

Based upon pairwise comparisons of 3,723 spruce and pine orthologues, we found an average synonymous genetic distance (dS) of 0.191, and an average dN/dS ratio of 0.314. Using a fossil-established divergence time of 140 million years between spruce and pine, we extrapolated a nucleotide substitution rate of 0.68 × 10(-9) synonymous substitutions per site per year. When compared to angiosperms, this indicates a dramatically slower rate of nucleotide substitution rates in conifers: on average 15-fold. Coincidentally, we found a three-fold higher dN/dS for the spruce-pine lineage compared to the poplar-Arabidopsis lineage. This joint occurrence of a slower evolutionary rate in conifers with higher dN/dS, and possibly positive selection, showcases the uniqueness of conifer genome evolution.

CONCLUSIONS

Our results are in line with documented reduced nucleotide diversity, conservative genome evolution and low rates of diversification in conifers on the one hand and numerous examples of local adaptation in conifers on the other hand. We propose that reduced levels of nucleotide mutation in large and long-lived conifer trees, coupled with large effective population size, were the main factors leading to slow substitution rates but retention of beneficial mutations.

Genetic drift widens the expected cline but narrows the expected cline width

Random genetic drift shifts clines in space, alters their width, and distorts their shape. Such random fluctuations complicate inferences from cline width and position. Notably, the effect of genetic drift on the expected shape of the cline is opposite to the naive (but quite common) misinterpretation of classic results on the expected cline. While random drift on average broadens the overall cline in expected allele frequency, it narrows the width of any particular cline. The opposing effects arise because locally, drift drives alleles to fixation--but fluctuations in position widen the expected cline. The effect of genetic drift can be predicted from standardized variance in allele frequencies, averaged across the habitat: . A cline maintained by spatially varying selection (step change) is expected to be narrower by a factor of √1- relative to the cline in the absence of drift. The expected cline is broader by the inverse of this factor. In a tension zone maintained by underdominance, the expected cline width is narrower by about 1- relative to the width in the absence of drift. Individual clines can differ substantially from the expectation, and we give quantitative predictions for the variance in cline position and width. The predictions apply to clines in almost one-dimensional circumstances such as hybrid zones in rivers, deep valleys, or along a coast line and give a guide to what patterns to expect in two dimensions.

On the fixation process of a beneficial mutation in a variable environment

A population that adapts to gradual environmental change will typically experience temporal variation in its population size and the selection pressure. On the basis of the mathematical theory of inhomogeneous branching processes, we present a framework to describe the fixation process of a single beneficial allele under these conditions. The approach allows for arbitrary time-dependence of the selection coefficient s(t) and the population size N(t), as may result from an underlying ecological model. We derive compact analytical approximations for the fixation probability and the distribution of passage times for the beneficial allele to reach a given intermediate frequency. We apply the formalism to several biologically relevant scenarios, such as linear or cyclic changes in the selection coefficient, and logistic population growth. Comparison with computer simulations shows that the analytical results are accurate for a large parameter range, as long as selection is not very weak.

Heterosis and inbreeding depression in bottlenecked populations: a test in the hermaphroditic freshwater snail Lymnaea stagnalis

Small population size is expected to induce heterosis, due to the random fixation and accumulation of mildly deleterious mutations, whereas within-population inbreeding depression should decrease due to increased homozygosity. Population bottlenecks, although less effective, may have similar consequences. We tested this hypothesis in the self-fertile freshwater snail Lymnaea stagnalis, by subjecting experimental populations to a single bottleneck of varied magnitude. Although patterns were not strong, heterosis was significant in the most severely bottlenecked populations, under stressful conditions. This was mainly due to hatching rate, suggesting that early acting and highly deleterious alleles were involved. Although L. stagnalis is a preferential outcrosser, inbreeding depression was very low and showed no clear relationship with bottleneck size. In the less reduced populations, inbreeding depression for hatching success increased under high inbreeding. This may be consistent with the occurence of synergistic epistasis between fitness loci, which may contribute to favour outcrossing in L. stagnalis.

Accumulation of beneficial mutations in one dimension

When beneficial mutations are relatively common, competition between multiple unfixed mutations can reduce the rate of fixation in well-mixed asexual populations. We introduce a one-dimensional model with a steady accumulation of beneficial mutations. We find a transition between periodic selection and multiple-mutation regimes. In the multiple-mutation regime, the increase of fitness along the lattice bears a striking similarity to surface growth phenomena, with power-law growth and saturation of the interface width. We also find significant differences compared to the well-mixed model. In our lattice model, the transition between regimes happens at a much lower mutation rate due to slower fixation times in one dimension. Also, the rate of fixation is reduced with increasing mutation rate due to the more intense competition, and it saturates with large population size.

Effective population size is positively correlated with levels of adaptive divergence among annual sunflowers

The role of adaptation in the divergence of lineages has long been a central question in evolutionary biology, and as multilocus sequence data sets have become available for a wide range of taxa, empirical estimates of levels of adaptive molecular evolution are increasingly common. Estimates vary widely among taxa, with high levels of adaptive evolution in Drosophila, bacteria, and viruses but very little evidence of widespread adaptive evolution in hominids. Although estimates in plants are more limited, some recent work has suggested that rates of adaptive evolution in a range of plant taxa are surprisingly low and that there is little association between adaptive evolution and effective population size in contrast to patterns seen in other taxa. Here, we analyze data from 35 loci for six sunflower species that vary dramatically in effective population size. We find that rates of adaptive evolution are positively correlated with effective population size in these species, with a significant fraction of amino acid substitutions driven by positive selection in the species with the largest effective population sizes but little or no evidence of adaptive evolution in species with smaller effective population sizes. Although other factors likely contribute as well, in sunflowers effective population size appears to be an important determinant of rates of adaptive evolution.

Origin of the fittest: link between emergent variation and evolutionary change as a critical question in evolutionary biology

In complex organisms, neutral evolution of genomic architecture, associated compensatory interactions in protein networks and emergent developmental processes can delineate the directions of evolutionary change, including the opportunity for natural selection. These effects are reflected in the evolution of developmental programmes that link genomic architecture with a corresponding functioning phenotype. Two recent findings call for closer examination of the rules by which these links are constructed. First is the realization that high dimensionality of genotypes and emergent properties of autonomous developmental processes (such as capacity for self-organization) result in the vast areas of fitness neutrality at both the phenotypic and genetic levels. Second is the ubiquity of context- and taxa-specific regulation of deeply conserved gene networks, such that exceptional phenotypic diversification coexists with remarkably conserved generative processes. Establishing the causal reciprocal links between ongoing neutral expansion of genomic architecture, emergent features of organisms' functionality, and often precisely adaptive phenotypic diversification therefore becomes an important goal of evolutionary biology and is the latest reincarnation of the search for a framework that links development, functioning and evolution of phenotypes. Here I examine, in the light of recent empirical advances, two evolutionary concepts that are central to this framework-natural selection and inheritance-the general rules by which they become associated with emergent developmental and homeostatic processes and the role that they play in descent with modification.

Wind pollination over mesoscale distances: an investigation with Scots pine

There is a gap between the order of magnitude of maximum documented distances of airborne tree pollen transport (up to 10(2)-10(3) km) and effective wind pollination (up to 10(1) km), which may partly derive from greater difficulties in detecting the latter. This study aims to assess wind pollination over scales closer to the maximum observed physical pollen transport distances. The origin of effective pollen immigrants into a strongly isolated Iberian Pinus sylvestris remnant was investigated using paternally inherited microsatellite markers and maximum-likelihood estimation combined with Monte Carlo assessment of parameter uncertainty. The results revealed significant effective pollen flow (up to 4.4%) from a large population located 100 km away, suggesting that the well-known mesoscale airborne transport of viable pine pollen can result in successful pollination over larger scales than previously reported for wind-pollinated tree species. This study supports the view that the gap between documented potential and effective wind pollen dispersal scales might not accurately reflect biological reality. Expanding the expected range of effective wind pollination has an impact on the assessment of a wide range of ecological and evolutionary processes, including reproductive assurance on fragmentation or colonization, metapopulation connectivity and interactions with local adaptation in heterogeneous habitats.

Heterozygosity-fitness correlations among wild populations of European tree frog (Hyla arborea) detect fixation load

Quantifying the impacts of inbreeding and genetic drift on fitness traits in fragmented populations is becoming a major goal in conservation biology. Such impacts occur at different levels and involve different sets of loci. Genetic drift randomly fixes slightly deleterious alleles leading to different fixation load among populations. By contrast, inbreeding depression arises from highly deleterious alleles in segregation within a population and creates variation among individuals. A popular approach is to measure correlations between molecular variation and phenotypic performances. This approach has been mainly used at the individual level to detect inbreeding depression within populations and sometimes at the population level but without consideration about the genetic processes measured. For the first time, we used in this study a molecular approach considering both the interpopulation and intrapopulation level to discriminate the relative importance of inbreeding depression vs. fixation load in isolated and non-fragmented populations of European tree frog (Hyla arborea), complemented with interpopulational crosses. We demonstrated that the positive correlations observed between genetic heterozygosity and larval performances on merged data were mainly caused by co-variations in genetic diversity and fixation load among populations rather than by inbreeding depression and segregating deleterious alleles within populations. Such a method is highly relevant in a conservation perspective because, depending on how populations lose fitness (inbreeding vs. fixation load), specific management actions may be designed to improve the persistence of populations.

Nonadaptive processes in primate and human evolution

Evolutionary biology has tended to focus on adaptive evolution by positive selection as the primum mobile of evolutionary trajectories in species while underestimating the importance of nonadaptive evolutionary processes. In this review, I describe evidence that suggests that primate and human evolution has been strongly influenced by nonadaptive processes, particularly random genetic drift and mutation. This is evidenced by three fundamental effects: a relative relaxation of selective constraints (i.e., purifying selection), a relative increase in the fixation of slightly deleterious mutations, and a general reduction in the efficacy of positive selection. These effects are observed in protein-coding, regulatory regions, and in gene expression data, as well as in an augmentation of fixation of large-scale mutations, including duplicated genes, mobile genetic elements, and nuclear mitochondrial DNA. The evidence suggests a general population-level explanation such as a reduction in effective population size (N(e)). This would have tipped the balance between the evolutionary forces of natural selection and random genetic drift toward genetic drift for variants having small selective effects. After describing these proximate effects, I describe the potential consequences of these effects for primate and human evolution. For example, an increase in the fixation of slightly deleterious mutations could potentially have led to an increase in the fixation rate of compensatory mutations that act to suppress the effects of slightly deleterious substitutions. The potential consequences of compensatory evolution for the evolution of novel gene functions and in potentially confounding the detection of positively selected genes are explored. The consequences of the passive accumulation of large-scale genomic mutations by genetic drift are unclear, though evidence suggests that new gene copies as well as insertions of transposable elements into genes can potentially lead to adaptive phenotypes. Finally, because a decrease in selective constraint at the genetic level is expected to have effects at the morphological level, I review studies that compare rates of morphological change in various mammalian and island populations where N(e) is reduced. Furthermore, I discuss evidence that suggests that craniofacial morphology in the Homo lineage has shifted from an evolutionary rate constrained by purifying selection toward a neutral evolutionary rate.

Fixation of a deleterious allele under mutation pressure and finite selection intensity

The mean fixation time of a deleterious mutant allele is studied beyond the diffusion approximation. As in Kimura's classical work [M. Kimura, Proc. Natl. Acad. Sci. USA. 77, 522 (1980)], that was motivated by the problem of fixation in the presence of amorphic or hypermorphic mutations, we consider a diallelic model at a single locus comprising a wild-type A and a mutant allele A' produced irreversibly from A at small uniform rate v. The relative fitnesses of the mutant homozygotes A'A', mutant heterozygotes A'A and wild-type homozygotes AA are 1-s, 1-h and 1, respectively, where it is assumed that v<<s. Here, we employ a WKB theory and directly treat the underlying Markov chain (formulated as a birth-death process) obeyed by the allele frequency (whose dynamics is prescribed by the Moran model). Importantly, this approach allows to accurately account for effects of large fluctuations. After a general description of the theory, we focus on the case of a deleterious mutant allele (i.e. s>0) and discuss three situations: when the mutant is (i) completely dominant (s=h); (ii) completely recessive (h=0), and (iii) semi-dominant (h=s/2). Our theoretical predictions for the mean fixation time and the quasi-stationary distribution of the mutant population in the coexistence state, are shown to be in excellent agreement with numerical simulations. Furthermore, when s is finite, we demonstrate that our results are superior to those of the diffusion theory, while the latter is shown to be an accurate approximation only when N(e)s(2)<<1, where N(e) is the effective population size.

G'ST and D do not replace FST

The genetic differentiation among populations is affected by mutation as well as by migration, drift and selection. For loci with high mutation rates, such as microsatellites, the amount of mutation can influence the values of indices of differentiation such as G(ST) and F(ST). For many purposes, this effect is undesirable, and as a result, new indices such as G'(ST) and D have been proposed to measure population differentiation. This paper shows that these new indices are not effective measures of the causes or consequences of population structure. Both G'(ST) and D depend heavily on mutation rate, but both are insensitive to any population genetic process when the mutation rate is high relative to the migration rate. Furthermore, D is specific to the locus being measured, and so little can be inferred about the population demography from D. However, at equilibrium, D may provide an index of whether a particular marker is more strongly affected by mutation than by migration. I argue that F(ST) is a more important summary of the effects of population structure than D and that R(ST) or other measures that explicitly account for the mutation process are much better than G(ST), G'(ST), or D for highly mutable markers. Markers with lower mutation rates will often be easier to interpret.

Fitness effects of derived deleterious mutations in four closely related wild tomato species with spatial structure

A key issue in evolutionary biology is an improved understanding of the genetic mechanisms by which species adapt to various environments. Using DNA sequence data, it is possible to quantify the number of adaptive and deleterious mutations, and the distribution of fitness effects of new mutations (its mean and variance) by simultaneously taking into account the demography of a given species. We investigated how selection functions at eight housekeeping genes of four closely related, outcrossing species of wild tomatoes that are native to diverse environments in western South America (Solanum arcanum, S. chilense, S. habrochaites and S. peruvianum). We found little evidence for adaptive mutations but pervasive evidence for strong purifying selection in coding regions of the four species. In contrast, the strength of purifying selection seems to vary among the four species in non-coding (NC) regions (introns). Using F(ST)-based measures of fixation in subdivided populations, we suggest that weak purifying selection has affected the NC regions of S. habrochaites, S. chilense and S. peruvianum. In contrast, NC regions in S. arcanum show a distribution of fitness effects with mutations being either nearly neutral or very strongly deleterious. These results suggest that closely related species with similar genetic backgrounds but experiencing contrasting environments differ in the variance of deleterious fitness effects.

Geographical variation in postzygotic isolation and its genetic basis within and between two Mimulus species

The aim of this study is to investigate the evolution of intrinsic postzygotic isolation within and between populations of Mimulus guttatus and Mimulus nasutus. We made 17 intraspecific and interspecific crosses, across a wide geographical scale. We examined the seed germination success and pollen fertility of reciprocal F(1) and F(2) hybrids and their pure-species parents, and used biometrical genetic tests to distinguish among alternative models of inheritance. Hybrid seed inviability was sporadic in both interspecific and intraspecific crosses. For several crosses, Dobzhansky-Muller incompatibilities involving nuclear genes were implicated, while two interspecific crosses revealed evidence of cytonuclear interactions. Reduced hybrid pollen fertility was found to be greatly influenced by Dobzhansky-Muller incompatibilities in five out of six intraspecific crosses and nine out of 11 interspecific crosses. Cytonuclear incompatibilities reduced hybrid fitness in only one intraspecific and one interspecific cross. This study suggests that intrinsic postzygotic isolation is common in hybrids between these Mimulus species, yet the particular hybrid incompatibilities responsible for effecting this isolation differ among the populations tested. Hence, we conclude that they evolve and spread only at the local scale.

Evolution in heterogeneous populations: from migration models to fixation probabilities

Although dispersal is recognized as a key issue in several fields of population biology (such as behavioral ecology, population genetics, metapopulation dynamics or evolutionary modeling), these disciplines focus on different aspects of the concept and often make different implicit assumptions regarding migration models. Using simulations, we investigate how such assumptions translate into effective gene flow and fixation probability of selected alleles. Assumptions regarding migration type (e.g. source-sink, resident pre-emption, or balanced dispersal) and patterns (e.g. stepping-stone versus island dispersal) have large impacts when demes differ in sizes or selective pressures. The effects of fragmentation, as well as the spatial localization of newly arising mutations, also strongly depend on migration type and patterns. Migration rate also matters: depending on the migration type, fixation probabilities at an intermediate migration rate may lie outside the range defined by the low- and high-migration limits when demes differ in sizes. Given the extreme sensitivity of fixation probability to characteristics of dispersal, we underline the importance of making explicit (and documenting empirically) the crucial ecological/ behavioral assumptions underlying migration models.

Spatial-temporal stratifications in natural populations and how they affect understanding and estimation of effective population size

The concept of effective population size (N(e) ) is based on an elegantly simple idea which, however, rapidly becomes very complex when applied to most real-world situations. In natural populations, spatial and temporal stratifications create different classes of individuals with different vital rates, and this in turn affects (generally reduces) N(e) in complex ways. I consider how these natural stratifications influence our understanding of effective size and how to estimate it, and what the consequences are for conservation and management of natural populations. Important points that emerge include the following: 1  The relative influences of local vs metapopulation N(e) depend on a variety of factors, including the time frame of interest. 2  Levels of diversity in local populations are strongly influenced by even low levels of migration, so these measures are not reliable indicators of local N(e) . 3  For long-term effective size, obtaining a reliable estimate of mutation rate is the most important consideration; unless this is accomplished, estimates can be biased by orders of magnitude. 4  At least some estimators of contemporary N(e) appear to be robust to relatively high (approximately 10%) equilibrium levels of migration, so under many realistic scenarios they might yield reliable estimates of local N(e) . 5  Age structure probably has little effect on long-term estimators of N(e) but can strongly influence contemporary estimates. 6  More research is needed in several key areas: (i) to disentangle effects of selection and drift in metapopulations connected by intermediate levels of migration; (ii) to elucidate the relationship between N(b) (effective number of breeders per year) and N(e) per generation in age-structured populations; (iii) to perform rigorous sensitivity analyses of new likelihood and coalescent-based methods for estimating demographic and evolutionary histories.

Assortative mating and mutation diffusion in spatial evolutionary systems

The influence of spatial structure on the equilibrium properties of a sexual population model defined on networks is studied numerically. Using a small-world-like topology of the networks as an investigative tool, the contributions to the fitness of assortative mating and of global mutant spread properties are considered. Simple measures of nearest-neighbor correlations and speed of spread of mutants through the system have been used to confirm that both of these dynamics are important contributory factors to the fitness. It is found that assortative mating increases the fitness of populations. Quick global spread of favorable mutations is shown to be a key factor increasing the equilibrium fitness of populations.

Inbreeding depression affects life-history traits but not infection by Plasmodium gallinaceum in the Asian tiger mosquito, Aedes albopictus

Emerging and re-emerging vector-borne diseases represent an increasingly significant public health challenge. While geographic variation among populations of vector species for susceptibility to pathogen infection and vector competence has been thoroughly documented, relatively little attention has been devoted to understanding the ultimate evolutionary causes of this intraspecific variation. Local genetic drift is known to influence genetic differentiation among populations for a variety of container-inhabiting mosquito species, including Aedes albopictus. Because genetic drift is expected to reduce genetic variation and lead to the accumulation of (partially) recessive deleterious alleles, we hypothesized that reduced genetic variation might affect susceptibility to pathogen infection in a model pathogen-vector system. We therefore created replicate inbred (two generations of full-sib mating, expected f=0.375) and control (expected f approximately 0.07) lines of Ae. albopictus and measured life-history traits including larval survivorship, adult longevity, and female wing length (body size) as well as susceptibility to infection by a model pathogen, Plasmodium gallinaceum. Inbred mosquitoes had significantly reduced larval survivorship and female adult longevity but inbreeding did not affect male adult longevity or female wing length (body size). Furthermore, there was no effect of inbreeding on susceptibility to infection by P. gallinaceum. Therefore, while our results did not support the hypothesis that reduced genetic variation influences susceptibility to pathogen infection in this system, we did find evidence for an effect of reduced genetic variation on female adult longevity, an important component of vectorial capacity. We suggest that additional research is needed to elucidate the genetic underpinnings of intraspecific variation in traits related to disease transmission and discuss the implications of our results for the efficacy of creating transgenic strains refractory to disease transmission.

Genome wide analyses reveal little evidence for adaptive evolution in many plant species

The relative contribution of advantageous and neutral mutations to the evolutionary process is a central problem in evolutionary biology. Current estimates suggest that whereas Drosophila, mice, and bacteria have undergone extensive adaptive evolution, hominids show little or no evidence of adaptive evolution in protein-coding sequences. This may be a consequence of differences in effective population size. To study the matter further, we have investigated whether plants show evidence of adaptive evolution using an extension of the McDonald-Kreitman test that explicitly models slightly deleterious mutations by estimating the distribution of fitness effects of new mutations. We apply this method to data from nine pairs of species. Altogether more than 2,400 loci with an average length of approximately 280 nucleotides were analyzed. We observe very similar results in all species; we find little evidence of adaptive amino acid substitution in any comparison except sunflowers. This may be because many plant species have modest effective population sizes.

Genome-wide evidence for efficient positive and purifying selection in Capsella grandiflora, a plant species with a large effective population size

Recent studies comparing genome-wide polymorphism and divergence in Drosophila have found evidence for a surprisingly high proportion of adaptive amino acid fixations, but results for other taxa are mixed. In particular, few studies have found convincing evidence for adaptive amino acid substitution in plants. To assess the generality of this finding, we have sequenced 257 loci in the outcrossing crucifer Capsella grandiflora, which has a large effective population size and low population structure. Using a new method that jointly infers selective and demographic effects, we estimate that 40% of amino acid substitutions were fixed by positive selection in this species, and we also infer a low proportion of slightly deleterious amino acid mutations. We contrast these estimates with those for a similar data set from the closely related Arabidopsis thaliana and find significantly higher rates of adaptive evolution and fewer nearly neutral mutations in C. grandiflora. In agreement with results for other taxa, genes involved in reproduction show the strongest evidence for positive selection in C. grandiflora. Taken together, these results imply that both positive and purifying selection are more effective in C. grandiflora than in A. thaliana, consistent with the contrasting demographic history and effective population sizes of these species.

A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates

Background

The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology.

Methods

The equation [p = 1 - (1 - (1 - (1 - u)^d)^k)^Nm ] calculates the probability of cancer (p) and contains five parameters: the number of divisions (d), the number of stem cells (N × m), the number of critical rate-limiting pathway driver mutations (k), and the mutation rate (u). In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell.

Results

When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk.

Conclusions

The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.

The dynamics of mutations associated with anti-malarial drug resistance in Plasmodium falciparum

The evolution of resistance in Plasmodium falciparum against safe and affordable drugs such as chloroquine (CQ) and sulfadoxine-pyrimethamine (SP) is a major global health threat. Investigating the dynamics of resistance against these antimalarial drugs will lead to approaches for addressing the problem of resistance in malarial parasites that are solidly based in evolutionary genetics and population biology. In this article, we discuss current developments in population biology modeling and evolutionary genetics. Despite great advancements achieved in the past decade, understanding the complex dynamics of mutations conferring drug resistance in P. falciparum requires approaches that consider the parasite population structure among other demographic processes.

A quantitative survey of local adaptation and fitness trade-offs

The long history of reciprocal transplant studies testing the hypothesis of local adaptation has shown that populations are often adapted to their local environments. Yet many studies have not demonstrated local adaptation, suggesting that sometimes native populations are no better adapted than are genotypes from foreign environments. Local adaptation may also lead to trade-offs, in which adaptation to one environment comes at a cost of adaptation to another environment. I conducted a survey of published studies of local adaptation to quantify its frequency and magnitude and the costs associated with local adaptation. I also quantified the relationship between local adaptation and environmental differences and the relationship between local adaptation and phenotypic divergence. The overall frequency of local adaptation was 0.71, and the magnitude of the native population advantage in relative fitness was 45%. Divergence between home site environments was positively associated with the magnitude of local adaptation, but phenotypic divergence was not. I found a small negative correlation between a population's relative fitness in its native environment and its fitness in a foreign environment, indicating weak trade-offs associated with local adaptation. These results suggest that populations are often locally adapted but stochastic processes such as genetic drift may limit the efficacy of divergent selection.

Allele fixation in a dynamic metapopulation: founder effects vs refuge effects

The fixation of mutant alleles has been studied with models assuming various spatial population structures. In these models, the structure of the metapopulation that we call the "landscape" (number, size and connectivity of subpopulations) is often static. However, natural populations are subject to repetitive population size variations, fragmentation and secondary contacts at different spatiotemporal scales due to geological, climatic and ecological processes. In this paper, we examine how such dynamic landscapes can alter mutant fixation probability and time to fixation. We consider three stochastic landscape dynamics: (i) the population is subject to repetitive bottlenecks, (ii) to the repeated alternation of fragmentation and fusion of demes with a constant population carrying capacity, (iii) idem with a variable carrying capacity. We show by deriving a variance, a coalescent and a harmonic mean population effective size, and with simulations that these landscape dynamics generate repetitive founder effects which counteract selection, thereby decreasing the fixation probability of an advantageous mutant but accelerate fixation when it occurs. For models (ii) and (iii), we also highlight an antagonistic "refuge effect" which can strongly delay mutant fixation. The predominance of either founder effects or refuge effects determines the time to fixation and mainly depends on the characteristic time scales of the landscape dynamics.

Variation at range margins across multiple spatial scales: environmental temperature, population genetics and metabolomic phenotype

Range margins are spatially complex, with environmental, genetic and phenotypic variations occurring across a range of spatial scales. We examine variation in temperature, genes and metabolomic profiles within and between populations of the subalpine perennial plant Arabidopsis lyrata ssp. petraea from across its northwest European range. Our surveys cover a gradient of fragmentation from largely continuous populations in Iceland, through more fragmented Scandinavian populations, to increasingly widely scattered populations at the range margin in Scotland, Wales and Ireland. Temperature regimes vary substantially within some populations, but within-population variation represents a larger fraction of genetic and especially metabolomic variances. Both physical distance and temperature differences between sites are found to be associated with genetic profiles, but not metabolomic profiles, and no relationship was found between genetic and metabolomic population structures in any region. Genetic similarity between plants within populations is the highest in the fragmented populations at the range margin, but differentiation across space is the highest there as well, suggesting that regional patterns of genetic diversity may be scale dependent.

Nucleotide polymorphism and within-gene recombination in Daphnia magna and D. pulex, two cyclical parthenogens

Theory predicts that partially asexual organisms may make the "best of both worlds": for the most part, they avoid the costs of sexual reproduction, while still benefiting from an enhanced efficiency of selection compared to obligately asexual organisms. There is, however, little empirical data on partially asexual organisms to test this prediction. Here we examine patterns of nucleotide diversity at eight nuclear loci in continentwide samples of two species of cyclically parthenogenetic Daphnia to assess the effect of partial asexual reproduction on effective population size and amount of recombination. Both species have high nucleotide diversities and show abundant evidence for recombination, yielding large estimates of effective population sizes (300,000-600,000). This suggests that selection will act efficiently even on mutations with small selection coefficients. Divergence between the two species is less than one-tenth of previous estimates, which were derived using a mitochondrial molecular clock. As the two species investigated are among the most distantly related species of the genus, this suggests that the genus Daphnia may be considerably younger than previously thought. Daphnia has recently received increased attention because it is being developed as a model organism for ecological and evolutionary genomics. Our results confirm the attractiveness of Daphnia as a model organism, because the high nucleotide diversity and low linkage disequilibrium suggest that fine-scale mapping of genes affecting phenotypes through association studies should be feasible.

Fundamental concepts in genetics: effective population size and patterns of molecular evolution and variation

The effective size of a population, N(e), determines the rate of change in the composition of a population caused by genetic drift, which is the random sampling of genetic variants in a finite population. N(e) is crucial in determining the level of variability in a population, and the effectiveness of selection relative to drift. This article reviews the properties of N(e) in a variety of different situations of biological interest, and the factors that influence it. In particular, the action of selection means that N(e) varies across the genome, and advances in genomic techniques are giving new insights into how selection shapes N(e).

Predicting the deleterious effects of mutation load in fragmented populations

Human-induced habitat fragmentation constitutes a major threat to biodiversity. Both genetic and demographic factors combine to drive small and isolated populations into extinction vortices. Nevertheless, the deleterious effects of inbreeding and drift load may depend on population structure, migration patterns, and mating systems and are difficult to predict in the absence of crossing experiments. We performed stochastic individual-based simulations aimed at predicting the effects of deleterious mutations on population fitness (offspring viability and median time to extinction) under a variety of settings (landscape configurations, migration models, and mating systems) on the basis of easy-to-collect demographic and genetic information. Pooling all simulations, a large part (70%) of variance in offspring viability was explained by a combination of genetic structure (F(ST)) and within-deme heterozygosity (H(S)). A similar part of variance in median time to extinction was explained by a combination of local population size (N) and heterozygosity (H(S)). In both cases the predictive power increased above 80% when information on mating systems was available. These results provide robust predictive models to evaluate the viability prospects of fragmented populations.

Diffusion approximations for one-locus multi-allele kin selection, mutation and random drift in group-structured populations: a unifying approach to selection models in population genetics

Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. These are analogous to the selection drift functions obtained with pure viability selection in a population with inbreeding. They give the changes of the allele frequencies in an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear combination of a symmetric matrix for allozygous individuals and a rank-one matrix for autozygous individuals. In the case of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization. The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition and the effective population size.

War and the evolution of belligerence and bravery

Tribal war occurs when a coalition of individuals use force to seize reproduction-enhancing resources, and it may have affected human evolution. Here, we develop a population-genetic model for the coevolution of costly male belligerence and bravery when war occurs between groups of individuals in a spatially subdivided population. Belligerence is assumed to increase an actor's group probability of trying to conquer another group. An actor's bravery is assumed to increase his group's ability to conquer an attacked group. We show that the selective pressure on these two traits can be substantial even in groups of large size, and that they may be driven by two independent reproduction-enhancing resources: additional mates for males and additional territory (or material resources) for females. This has consequences for our understanding of the evolution of intertribal interactions, as hunter-gatherer societies are well known to have frequently raided neighbouring groups from whom they appropriated territory, goods and women.

The fixation probability of beneficial mutations

The fixation probability, the probability that the frequency of a particular allele in a population will ultimately reach unity, is one of the cornerstones of population genetics. In this review, we give a brief historical overview of mathematical approaches used to estimate the fixation probability of beneficial alleles. We then focus on more recent work that has relaxed some of the key assumptions in these early papers, providing estimates that have wider applicability to both natural and laboratory settings. In the final section, we address the possibility of future work that might bridge the gap between theoretical results to date and results that might realistically be applied to the experimental evolution of microbial populations. Our aim is to highlight the concrete, testable predictions that have arisen from the theoretical literature, with the intention of further motivating the invaluable interplay between theory and experiment.

A metapopulation model for the introgression from genetically modified plants into their wild relatives

Most models on introgression from genetically modified (GM) plants have focused on small spatial scales, modelling gene flow from a field containing GM plants into a single adjacent population of a wild relative. Here, we present a model to study the effect of introgression from multiple plantations into the whole metapopulation of the wild relative. The most important result of the model is that even very low levels of introgression and selection can lead to a high probability that the transgene goes to fixation in the metapopulation. Furthermore, the overall frequency of the transgene in the metapopulation, after a certain number of generations of introgression, depends on the population dynamics. If there is a high rate of migration or a high rate of population turnover, the overall transgene frequency is much higher than with lower rates. However, under an island model of population structure, this increased frequency has only a very small effect on the probability of fixation of the transgene. Considering these results, studies on the potential ecological risks of introgression from GM plants should look not only at the rate of introgression and selection acting on the transgene, but also at the metapopulation dynamics of the wild relative.

The fixation of locally beneficial alleles in a metapopulation

Extinction, recolonization, and local adaptation are common in natural spatially structured populations. Understanding their effect upon genetic variation is important for systems such as genetically modified organism management or avoidance of drug resistance. Theoretical studies on the effect of extinction and recolonization upon genetic variance started appearing in the 1970s, but the role of local adaptation still has no good theoretical basis. Here we develop a model of a haploid species in a metapopulation in which a locally adapted beneficial allele is introduced. We study the effect of different spatial patterns of local adaptation, and different metapopulation dynamics, upon the fixation probability of the beneficial allele. Controlling for the average selection pressure, we find that a small area of positive selection can significantly increase the global probability of fixation. However, local adaptation becomes less important as extinction rate increases. Deme extinction and recolonization have a spatial smoothing effect that effectively reduces spatial variation in fitness.

Quantifying the threat of extinction from Muller's ratchet in the diploid Amazon molly (Poecilia formosa)

BACKGROUND

The Amazon molly (Poecilia formosa) is a small unisexual fish that has been suspected of being threatened by extinction from the stochastic accumulation of slightly deleterious mutations that is caused by Muller's ratchet in non-recombining populations. However, no detailed quantification of the extent of this threat is available.

RESULTS

Here we quantify genomic decay in this fish by using a simple model of Muller's ratchet with the most realistic parameter combinations available employing the evolution@home global computing system. We also describe simple extensions of the standard model of Muller's ratchet that allow us to deal with selfing diploids, triploids and mitotic recombination. We show that Muller's ratchet creates a threat of extinction for the Amazon molly for many biologically realistic parameter combinations. In most cases, extinction is expected to occur within a time frame that is less than previous estimates of the age of the species, leading to a genomic decay paradox.

CONCLUSION

How then does the Amazon molly survive? Several biological processes could individually or in combination solve this genomic decay paradox, including paternal leakage of undamaged DNA from sexual sister species, compensatory mutations and many others. More research is needed to quantify the contribution of these potential solutions towards the survival of the Amazon molly and other (ancient) asexual species.

Quasi-species evolution in subdivided populations favours maximally deleterious mutations

Most models of quasi-species evolution predict that populations will evolve to occupy areas of sequence space with the greatest concentration of neutral sequences, thus minimizing the deleterious mutation rate and creating mutationally 'robust' genomes. In contrast, empirical studies of the principal model of quasi-species evolution, RNA viruses, suggest that the effects of deleterious mutations are more severe than in similar DNA-based microbes. We demonstrate that populations divided into discrete patches connected by dispersal may favour genotypes where the deleterious effect of non-neutral mutations is maximized. This effect is especially strong in the absence of back mutation and when the amount of time spent in hosts prior to dispersal is intermediate. Our results indicate that RNA viruses that produce acute infections initiated by a small number of virions are expected to evolve fragile genetic architectures when compared with other RNA viruses.

The analysis of bi-level evolutionary graphs

Evolutionary graphs (EGs), in which evolutionary dynamic is arranged on a graph, were initially proposed by Lieberman et al. [Lieberman, E., Hauert, C., Nowak, M.A., 2005. Evolutionary dynamics on graphs. Nature 433, 312-316] in the biological field and many biological phenomena are successfully explained. EGs on two levels (or bi-level EGs), based on some biological phenomena, are considered in this paper. The bi-level EGs are compared with the one-rooted EGs in two cases. One has the identical numbers of the followers, the other with the same numbers of total individuals. Then, some properties of the bi-level EGs are obtained. It is showed that bi-level EGs are more stable, and the bi-level EGs with just two leaders are the most stable, if they have identical followers respectively. The bi-level EGs theory can successfully explain the phenomena of symbiosis in biology.