When Does Frequency-Independent Selection Maintain Genetic Variation?

Game changing mutation

We present a model of the effect of mutation on haploid sexually reproducing populations by modelling the reproductive dynamics as occurring in the context of a common interests game played by the loci, with the alleles in the role of pure actions. Absent mutations, the population will deterministically converge to a pure Nash equilibrium of the game. A novel mutation adds new alleles, hence is tantamount to a change of the game by the addition of new actions. If the new game defined by the mutation removes the former pure Nash equilibrium the game changing mutation becomes in addition a Nash equilibrium changing mutation, as the population will then move to a new equilibrium with an increase in fitness. A graph of common interests games is defined, and evolution by mutation is modelled as a path through this graph. We discuss two applications-fitness valley crossing and evolutionary contingency.

A Wright-Fisher graph model and the impact of directional selection on genetic variation

We introduce a multi-allele Wright-Fisher model with mutation and selection such that allele frequencies at a single locus are traced by the path of a hybrid jump-diffusion process. The state space of the process is given by the vertices and edges of a topological graph, i.e. edges are unit intervals. Vertices represent monomorphic population states and positions on the edges mark the biallelic proportions of ancestral and derived alleles during polymorphic segments. In this setting, mutations can only occur at monomorphic loci. We derive the stationary distribution in mutation-selection-drift equilibrium and obtain the expected allele frequency spectrum under large population size scaling. For the extended model with multiple independent loci we derive rigorous upper bounds for a wide class of associated measures of genetic variation. Within this framework we present mathematically precise arguments to conclude that the presence of directional selection reduces the magnitude of genetic variation, as constrained by the bounds for neutral evolution.

Eco-evolutionary maintenance of diversity in fluctuating environments

Growing evidence suggests that temporally fluctuating environments are important in maintaining variation both within and between species. To date, however, studies of genetic variation within a population have been largely conducted by evolutionary biologists (particularly population geneticists), while population and community ecologists have concentrated more on diversity at the species level. Despite considerable conceptual overlap, the commonalities and differences of these two alternative paradigms have yet to come under close scrutiny. Here, we review theoretical and empirical studies in population genetics and community ecology focusing on the 'temporal storage effect' and synthesise theories of diversity maintenance across different levels of biological organisation. Drawing on Chesson's coexistence theory, we explain how temporally fluctuating environments promote the maintenance of genetic variation and species diversity. We propose a further synthesis of the two disciplines by comparing models employing traditional frequency-dependent dynamics and those adopting density-dependent dynamics. We then address how temporal fluctuations promote genetic and species diversity simultaneously via rapid evolution and eco-evolutionary dynamics. Comparing and synthesising ecological and evolutionary approaches will accelerate our understanding of diversity maintenance in nature.

Evolution with recombination as Gibbs sampling

This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions without resorting to diffusion approximations. Tractability is achieved by generating new offspring using n-parent rather than 2-parent recombination. While this enforces linkage equilibrium among offspring, it allows analysis of the whole population under linkage disequilibrium. We derive a general and exact relationship between fitness fluctuations and response to selection. Our assumptions allow analytical calculation of the stationary distribution of the model for a variety of non-trivial fitness functions. These results allow us to speak to genetic architecture, i.e., what stationary distributions result from different fitness functions. This paper presents methods for exactly deriving stationary states for finite and infinite populations. This method can be applied to many fitness functions, and we give exact calculations for four of these. These results allow us to investigate metastability, tradeoffs between fitness functions, and even consider error-correcting codes.

Fluctuating selection on bacterial iron regulation in the mammalian gut

Iron is critical in host-microbe interactions, and its availability is tightly regulated in the mammalian gut. Antibiotics and inflammation can perturb iron availability in the gut, which could alter host-microbe interactions. Here, we show that an adaptive allele of iscR, a major regulator of iron homeostasis of Escherichia coli, is under fluctuating selection in the mouse gut. In vivo competitions in immune-competent, immune-compromised, and germ-free mice reveal that the selective pressure on an iscR mutant E. coli is modulated by the presence of antibiotics, the microbiota, and the immune system. In vitro assays show that iron availability is an important mediator of the iscR allele fitness benefits or costs. We identify Lipocalin-2, a host's immune protein that prevents bacterial iron acquisition, as a major host mechanism underlying fluctuating selection of iscR. Our results provide a remarkable example of strong fluctuating selection acting on bacterial iron regulation in the mammalian gut.

Quantifying the relationship between genetic diversity and population size suggests natural selection cannot explain Lewontin's Paradox

Neutral theory predicts that genetic diversity increases with population size, yet observed levels of diversity across metazoans vary only two orders of magnitude while population sizes vary over several. This unexpectedly narrow range of diversity is known as Lewontin's Paradox of Variation (1974). While some have suggested selection constrains diversity, tests of this hypothesis seem to fall short. Here, I revisit Lewontin's Paradox to assess whether current models of linked selection are capable of reducing diversity to this extent. To quantify the discrepancy between pairwise diversity and census population sizes across species, I combine previously-published estimates of pairwise diversity from 172 metazoan taxa with newly derived estimates of census sizes. Using phylogenetic comparative methods, I show this relationship is significant accounting for phylogeny, but with high phylogenetic signal and evidence that some lineages experience shifts in the evolutionary rate of diversity deep in the past. Additionally, I find a negative relationship between recombination map length and census size, suggesting abundant species have less recombination and experience greater reductions in diversity due to linked selection. However, I show that even assuming strong and abundant selection, models of linked selection are unlikely to explain the observed relationship between diversity and census sizes across species.

Making the most of potential: potential games and genotypic convergence

We consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even under genetic linkage between loci) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum-Eagon Theorem. To analyse varying environments, we introduce the concept of 'virtual convergence', under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.

Loss of genetic variation in the two-locus multiallelic haploid model

In the evolutionary biology literature, it is generally assumed that for deterministic frequency-independent haploid selection models, no polymorphic equilibrium can be stable in the absence of variation-generating mechanisms such as mutation. However, mathematical analyses that corroborate this claim are scarce and almost always depend upon additional assumptions. Using ideas from game theory, we show that a monomorphism is a global attractor if one of its alleles dominates all other alleles at its locus. Further, we show that no isolated equilibrium exists, at which an unequal number of alleles from two loci is present. Under the assumption of convergence of trajectories to equilibrium points, we resolve the two-locus three-allele case for a fitness scheme formally equivalent to the classical symmetric viability model. We also provide an alternative proof for the two-locus two-allele case.

Legacy of prior host and soil selection on rhizobial fitness in planta

Measuring selection acting on microbial populations in natural or even seminatural environments is challenging because many microbial populations experience variable selection. The majority of rhizobial bacteria are found in the soil. However, they also live symbiotically inside nodules of legume hosts and each nodule can release thousands of daughter cells back into the soil. We tested how past selection (i.e., legacies) by two plant genotypes and by the soil alone affected selection and genetic diversity within a population of 101 strains of Ensifer meliloti. We also identified allelic variants most strongly associated with soil- and host-dependent fitness. In addition to imposing direct selection on rhizobia populations, soil and host environments had lasting effects across host generations. Host presence and genotype during the legacy period explained 22% and 12% of the variance in the strain composition of nodule communities in the second cohort, respectively. Although strains with high host fitness in the legacy cohort tended to be enriched in the second cohort, the diversity of the strain community was greater when the second cohort was preceded by host rather than soil legacies. Our results indicate the potential importance of soil selection driving the evolution of these plant-associated microbes.

Seasonally fluctuating selection can maintain polymorphism at many loci via segregation lift

Most natural populations are affected by seasonal changes in temperature, rainfall, or resource availability. Seasonally fluctuating selection could potentially make a large contribution to maintaining genetic polymorphism in populations. However, previous theory suggests that the conditions for multilocus polymorphism are restrictive. Here, we explore a more general class of models with multilocus seasonally fluctuating selection in diploids. In these models, the multilocus genotype is mapped to fitness in two steps. The first mapping is additive across loci and accounts for the relative contributions of heterozygous and homozygous loci-that is, dominance. The second step uses a nonlinear fitness function to account for the strength of selection and epistasis. Using mathematical analysis and individual-based simulations, we show that stable polymorphism at many loci is possible if currently favored alleles are sufficiently dominant. This general mechanism, which we call "segregation lift," requires seasonal changes in dominance, a phenomenon that may arise naturally in situations with antagonistic pleiotropy and seasonal changes in the relative importance of traits for fitness. Segregation lift works best under diminishing-returns epistasis, is not affected by problems of genetic load, and is robust to differences in parameters across loci and seasons. Under segregation lift, loci can exhibit conspicuous seasonal allele-frequency fluctuations, but often fluctuations may be small and hard to detect. An important direction for future work is to formally test for segregation lift in empirical data and to quantify its contribution to maintaining genetic variation in natural populations.