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The majority of highly polymorphic genes are related to immune functions and with over 100 alleles within a population, genes of the major histocompatibility complex (MHC) are the most polymorphic loci in vertebrates. How such extraordinary polymorphism arose and is maintained is controversial. One possibility is heterozygote advantage (HA), which can in principle maintain any number of alleles, but biologically explicit models based on this mechanism have so far failed to reliably predict the coexistence of significantly more than ten alleles. We here present an eco-evolutionary model showing that under HA evolution can result in the emergence and maintenance of more than 100 alleles if the following two assumptions are fulfilled: first, pathogens are lethal in the absence of an appropriate immune defence; second, the combined effect of multiple pathogens on host survival exceeds the sum of the effects of each pathogen alone. Thus, our results show that HA can be a more potent force in explaining the extraordinary polymorphism found at MHC loci than currently recognized.

In patch- or habitat-structured populations, different processes can favor adaptive polymorphism at different scales. While spatial heterogeneity can generate spatially disruptive selection favoring variation between patches, local competition can lead to locally disruptive selection promoting variation within patches. So far, almost all theory has studied these two processes in isolation. Here, we use mathematical modeling to investigate how resource variation within and between habitats influences the evolution of variation in a consumer population where individuals compete in finite patches connected by dispersal. We find that locally and spatially disruptive selection typically act in concert, favoring polymorphism under a wider range of conditions than when in isolation. But when patches are small and dispersal between them is low, kin competition inhibits the emergence of polymorphism, especially when the latter is driven by local competition for resources. We further use our model to clarify what comparisons between trait and neutral genetic differentiation (QST/FST comparisons) can tell about the nature of selection. Overall, our results help us understand the interaction between two major drivers of polymorphism: locally and spatially disruptive selection, and how this interaction is modulated by the unavoidable effects of kin selection under limited dispersal.

Most animals undergo ontogenetic niche shifts during their life. Yet, standard ecological theory builds on models that ignore this complexity. Here, we study how complex life cycles, where juvenile and adult individuals each feed on different sets of resources, affect community richness. Two different modes of community assembly are considered: gradual adaptive evolution and immigration of new species with randomly selected phenotypes. We find that under gradual evolution complex life cycles can lead to both higher and lower species richness when compared to a model of species with simple life cycles that lack an ontogenetic niche shift. Thus, complex life cycles do not per se increase the scope for gradual adaptive diversification. However, complex life cycles can lead to significantly higher species richness when communities are assembled trough immigration, as immigrants can occupy isolated peaks of the dynamic fitness landscape that are not accessible via gradual evolution.

Meiotic drivers (MDs) are selfish genetic elements that are able to become overrepresented among the products of meiosis. This transmission advantage makes it possible for them to spread in a population even when they impose fitness costs on their host organisms. Whether an MD can invade a population, and subsequently reach fixation or coexist in a stable polymorphism, depends on the one hand on the biology of the host organism, including its life cycle, mating system, and population structure, and on the other hand on the specific fitness effects of the driving allele on the host. Here, we present a population genetic model for spore killing, a type of drive specific to fungi. We show how ploidy level, rate of selfing, and efficiency of spore killing affect the invasion probability of a driving allele and the conditions for its stable coexistence with a nondriving allele. Our model can be adapted to different fungal life cycles, and is applied here to two well-studied genera of filamentous ascomycetes known to harbor spore-killing elements, Neurospora and Podospora. We discuss our results in the light of recent empirical findings for these two systems.

Consumers regularly experience trade-offs in their ability to find, handle, and digest different resources. Evolutionary ecologists recognized the significance of this observation for the evolution and maintenance of biological diversity long ago and continue to elaborate on the conditions under which to expect one or several specialists, generalists, or combinations thereof. Existing theory based on a single evolving trait predicts that specialization requires strong trade-offs such that generalists perform relatively poorly, while weak trade-offs favor a single generalist. Here, we show that this simple dichotomy does not hold true under joint evolution of two or more foraging traits. In this case, the boundary between trade-offs resulting in resource specialists and resource generalists is shifted toward weaker trade-off curvatures. In particular, weak trade-offs can result in evolutionary branching, leading to the evolution of two coexisting resource specialists, while the evolution of a single resource generalist requires particularly weak trade-offs. These findings are explained by performance benefits due to epistatic trait interactions enjoyed by phenotypes that are specialized in more than one trait for the same resource.

We derive how directional and disruptive selection operate on scalar traits in a heterogeneous group-structured population for a general class of models. In particular, we assume that each group in the population can be in one of a finite number of states, where states can affect group size and/or other environmental variables, at a given time. Using up to second-order perturbation expansions of the invasion fitness of a mutant allele, we derive expressions for the directional and disruptive selection coefficients, which are sufficient to classify the singular strategies of adaptive dynamics. These expressions include first- and second-order perturbations of individual fitness (expected number of settled offspring produced by an individual, possibly including self through survival); the first-order perturbation of the stationary distribution of mutants (derived here explicitly for the first time); the first-order perturbation of pairwise relatedness; and reproductive values, pairwise and three-way relatedness, and stationary distribution of mutants, each evaluated under neutrality. We introduce the concept of individual k-fitness (defined as the expected number of settled offspring of an individual for which k - 1 randomly chosen neighbors are lineage members) and show its usefulness for calculating relatedness and its perturbation. We then demonstrate that the directional and disruptive selection coefficients can be expressed in terms individual k-fitnesses with k = 1, 2, 3 only. This representation has two important benefits. First, it allows for a significant reduction in the dimensions of the system of equations describing the mutant dynamics that needs to be solved to evaluate explicitly the two selection coefficients. Second, it leads to a biologically meaningful interpretation of their components. As an application of our methodology, we analyze directional and disruptive selection in a lottery model with either hard or soft selection and show that many previous results about selection in group-structured populations can be reproduced as special cases of our model.

Sexual selection can promote adaptation if sexually selected traits are reliable indicators of genetic quality. Moreover, models of good genes sexual selection suggest that, by operating more strongly in males than in females, sexual selection may purge deleterious alleles from the population at a low demographic cost, offering an evolutionary benefit to sexually reproducing populations. Here, we investigate the effect of good genes sexual selection on adaptation following environmental change. We show that the strength of sexual selection is often weakened relative to fecundity selection, reducing the suggested benefit of sexual reproduction. This result is a consequence of incorporating a simple and general mechanistic basis for how sexual selection operates under different mating systems, rendering selection on males frequency-dependent and dynamic with respect to the degree of environmental change. Our model illustrates that incorporating the mechanism of selection is necessary to predict evolutionary outcomes and highlights the need to substantiate previous theoretical claims with further work on how sexual selection operates in changing environments.

Over the last two decades evolutionary branching has emerged as a possible mathematical paradigm for explaining the origination of phenotypic diversity. Although branching is well understood for one-dimensional trait spaces, a similarly detailed understanding for higher dimensional trait spaces is sadly lacking. This note aims at getting a research program of the ground leading to such an understanding. In particular, we show that, as long as the evolutionary trajectory stays within the reign of the local quadratic approximation of the fitness function, any initial small scale polymorphism around an attracting invadable evolutionarily singular strategy (ess) will evolve towards a dimorphism. That is, provided the trajectory does not pass the boundary of the domain of dimorphic coexistence and falls back to monomorphism (after which it moves again towards the singular strategy and from there on to a small scale polymorphism, etc.). To reach these results we analyze in some detail the behavior of the solutions of the coupled Lande-equations purportedly satisfied by the phenotypic clusters of a quasi-n-morphism, and give a precise characterisation of the local geometry of the set in trait space squared harbouring protected dimorphisms. Intriguingly, in higher dimensional trait spaces an attracting invadable ess needs not connect to . However, for the practically important subset of strongly attracting ess-es (i.e., ess-es that robustly locally attract the monomorphic evolutionary dynamics for all possible non-degenerate mutational or genetic covariance matrices) invadability implies that the ess does connect to , just as in 1-dimensional trait spaces. Another matter is that in principle there exists the possibility that the dimorphic evolutionary trajectory reverts to monomorphism still within the reign of the local quadratic approximation for the invasion fitnesses. Such locally unsustainable branching cannot occur in 1- and 2-dimensional trait spaces, but can do so in higher dimensional ones. For the latter trait spaces we give a condition excluding locally unsustainable branching which is far stricter than the one of strong convergence, yet holds good for a relevant collection of published models. It remains an open problem whether locally unsustainable branching can occur around general strongly attracting invadable ess-es.

Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that fluctuates in space and time, and derive an analytical condition for when these fluctuations promote genetic diversification. As ecological scenario we use a generalized island model with soft selection within patches in which we incorporate generation overlap. We allow for arbitrary fluctuations in the environment including spatio-temporal correlations and any functional form of selection on the trait. Using the concepts of invasion fitness and evolutionary branching, we derive a simple and transparent condition for the adaptive evolution and maintenance of genetic diversity. This condition relates the strength of selection within patches to expectations and variances in the environmental conditions across space and time. Our results unify, clarify, and extend a number of previous results on the evolution and maintenance of genetic variation under fluctuating selection. Individual-based simulations show that our results are independent of the details of the genetic architecture and whether reproduction is clonal or sexual. The onset of increased genetic variance is predicted accurately also in small populations in which alleles can go extinct due to environmental stochasticity.

We present two theoretical approaches to investigate whether organismal complexity, defined as the number of quantitative traits determining fitness, and the potential for adaptive diversification are correlated. The first approach is independent of any specific ecological model and based on curvature properties of the fitness landscape as a function of the dimension of the trait space. This approach indeed suggests a positive correlation between complexity and diversity. An assumption made in this first approach is that the potential for any pair of traits to interact in their effect on fitness is independent of the dimension of the trait space. In the second approach, we circumvent making this assumption by analyzing the evolutionary dynamics in an explicit consumer-resource model in which the shape of the fitness landscape emerges from the underlying mechanistic ecological model. In this model, consumers are characterized by several quantitative traits and feed on a multidimensional resource distribution. The consumer's feeding efficiency on the resource is determined by the match between consumer phenotype and resource item. This analysis supports a positive correlation between the complexity of the evolving consumer species and its potential to diversify with the additional insight that also increasing resource complexity facilitates diversification.