The basic idea of evolutionary game theory is that payoff determines reproductive rate. Successful individuals have a higher payoff and produce more offspring. But in evolutionary and ecological situations there is not only reproductive rate but also carrying capacity. Individuals may differ in their exposure to density limiting effects. Here we explore an alternative approach to evolutionary game theory by assuming that the payoff from the game determines the carrying capacity of individual phenotypes. Successful strategies are less affected by density limitation (crowding) and reach higher equilibrium abundance. We demonstrate similarities and differences between our framework and the standard replicator equation. Our equation is defined on the positive orthant, instead of the simplex, but has the same equilibrium points as the replicator equation. Linear stability analysis produces the classical conditions for asymptotic stability of pure strategies, but the stability properties of internal equilibria can differ in the two frameworks. For example, in a two-strategy game with an internal equilibrium that is always stable under the replicator equation, the corresponding equilibrium can be unstable in the new framework resulting in a limit cycle.

Frequency-independent selection is generally considered as a force that acts to reduce the genetic variation in evolving populations, yet rigorous arguments for this idea are scarce. When selection fluctuates in time, it is unclear whether frequencyindependent selection may maintain genetic polymorphism without invoking additional mechanisms. We show that constant frequency-independent selection with arbitrary epistasis on a well-mixed haploid population eliminates genetic variation if we assume linkage equilibrium between alleles. To this end, we introduce the notion of frequency-independent selection at the level of alleles, which is sufficient to prove our claim and contains the notion of frequency-independent selection on haploids. When selection and recombination are weak but of the same order, there may be strong linkage disequilibrium; numerical calculations show that stable equilibria are highly unlikely. Using the example of a diallelic two-locus model, we then demonstrate that frequency-independent selection that fluctuates in time can maintain stable polymorphism if linkage disequilibrium changes its sign periodically. We put our findings in the context of results from the existing literature and point out those scenarios in which the possible role of frequency-independent selection in maintaining genetic variation remains unclear.

Mutator strains are expected to evolve when the availability and effect of beneficial mutations are high enough to counteract the disadvantage from deleterious mutations that will inevitably accumulate. As the population becomes more adapted to its environment, both availability and effect of beneficial mutations necessarily decrease and mutation rates are predicted to decrease. It has been shown that certain molecular mechanisms can lead to increased mutation rates when the organism finds itself in a stressful environment. While this may be a correlated response to other functions, it could also be an adaptive mechanism, raising mutation rates only when it is most advantageous. Here, we use a mathematical model to investigate the plausibility of the adaptive hypothesis. We show that such a mechanism can be mantained if the population is subjected to diverse stresses. By simulating various antibiotic treatment schemes, we find that combination treatments can reduce the effectiveness of second-order selection on stress-induced mutagenesis. We discuss the implications of our results to strategies of antibiotic therapy.

Understanding the evolution of dispersal is essential for understanding and predicting the dynamics of natural populations. Two main factors are known to influence dispersal evolution: spatio-temporal variation in the environment and relatedness between individuals. However, the relation between these factors is still poorly understood, and they are usually treated separately. In this article, I present a theoretical framework that contains and connects effects of both environmental variation and relatedness, and reproduces and extends their known features. Spatial habitat variation selects for balanced dispersal strategies, whereby the population is kept at an ideal free distribution. Within this class of dispersal strategies, I explain how increased dispersal is promoted by perturbations to the dispersal type frequencies. An explicit formula shows the magnitude of the selective advantage of increased dispersal in terms of the spatial variability in the frequencies of the different dispersal strategies present. These variances are capable of capturing various sources of stochasticity and hence establish a common scale for their effects on the evolution of dispersal. The results furthermore indicate an alternative approach to identifying effects of relatedness on dispersal evolution.

BackgroundIndirect genetic effects (IGEs) occur when genes expressed in one individual alter the expression of traits in social partners. Previous studies focused on the evolutionary consequences and evolutionary dynamics of IGEs, using equilibrium solutions to predict phenotypes in subsequent generations. However, whether or not such steady states may be reached may depend on the dynamics of interactions themselves.ResultsIn our study, we focus on the dynamics of social interactions and indirect genetic effects and investigate how they modify phenotypes over time. Unlike previous IGE studies, we do not analyse evolutionary dynamics; rather we consider within-individual phenotypic changes, also referred to as phenotypic plasticity. We analyse iterative interactions, when individuals interact in a series of discontinuous events, and investigate the stability of steady state solutions and the dependence on model parameters, such as population size, strength, and the nature of interactions. We show that for interactions where a feedback loop occurs, the possible parameter space of interaction strength is fairly limited, affecting the evolutionary consequences of IGEs. We discuss the implications of our results for current IGE model predictions and their limitations.

Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatio-temporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes and show that under the assumption of maintenance of spatially homogeneous total population the dynamics of the frequency of one of the genotypes is approximately described by the generalized Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation. This generalized FKPP equation with (nonlinear) frequency dependent diffusion and advection terms admits traveling wave solutions (fronts/clines) that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the FKPP with constant coefficients. Moreover for the particular case of the quadratic (monostable) nonlinear growth-decay rate in the generalized FKPP we study in details the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.

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