Evolutionary branching of a magic trait

Revisiting implementation of multiple natural enemies in pest management

A major goal of biological control is the reduction and/or eradication of pests using various natural enemies, in particular, via deliberate infection of the target species by parasites. To enhance the biological control, a promising strategy seems to implement a multi-enemy assemblage rather than a single control agent. Although a large body of theoretical studies exists on co-infections in epidemiology and ecology, there is still a big gap in modelling outcomes of multi-enemy biological control. Here we theoretically investigate how the efficiency of biological control of a pest depends on the number of natural enemies used. We implement a combination of eco-epidemiological modelling and the Adaptive Dynamics game theory framework. We found that a progressive addition of parasite species increases the evolutionarily stable virulence of each parasite, and thus enhances the mortality of the target pest. However, using multiple enemies may have only a marginal effect on the success of biological control, or can even be counter-productive when the number of enemies is excessive. We found the possibility of evolutionary suicide, where one or several parasite species go extinct over the course of evolution. Finally, we demonstrate an interesting scenario of coexistence of multiple parasites at the edge of extinction.

Establishment process of a magic trait allele subject to both divergent selection and assortative mating

Sexual selection and divergent selection are among the major driving forces of reproductive isolation, which could eventually result in speciation. A magic trait is defined such that a single trait is subject to both divergent selection and mate choice through phenotype-based assortative mating. We are here interested in the evolutionary behavior of alleles at a genetic locus responsible for a magic trait in a finite population. We assume that, in a pair of homogeneous subpopulations, a mutant allele arises at the magic trait locus, and theoretically obtain the probability that the new allele establishes in the population, or the establishment probability. We also show an analytical expression for the trajectory of allele frequency along the establishment, from which the time required for the establishment is obtained, or the establishment time. Under this model, divergent selection simply favors the new allele to fix where it is beneficial, whereas assortative mating works against rare alleles. It is theoretically demonstrated that the fate of the new allele is determined by the relative contributions of the two selective forces, divergent selection and assortative mating, when the allele is rare so that the two selective forces counteract. Our theoretical results for the establishment probability and time allow us to understand the relative role of random genetic drift in the establishment process of a magic trait allele in a finite population.

Revealing Evolutionarily Optimal Strategies in Self-Reproducing Systems via a New Computational Approach

Modelling the evolution of complex life history traits and behavioural patterns observed in the natural world is a challenging task. Here, we develop a novel computational method to obtain evolutionarily optimal life history traits/behavioural patterns in population models with a strong inheritance. The new method is based on the reconstruction of evolutionary fitness using underlying equations for population dynamics and it can be applied to self-reproducing systems (including complicated age-structured models), where fitness does not depend on initial conditions, however, it can be extended to some frequency-dependent cases. The technique provides us with a tool to efficiently explore both scalar-valued and function-valued traits with any required accuracy. Moreover, the method can be implemented even in the case where we ignore the underlying model equations and only have population dynamics time series. As a meaningful ecological case study, we explore optimal strategies of diel vertical migration (DVM) of herbivorous zooplankton in the vertical water column which is a widespread phenomenon in both oceans and lakes, generally considered to be the largest synchronised movement of biomass on Earth. We reveal optimal trajectories of daily vertical motion of zooplankton grazers in the water column depending on the presence of food and predators. Unlike previous studies, we explore both scenarios of DVM with static and dynamic predators. We find that the optimal pattern of DVM drastically changes in the presence of dynamic predation. Namely, with an increase in the amount of food available for zooplankton grazers, the amplitude of DVM progressively increases, whereas for static predators DVM would abruptly cease.

Singularity theory of fitness functions under dimorphism equivalence

We apply singularity theory to classify monomorphic singular points as they occur in adaptive dynamics. Our approach is based on a new equivalence relation called dimorphism equivalence, which is the largest equivalence relation on strategy functions that preserves ESS singularities, CvSS singularities, and dimorphisms. Specifically, we classify singularities up to topological codimension two and compute their normal forms and universal unfoldings. These calculations lead to the classification of local mutual invasibility plots that can be seen generically in systems with two parameters.

Modeling the Population-Level Processes of Biodiversity Gain and Loss at Geological Timescales

The path of species diversification is commonly observed by inspecting the fossil record. Yet, how species diversity changes at geological timescales relate to lower-level processes remains poorly understood. Here we use mathematical models of spatially structured populations to show that natural selection and gradual environmental change give rise to discontinuous phenotype changes that can be connected to speciation and extinction at the macroevolutionary level. In our model, new phenotypes arise in the middle of the environmental gradient, while newly appearing environments are filled by existing phenotypes shifting their adaptive optima. Slow environmental change leads to loss of phenotypes in the middle of the extant environmental range, whereas fast change causes extinction at one extreme of the environmental range. We compared our model predictions against a well-known yet partially unexplained pattern of intense hoofed mammal diversification associated with grassland expansion during the Late Miocene. We additionally used the model outcomes to cast new insight into Cope's law of the unspecialized. Our general finding is that the rate of environmental change determines where generation and loss of diversity occur in the phenotypic and physical spaces.

Geography, assortative mating, and the effects of sexual selection on speciation with gene flow

Theoretical and empirical research on the evolution of reproductive isolation have both indicated that the effects of sexual selection on speciation with gene flow are quite complex. As part of this special issue on the contributions of women to basic and applied evolutionary biology, I discuss my work on this question in the context of a broader assessment of the patterns of sexual selection that lead to, versus inhibit, the speciation process, as derived from theoretical research. In particular, I focus on how two factors, the geographic context of speciation and the mechanism leading to assortative mating, interact to alter the effect that sexual selection through mate choice has on speciation. I concentrate on two geographic contexts: sympatry and secondary contact between two geographically separated populations that are exchanging migrants and two mechanisms of assortative mating: phenotype matching and separate preferences and traits. I show that both of these factors must be considered for the effects of sexual selection on speciation to be inferred.

Three modes of adaptive speciation in spatially structured populations

Adaptive speciation with gene flow via the evolution of assortative mating has classically been studied in one of two different scenarios. First, speciation can occur if frequency-dependent competition in sympatry induces disruptive selection, leading to indirect selection for mating with similar phenotypes. Second, if a subpopulation is locally adapted to a specific environment, then there is indirect selection against hybridizing with maladapted immigrants. While both of these mechanisms have been modeled many times, the literature lacks models that allow direct comparisons between them. Here we incorporate both frequency-dependent competition and local adaptation into a single model and investigate whether and how they interact in driving speciation. We report two main results. First, we show that individually, the two mechanisms operate under separate conditions, hardly influencing each other when one of them alone is sufficient to drive speciation. Second, we also find that the two mechanisms can operate together, leading to a third speciation mode in which speciation is initiated by selection against maladapted migrants but completed by within-deme competition in a distinct second phase. While this third mode bears some similarity to classical reinforcement, it is considerably faster, and both newly formed species go on to coexist in sympatry.

Experimental confirmation that body size determines mate preference via phenotype matching in a stickleback species pair

Mate choice by phenotype matching, whereby individuals prefer a mate whose phenotype is similar to their own, should facilitate speciation with gene flow. This is because the genes that control mate signal (the phenotype being matched) also determine the preferred mate signal ("mate preference"). Speciation is made even easier if phenotype matching is based on a trait under divergent natural selection. In this case, assortative mating should readily evolve as a byproduct of divergent selection on the trait. Previous observational studies of assortative mating between sympatric, hybridizing threespine stickleback species (Gasterosteus aculeatus complex) suggested that phenotype matching might occur by body size, a trait under divergent natural selection. To test this, we used experimental manipulation of body size to rule out the effects of confounding variables. We found that size-manipulated benthic and limnetic stickleback females prefer mates whose body size more closely matches their own. It is thus likely that assortative mating by phenotype matching has facilitated the origin and persistence of benthic and limnetic threespine sticklebacks in the face of gene flow.

On invasion boundaries and the unprotected coexistence of two strategies

In this paper we present, in terms of invasion fitness functions, a sufficient condition for a coexistence of two strategies which are not protected from extinction when rare. In addition, we connect the result to the local characterization of singular strategies in the theory of adaptive dynamics. We conclude with some illustrative examples.