Polymorphic evolution sequence and evolutionary branching

We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems

20 questions on Adaptive Dynamics

Abstract Adaptive Dynamics is an approach to studying evolutionary change when fitness is density or frequency dependent. Modern papers identifying themselves as using this approach first appeared in the 1990s, and have greatly increased up to the present. However, because of the rather technical nature of many of the papers, the approach is not widely known or understood by evolutionary biologists. In this review we aim to remedy this situation by outlining the methodology and then examining its strengths and weaknesses. We carry this out by posing and answering 20 key questions on Adaptive Dynamics. We conclude that Adaptive Dynamics provides a set of useful approximations for studying various evolutionary questions. However, as with any approximate method, conclusions based on Adaptive Dynamics are valid only under some restrictions that we discuss

Speciation Along Environmental Gradients

Traditional discussions of speciation are based on geographical patterns of species ranges. In allopatric speciation, long-term geographical isolation generates reproductively isolated and spatially segregated descendant species. In the absence of geographical barriers, diversification is hindered by gene flow. Yet a growing body of phylogenetic and experimental data suggests that closely related species often occur in sympatry or have adjacent ranges in regions over which environmental changes are gradual and do not prevent gene flow. Theory has identified a variety of evolutionary processes that can result in speciation under sympatric conditions, with some recent advances concentrating on the phenomenon of evolutionary branching. Here we establish a link between geographical patterns and ecological processes of speciation by studying evolutionary branching in spatially structured populations. We show that along an environmental gradient, evolutionary branching can occur much more easily than in non-spatial models. This facilitation is most pronounced for gradients of intermediate slope. Moreover, spatial evolutionary branching readily generates patterns of spatial segregation and abutment between the emerging species. Our results highlight the importance of local processes of adaptive divergence for geographical patterns of speciation, and caution against pitfalls of inferring past speciation processes from present biogeographical patterns

Malthusian assumptions, Boserupian response in models of the transitions to agriculture

In the many transitions from foraging to agropastoralism it is debated whether the primary drivers are innovations in technology or increases of population. The driver discussion traditionally separates Malthusian (technology driven) from Boserupian (population driven) theories. I present a numerical model of the transitions to agriculture and discuss this model in the light of the population versus technology debate and in Boserup's analytical framework in development theory. Although my model is based on ecological -Neomalthusian- principles, the coevolutionary positive feedback relationship between technology and population results in a seemingly Boserupian response: innovation is greatest when population pressure is highest. This outcome is not only visible in the theory-driven reduced model, but is also present in a corresponding "real world" simulator which was tested against archaeological data, demonstrating the relevance and validity of the coevolutionary model. The lesson to be learned is that not all that acts Boserupian needs Boserup at its core.Comment: Chapter in: "Society, Nature and History: The Legacy of Ester Boserup", Springer, Vienna (in press

Spatial Pattern Switching Enables Cyclic Evolution in Spatial Epidemics

Infectious diseases often spread as spatial epidemic outbreak waves. A number of model studies have shown that such spatial pattern formation can have important consequences for the evolution of pathogens. Here, we show that such spatial patterns can cause cyclic evolutionary dynamics in selection for the length of the infectious period. The necessary reversal in the direction of selection is enabled by a qualitative change in the spatial pattern from epidemic waves to irregular local outbreaks. The spatial patterns are an emergent property of the epidemic system, and they are robust against changes in specific model assumptions. Our results indicate that emergent spatial patterns can act as a rich source for complexity in pathogen evolution

Competition-Colonization Trade-Offs, Competitive Uncertainty, and the Evolutionary Assembly of Species

We utilize a standard competition-colonization metapopulation model in order to study the evolutionary assembly of species. Based on earlier work showing how models assuming strict competitive hierarchies will likely lead to runaway evolution and self-extinction for all species, we adopt a continuous competition function that allows for levels of uncertainty in the outcome of competition. We then, by extending the standard patch-dynamic metapopulation model in order to include evolutionary dynamics, allow for the coevolution of species into stable communities composed of species with distinct limiting similarities. Runaway evolution towards stochastic extinction then becomes a limiting case controlled by the level of competitive uncertainty. We demonstrate how intermediate competitive uncertainty maximizes the equilibrium species richness as well as maximizes the adaptive radiation and self-assembly of species under adaptive dynamics with mutations of non-negligible size. By reconciling competition-colonization tradeoff theory with co-evolutionary dynamics, our results reveal the importance of intermediate levels of competitive uncertainty for the evolutionary assembly of species

Where Two Are Fighting, the Third Wins: Stronger Selection Facilitates Greater Polymorphism in Traits Conferring Competition-Dispersal Tradeoffs

A major conundrum in evolution is that, despite natural selection, polymorphism is still omnipresent in nature: Numerous species exhibit multiple morphs, namely several abundant values of an important trait. Polymorphism is particularly prevalent in asymmetric traits, which are beneficial to their carrier in disruptive competitive interference but at the same time bear disadvantages in other aspects, such as greater mortality or lower fecundity. Here we focus on asymmetric traits in which a better competitor disperses fewer offspring in the absence of competition. We report a general pattern in which polymorphic populations emerge when disruptive selection increases: The stronger the selection, the greater the number of morphs that evolve. This pattern is general and is insensitive to the form of the fitness function. The pattern is somewhat counterintuitive since directional selection is excepted to sharpen the trait distribution and thereby reduce its diversity (but note that similar patterns were suggested in studies that demonstrated increased biodiversity as local selection increases in ecological communities). We explain the underlying mechanism in which stronger selection drives the population towards more competitive values of the trait, which in turn reduces the population density, thereby enabling lesser competitors to stably persist with reduced need to directly compete. Thus, we believe that the pattern is more general and may apply to asymmetric traits more broadly. This robust pattern suggests a comparative, unified explanation to a variety of polymorphic traits in nature.ope

Nonlinear and Multiplayer Evolutionary Games

Classical evolutionary game theory has typically considered populations within which randomly selected pairs of individuals play games against each other, and the resulting payoff functions are linear. These simple functions have led to a number of pleasing results for the dynamic theory, the static theory of evolutionarily stable strategies, and the relationship between them. We discuss such games, together with a basic introduction to evolutionary game theory, in Sect. 5.1. Realistic populations, however, will generally not have these nice properties, and the payoffs will be nonlinear. In Sect. 5.2 we discuss various ways in which nonlinearity can appear in evolutionary games, including pairwise games with strategy-dependent interaction rates, and playing the field games, where payoffs depend upon the entire population composition, and not on individual games. In Sect. 5.3 we consider multiplayer games, where payoffs are the result of interactions between groups of size greater than two, which again leads to nonlinearity, and a breakdown of some of the classical results of Sect. 5.1. Finally in Sect. 5.4 we summarise and discuss the previous sections