EVOP Subgroup Contributed Talks

Hong Duong

University of Birmingham

"Statistics of the number of equilibria: Evolutionary Game Theory meets Random Polynomial Theory"

Random evolutionary games, where the payoff entries are random variables, play an important role in the modelling of social and biological systems under uncertainty which is due to, for instance, the lack of information or the rapidly change of environment. As in classical game theory with the foundational concept of Nash equilibrium, the analysis of equilibrium points in evolutionary game theory has been of special interest because these equilibrium points provide essential understanding of complexity in a dynamical system, such as its behavioural, cultural or biological diversity and the maintenance of polymorphism.In this talk, I will discuss our recent works on the statistics of the number of equilibriums in multi-player multi-strategy games. Existing methods in the literature involve solving a system of polynomial equations, thus are restricted to systems consisting of small numbers of players and/or strategies due to Abel's impossibility theorem. By connecting to the rich theory of random polynomial theory, our approach allows overcoming this difficulty, enabling us to study general systems with arbitrarily large numbers of strategies and players.

Enrico Di Gaspero

Bielefeld University

"Phylogeny and population genetics: The mutation process on the ancestral line"

We consider a well-known observation at the interface of phylogeny and population genetics: Mutation rates estimated via phylogenetic methods tend to be much smaller than direct estimates from pedigree studies. To understand this, we consider the Moran model with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the distant past, far beyond the most recent common ancestor of the population (thus connecting population genetics to phylogeny) and analyze the mutation process along this line. We use a probabilistic tool, namely the pruned lookdown ancestral selection graph, which consists of the set of potential ancestors of the sampled individual at any given time. A crucial observation is that the mutation process on the ancestral line is not a Markov process by itself, but it becomes Markov when consindering a broader state space. Relative to the neutral case (that is, without selection), we obtain a general bias towards beneficial mutations, while (depending on the parameters) both a speedup and a slowdown of the mutation process are possible. These results shed new light on previous analytical findings of Fearnhead (2002).

Yuriy Pichugin

Max Planck Institute for Evolutionary Biology

"Mass conservation restricts the possible modes of microbial reproduction"

Multiple modes of asexual reproduction are observed among microbial organisms in natural populations. These modes are not only subject to evolution, but may drive evolutionary competition directly through their impact on population growth rates. The most prominent transition between two such modes is the one from unicellularity to multicellularity. So far, an analysis of general reproduction modes in terms of the optimality of the biomass distribution between daughter organisms is missing. We found that such considerations can greatly reduce the number of possible reproduction modes. This has important direct implications on microbial life: For unicellular species, the interplay between cell shape and kinetics of the cell growth implies that the largest and the smallest possible cells should be rod-shaped rather than spherical. For primitive multicellular species, these considerations can explain why rosette cell colonies evolved a mechanistically complex binary split reproduction. Finally, we show that the loss of organism mass during sporulation can explain the macroscopic sizes of the formally unicellular microorganism Myxomycetes plasmodium. Our findings demonstrate that a number of seemingly unconnected phenomena observed in unrelated species may be different manifestations of the same underlying process.

Max Schmid

University of Lausanne, Switzerland

"Spatial heterogeneity and frequency-dependent selection under limited dispersal: Where kin, divergent and disruptive selection meet"

Different ecological processes lead to polymorphism at different spatial scales. While spatially divergent selection favors phenotypic differentiation between habitats, competitive exclusion promotes variation within patches. Both of these processes have been shown to depend on dispersal. High dispersal can restrict spatial phenotypic variation when counteracting local adaptation, while facilitating phenotypic variation within groups when reducing kin competition. Here, we investigate the evolution of quantitative traits that control the feeding rate on resources when both processes act in concert. Using the adaptive dynamics framework, we study intra-specific competition for locally and globally varying resources that triggered both divergent and negative frequency-dependent selection. We derive explicit expressions for the selection gradient and the disruptive selection coefficient for an infinite island model, while accounting for kin selection when patch sizes were small. We further tested the analytical predictions using individual-based simulations. Our results illustrate the relationship between the spatial scale of resource variation and the resulting intra-specific polymorphism in consumer traits. We further discuss how phenotypic polymorphism varies with regard to dispersal rate, patch size, and life history. All in all, our results shed light on the interaction between two major drivers of biological diversity in spatially varying environments when dispersal was limited.