EVOP Subgroup Contributed Talks

Laurence Ketchemen Tchouaga

University of Ottawa

"Population density in fragmented landscapes under monostable and bistable dynamics"

A model for a single species population which propagates in a heterogeneous landscape in a one dimensional space is presented. The landscape is composed of two kind of patches with different diffusivities. The dynamics of the population is studied through a reaction diffusion model on which the net growth function can be a monostable or bistable function. In addition, we consider that at the interface between patch types, individuals may show preference for more favorable regions. We study the different nonlinear steady state models. We prove existence of monotone solution in each model and classify their qualitative shape. An analysis is done to study the effect of the diffusivity coefficient. A stability analysis is also done for each model.

Luigi Esercito

Bielefeld University

"Lines of descent in a Moran model with frequency-dependent selection and mutation"

Dealing with the interplay of mutation and selection is one of the important challenges in population genetics. We consider two variants of the two-type Moran model with mutation and frequency-dependent selection, namely a scheme with nonlinear dominance and another with what we name fittest-type-wins scheme. We show the equivalence of the two variants and pursue the latter for further analysis.In particular, we trace the genealogy of a sample of individuals backward in time, via an appropriate version of the so-called ancestral selection graph (ASG), originally introduced by Krone and Neuhauser. We use the information contained in mutation events to reduce the ASG to the parts informative with respect to the type distribution of the present population and their ancestors, respectively. This leads to the killed ASG and the pruned lookdown ASG in this setting, which we use to derive representations for the (factorial) moments of the type distribution and the ancestral type distribution by connecting forward and backward graphical models via duality relationships.Finally, we show how the results carry over to the diffusion limit.[1] Baake, Ellen, Luigi Esercito, and Sebastian Hummel. 'Lines of descent in a Moran model with frequency-dependent selection and mutation.' textit{arXiv preprint arXiv:2011.08888} (2020).

Léonard Dekens

Institut Camille Jordan, Université Claude Bernard Lyon 1

"Quantitative Trait in a Patchy Environment: Beneath the Gaussian Approximation"

Assuming Gaussian trait distributions is central in quantitative genetic models in order to describe complex evolutionary dynamics, like source-sink scenarii in heterogeneous environments. However, the mechanisms of why and when this is a reasonable approximation remain unclear. Here, we investigate the underlying role of sexual reproduction by introducing a new framework that directly involves the dynamics of the trait distributions. We opt for an infinitesimal model operator to model the transmission of a complex trait under sexual reproduction. We apply this approach to revisit a classical study in a patchy environment (following Ronce and Kirkpatrick 2001). We first justify the Gaussian assumption in a small variance regime with perturbative techniques. We next perform a rigorous separation of ecological and evolutionary time scales to complete the analytical description of source-sink type equilibria, numerically described in Ronce and Kirkpatrick 2001. Our analysis highlights the relative influence of the blending effects of migration and sexual reproduction on local adaptation patterns.