Disentangling eco-evolutionary effects on trait fixation

Abstract

In population genetics, fixation of traits in a demographically changing population under frequencyindependent selection has been extensively analyzed. In evolutionary game theory, models of fixation have typically focused on fixed population sizes and frequency-dependent selection. However, combining ecological fluctuations with frequency-dependent interactions such as Lotka-Volterra dynamics and thus the analysis of eco-evolutionary fixation has received comparatively little attention. Here, we consider a two-type stochastic competitive Lotka-Volterra model with higher order interactions. The emerging individual based model allows for stochastic fluctuations not just in the frequencies of the two types but the total population size as well. Assuming weak selective di↵erences between the traits we approximate the fixation probability for di↵ering competition coe cients. We find that it resembles qualitatively the corresponding evolutionary deterministic dynamics within a population of fixed size. Furthermore, we analyze and partially disentangle the selection e↵ects into their ecological and evolutionary components. Concretely, we show that the evolutionary selection intensity has a larger e↵ect on the predictive power of our approximation than the ecological selection. However, the fixed points themselves are also a↵ected by the selection intensity which implies that a clean separation of the ecological and evolutionary impacts on the evolutionary outcome of the model is not possible. The entanglement of eco-evolutionary processes in a co-evolutionary system is thus a reality which needs to be considered when determining the fixation properties in populations of fluctuating size.

From Fixation Probabilities to d-player Games: An Inverse Problem in Evolutionary Dynamics

“…Indeed, we will show that almost any arbitrary interaction can be modelled by d-player game theory, provided we do not impose any restriction on the game size. As already observed Wu et al, 2013;Pena et al, 2014;Souza, 2016, 2017;Czuppon and Gokhale, 2018;Chalub and Souza, 2018), d-player games with d ≥ 3 can exhibit quite distinct behaviour from the 2-player ones. In the multi-type case, we expect that a similar approach might work, but much remains to be done-indeed, multi-type evolution is an important source of open mathematical problems.…”

Neutral competition in a deterministically changing environment: Revisiting continuum approaches

“…This assumption greatly simplifies the resulting mathematics by reducing the number of stochastic variables by one. Separately, there is a growing literature on stochastic competition models that relax this constant-population assumption, but do not consider environmental effects [31,32,33,34,35,36,37,38,39]. A natural way to simultaneously approach both a fluctuating environment and a variable population size is to incorporate the changing environment deterministically, as we do in this work.…”

Understanding evolutionary and ecological dynamics using a continuum limit

“…Applications of these finite population size approximations are abundant and cover diverse topics (e.g. Reichenbach et al, 2007;Assaf and Mobilia, 2011;Houchmandzadeh, 2015;Constable et al, 2016;Débarre and Otto, 2016;Kang and Park, 2017;Koopmann et al, 2017;Serrao and Täuber, 2017;Czuppon and Gokhale, 2018;Czuppon and Traulsen, 2018;Parsons et al, 2018;McLeod and Day, 2019;Schenk et al, 2019).…”