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Abstract

In population genetics, fixation of traits in a demographically changing population under frequency-independent 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 differences between the traits we approximate the fixation probability for differing competition coefficients. 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 effects into their ecological and evolutionary components. Concretely, we show that the evolutionary selection intensity has a larger effect on the predictive power of our approximation than the ecological selection. However, the fixed points themselves are also affected 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.