Fixation in the stochastic Lotka-Volterra model with small fitness trade-offs

Glenn Young; Andrew Belmonte

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arXiv · 1809.06917

Fixation in the stochastic Lotka-Volterra model with small fitness trade-offs

Glenn Young·Andrew Belmonte

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Abstract

We study the probability of fixation in a stochastic two-species competition model. By identifying a naturally occurring fast timescale, we derive an approximation to the associated backward Kolmogorov equation that allows us to obtain an explicit closed form solution for the probability of fixation of either species. We use our result to study fitness tradeoff strategies and show that, despite some tradeoffs having nearly negligible effects on the corresponding deterministic dynamics, they can have large implications for the outcome of the stochastic system.

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Glenn Young, Andrew Belmonte. 2018-09-18. Fixation in the stochastic Lotka-Volterra model with small fitness trade-offs. https://arxiv.org/abs/1809.06917

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