Neutral competition in a deterministically changing environment: Revisiting continuum approaches

Abstract

Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an environment that fluctuates periodically in time. We adapt methods from work on these classical models to investigate the effects of the magnitude and frequency of environmental fluctuations on two important population statistics: the probability of fixation and the mean time to fixation. In particular, we find that for small frequencies, the system behaves similar to a system with a constant fitness difference between the two species, and for large frequencies, the system behaves similar to a neutrally competitive model. Most interestingly, the system exhibits nontrivial behavior for intermediate frequencies.We conclude by showing that our results agree quite well with recent theoretical work on competitive models with a stochastically changing environment, and discuss how the methods we develop ease the mathematical analysis required to study such models.

Species coexistence and temporal environmental fluctuations: a quantitative comparison between stochastic and seasonal variations

“…This is an old result, first obtained in Kimura [39]. Interestingly, Murray and Young [40] obtained this neutral-like results, for both the chace of ultimate fixation and the persistence time, using a model with global competition. They consider the parameter regime in which γ 2 is negligible, so the expressions in (10) reduce to those of (9).…”

How the storage effect and the number of temporal niches affect biodiversity in stochastic and seasonal environments

“…This is an old result, first obtained in [ 42 ], and we expect this behavior also in the local-periodic case. Interestingly, [ 43 ] obtained this neutral-like results, for both the chance of ultimate fixation and the persistence time, using a model with global competition. They consider the parameter regime in which γ 2 is negligible, so the expressions in (10) reduce to those of (9) .…”

Proposal of an open-source computational toolbox for solving PDEs in the context of chemical reaction engineering using FEniCS and complementary components

“…The FEniCS Project has been used within a wide range of research fields, such as tidal energy, geoscience, fluid mechanics, theoretical biology, strain gradient elasticity, biophysics and metamodelling (Abali, 2019;Epanchintsev et al, 2016;Funke et al, 2019;Goodwin et al, 2019;Haagenson et al, 2020;Jane cka et al, 2019;Lejeune, 2020;Murray and Young, 2020;Phunpeng and Baiz, 2015;Zhu and Yan, 2019). Abali (2017), for instance, demonstrated several modelling examples with different engineering applications through a continuum mechanics approach.…”