| Abstract: |
| The question of how competing species coexist remains a major challenge in theoretical and mathematical ecology. Disturbance and the subsequent progression of competitive dynamics--or /textit{aging} of patches--have been posited as creating opportunities for coexistence. However, prior work studying this possibility has limitations. Most importantly it has not clearly delineated coexistence opportunities that arise from explicit consideration of the progression of competitive dynamics with patch aging. Here we study a nonlinear PDE model which accounts for patch aging while remaining analytically tractable in many cases. We consider two types of density-dependence under disturbance: $1$) on reproduction and $2$) on recruitment. We analyze when the models allow coexistence that is \textit{feasible} (both species have positive populations) and \textit{stable} (mutual positive long-term invasions). We confirm our results using a $2$nd order flux limiter numerical method. Under density-dependent recruitment, our model does not permit feasible coexistence. Under density-dependent reproduction, a reproduction-survival trade-off allows for feasible and stable coexistence. One species must have both higher reproduction and higher mortality than the other. Intermediate relative reproduction and death rates--which could arise from intermediate values of disturbance--lead to a wider coexistence region. |
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