The question of how competing species coexist remains a major challenge for theoretical and mathematical ecology. Disturbance, and the subsequent progression of competitive dynamics, or ‘aging’ of patches, have been posited as creating opportunities for coexistence of species competing on a landscape if they differ in life history strategy. However, models used to study this possibility lie at two extremes. The first: simple, analytically tractable models that do not model patch aging explicitly and are limited in delineating the explicit life history differences needed. The second: much more complex models with forests in mind. However, these require extensive simulation and also include size structure and hence do not delineate life-history differences enabling coexistence that may not require size structure. Here we study a simple partial differential equation (PDE) model that is still analytically tractable, but allows explicit consideration of the progression of competitive dynamics as patches age after disturbance. We consider two possible types of density-dependence for their importance in coexistence under disturbance: 1) on reproduction and 2) on recruitment. We analyze when the model allows coexistence that is feasible (both species have positive population sizes) and ‘stable’ in the sense of mutual positive long-term invasion growth rates.
Results/Conclusions
Rescaling of time in our model reveals that outcomes are determined entirely by ‘relative’ reproduction and death rates, measured relative to the disturbance rate. Under density-dependent recruitment, our model does not permit feasible coexistence. However, under density-dependent reproduction, variation between two species along a reproduction-survival trade-off allows for coexistence that is feasible and ‘stable’ (as defined above). One species must have both higher reproduction and higher mortality than the other species in order for coexistence to occur. Intermediate relative reproduction and death rates, which could arise from intermediate values of disturbance, lead to a wider coexistence region. We show that outside of the feasible coexistence region a species may initially increase but then declines to extinction rather quickly (due to the possibility that it may initially have more potential recruits in relatively empty patches, where they will be highly successful) once population dynamics proceed. Our results contrast importantly with the classical competition-colonization tradeoff model by elucidating that it is a combination of species’ reproduction and death rates that influence their coexistence under disturbance.
