Reduction of species coexistence through mixing in a spatial competition model

Background/Question/Methods

A long-standing question in ecology has been to identify mechanisms that maintain biodiversity. Numerous theoretical models to date have shown that inclusion of spatial structure can result in species coexistence when dispersal and interactions are strictly local.  Much of this work has been restricted to non-transitive interactions whereby different species aggregate and form cyclical patterns that lead to species coexistence. However, diversity declines when dispersal rates are high and interactions are no longer local. In such well-mixed systems, species rapidly exclude each other from sites and subsequently reduce diversity. While the effects of spatial structure on species coexistence have been studied in non-transitive systems (i.e. cyclical patterns), we lack information on other spatial mechanisms that can possibly contribute to species coexistence.

We studied the effects of spatial structure on species coexistence under varying rates of dispersal in well-mixed systems. We specifically addressed how different types of spatial patterns impacted species diversity under varying dispersal rates. Furthermore, we examined how initial extinction rates varied under different dispersal rates. To this extent, we developed a stochastic cellular automata model to investigate how different spatial mechanisms contribute to species diversity under varying dispersal rates.

Results/Conclusions

We present simulation results of our model investigating species coexistence in a well-mixed system. We found that diversity is significantly reduced when species form cyclical spatial patterns, while diversity declines at a slower rate when species form mosaic spatial patterns. In the case of cyclical spatial patterns, species diversity gets rapidly lost when dispersal rates incrementally increase (i.e. local neighbors get gradually replaced by distant neighbors). Alternatively, we observe that diversity decreases at a much slower pace when species form mosaic spatial patterns. We observed significant differences in the initial extinction rates as we gradually increased stochasticity in the competition matrix. The rate of initial extinctions occurred at a much faster rate for cyclical spatial patterns. Our results have important implications for biodiversity maintenance. Our findings are in agreement with previous studies demonstrating loss of diversity when dispersal rates are high. However, we show that this fundamentally depends on the spatial mechanisms at play. While species forming cyclical spatial patterns lead to loss of diversity in well-mixed systems, we found the opposite pattern with spatial mosaic patterns. As a result, the continuum from spatial cyclical patterns to mosaic patterns provides us with important insights into the possible mechanisms of biodiversity.