Modeling non-competitive and competitive ecological interactions: Implications for coexistence, invasion, and the importance of spatial scale of interactions.
Eppstein, Margaret*,1, Molofsky, Jane2, 1 Department of Computer Science, Burlington, Vermont2 Department of Botany, Burlington, Vermont
ABSTRACT- Previous models of ecological community dynamics have largely focused on competitive interactions. Spatially explicit formulations of these models have shown that changing the scale of spatial interactions alters the region of the parameter space where equilibrium coexistence can occur. While reductions in scale generally reduce the regions of coexistence, certain asymmetric differences in scale of intra- and inter-specific competitive interactions have also been shown to promote coexistence where not predicted by a mean-field approximation. Molofsky and colleagues have proposed a spatially explicit model that focuses on symmetric intra-specific non-competitive frequency dependent interactions. One important finding of the latter model is that strong symmetric positive intra-specific frequency dependent interactions over limited spatial range can result in cluster formation that promotes coexistence. However, Molofsky's previous model of non-competitive interactions assumes symmetric intra-specific interactions, with no inter-specific interactions. Here, we present a general multi-species model that incorporates universal inter- and intra-specific competitive interactions as well as frequency and/or density dependent non-competitive interactions, each of which can occur over unique spatial scales. By judicious choices of parameter values, we show how this new model can be made to reduce to (and is therefore more general than) the Lotka-Volterra model, the voter model, and the frequency dependent model of Molofsky. As an initial application of the model, we focus on the outcome of asymmetric non-competitive interactions in simulated two species annual plant communities and compare simulated mean field results with spatially explicit formulations. We find that in certain regions of this previously unexplored parameter space, limiting the spatial range of interactions can either promote or prevent coexistence or invasiveness, relative to mean-field approximations. These results have important implications for understanding what maintains diversity in ecological communities.
Key words: non-competitive interactions, spatially explicit, population dynamics, community structure
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