Understanding the multiple processes that allow species to coexist is a fundamental goal of community ecology and a necessity for ecosystem management and conservation. Stable coexistence is jointly determined by stabilizing niche differences and fitness differences, such that the strength of stabilizing niche differences must be large enough to overcome fitness differences and prevent competitive exclusion. Currently, quantifying the strength of unique stabilizing niche differences requires simplistic mathematical models, such as the lottery model, that can be analytically solved. Here, we present a simulation-based technique for quantifying the strength of the two stabilizing spatial coexistence mechanisms of Chesson: (1) fitness-density covariance, a concentration effect measuring the importance of intraspecific aggregation of individuals, and (2) the spatial storage effect, the co-variation in abiotic conditions and competition between species. This method is not only appropriate for simple models, but also for complex models, such as those fit to specific ecosystems that have no analytical solution. We present the details of the method, show that it recovers the analytical solutions for stabilizing spatial mechanisms in a metacommunity model, and demonstrate its versatility by applying it to a complex, individual based grassland model.
Results/Conclusions
The spatial storage effect is the product of the subadditivity and covariance between environment and competition. To calculate the subadditivity, we numerically calculate the limit for both the environmental and competitive terms simultaneously. We calculate the covariance between the environment and competition by simulating the invader’s growth rate in the absence of competition, representing the environmental term, and again with the rest of the community at equilibrium, representing the competitive term. Finally, we determine fitness-density covariance by directly measuring the covariance of the invader’s growth rate and number of individuals across all locations. The method accurately recovers the strength of fitness-density covariance and the spatial storage effect when compared to previously derived analytical solutions for a metacommunity model, regardless of parameterization. We further explore the versatility of the method by applying it to an individual based grassland model, the complexity of which precludes the use of current analytical methods. We instead use the simulation-based technique to explore when below-ground and above-ground tradeoffs increase stabilizing spatial niche differences in a heterogeneous metacommunity. Our results emphasize the versatility and generality of a simulation-based method for calculating the strength of stabilizing spatial coexistence mechanisms.