Density dependence and a colonization rule predict spatial patterning

Abstract

Spatial patterns in ecology contain useful information about underlying mechanisms and processes. Although there are many summary statistics used to quantify these spatial patterns, there are far fewer models that directly link explicit ecological mechanisms to observed patterns easily derived from available data. We present a model of intraspecific spatial aggregation that quantitatively relates static spatial patterning to negative density dependence. Individuals are placed according to the colonization rule consistent with the Maximum Entropy Theory of Ecology (METE), and die with probability proportional to their abundance raised to a power , a parameter indicating the degree of density dependence. Our model shows quantitatively and generally that increasing density dependence randomizes spatial patterning. = 1 recovers the strongly aggregated METE distribution that is consistent with many ecosystems empirically, and as [->] 2 our prediction approaches the binomial distribution consistent with random placement. In between our model predicts less aggregation than METE, but more than random placement. We additionally relate our mechanistic parameter to the statistical aggregation parameter k in the negative binomial distribution, giving it an ecological interpretation in the context of density dependence. We use our model to analyze two contrasting datasets, a 50 ha tropical forest and a 64 m2 serpentine grassland plot. For each dataset, we infer for individual species as well as a community parameter. We find that is generally larger in the tightly packed forest than the sparse grassland, and the degree of density dependence increases at smaller scales. These results are consistent with current understanding in both ecosystems, and we infer this underlying density dependence using only empirical spatial patterns. Our model can easily be applied to other datasets where spatially explicit data are available.