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 α, a parameter indicating the degree of density dependence. This model can therefore be interpreted as a hybridization of MaxEnt and mechanism. Our model shows quantitatively and generally that increasing density dependence randomizes spatial patterning. α = 1 recovers the strongly aggregated METE distribution that is consistent with many ecosystems empirically, and as α → 2 our prediction approaches the binomial distribution consistent with random placement. For 1 < α < 2, our model predicts more aggregation than random placement but less than METE. We additionally relate our mechanistic parameter α 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 α for individual species as well as a community α parameter. We find that α 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.
Highlights
Spatial patterns in ecology have been studied extensively (e.g., Wiegand and Moloney, 2013; Diggle, 2014), and contain useful information about what processes shape ecosystems (Law et al, 2009; Brown et al, 2011; Münkemüller et al, 2020)
Our model predicts that increasing negative density dependence leads to more random spatial patterning, and less density dependence leads to stronger aggregation
For both serpentine and Barro Colorado Island (BCI) at all scales considered, we find that the Akaike Information Criterion (AIC) is lower with species-level α compared to a single community α, despite the inclusion of 9 more parameters in the case of the serpentine data and 228 more parameters in the case of the BCI data
Summary
Spatial patterns in ecology have been studied extensively (e.g., Wiegand and Moloney, 2013; Diggle, 2014), and contain useful information about what processes shape ecosystems (Law et al, 2009; Brown et al, 2011; Münkemüller et al, 2020). Quantitative understanding of these patterns can be used to infer the importance of various mechanisms, and illuminate underlying. A common approach to quantifying these patterns is the use of various summary statistics (Wiegand et al, 2013), which have been shown to be able to distinguish different ecological mechanisms (Brown et al, 2016). We focus on the effects of this ecological mechanism on spatial patterning
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