Relating the Strength of Density Dependence and the Spatial Distribution of Individuals

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.

Investigating spatiotemporal patterns, spatial density dependence and fruit quality in a plant-bruchine-parasitoids system

“…However, inverse spatial densitydependent patterns have also been shown to be relevant for population regulation, both in space and time (Hassell 2000;White 2011), particularly because some natural enemies can find their hosts or prey at low densities, thus avoiding population outbreaks. Thus, for any natural system, the search for density-dependent patterns is fundamentally relevant for understanding the processes that contribute to population stability (Johnson 2006;Brush and Harte 2021). Historically, however, the detection of the density dependence has not been trivial.…”

Spatial patterning of Wyoming big sagebrush indicates negative density dependence

“…Some dryland plant communities display a distinct patchiness controlled by an ever‐shifting balance of facilitation and competition (Aguiar & Sala, 1999), where plant cover is relatively low and bare “interspaces” often comprise more than 60% of cover (Sala & Aguiar, 1995; Figure 2). The spatial patterning of desert shrubs has been found to exhibit an aggregated dispersion pattern in early successional stages, which shift toward a more regular or random as plants mature (Brush & Harte, 2021; Greig‐Smith & Chadwick, 1965; Figure 1). Phillips and MacMahon (1981) found that as they grew, shrubs in the Mojave Desert transitioned from clumped, to random, to regular dispersion.…”