A general framework for the distance-decay of similarity in ecological communities

Abstract

Species spatial turnover, or beta-diversity, induces a decay of community similarity with geographic distance known as the distance-decay relationship. Although this relationship is central to biodiversity and biogeography, its theoretical underpinnings remain poorly understood. Here, we develop a general framework to describe how the distance-decay relationship is influenced by population aggregation and the landscape-scale species-abundance distribution. We utilize this general framework and data from three tropical forests to show that rare species have a weak influence on distance-decay curves, and that overall similarity and rates of decay are primarily influenced by species abundances and population aggregation respectively. We illustrate the utility of the framework by deriving an exact analytical expression of the distance-decay relationship when population aggregation is characterized by the Poisson Cluster Process. Our study provides a foundation for understanding the distance-decay relationship, and for predicting and testing patterns of beta-diversity under competing theories in ecology.

Figure 1

Example of (a) the relative neighbourhood density Ω and (b) the neighbourhood occurrence probability curves ψ* for (c) four tropical forest species in Korup National Park, Cameroon. Ω and ψ* are tightly linked: when a species is aggregated (i.e. Crotonogyne strigosa, Rinorea thomasii), both the relative neighbourhood density Ω and the neighbourhood occurrence probability ψ* are decreasing functions of distance. When a species is uniformly distributed (i.e. Diospyros gabunensis, Mareyopsis longifolia), neither Ω nor ψ* depend on distance. Aggregation mainly influences the shape of ψ*, and abundance its overall value. Here, ψ* is calculated in a 20 × 20 m quadrat nested in the 50-ha plot (a = 0.0008).

Figure 2

Conceptual figure illustrating the hypothetical influence of landscape-scale abundances, sampling and population aggregation on the distance–decay relationship, as suggested by eqn 2. We consider abundance n and sample area a in parallel because they are expected to have the same effect on the distance–decay relationship (community similarity at a given distance is a function of the average number of individuals in a sample an). From left to right: with comparable landscape-scale species abundances and sample area, increased aggregation (steeper decays of Ω with distance) induces steeper decays in community similarity and lower similarity values at large distances. From bottom to top: with comparable aggregation, increased landscape-scale abundances (or equivalently increased sample areas), induce high overall similarity. Dashed lines: long dashed lines reflect high aggregation, dotted lines reflect moderate aggregation. In highly aggregated communities, the distance–decay slope can be influenced by abundance and sampling at the boundaries of low and high similarity values.

Figure 3

Influence of landscape-scale abundance, population aggregation and sampling on the distance–decay relationship in Korup. (a) An increasing proportion of the rarest (lines going up) or most abundant (lines going down) species are removed from the forest. Removing species with fewer than 50 individuals corresponds to considering only 55% of the landscape-scale species pool, yet this removal has very little effect on the relationship. At the other side of the spectrum, removing only 2% of the most abundant species substantially affects overall similarity. (b) An increasing proportion of the most aggregated (lines going up) or least aggregated (lines going down) species is removed from the forest. Only species with > 50 individuals are considered (Condit et al. 2000). (c) Sample area substantially influence rate of decays only at the smallest sample area. In (a) and (b), distance–decay plots correspond to 20 × 20 m samples nested in the 50 ha plot (A = 0.04 ha, a = 0.0008). See Appendix SD for similar results in BCI and Yasuni and log-linear plots emphasizing the effect of aggregation.

Figure 4

Distributions of clustering parameters estimated by the Poisson Cluster Process (a) The distributions of mean clump radius appear log-normal (in Yasuni) to right-skewed log-normal (in BCI and Korup); plotted on a linear scale, they are characterized by left-skewed shapes similar to those observed by Plotkin et al. (2000) (their fig. 5; see Appendix SE). (b–c) The distributions of number of clumps ρA₀ and number of individuals per clump μ vary greatly between forests: species with few clusters and many individuals per cluster are common in Korup, but scarce in Yasuni, where species tend to be clumped in more clusters with fewer individuals. (d) Topographic maps and typical spatial distributions for trees in Yasuni, BCI and Korup.

Figure 5

Dependence of (a) the mean clump radius (b) the number of clumps ρA₀, (c) the mean number of individuals per clump μ and (d) the relative neighbourhood density Ω_0-10 on a species’ abundance n. All correlations are significant (Spearman test, P < 0.05); b-values correspond to the slope of the log–log regression of the parameters against abundance.

Figure 6

Comparison of theory with data in Yasuni, BCI and Korup (a) distance–decay curves reported for 25 × 25 m samples (A = 0.0625 ha), (b) species–area curves, (c) species-abundance distributions. The diamonds represent observed data. The red solid lines represent curves predicted by the Poisson Cluster Process (eqn 5). The white area represents the 95% confidence intervals produced by simulation of the Poisson Cluster Process. The green dashed lines represent curves predicted when assuming random placement (Appendix SF). The sensitivity of the results to sample area is presented in Appendix SF.