Scale dependency in the functional form of the distance decay relationship

We examine a novel mathematical approach which posits that the decay of similarity in community composition with increasing distance (aka distance decay) can be modeled as the sum of individual species joint‐probability vs distance relationships. Our model, supported by analyses of these curves from three datasets (North American breeding birds, North American taiga plants, and tropical forest trees), suggest that when sampling grain is large enough to avoid absences due to stochastic sampling effects, and/or sampling extent is large enough to generate species turnover through the deterministic crossing of environmental and/or geographical range limits, species joint‐probability over increasing distance will generally exhibit exponential decay. However, at small scales where occurrence is driven more by stochastic sampling effects, species joint‐probability curves exhibit a power‐law decay form. Lacking a theoretical prediction of how individual species joint‐probability relationships combine to generate community distance decay, we also performed a meta‐analysis of 26 ecological and 4 human‐system datasets, using non‐linear regression to mean and quantile non‐linear regression at tau = 0.95 for linear, exponential, and power‐law decay forms. These analyses demonstrate that the functional form of community distance decay – as shown by comparison of AIC ranks – is largely determined by observational scale, with power law decay prevailing within domains where the species pool remains constant, while exponential decay prevails at larger scales over which the species pool varies, paralleling the patterns predicted in our mathematical approach.