Scale dependency in the functional form of the distance decay relationship

Abstract

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.

β‐diversity scaling patterns are consistent across metrics and taxa

“…The fact that species replacement, rather than change in species richness, was the main driver of compositional change across the scale gradient offers important insights for the underlying processes driving β‐diversity at different spatial scales. It also has implications for both our understanding of spatiotemporal dynamics of biodiversity change and conservation (Baselga , Dornelas et al , Magurran et al , McGill et al , Socolar et al 2016), highlighting that substantial changes in community composition might be occurring, despite species richness remaining seemingly stable. A recent meta‐analysis by Soininen et al (2017) also found turnover to be the dominant component of β‐diversity across different latitudes, spatial extents and taxa.…”

“…not spatially explicit), while the second approach typically regresses pairwise site comparisons vs geographic distance (distance–decay relationship (DDR); Nekola and White 1999, Morlon et al ). DDR are often well fitted by exponential or power law curves, and β‐diversity is then summarized as the rate of change from this curve (Nekola and McGill ). Additionally, β‐diversity may reflect two underlying phenomena – turnover and nestedness.…”

Variation among European beetle taxa in patterns of distance decay of similarity suggests a major role of dispersal processes

“…Each of these presence/ absence tables was used to compute the similarity between pairs of territories using the Simpson's similarity index (1 − β sim  a/[a + min(b,c)]) in R package 'betapart' (Baselga and Orme 2012), where a is the number of species present in both territories, and b and c the number of species unique to one or another, respectively. Theory suggests that the negative exponential model should better describe distance decay patterns at large spatial scales (Nekola and McGill 2014), as the one we are studying. Then, for each taxon and region (i.e.…”

First evidence for long‐term stasis in wet‐tropics land snail community composition

“…Here we compare species turnover and accumulation patterns in comparable temperate (Slovakia and the Czech Republic) and tropical (Malaysian Borneo) land snail datasets. Such directional change in the regional species pool is supported by extensive fossil evidence (Ložek 1964) and is further documented by the exponential form of the temporal DD relationship (Nekola and McGill 2014). Highly significant temporal distance decay (DD) in species composition was noted ( Fig.…”

“…Such directional change in the regional species pool is supported by extensive fossil evidence (Ložek 1964) and is further documented by the exponential form of the temporal DD relationship (Nekola and McGill 2014). Observed turnover in the temperate system was expected given regional biome change from the cold and dry LGM to wet and warm modern.…”