Two of the most iconic patterns in spatial ecology are the manner in which diversity changes as plot area changes (scaling metrics, such as the species-area relationship) and the manner in which the similarity in diversity between two plots changes as the distance between those plots changes (turnover metrics, such as the Sorensen index). It has long been wondered whether these scaling and turnover patterns are fundamentally related, or whether they are free to vary independently in any given community. Here I demonstrate that in the single species context, these two patterns are quantitatively linked, such that equations describing a plot-scaling pattern can be used to calculate a plot-turnover pattern, or vice versa. Specifically, I show that the spatial form of Taylor’s Law, the relationship between the mean and variance in abundance in a plot, can be exactly related to a turnover metric defined as the conditional probability that a species will be present in one plot given its presence in another plot at some distance away (a single-species analogue to the Sorensen index). This relationship is very general, requiring only knowledge of Taylor’s Law and the parametric form, but not the parameters, of an appropriate bivariate abundance distribution for two plots.
Results/Conclusions
For the case of two linear plots, such as two segments along a stream separated by a known distance, many results can be derived and expressed in simple terms. Results for square plots are more difficult to express in simple forms but are qualitatively similar. The turnover metric decreases with a decrease in the slope of Taylor’s Law, an increase in its intercept, or an increase in inter-plot distance. For many realistic combinations of parameters, turnover reaches a steady state value, with presences in the two plots being independent, before inter-plot distances reach one thousand times the plot width. However, relatively large but realistic intercepts and slopes of Taylor’s Law lead to a longer-tailed decline, with turnover not reaching its limit until up to 108 times plot width. This suggests that, at least in some communities, plot abundances may have the potential to be correlated at distances far larger than usually assumed. These findings demonstrate broadly that plot scaling and turnover patterns are fundamentally related, pointing the way towards more flexible biodiversity sampling designs and the development of multi-patch, multi-species scaling and turnover metrics.