Beta diversity as a function of sample size and distance

When taking spatially explicit data on species diversity, distance and sample size are inherently confounded. When we increase the size of two samples of individuals from the same geographical region, we expect the similarity in the species composition of the two samples to increase (or beta diversity to decrease). On the other hand, when we increase the distance between the samples' locations, we expect the similarity in the species composition to decrease (or beta diversity to increase). This will happen, for example, if one takes transect data in opposite directions from a central starting point. In this case, sample size increases as the length of the transect increases, and the average separation between samples along the transect also increases. In this and similar situations, we predict that turnover indices, such as the Jaccard index, will first increase, reach a maximum, and then decrease. Data on North America tree species ranges confirm the humped-shaped curves for the turnover indices, but also that these curves can take many shapes depending upon how beta diversity patterns vary among different communities. Using simulations based on neutral theory, we also recovered the same qualitative patterns. In addition we show that when species are more spatially aggregated, then the minimum in beta diversity occurs for smaller sample sizes.