Extended Data Fig. 1: Simulations of the null expectation under the random sampling hypothesis for varying degrees of within-species aggregation.

To evaluate the robustness of the null expectation of a zero slope of biodiversity patterns in standardized samples with fragment size, we took different-sized samples from a simulated landscape and estimated biodiversity patterns. a, Examples of landscapes with different levels of intraspecific aggregation (left to right is from completely random to most-aggregated). From within each of these landscapes, we illustrate four different fragment sizes (shaded squares), and then take standardized (constant-sized) samples from each fragment. b, Density plots showing slope estimates of linear models fit to numbers of individuals (top), species richness (centre) and evenness (bottom) as a function of fragment areas for 2,000 simulated landscapes of each level of aggregation. Both the response and fragment area were log-transformed before model fitting. Densities are shaded by quantiles and the black diamond shows the median for each combination of aggregation and metric; vertical dashed line shows the zero expectation and the median result is given. In some cases, the median result lies very slightly above or below zero (though this does not seem to be associated with levels of aggregation). This is an outcome of the stochastic simulation we performed, and is sensitive to parameters and numbers of iterations, and thus we do not perform statistical tests.