Efficient algorithms for sampling feasible sets of macroecological patterns

Ecological variables such as species richness (S) and total abundance (N) can strongly influence the forms of macroecological patterns. For example, the majority of variation in the species abundance distribution (SAD) can often be explained by the majority of possible forms having the same N and S, i.e. the feasible set. The feasible set reveals how variables such as N and S determine observable variation and whether empirical patterns are exceptional to the majority of possible forms. However, this approach has currently only been applied to the SAD using relatively inefficient random sampling algorithms. We extend the use of the feasible set approach by developing new algorithms to efficiently generate random samples of the feasible set for the SAD and the intraspecific spatial abundance distribution (SSAD). These algorithms are often several orders of magnitude faster than a previous method, which greatly increases the size and diversity of communities that can be examined.