Coherence, species turnover, and boundary clumping: elements of meta-community structure

Ecologists have identified several kinds of pattern in the distribution of species among sites, including a) nested subsets, b) checkerboards, c) Clementsian gradients, d) Gleasonian gradients, and e) evenly spaced gradients. Most past efforts to diagnose such patterns have focused on only one at a time, often contrasted with a sixth type of pattern, f) "randomness". While there are statistical tests to distinguish each of the first five patterns from randomness, there are currently no established methods for discriminating among these first five patterns in a given data set. Here we propose a method that will identify which of these possibilities is most prevalent in a site-by-species incidence matrix based on three basic aspects of meta-community structure. Our method is based on first ordinating the incidence matrix to identify the dominant axis of variation and identifying three aspects variation along this dominant axis. The first aspect, "coherence", is the degree to which pattern can be collapsed into a single dimension. The second, "species turnover", describes the number of species replacements along this dimension. The third aspect, "boundary clumping", has to do with how the edges of species boundaries are distributed along this dimension. We present methods for analyzing these three aspects of meta-community structure, use them to identify the six different patterns, and illustrate them with a representative set of cases drawn from previously published data.