The checkerboard score and species distributions

Abstract

There has been an ongoing controversy over how to decide whether the distribution of species is "random" - i.e., whether it is not greatly different from what it would be if species did not interact. We recently showed (Roberts and Stone (1990)) that in the case of the Vanuatu (formerly New Hebrides) avifauna, the number of islands shared by species pairs was incompatible with a "random" null hypothesis. However, it was difficult to determine the causes or direction of the community's exceptionality. In this paper, the latter problem is examined further. We use Diamond's (1975) notion of checkerboard distributions (originally developed as an indicator of competition) and construct a C-score statistic which quantifies "checkerboardedness". This statistic is based on the way two species might colonise a pair of islands; whenever each species colonises a different island this adds 1 to the C-score. Following Connor and Simberloff (1979) we generate a "control group" of random colonisation patterns (matrices), and use the C-score to determine their checkerboard characteristics. As an alternative mode of enquiry, we make slight alterations to the observed data, repeating this process many times so as to obtain another "control group". In both cases, when we compare the observed data for the Vanuatu avifauna and the Antillean bat communities with that given by their respective "control group", we find that these communities have significantly large checkerboard distributions, making implausible the hypothesis that their species distributions are a product of random colonisation.

Assembly rules in Muscid Fly assemblages in the grasslands Biome of Southern Brazil

“…On the other hand, if the co-occurrence index of the original matrix is above the 95% confi dence interval of the randomized matrices, the null hypothesis should be rejected and the role of competition in structuring the studied competitions is confi rmed. Finally, if the observed C-score is smaller than that estimated in the null model, the observed occurrence patterns are most consistent with aggregation that with segregation (Stone & Roberts 1990).…”

“…The C-score was used as the community structure index based on species interactions (Stone & Roberts 1990). This index is the average of the "checkerboard units" calculated for all species pairs that occurred at least once in the same group.…”

“…All simulations were carried out using the "swap" algorithm, in which the original matrix is resample repeatedly, generating random submatrices (Stone & Roberts 1990, but see Gotelli 2000, Gotelli & Entsminger 2001b.…”

A poke into the diversity and associations within human anterior nare microbial communities

“…Only relationships between phylotypes that were present in at least 10% and no more than 80% of samples were evaluated (yielding a list of 11 available phylotypes and thus 55 pairwise comparisons). Random matrices for generating standardized scores (C-score) (Stone and Roberts, 1990) and significance levels (P-values) were obtained using the fixed row (phylotypes)-fixed column (anterior nare samples) constraints algorithm, and 100 random matrices were computed from the binary data matrix. Significant species underdispersion or overdispersion results in Z-transformed scores (observed C-score-expected C-score/standard deviation) above 1.96 or below À1.96 (at the 5% error level) (Ulrich and Zalewski, 2006).…”

River organic matter shapes microbial communities in the sediment of the Rhône prodelta

“…The significance was tested against a null model (999 random permutations across the entire phylogeny). To check for nonrandom co-occurrence patterns, a checkerboard score (C-score) (Stone and Roberts 1990;Horner-Devine et al, 2007) was calculated for the different OTU tables. This was tested for significance against a null model preserving sample frequencies.…”