In biodiversity studies, the checkerboard score or C-score is a statistic which determines the randomness of the distribution of two or more species through a collection of biomes. The statistic, first published by Stone and Roberts in 1990, expands on the earlier work of Diamond that defined a notion of "checkerboard distributions" as an indicator of species competition.
A low c-score indicates a higher randomness, i.e. a greater likelihood that the distribution of one species has not been directly affected by the presence of other species.
Definition and calculation
Given two species sp1, sp2 and n islands, an incident matrix is built. In the 2xn incident matrix, each row represents one of the two species and each column represents a different island. The matrix is then filled with each cell being set to either 0 or 1. Cell with the value of 0 means that a given species doesn't exist in the given island whilst the value of 1 means that the species do exist in the given island.
The calculation of the co-occurrence of two species sp1, sp2 in the given set of islands is done as follows:
The checkerboard score (c-score) for the colonisation pattern is then calculated as the mean number of checkerboard units per species-pair in the community:
For M species, there are P = M(M-1)/2 species-pairs, so C-score is calculated:
The C-score is sensitive to the proportion of islands that are occupied, thereby confounding comparisons between matrices or sets of species pairs within them. An extension of the C-score therefore standardizes by the number of islands each species-pair occupies using: