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 2 × n {\displaystyle 2\times n} 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 does 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:
C i j = ( r i − S i j ) ( r j − S i j ) {\displaystyle C_{ij}=(r_{i}-S_{ij})(r_{j}-S_{ij})}
Cij - C-score for the two species sp1, sp2 in the given set of islands Sij - The number of co-occurrences of sp1, sp2 ri - Number of islands in which sp1 has 1 rj - Number of islands in which sp2 has 1 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:
C = ∑ j = 0 M ∑ i < j C i j / P {\displaystyle C=\sum _{j=0}^{M}\sum _{i<j}C_{ij}/P}
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:
C i j = ( r i − S i j ) ( r j − S i j ) / ( r i + r j − S i j ) {\displaystyle C_{ij}=(r_{i}-S_{ij})(r_{j}-S_{ij})/(r_{i}+r_{j}-S_{ij})}
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