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,[1] expands on the earlier work of Diamond[2] 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.
Given two species sp1, sp2 and n islands, an incident matrix is built.In the
2 x n
The calculation of the co-occurrence of two species sp1, sp2 in the given set of islands is done as follows:
Cij=(ri-Sij)(rj-Sij)
- C-score for the two species sp1, sp2 in the given set of islands
- The number of co-occurrences of sp1, sp2
- Number of islands in which sp1 has 1
- 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 species-pairs, so C-score is calculated:
C
| M | |
| =\sum | |
| j=0 |
\sumi<jCij/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:[3]
Cij=(ri-Sij)(rj-Sij)/(ri+rj-Sij)