Checkerboard score

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.

Definition and calculation

Given two species sp₁, sp₂ and n islands, an incident matrix is built. In the $2\times n$ 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 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:

C_{ij}=(r_{i}-S_{ij})(r_{j}-S_{ij})

C ij

- C-score for the two species sp₁, sp₂ in the given set of islands

S ij

- The number of co-occurrences of sp₁, sp₂

r i

- Number of islands in which sp₁ has 1

r j

- 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=\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:[3]

C_{ij}=(r_{i}-S_{ij})(r_{j}-S_{ij})/(r_{i}+r_{j}-S_{ij})

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gollark: (and all-round convenience)

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References

Stone, Lewis; Roberts, Alan (1990). "The checkerboard score and species distributions". Oecologia. 85 (1): 74–79. Bibcode:1990Oecol..85...74S. doi:10.1007/BF00317345. ISSN 0029-8549. PMID 28310957.
Diamond, JM (1975). "Assembly of species communities". In Cody, ML; Diamond, JM (eds.). Ecology and evolution of communities. Belknap Press. pp. 342–444.
Novak, Mark; Moore, Jonathan W.; Leidy, Robert A. (2011). "Nestedness patterns and the dual nature of community reassembly in California streams: a multivariate permutation-based approach". Global Change Biology. 17 (12): 3714–3723. Bibcode:2011GCBio..17.3714N. doi:10.1111/j.1365-2486.2011.02482.x.

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[StoneRoberts1990-1] Stone, Lewis; Roberts, Alan (1990). "The checkerboard score and species distributions". Oecologia. 85 (1): 74–79. Bibcode:1990Oecol..85...74S. doi:10.1007/BF00317345. ISSN 0029-8549. PMID 28310957.

[2] Diamond, JM (1975). "Assembly of species communities". In Cody, ML; Diamond, JM (eds.). Ecology and evolution of communities. Belknap Press. pp. 342–444.

[Novaketal2011-3] Novak, Mark; Moore, Jonathan W.; Leidy, Robert A. (2011). "Nestedness patterns and the dual nature of community reassembly in California streams: a multivariate permutation-based approach". Global Change Biology. 17 (12): 3714–3723. Bibcode:2011GCBio..17.3714N. doi:10.1111/j.1365-2486.2011.02482.x.