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Checkerboard score : ウィキペディア英語版
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, expands on the earlier work of Diamond〔
〕 that defined a notion of "checkerboard distributions" as an indicator of species competition.
A higher c-score indicates a lower randomness, i.e. a greater likelihood that the distribution of one species has 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:
:C_ = (r_i- S_) (r_j - S_ )
: - 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 =\sum_^ \sum_C_ / 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_ = (r_i- S_) (r_j - S_ )/(r_i + r_j - S_)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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