Takes a resource utilization matrix as input and returns the average pairwise Pianka's niche overlap index.
a matrix of resource utilization values.
Pianka's niche overlap index is averaged over each unique species pair. The index is symmetric, with a normalization term in the denominator for the overlap between species 1 and 2. Values of Pianka's niche overlap index close to 0.0 reflect usage of exclusive resource categories, whereas values close to 1.0 reflect similar resource utilization spectra.
O_jk = O_kj = sum(p_ij*p_jk) / sqrt(sum((p_ij)^2)sum((p_jk)^2))
Returns the average pairwise niche overlap.
The resource utilization matrix (rows = species, columns = discrete resource categories) may include zeroes, but no negative numbers or missing values. Relative resource within a species is first calculated, so the rows need not sum to 1.0.
Pianka, E. 1973. The structure of lizard communities. Annual Review of Ecology and Systematics 4:53-74.
Winemiller, K.O. and E.R. Pianka. 1990. Organization in natural assemblages of desert lizards and tropical fishes. Ecological Monographs 60: 27-55.
czekanowski niche overlap index.
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