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Creates a pairwise site by site commonness matrix from estimates of species richness and Bray-Curtis dissimilarity.

Usage

generate_commonness_matrix_from_gdm(gdm_predictions, alpha_list)

Arguments

gdm_predictions

a square pairwise matrix of Bray-Curtis dissimilarity estimates between site pairs. We recommend using the gdm-package (Fitzpatrick et al. 2020) to generate this matrix

alpha_list

a vector of species richness for every site in the study area. The length of this vector must be equivalent to one of the dimensions of the gdm_predictions

Value

A pairwise site by site matrix of the number of species in common between each site pair, with dimensions equal to that of the provided dissimilarity matrix.

Details

generate_commonness_matrix_from_gdm uses a vector of estimated species richness per site and a pairwise matrix of site by site Bray-Curtis dissimilarity (we recommend using the gdm-package (Fitzpatrick et al. 2020) to generate this matrix) to produce a matrix of the estimated species in common between site pairs (referred to as a commonness matrix). The commonness between sites is calculated using $$C_{ij}=(1-\beta_{ij})(S_{i} + S_{j})/2$$ Where \(\beta_{ij}\) is the dissimilarity between sites, \(C_{ij}\) is the species in common between sites, and S is the number of species in each site. For more details see Mokany et al 2011.

References

Mokany, K., Harwood, T.D., Overton, J.M., Barker, G.M., & Ferrier, S. (2011). Combining \(\alpha\) and \(\beta\) diversity models to fill gaps in our knowledge of biodiversity. Ecology Letters, 14(10), 1043-1051.