Compute similarity metrics between sites based on species composition

This function generates a data.frame where each row provides one or several similarity metrics between pairs of sites, based on a co-occurrence matrix with sites as rows and species as columns.

Usage

similarity(comat, metric = "Simpson", formula = NULL, method = "prodmat")

Arguments

comat

A co-occurrence matrix with sites as rows and species as columns.

metric

A character vector or a single character string specifying the metrics to compute (see Details). Available options are "abc", "ABC", "Jaccard", "Jaccardturn", "Sorensen", "Simpson", "Bray", "Brayturn", and "Euclidean". If "all" is specified, all metrics will be calculated. Can be set to NULL if formula is used.

formula

A character vector or a single character string specifying custom formula(s) based on the a, b, c, A, B, and C quantities (see Details). The default is NULL.

method

A character string specifying the method to compute abc (see Details). The default is "prodmat", which is more efficient but memory-intensive. Alternatively, "loops" is less memory-intensive but slower.

Value

A data.frame with the additional class bioregion.pairwise.metric, containing one or several similarity metrics between pairs of sites. The first two columns represent the pairs of sites. There is one column per similarity metric provided in metric and formula, except for the abc and ABC metrics, which are stored in three separate columns (one for each letter).

Details

With a the number of species shared by a pair of sites, b species only present in the first site and c species only present in the second site.

Jaccard = 1 - (b + c) / (a + b + c)

Jaccardturn = 1 - 2min(b, c) / (a + 2min(b, c)) (Baselga, 2012)

Sorensen = 1 - (b + c) / (2a + b + c)

Simpson = 1 - min(b, c) / (a + min(b, c))

If abundances data are available, Bray-Curtis and its turnover component can also be computed with the following equation:

Bray = 1 - (B + C) / (2A + B + C)

Brayturn = 1 - min(B, C) / (A + min(B, C)) (Baselga, 2013)

with A the sum of the lesser values for common species shared by a pair of sites. B and C are the total number of specimens counted at both sites minus A.

formula can be used to compute customized metrics with the terms a, b, c, A, B, and C. For example formula = c("1 - pmin(b,c) / (a + pmin(b,c))", "1 - (B + C) / (2*A + B + C)") will compute the Simpson and Bray-Curtis similarity metrics, respectively. Note that pmin is used in the Simpson formula because a, b, c, A, B and C are numeric vectors.

Euclidean computes the Euclidean similarity between each pair of site following this equation:

Euclidean = 1 / (1 + d_ij)

Where d_ij is the Euclidean distance between site i and site j in terms of species composition.

References

Baselga A (2012) The Relationship between Species Replacement, Dissimilarity Derived from Nestedness, and Nestedness. Global Ecology and Biogeography 21, 1223–1232.

Baselga A (2013) Separating the two components of abundance-based dissimilarity: balanced changes in abundance vs. abundance gradients. Methods in Ecology and Evolution 4, 552–557.

See also

For more details illustrated with a practical example, see the vignette: https://biorgeo.github.io/bioregion/articles/a3_pairwise_metrics.html.

Associated functions: dissimilarity similarity_to_dissimilarity

Author

Maxime Lenormand (maxime.lenormand@inrae.fr)
Pierre Denelle (pierre.denelle@gmail.com)
Boris Leroy (leroy.boris@gmail.com)

Examples

comat <- matrix(sample(0:1000, size = 50, replace = TRUE,
prob = 1 / 1:1001), 5, 10)
rownames(comat) <- paste0("Site", 1:5)
colnames(comat) <- paste0("Species", 1:10)

sim <- similarity(comat, metric = c("abc", "ABC", "Simpson", "Brayturn"))

sim <- similarity(comat, metric = "all",
formula = "1 - (b + c) / (a + b + c)")