The function specieseve calculates evenness indices that rely on relative or absolute species abundance.
specieseve(comm, method = "full", tol = 1e-8)Function specieseve returns a matrix with communities as rows and the evenness indices as columns.
a data frame or a matrix typically with communities as rows, species as columns and abundance as entry.
a string or a vector of strings: one or several of "GiniSimpson", "Simpson", "Shannon", "Heip", "McIntosh", "SmithWilson", "full". See details.
a tolerance threshold (a value between -tol and tol is considered equal to zero)
Sandrine Pavoine sandrine.pavoine@mnhn.fr
Let S_i be the number of species in community i, \(n_{ij}\) be the absolute abundance of species j in community i, \(N_i\) the sum of all species abundance in community i (\(N_i=\sum_j n_{ij}\); the sum of row i in comm), \(p_{ij}\) the relative abundance of species j in community i (\(p_{ij}=n_{ij}/N_i\)).
If method="GiniSimpson", the evenness index is that associated with Gini (1912) and Simpson (1949) diversity index: \((1-\sum_j p_{ij}^2)*S_i/(S_i-1)\).
If method="Simpson", the evenness index is (Simpson 1949; Magurran 2004): \((1/\sum_j p_{ij}^2)/S_i\).
If method="Shannon", the evenness index is that associated with Shannon (1948) diversity index with neperian logarithm: \((-\sum_j p_{ij}ln(p_{ij}))/ln(S_i)\).
If method="Heip", the evenness index is that of Heip (1974) (Magurran 2004): \([exp(-\sum_j p_{ij}log(p_{ij})) - 1]/(S_i-1)\).
If method="McIntosh", the evenness index is that of Pielou (1975) associated with McIntosh (1967) index of diversity: \((N_i-\sqrt{\sum_j n_{ij}^2})/(N_i-N_i/\sqrt{S_i})\).
If method="SmithWilson", the Smith and Wilson (1996) evenness index is calculated (Magurran 2004): \(1-[(2/\pi)(arctan(\sum_{j=1}^{S_i} (log n_{ij} - \sum_{k=1}^{S_i} log n_{ik}/S_i)^2/S_i))]\). The function uses neperian logarithm for all indices. If one of the strings is "full", then all indices are calculated.
Gini, C. (1912) Variabilita e mutabilita. Studi economicoaguridici delle facoltta di giurizprudenza dell, Universite di Cagliari III, Parte II.
Heip, C. (1974) A new index measuring evenness. Journal of the Marine Biological Association UK, 54, 555--557.
Magurran, A.E. (2004) Measuring biological diversity. Oxford, UK: Blackwell Publishing.
McIntosh, R.P. (1967) An index of diversity and the relation of certain conepts to diversity. Ecology, 48, 392--404.
Pielou, E.C. (1975) Ecological diversity. New York: Wiley InterScience.
Shannon, C.E. (1948) A mathematical theory of communication. Bell System technical journal, 27, 379--423, 623--656.
Simpson, E.H. (1949) Measurement of diversity. Nature, 163, 688.
Smith, B. and Wilson, J.B. (1996) A consumer's guide to evenness measures. Oikos, 76, 70--82.
data(batcomm)
ab <- batcomm$ab
specieseve(ab)
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