Effective Numbers for Alpha, Beta, and Gamma Diversity Indices

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Description

The function dz calculates the 'effective number' of traits or species in terms of multiplicative alpha, beta, or gamma diversity for any order of q (Hill 1973; Jost 2006, 2007). As the order q increases, the diversity calculated by dz becomes increasingly sensitive to differential abundance or amount; rare or low-abundance traits/species become downweighted in importance.

Usage

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dz(abundances, lev = "beta", q = 1)

Arguments

abundances

A matrix of community or phenotypic data where columns are individual species or traits and rows are replicates (e.g., sites, individuals, groups). Matrix elements are abundances or amounts (e.g., concentrations, counts).

lev

Partitioning level of diversity. Can be "alpha," "beta," or "gamma".

q

Order of diversity. Default is the exponential of Shannon's entropy where q = 1.

Details

dz is a direct modification of the d function from the vegetarian package (Charney & Record 2012). The function was optimized to work with hierDiversity to return the desired multiplicative diversity partition of interest for a given order q.

The diversity orders most familiar to ecologists are q = 0 (richness), q = 1 (Shannon entropy), and q = 2 (Simpson's probability of identity). As q increases, the diversity measure becomes less sensitive to rare subcomponents of low amount, while components of high abundance are increasingly upweighted (Jost 2006, 2007).

Value

D.VALUE

A scalar that gives the effective number of alpha, beta, or gamma diversity for the desired order of q.

Note

If abundances is a class other than a matrix or vector, dz will return an error.

Author(s)

Zachary Marion zmarion@vols.utk.edu, James Fordyce jfordyce@utk.edu, and Benjamin Fitzpatrick benfitz@utk.edu

References

Charney, N. and S. Record. (2012). vegetarian: Jost Diversity Measures for Community Data. R package version 1.2.

Hill, M.O. (1973). Diversity and evenness: a unifying notation and its consequences. Ecology, 54(2):427–432.

Jost, L. (2006). Entropy and diversity. Oikos, 113(2):363–375.

Jost, L. (2007). Partitioning diversity into independent alpha and beta components. Ecology, 88(10):2427–2439.

See Also

hierDiversity, d

Examples

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set.seed(2)
dat <- matrix(rpois(100, lambda = 3), nrow = 10)
dz(abundances = dat, lev = "beta", q = 2)
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