Effective Numbers for Alpha, Beta, and Gamma Diversity Indices
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.
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).
Partitioning level of diversity. Can be "alpha," "beta," or "gamma".
Order of diversity. Default is the exponential of Shannon's entropy where q = 1.
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).
A scalar that gives the effective number of alpha, beta, or gamma diversity for the desired order of q.
abundances is a class other than a matrix or vector,
dz will return an error.
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.
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