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