Common indices of biodiversity, expressed as the number of common species.
1 2 3 4  biodSimpson(abVec, correct = TRUE)
biodShannon(abVec)
biodBerger(abVec)
biodBrillouin(cntVec)

abVec 
a vector of measures of abundance, eg. counts of individuals or biomass, one element per species; or a corresponding matrix or data frame, which will be converted to a vector with 
cntVec 
a vector (or matrix or data frame) of counts of individuals, one element per species. Nonintegers will be rounded without warning. 
correct 
if TRUE, a small sample correction is applied, and in that case 
Inverse of Simpson's (1949) index of dominance. If correct = TRUE
, a smallsample correction is applied, giving Hurlbert's (1971) diversity index. Otherwise, the result is equivalent to Hill's (1973) N_2.
Exponential form of Shannon's (1948) entropy measure, equivalent to Hill's (1973) N_1.
Inverse of Berger & Parker's (1970) index of dominance, equivalent to Hill's (1973) N_Inf.
Exponential form of Brillouin's index: for small, completely censused populations, Brillouin's index is a more appropriate measure of entropy than Shannon's measure (Maurer & McGill 2011:61).
The relevant index.
It is important that the proportions of each species in the sample represent those in the population from which it is drawn. This will not be the case if probability of inclusion varies among species, as often occurs when samples are collected in the field.
Mike Meredith
Berger, W H; F L Parker. 1970. Diversity of planktonic Foramenifera in deep sea sediments. Science 168:13451347.
Hill, M O. 1973. Diversity and evenness: a unifying notation and its consequences. Ecology 54:427431.
Hurlbert, S H. 1971. The nonconcept of species diversity: A critique and alternative parameters. Ecology 52:577586.
Maurer, B A; B J McGill. 2011. Measurement of species diversity. 5564 in Magurran, A E, and B J McGill, editors. Biological diversity: frontiers in measurement and assessment. Oxford University Press, Oxford, New York NY
Shannon, C E. 1948. A mathematical theory of communication. Bell System Technical Journal 27:379423
Simpson, E H. 1949. Measurement of diversity. Nature 163:688.
richSobs
and Species richness estimators for alternatives to indices.
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