MacArthur's Homogeneity Measure

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Description

Macarthur's homogeneity measure provides a gauge of the amount of total diversity contained in an average community or sample (MacArthur 1965). It can be derived from a transformation of the true beta diversity of order 1, the numbers equivalent of the beta Shannon entropy (Jost 2007 Equation 18). If the N communities being compared are equally weighted, then other values of q can be specified to calculate other familiar similarity indices (e.g. Jaccard index when q=0, Morisita-Horn index when q=2) (Jost 2006).

Usage

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M.homog(abundances, abundances2 = NULL, q = 1, std = FALSE, boot = FALSE, boot.arg = list(s.sizes = NULL, num.iter = 100))

Arguments

abundances

Community data as a matrix where columns are individual species and rows are sites or a vector of different species within a site. Matrix and vector elements are abundance data (e.g. counts, percent cover estimates).

abundances2

Community data, a vector of different species within a site. Vector elements are abundance data (e.g. counts, percent cover estimates). If abundances is given a matrix, then abundances2 defaults to NULL.

q

Order of the diversity measure. Defaults to the Shannon case where q = 1.

std

Logical statement. If std = TRUE, then the data is standardized, so that the value returned is bounded between zero and one. The default is std = FALSE where there is no standardization of the data, and lower and upper limits of the value returned are 1/N and one, respectively.

boot

Logical indicating whether to use bootstrapping to estimate uncertainty.

boot.arg

(optional) List of arguments to pass bootstrapping function: list(s.sizes=number you specify, num.iter=number you specify)

Value

M

A scalar, MacArthur's homogeneity measure, where the lower limit (either 1/N or zero depending on the specification of the argument std) is the case when all communities are distinct and the upper limit (unity) occurs when all communities are exactly identical.

StdErr

(optional) Standard error of value estimated through bootstrapping.

Author(s)

Noah Charney, Sydne Record

References

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.

Hill, M. 1973. Diversity and evenness: A unifying notation and its consequences. Ecology 54: 427-432.

See Also

Rel.homog bootstrap

Examples

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data(simesants)
M.homog(simesants[1:2,-1])
hemlock<-subset(simesants,Habitat=="Hemlock")[,-1]
hardwood<-subset(simesants,Habitat=="Hardwood")[,-1]
M.homog(abundances=hemlock,abundances2=hardwood)
M.homog(simesants[1:2,-1], q=2,std=TRUE,boot=TRUE)