# M.homog: MacArthur's Homogeneity Measure In vegetarian: Jost Diversity Measures for Community Data

## 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

 `1` ```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.

`Rel.homog` `bootstrap`
 ```1 2 3 4 5 6``` ```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) ```