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).

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`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) |

`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. |

Noah Charney, Sydne Record

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.

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