morisita {abdiv}

The Morisita index and Horn-Morisita index

Description

The Morisita and the Horn-Morisita indices measure the probability that individuals drawn one from each vector will belong to different species, relative to drawing from each vector separately. The Morisita index is formulated for count data only, whereas the Horn-Morisita index can be used with transformed counts or proportions.

Usage

morisita(x, y)

horn_morisita(x, y)

Arguments

x, y

Numeric vectors

Details

For two vectors x and y, the Morisita index of dissimilarity is

d(x,y) = 1 - \frac{2 \sum_i x_i y_i}{(\lambda_x + \lambda_y) N_x N_y},

where

\lambda_x = \frac{\sum_i x_i (x_i - 1)}{N_x (N_x - 1)}

and N_x = \sum_i x_i The formula for \lambda_x is the unbiased estimate for the probability of drawing two individuals of the same species from x, without replacement. The correction for sampling without replacement only makes sense for species count data.

Relation of morisita() to other definitions:

• Equivalent to vegdist() with method = "morisita".

Horn (1966) reformulated the index to use the equations for sampling with replacement in \lambda_x and \lambda_y:

\lambda_x = \frac{\sum_i x_i^2}{N_x^2}

With this modification, the index is valid for proportions or transformed count data.

Relation of horn_morisita() to other definitions:

• Equivalent to vegdist() with method = "horn".

• Equivalent to the morisitahorn calculator in Mothur.

Value

The Morisita or Horn-Morisita index between x and y. Both are undefined if x or y have no nonzero elements, in which case we return NaN.

References

Mosrisita M. Measuring of interspecific association and similarity between communities. Memoirs of the Faculty of Science, Kyushu Univ., Series E (Biology). 1959;3:65-80.

Horn HS. Measurement of "Overlap" in Comparative Ecological Studies. The American Naturalist, 1966;100(914):419-424.