# MoranI: Moran's I Autocorrelation Index In ape: Analyses of Phylogenetics and Evolution

## Description

This function computes Moran's I autocorrelation coefficient of `x` giving a matrix of weights using the method described by Gittleman and Kot (1990).

## Usage

 ```1 2``` ``` Moran.I(x, weight, scaled = FALSE, na.rm = FALSE, alternative = "two.sided") ```

## Arguments

 `x` a numeric vector. `weight` a matrix of weights. `scaled` a logical indicating whether the coefficient should be scaled so that it varies between -1 and +1 (default to `FALSE`). `na.rm` a logical indicating whether missing values should be removed. `alternative` a character string specifying the alternative hypothesis that is tested against the null hypothesis of no phylogenetic correlation; must be of one "two.sided", "less", or "greater", or any unambiguous abbrevation of these.

## Details

The matrix `weight` is used as “neighbourhood” weights, and Moran's I coefficient is computed using the formula:

\code{I = n/S0 * (sum{i=1..n} sum{j=1..n} wij(yi - ym))(yj - ym) / (sum{i=1..n} (yi - ym)^2)}

with

• yi = observations

• wij = distance weight

• n = number of observations

• S0 = \code{sum_{i=1..n} sum{j=1..n} wij}

The null hypothesis of no phylogenetic correlation is tested assuming normality of I under this null hypothesis. If the observed value of I is significantly greater than the expected value, then the values of `x` are positively autocorrelated, whereas if Iobserved < Iexpected, this will indicate negative autocorrelation.

## Value

A list containing the elements:

 `observed` the computed Moran's I. `expected` the expected value of I under the null hypothesis. `sd` the standard deviation of I under the null hypothesis. `p.value` the P-value of the test of the null hypothesis against the alternative hypothesis specified in `alternative`.

## Author(s)

Julien Dutheil [email protected] and Emmanuel Paradis

## References

Gittleman, J. L. and Kot, M. (1990) Adaptation: statistics and a null model for estimating phylogenetic effects. Systematic Zoology, 39, 227–241.

`weight.taxo`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```tr <- rtree(30) x <- rnorm(30) ## weights w[i,j] = 1/d[i,j]: w <- 1/cophenetic(tr) ## set the diagonal w[i,i] = 0 (instead of Inf...): diag(w) <- 0 Moran.I(x, w) Moran.I(x, w, alt = "l") Moran.I(x, w, alt = "g") Moran.I(x, w, scaled = TRUE) # usualy the same ```