ape: MoranI – R documentation

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MoranI

Moran's I Autocorrelation Index

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

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 dutheil@evolbio.mpg.de 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.

Examples

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

ape

Analyses of Phylogenetics and Evolution

v5.5

GPL-2 | GPL-3

Authors

Emmanuel Paradis [aut, cre, cph] (<https://orcid.org/0000-0003-3092-2199>), Simon Blomberg [aut, cph] (<https://orcid.org/0000-0003-1062-0839>), Ben Bolker [aut, cph] (<https://orcid.org/0000-0002-2127-0443>), Joseph Brown [aut, cph] (<https://orcid.org/0000-0002-3835-8062>), Santiago Claramunt [aut, cph] (<https://orcid.org/0000-0002-8926-5974>), Julien Claude [aut, cph] (<https://orcid.org/0000-0002-9267-1228>), Hoa Sien Cuong [aut, cph], Richard Desper [aut, cph], Gilles Didier [aut, cph] (<https://orcid.org/0000-0003-0596-9112>), Benoit Durand [aut, cph], Julien Dutheil [aut, cph] (<https://orcid.org/0000-0001-7753-4121>), RJ Ewing [aut, cph], Olivier Gascuel [aut, cph], Thomas Guillerme [aut, cph] (<https://orcid.org/0000-0003-4325-1275>), Christoph Heibl [aut, cph] (<https://orcid.org/0000-0002-7655-3299>), Anthony Ives [aut, cph] (<https://orcid.org/0000-0001-9375-9523>), Bradley Jones [aut, cph] (<https://orcid.org/0000-0003-4498-1069>), Franz Krah [aut, cph] (<https://orcid.org/0000-0001-7866-7508>), Daniel Lawson [aut, cph] (<https://orcid.org/0000-0002-5311-6213>), Vincent Lefort [aut, cph], Pierre Legendre [aut, cph] (<https://orcid.org/0000-0002-3838-3305>), Jim Lemon [aut, cph], Guillaume Louvel [aut, cph] (<https://orcid.org/0000-0002-7745-0785>), Eric Marcon [aut, cph] (<https://orcid.org/0000-0002-5249-321X>), Rosemary McCloskey [aut, cph] (<https://orcid.org/0000-0002-9772-8553>), Johan Nylander [aut, cph], Rainer Opgen-Rhein [aut, cph], Andrei-Alin Popescu [aut, cph], Manuela Royer-Carenzi [aut, cph], Klaus Schliep [aut, cph] (<https://orcid.org/0000-0003-2941-0161>), Korbinian Strimmer [aut, cph] (<https://orcid.org/0000-0001-7917-2056>), Damien de Vienne [aut, cph] (<https://orcid.org/0000-0001-9532-5251>)

Initial release

2021-04-24