mantel {vegan} | R Documentation |

Function `mantel`

finds the Mantel statistic as a matrix
correlation between two dissimilarity matrices, and function
`mantel.partial`

finds the partial Mantel statistic as the
partial matrix correlation between three dissimilarity matrices. The
significance of the statistic is evaluated by permuting rows and
columns of the first dissimilarity matrix.

mantel(xdis, ydis, method="pearson", permutations=999, strata) mantel.partial(xdis, ydis, zdis, method = "pearson", permutations = 999, strata)

`xdis, ydis, zdis` |
Dissimilarity matrices or a `dist` objects. |

`method` |
Correlation method, as accepted by `cor` :
`"pearson"` , `"spearman"` or `"kendall"` . |

`permutations` |
Number of permutations in assessing significance. |

`strata` |
An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata. |

Mantel statistic is simply a correlation between entries of two
dissimilarity matrices (some use cross products, but these are linearly
related). However, the significance cannot be directly assessed,
because there are *N(N-1)/2* entries for just *N* observations.
Mantel developed asymptotic test, but here we use permutations of
*N* rows and columns of dissimilarity matrix.

Partial Mantel statistic uses partial correlation
conditioned on the third matrix. Only the first matrix is permuted so
that the correlation structure between second and first matrices is
kept constant. Although `mantel.partial`

silently accepts other
methods than `"pearson"`

, partial correlations will probably be
wrong with other methods.

The function uses `cor`

, which should accept
alternatives `pearson`

for product moment correlations and
`spearman`

or `kendall`

for rank correlations.

The function returns a list of class `mantel`

with following
components:

`Call ` |
Function call. |

`method ` |
Correlation method used, as returned by
`cor.test` . |

`statistic` |
The Mantel statistic. |

`signif` |
Empirical significance level from permutations. |

`perm` |
A vector of permuted values. |

`permutations` |
Number of permutations. |

Legendre & Legendre (1998) say that partial Mantel correlations often are difficult to interpret.

Jari Oksanen

The test is due to Mantel, of course, but the current implementation is based on Legendre and Legendre.

Legendre, P. and Legendre, L. (1998) *Numerical Ecology*. 2nd English
Edition. Elsevier.

`cor`

for correlation coefficients,
`protest`

(``Procrustes test'') for an alternative with
ordination diagrams, `anosim`

and `mrpp`

for comparing dissimilarities against
classification. For dissimilarity matrices, see `vegdist`

or `dist`

. See `bioenv`

for selecting
environmental variables.

## Is vegetation related to environment? data(varespec) data(varechem) veg.dist <- vegdist(varespec) # Bray-Curtis env.dist <- vegdist(scale(varechem), "euclid") mantel(veg.dist, env.dist) mantel(veg.dist, env.dist, method="spear")

[Package *vegan* version 1.16-32 Index]