Description Usage Arguments Details Value Acknowledgements Note Author(s) References See Also Examples

Function `mpmcorrelogram`

computes both multivariate and multivariate partial
Mantel correlograms. Multivariate Mantel correlograms were proposed by Sokal
(1986) and Oden and Sokal (1986) and popularized among ecologists by Legendre
and Legendre (1998, pp. 736-738). Multivariate partial Mantel correlograms
are described and employed by Matesanz et al. (2011).

1 2 3 4 5 6 7 8 | ```
mpmcorrelogram(xdis, geodis, zdis = NULL, method = "pearson",
alfa = 0.05, nclass = NULL, breaks = NULL,
permutations = 999, strata, simil = FALSE,
plot = TRUE, print = TRUE)
## S3 method for class 'mpmcorrelogram'
plot(x, pch = c(15, 22), xlim = NULL, ylim = NULL,
ylab = NULL, xlab = NULL, alfa = 0.05, ...)
``` |

`xdis, geodis, zdis` |
Multivariate distance (or similarity) matrices or their as.dist representation |

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

`alfa` |
Significance level for the points drawn with black symbols in the
correlogram. By default |

`nclass` |
Number of distance classes. Deafult |

`breaks` |
Vector with break points of the distance classes. |

`permutations` |
Number of permutations for the tests of significance. |

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

`simil` |
Logical. Is the first matrix a similarity matrix? Default= |

`plot` |
Logical. Should the correlogram be ploted?. |

`print` |
Logical. Should the results be printed? |

`x` |
An object of class mpmcorrelogram, i.e. resulting from function mpmcorrelogram. |

`pch` |
Vector with two integers (or two single characters) specifying the symbols
(or characters) to plot respectively the significant
and non-significant |

`xlim` |
Vector with the limits for the x-axis. |

`ylim` |
Vector with the limits for the y-axis. |

`ylab` |
Label for the y-axis. |

`xlab` |
Label for the x-axis. |

`...` |
Other parameters passed to print and plot methods. |

The function `mpmcorrelogram`

computes both Mantel correlograms and
*partial* Mantel correlograms.
A correlogram is a graph in which spatial correlation values are plotted,
on the ordinate, as a function of the geographic distance classes among
the study units along the abscissa. In a "classical" Mantel correlogram,
a Mantel correlation (Mantel 1967) is computed between a multivariate
(e.g. multi-species or multi-locus) distance or similarity matrix
and a design matrix representing each of the geographic distance classes
in turn. The Mantel statistic is tested through a permutational Mantel test
performed by vegan's mantel function.

In a partial Mantel correlogram, a partial correlation conditioned on a third matrix is computed between the focal matrix and the design matrix representing each of the geographic distance classes. In this case, the partial Mantel statistic is tested through a permutational test performed by vegan's mantel.partial function.

A practical application of the use of the partial Mantel correlogram can be seen in Matesanz et al. (2011).

If the arguments `plot`

and `print`

are both `TRUE`

,
`mpmcorrelogram`

by default will draw a correlogram where solid squares
indicate significant `rM`

values and void squares indicate non-significant ones.
It will also print the results as a table. In any case, `mpmcorrelogram`

will return an object of `class mpmcorrelogram`

, i.e. a list with the
following elements:

`breaks` |
Vector with the break points of the distance classes considered. |

`rM` |
Vector with the computed Mantel correlations for each distance class. |

`signif` |
The value of the selected |

`pvalues` |
Vector with the p-values computed for each distance class. |

`pval.Bonferroni` |
Vector with the p-values after a progressive Bonferroni correction. |

`clases` |
Alfanumeric vector with the range of each distance class. |

This package has been developed thaks to the subvention 099/RN08/02.1 of the Spanish Ministerio de Medio Ambiente, Medio Rural y Marino.

The implementation of the Mantel correlogram computation in
the function `mpmcorrelogram`

(and that of Mantel correlation performed
by vegan's mantel.partial and mantel
functions) are based on the description of Legendre and Legendre (1998).
Following these approaches, positive Mantel statistics correspond to
positive autocorrelation when the focal matrix (i.e. `xdis`

)
is a similarity matrix and to negative values when it is a
distance matrix. As most of the designed tools in **R** for summarizing
relationships between the rows of data matrices return distance objects,
the argument `simil`

in `mpmcorrelogram`

is set by default to
`FALSE`

. See the examples for the use with a similarity matrix.

Marcelino de la Cruz Rot marcelino.delacruz@upm.es

Legendre, P. and L. Legendre. 1998. *Numerical ecology*, 2nd English
edition. Elsevier Science BV, Amsterdam.

Mantel, N. 1967. The detection of disease clustering and a generalized
regression approach. *Cancer Res.* 27: 209-220.

Matesanz S., Gimeno T.E., de la Cruz M., Escudero A. and Valladares F. 2011.
Competition may explain the fine-scale spatial patterns and genetic structure
of two co-occurring plant congeners. *J. Ecol.* 99: 838-848

Oden, N. L. and R. R. Sokal. 1986. Directional autocorrelation: an extension
of spatial correlograms to two dimensions. *Syst. Zool.* 35: 608-617.

Sokal, R. R. 1986. Spatial data analysis and historical processes.
29-43 in: E. Diday et al. (eds.) *Data analysis and informatics*,
IV. North-Holland, Amsterdam.

vegan's mantel.correlog for another implementation of (non-partial) Mantel correlograms.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | ```
# Example from Figure 13.12 of Legendre and Legendre (1998):
# Get similarity matrix based on assemblage composition.
data(S)
# Get euclidean distance between sites.
data(D)
# Compute Multivariate Mantel Correlogram
# as in Fig. 13.12 of Legendre and Legendre
## Not run:
result <- mpmcorrelogram(S, D, simil=TRUE)
## End(Not run)
# A Multivariate Partial examle.
# Get distance matrix of "covariate" attributes
data(Zd)
# Compute multivariate partial Mantel correlogram
## Not run:
result <- mpmcorrelogram(S, D, Zd, simil=TRUE)
## End(Not run)
# Change the appearance of the plot
## Not run:
plot(result, pch=c(17,24))
## End(Not run)
``` |

```
Loading required package: vegan
Loading required package: permute
Loading required package: lattice
This is vegan 2.5-4
evaluating distance class 1, 2, 3, 4, 5, 6,
class distance.range rM p p.Bonferroni
1 1 0.12 - 0.267 0.5384651 0.001 0.001
2 2 0.267 - 0.413 0.4200693 0.001 0.002
3 3 0.413 - 0.56 0.1029263 0.233 0.699
4 4 0.56 - 0.707 -0.3087466 0.021 0.084
5 5 0.707 - 0.853 -0.4010639 0.005 0.025
6 6 0.853 - 2 -0.4262626 0.001 0.006
evaluating distance class 1, 2, 3, 4, 5, 6,
class distance.range rM p p.Bonferroni
1 1 0.12 - 0.267 0.06626292 0.337 0.337
2 2 0.267 - 0.413 0.52481294 0.001 0.002
3 3 0.413 - 0.56 0.31878713 0.014 0.042
4 4 0.56 - 0.707 -0.25568078 0.066 0.264
5 5 0.707 - 0.853 -0.32226995 0.013 0.065
6 6 0.853 - 2 -0.42087234 0.001 0.006
```

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