bgdispersal {vegan} | R Documentation

## Coefficients of Biogeographical Dispersal Direction

### Description

This function computes coefficients of dispersal direction between geographically connected areas, as defined by Legendre and Legendre (1984), and also described in Legendre and Legendre (1998, section 13.3.4).

### Usage

    bgdispersal(mat, PAonly = FALSE)

### Arguments

`mat` | Data frame or matrix containing a community composition data table (species presence-absence or abundance data)
`PAonly` | `FALSE` if the four types of coefficients, DD1 to DD4, are requested; `TRUE` if DD1 and DD2 only are sought (see Details).

### Details

The signs of the DD coefficients indicate the direction of dispersal, provided that the asymmetry is significant. A positive sign indicates dispersal from the first (row in DD tables) to the second region (column); a negative sign indicates the opposite. Coefficients DD1 and DD2 are computed from presence-absence data. The function converts abundance data to presence-absence if necessary. Coefficients DD3 and DD4 are computed on abundance data if available. A McNemar test of asymmetry is computed from the presence-absence data to test the hypothesis of a significant asymmetry between the two areas under comparison.

In the input data table, the rows are sites or areas, the columns are taxa. Most often, the taxa are species, but the coefficients can be computed from genera or families as well. DD1 and DD2 only are computed for presence-absence data. The four types of coefficients are computed for quantitative data, which are converted to presence-absence for the computation of DD1 and DD2. `PAonly = FALSE` indicates that the four types of coefficients are requested. `PAonly = TRUE` if DD1 and DD2 only are sought.

### Value

Function `dispersion` returns a list containing the following matrices:

`DD1` | DD1[j,k] = (a * (b - c))/((a + b + c)^2)
`DD2` | DD2[j,k] = (2*a * (b - c))/((2*a + b + c) * (a + b + c)) where a, b, and c have the same meaning as in the same meaning as in the computation of binary similarity coefficients.
`DD3` | DD3[j,k] = W*(A-B) / ((A+B-W)^2)
`DD4` | DD4[j,k] = 2*W*(A-B) / ((A+B)*(A+B-W)) where `W = sum(pmin(vector1, vector2))`, `A = sum(vector1)`, `B = sum(vector2)`
`McNemar` | McNemar chi-square statistic of asymmetry with correction for continuity (Siegel and Castellan 1988): (abs(b - c) - 1)^2 / (b + c)
`prob.McNemar` | probabilities associated with McNemar statistics, chi-square test. H0: no asymmetry in (b-c).

### Author(s)

Pierre Legendre, Departement de Sciences Biologiques, Universite de Montreal

### References

Legendre, P. and V. Legendre. 1984. Postglacial dispersal of freshwater fishes in the Québec peninsula. Can. J. Fish. Aquat. Sci. 41: 1781-1802.

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

Siegel, S. and N. J. Castellan, Jr. 1988. Nonparametric statistics for the behavioral sciences. 2nd edition. McGraw-Hill, New York.

### Examples

    mat <- matrix(c(32,15,14,10,70,30,100,4,10,30,25,0,18,0,40,
      0,0,20,0,0,0,0,4,0,30,20,0,0,0,0,25,74,42,1,45,89,5,16,16,20),
      4, 10, byrow=TRUE)
    bgdispersal(mat)

[Package vegan version 1.8-6 Index]