beals {vegan} | R Documentation

## Beals Smoothing and Degree of Absence

### Description

Beals smoothing replaces each entry in the community data with a probability of target species occurring in that particular site, based on the joint occurrences of target species with the species that actually occur in the site. Swan's (1970) degree of absence applies Beals smoothing to zero items so long that all zeros are replaced with smoothed values.

### Usage

    beals(x)
    swan(x)

### Arguments

`x` | Community data frame or matrix

### Details

The Beals smoothing is the estimated probability p[ij] that species j occurs in site i. It is defined as p[ij] = 1/S[i] Sum(k) N[jk] I[ik] / N[k], where S is the number of species on a site, N[jk] is the number of joint occurrences of species j and k, and N[k] is the number of occurences of species k, and I is the incidence (0 or 1) of species (this last term is usually omitted from the equation, but it is necessary).

Beals smoothing was originally suggested as a method of data transformation to remove excessive zeros (Beals 1984, McCune 1994). However, it is not a suitable method for this purpose since it does not maintain the information on species presences: A species may have a higher probability of occurrence in a site where it does not occur than in sites where it occurs. Moreover, it regularizes data too strongly. The method may be useful in identifying species that belong to the species pool (Ewald 2002) or to identify suitable unoccupied patches in metapopulation analysis (Münzbergová & Herben 2004). The function is provided here for the brave.

Swan (1970) suggested replacing zero values with degrees of absence of a species in a community data matrix. Swan expressed the method in terms of similarity matrix, but it is equivalent to applying Beals smoothing to zero values, at each step shifting smallest initially non-zero item to value one, and repeating this so many times that there are no zeros left in the data. This actually is very similar to extended dissimilarities (implemented in function `stepacross`), but very rarely used.

### Value

The function returns a transformed data matrix.

### Note

The current function is modelled as closely as possible after Beals (1984) and McCune (1994). It seems that Münzbergová and Herben (2004) use slightly different formulation.

### Author(s)

Jari Oksanen

### References

Beals, E.W. 1984. Bray-Curtis-ordination: an effective strategy for analysis of multivariate ecological data. Adv. Ecol. Res. 14: 1-55.

Ewald, J. 2002. A probabilistic approach to estimating species pools from large compositional matrices. J. Veg. Sci. 13: 191-198.

McCune, B. 1994. Improving community ordination with the Beals smoothing function. Ecoscience 1: 82-86.

Münzbergová, Z. & Herben, T. 2004. Identification of suitable unoccupied habitats in metapopulation studies using co-occurrence of species. Oikos 105: 408-414.

Swan, J.M.A. (1970) An examination of some ordination problems by use of simulated vegetational data. Ecology 51, 89–102.

### See Also

`decostand` for proper standardization methods, `specpool` for an attempt to assess the size of species pool.

### Examples

    data(dune)
    x <- beals(dune)
    ## Smoothed values against presence or absence of species
    pa <- decostand(dune, "pa")
    boxplot(as.vector(x) ~ unlist(pa), xlab="Presence", ylab="Beals")

[Package vegan version 1.8-8 Index]