beals {vegan} | R Documentation |

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.

beals(x, species = NA, reference = x, type = 0, include = TRUE) swan(x)

`x` |
Community data frame or matrix. |

`species` |
Column index used to compute Beals function for a single species.
The default (`NA` ) indicates that the function will be computed for all species. |

`reference` |
Community data frame or matrix to be used to compute
joint occurrences. By default, `x` is used as reference to
compute the joint occurrences. |

`type` |
Numeric. For function `beals` it specifies if and how abundance
values have to be used. See details for more explanation. |

`include` |
This logical flag indicates whether the target species has to be
included when computing the mean of the conditioned probabilities. The
original Beals (1984) definition is equivalent to `include=TRUE` ,
while the formulation of Münzbergová and Herben is
equal to `include=FALSE` . |

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[i]* is the number of
species on site *i*, *N[jk]* is the number of joint
occurrences of species *j* and *k*, *N[k]* is the
number of occurrences 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). As *N[jk]* can be
interpreted as a mean of conditional probability, the `beals`

function can be interpreted as a mean of conditioned probabilities (De
Cáceres & Legendre 2008). The current function is
generalized to abundance values (De Cáceres & Legendre
2008).

The `type`

argument specifies if and how abundance values have to be
used. `type = 0`

presence/absence mode. `type = 1`

abundances in `reference`

(or `x`

) are used to compute
conditioned probabilities. `type = 2`

abundances in `x`

are
used to compute weighted average of conditioned
probabilities. `type = 3`

abundances are used to compute both
conditioned probabilities and the weighted average.

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). In this case, the function should be called with ```
include
= FALSE
```

for cross-validatory smoothing for species, and argument
`species`

can be used if only one species was studied.

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 a similarity matrix, but it is equivalent to applying Beals
smoothing to zero values, at each step shifting the smallest initially
non-zero item to value one, and repeating this so many times that
there are no zeros left in the data. This is actually very similar to
extended dissimilarities (implemented in function
`stepacross`

), but very rarely used.

The function returns a transformed data matrix or a vector in case of asking Beals smoothing for a single species.

Miquel De Cáceres and Jari Oksanen

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

De Cáceres, M. & Legendre, P. 2008. Beals smoothing
revisited. *Oecologia* 156: 657–669.

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.

`decostand`

for proper standardization methods,
`specpool`

for an attempt to assess the size of species
pool. Function `indpower`

assesses the power of each species
to estimate the probabilities predicted by `beals`

.

data(dune) ## Default x <- beals(dune) ## Remove target species x <- beals(dune, include = FALSE) ## Smoothed values against presence or absence of species pa <- decostand(dune, "pa") boxplot(as.vector(x) ~ unlist(pa), xlab="Presence", ylab="Beals") ## Remove the bias of tarbet species: Yields lower values. beals(dune, type =3, include = FALSE) ## Uses abundance information. ## Vector with beals smoothing values corresponding to the first species ## in dune. beals(dune, species=1, include=TRUE)

[Package *vegan* version 1.16-32 Index]