enfa: Ecological Niche Factor Analysis

Description

enfa performs an Ecological Niche Factor Analysis. hist.enfa draws histograms of the row scores or of the initial variables of the ENFA.

Usage

enfa(dudi, pr, scannf = TRUE, nf = 1)
# S3 method for enfa
hist(x, scores = TRUE, type = c("h", "l"), adjust = 1,
                    Acol, Ucol, Aborder, Uborder, Alwd = 1, Ulwd = 1, ...)

Value

enfa returns a list of class enfa containing the following components:

call: original call.
tab: a data frame with n rows and p columns.
pr: a vector of length n containing the number of points in each pixel of the map.
nf: the number of kept specialization axes.
m: the marginality (squared length of the marginality vector).
s: a vector with all the eigenvalues of the analysis.
lw: row weights, a vector with n components.
li: row coordinates, data frame with n rows and nf columns.
cw: column weights, a vector with p components.
co: column coordinates, data frame with p rows and nf columns.
mar: coordinates of the marginality vector.

Arguments

dudi: a duality diagram, object of class dudi (see Details)
pr: a vector giving the utilization weights associated to each unit
scannf: logical. Whether the eigenvalues barplot should be displayed
nf: an integer indicating the number of kept specialization axes
x: an object of class enfa
scores: logical. If TRUE, the histograms display the row scores of the ENFA. If FALSE, they display the niche on the environmental variables (in this case, this is equivalent to histniche)
type: what type of plot should be drawn. Possible types are:
"h" for histograms,
"l" for kernel density estimates (see ?density).
By default, type = "h" is used. If type = "l" is used, the position of the mean of each distribution is indicated by dotted lines
adjust: if type = "l", a parameter used to control the bandwidth of the density estimates (see ?density)
Acol: if type = "h", a color to be used to fill the histogram of the available pixels. if type = "l", a color to be used for the kernel density estimates of the available pixels
Ucol: if type = "h", a color to be used to fill the histogram of the used pixels. if type = "l", a color to be used for the kernel density estimates of the used pixels
Aborder: color for the border of the histograms of the available pixels
Uborder: color for the border of the histograms of the used pixels
Alwd: if type = "l", the line width of the kernel density estimates of the available pixels
Ulwd: if type = "l", the line width of the kernel density estimates of the used pixels
...: further arguments passed to or from other methods

Author

Mathieu Basille basille@ase-research.org

Details

The niche concept, as defined by Hutchinson (1957), considers the ecological niche of a species as an hypervolume in the multidimensional space defined by environmental variables, within which the populations of a species can persist. The Ecological Niche Factor Analysis (ENFA) has been developped by Hirzel et al. (2002) to analyse the position of the niche in the ecological space. Nicolas Perrin (1984) described the position of the niche in the n-dimensional space using two measures: the M-specialization (hereafter termed marginality) and the S-specialization (hereafter termed specialization). The marginality represents the squared distance of the niche barycentre from the mean available habitat. A large specialization corresponds to a narrow niche relative to the habitat conditions available to the species.

The ENFA first extracts an axis of marginality (vector from the average of available habitat conditions to the average used habitat conditions). Then the analysis extracts successives orthogonal axes (i.e. uncorrelated), which maximises the specialization of the species. The calculations used in the function are described in Hirzel et al. (2002).

The function enfa can be used on both quantitative variables and qualitative variables (though the interpretation of the results of the ENFA for qualitative variables is still under research), provided that the table containing the values of habitat variables (columns) for each resource unit (rows) is correctly transformed (e.g. column-centered and standardised for tables containing only quantitative variables), and that appropriate column weights are given (e.g. the sum of the weights for the levels of a factor should be the same as the weight of one quantitative variable). Therefore, the function enfa requires that a preliminary multivariate analysis is performed on the table (using analysis of the family of duality diagram, e.g. principal component analysis or Hill and Smith analysis). The object returned by this preliminary analysis contains the appropriate weights and transformation of the original data frame. For example, the function dudi.mix can be used first on the data.frame containing the value of both quantitative (e.g. slope, elevation) and qualitative habitat variables (e.g. vegetation) for each pixel of a raster map. The result of this analysis can then be passed as argument to the function enfa (see examples below).

References

Hutchinson, G.E. (1957) Concluding Remarks. Cold Spring Harbor Symposium on Quantitative Biology, 22: 415--427.

Perrin, N. (1984) Contribution a l'ecologie du genre Cepaea (Gastropoda) : Approche descriptive et experimentale de l'habitat et de la niche ecologique. These de Doctorat. Universite de Lausanne, Lausanne.

Hirzel, A.H., Hausser, J., Chessel, D. and Perrin, N. (2002) Ecological-niche factor analysis: How to compute habitat-suitability maps without absence data? Ecology, 83, 2027--2036.

Basille, M., Calenge, C., Marboutin, E., Andersen, R. and Gaillard, J.M. (2008) Assessing habitat selection using multivariate statistics: Some refinements of the ecological-niche factor analysis. Ecological Modelling, 211, 233--240.

Examples

Run this code


data(lynxjura)

map <- lynxjura$map

## We keep only "wild" indices.
locs <- lynxjura$locs
locs <- locs[slot(locs, "data")[,2]!="D",]

hist(map, type = "l")
## The variable artif is far from symetric

## We perform a square root transformation
## of this variable
## We therefore normalize the variable 'artif'
slot(map,"data")[,4] <- sqrt(slot(map,"data")[,4])
hist(map, type = "l")

## We prepare the data for the ENFA
tab <- slot(map, "data")
pr <- slot(count.points(locs, map), "data")[,1]


## We then perform the PCA before the ENFA
pc <- dudi.pca(tab, scannf = FALSE)

## The object 'pc' contains the transformed table (i.e.
## centered so that all columns have a mean of 0
## and scaled so that all columns have a variance of 1
## 'pc' also contains the weights of the habitat variables,
## and the weights of the pixels in the analysis

(enfa1 <- enfa(pc, pr,
               scannf = FALSE))
hist(enfa1)
hist(enfa1, scores = FALSE, type = "l")


## scatterplot
scatter(enfa1)


## randomization test
if (FALSE) {
(renfa <- randtest(enfa1))
plot(renfa)
}

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