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.
data2enfa prepares data (kasc and localizations) to be analyzed by the ENFA.

Usage

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enfa(dudi, pr, scannf = TRUE, nf = 1)
## S3 method for class 'enfa'
hist(x, scores = TRUE, type = c("h", "l"), adjust = 1, Acol, Ucol, 
          Aborder, Uborder, Alwd = 1, Ulwd = 1, ...)
data2enfa(kasc, pts)

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

kasc

a raster map of class kasc

pts

a data frame with two columns, giving the coordinates of the species locations

...

further arguments passed to or from other methods

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).

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.

data2enfa returns a list of class dataenfa containing the following components:

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.

index

an integer vector giving the position of the rows of tab in the initial object of class kasc.

attr

an object of class mapattr with the attributes of the initial kasc.

Author(s)

Mathieu Basille basille@ase-research.org

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.

See Also

niche, kselect for other types of analysis of the niche, when several species are under studies, niche.test to perform a test of the marginality and the tolerance of the niche, and scatter.enfa to have a graphical display of objects of class enfa. See madifa for another factorial analysis of the ecological niche.

Examples

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data(lynxjura)

map <- lynxjura$map

## We keep only "wild" indices.
tmp <- lynxjura$locs[,4]!="D"
locs <- lynxjura$locs[tmp, c("X","Y")]
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'
map[,4] <- sqrt(map[,4])
hist(map, type = "l")

## We prepare the data for the ENFA
(dataenfa1 <- data2enfa(map, locs))

## We then perform the PCA before the ENFA
pc <- dudi.pca(dataenfa1$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, dataenfa1$pr,
               scannf = FALSE))
hist(enfa1)
hist(enfa1, scores = FALSE, type = "l")

## randomization test and scatterplot
## Not run: 
(renfa <- randtest(enfa1))
plot(renfa)
scatter(enfa1)

## End(Not run)

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