# wi {adehabitat}

### Description

These functions compute the resource selection ratios (wi) for design I, II and III data types, with resources defined by several categories. Basic tests are also provided.

### Usage

widesI(u, a, avknown = TRUE, alpha = 0.05) widesII(u, a, avknown = TRUE, alpha = 0.05) widesIII(u, a, avknown = TRUE, alpha = 0.05) ## S3 method for class 'wiI': print((x, ...)) ## S3 method for class 'wiII': print((x, ...)) ## S3 method for class 'wiIII': print((x, ...)) ## S3 method for class 'wi': plot((x, caxis = 0.7, clab = 1, ylog = FALSE, errbar = c("CI", "SE"), main = "Manly selectivity measure", noorder = TRUE, ...))

### Arguments

- u
- for
`widesI`

, a vector with named elements describing the sample of used resource units. For`widesII`

and`widesIII`

a matrix or a data frame giving the number of used resource units for each animal (in rows) in each resource category (in columns) - a
- for
`widesI`

and`widesII`

, a vector with named elements describing the sample or the proportion of available resource units. For`widesIII`

a matrix or a data frame giving the number or the proportion of available resource units for each animal (in rows) in each resource category (in columns) - avknown
- logical.
`TRUE`

if the available proportions are known, and`FALSE`

if they are estimated - alpha
- the threshold value for the tests and confidence intervals
- x
- an object of class
`wi`

- caxis
- character size on axes to be passed to
`par("cex.axis")`

- clab
- character size of axes labels to be passed to
`par("cex.lab")`

- ylog
- logical. If
`TRUE`

, the selection ratios are plotted on a log scale - errbar
- a character string. Type of error bars: either
`"CI"`

for confidence intervals or`"SE"`

for standard errors - main
- a character string. The title of the graph
- noorder
- logical. If
`TRUE`

, the habitat categories are ordered on the graph in decreasing order of their preference. If FALSE, they are not ordered (i.e. they are in the same order as the columns in`used`

and`available`

- ...
- additionnal arguments to be passed to the function
`plot`

### Details

`widesI`

may be used to explore resource selection by animals, when designs I are involved (habitat use and availability are measured at the population level - animals are not identified). The function tests habitat selection with the Khi2 of Pearson and log-likelihood Khi2 (recommended, see Manly et al. 2003). The Manly selectivity measure (selection ratio = used/available) is computed, the preference / avoidance is tested for each habitat, and the differences between selection ratios are computed and tested.

`widesII`

computes the selection ratios with design II data (same availability for all animals, but use measured for each one). Tests of identical habitat use for all animals, and of habitat selection are also provided.

`widesIII`

computes the selection ratios for design III data (when the use and the availability are measured for each animal - see examples on the wild boar below). Habitat selection is tested using a Chi-square for each animal, and the overall habitat selection is also tested.

Note that all these methods rely on the following hypotheses: (i) independence between animals, and (ii) all animals are selecting habitat in the same way (in addition to "traditional" hypotheses in these kinds of studies: no territoriality, all animals having equal access to all available resource units, etc., see Manly et al. 2002 for further details).

### Values

`widesI`

returns a list of the class `wiI`

. `widesII`

returns a list of class `wiII`

. `widesIII`

returns a list of class `wiIII`

. These objects are all inheriting from the class `wi`

. They have the following components:

- used.prop
- the proportion of use for each resource type.
- avail.prop
- the proportion of available resources.
- wi
- the Manly selectivity measure (selection ratio: used/available).
- se.wi
- the standard error of the selection ratios.
- comparisons
- a list with the following components:

`diffwi`

- a matrix with the differences of the selection ratios for each pair of resource type.
`ICdiffupper`

- a matrix containing the upper limit of confidence interval on the differences of the selection ratios between each pair of resource type.
`ICdifflower`

- a matrix containing the lower limit of confidence interval on the differences of the selection ratios between each pair of resource type.
`signif`

- the ranking matrix, with the sign of the differences between the resource type in row and the resource type in column. When the difference is significant, the sign is tripled.

- profile
- the profile of preferences: resource types are sorted so that the left type is the most preferred and the right type is the most avoided. Habitats for which the selection ratios are not significant are connected by a line.
- alpha
- the parameter
`alpha`

of this function. - avknown
- the parameter
`avknown`

of this function. - se.used
- only for designs I, the standard error of the proportion of use.
- se.avail
- only for designs I, the standard error of the available proportion.
- chisquwi
- only for designs I, the results of Chi-Square tests of the hypothesis that the selection ratios are in average equals to zero.
- Bi
- only for designs I, equals to
`wi/sum(wi)`

. - Khi2P
- only for designs I, test of random resource use (Pearson statistic).
- Khi2L
- For designs I, test of random resource use (Log-likelihood statistic). For design III, global test of random resource use (Log-likelihood statistic)
- Khi2L1
- only for designs II, test of identical use of habitat by all animals.
- Khi2L2
- only for designs II, test of overall habitat selection.
- Khi2L2MinusL1
- only for designs II, test of hypothesis that animals are on average using resources in proportion to availability, irrespective of whether they are the same or not (= Khi2L2 - Khi2L1).
- wij
- only for designs II and III, a matrix with the selection ratios for all animals and all resource categories.
- ICwiupper
- only for designs II and III, the upper limit of the confidence intervals on the selection ratios.
- ICwilower
- only for designs II and III, the lower limit of the confidence intervals on the selection ratios.
- Khi2Lj
- only for designs III, the test of habitat selection for each animal.

### References

Manly B.F.J., McDonald L.L., Thomas, D.L., McDonald, T.L. & Erickson, W.P. (2003) *Resource selection by animals - Statistical design and Analysis for field studies. Second edition* London: Kluwer academic publishers.

Thomas D. L. and Taylor E. J. (1990) Study designs and tests for comparing resource use and availability. *Journal of Wildlife Management*, **54**, 322--330.

### See Also

`compana`

for compositional analysis, and `eisera`

to perform an eigenanalysis of selection ratios.

### Examples

############################ ## Example of moose (Manly et al., 2003, p.52) ## Known available proportions on design I data moose.avail <- c(0.34, 0.101, 0.104, 0.455) moose.used <- c(25, 22, 30, 40) names(moose.used) <- c("InBurnInterior", "InBurnEdge", "OutOfBurnEdge", "OutOfBurnFurther") names(moose.avail) <- names(moose.used) ## Computation of wi (wiRatio <- widesI(moose.used, moose.avail)) ## plot the values of the selection ratios opar <- par(mfrow=c(2,2)) plot(wiRatio) par(opar) ############################ ## Example of Elk (Manly et al., 2003, p.62) ## Estimated available proportions on design I data elk.avail <- c(15, 61, 84, 40) elk.used <- c(3, 90, 181, 51) names(elk.used) <- c("0%", "1-25%", "26-75%", ">75%") names(elk.avail) <- names(elk.used) ## Computation of wi (wiRatio <- widesI(elk.used, elk.avail, avknown=FALSE)) ## plot the values of the selection ratios opar <- par(mfrow=c(2,2)) plot(wiRatio) par(opar) ############################ ## Example of Bighorn (Manly et al., 2003, p.67) ## Known available proportions on design II data data(bighorn) ## Computation of wi (wi <- widesII(bighorn$used, bighorn$availT, alpha = 0.1)) ## plot the values of the selection ratios opar <- par(mfrow=c(2,2)) plot(wi) ############################ ## Example of Bighorn (Manly et al., 2003, p.74) ## Estimated available proportions on design II data ## Computation of wi (wi <- widesII(bighorn$used, bighorn$availE, avknown = FALSE, alpha = 0.1)) ## plot the values of the selection ratios plot(wi) par(opar) ############################ ## Example of Wild boar ## Estimated available proportions on design III data data(puechdesIII) used <- puechdesIII$used available <- puechdesIII$available ## calculation of the selectio ratios ## with sampled availability (i <- widesIII(used,available, avknown = FALSE, alpha = 0.1)) opar <- par(mfrow = c(2,2)) plot(i) par(opar)

Documentation reproduced from package adehabitat, version 1.8.12. License: GPL (>= 2)