# Compute Schoener's ratio

### Description

`schoener`

computes the Schoener's ratio on radio-tracking data.

`schoener.rtest`

performs a randomization test of the equality of
the Schoener's ratio to 2

### Usage

1 2 | ```
schoener(tr, keep, byburst = TRUE)
schoener.rtest(tr, keep, byburst = TRUE, nrep = 500)
``` |

### Arguments

`tr` |
an object of class |

`keep` |
a vector of length 2, giving the lower and the upper bound of the time interval for which a pair of relocations is considered in the computation of t\^2 (see details). These values are given in seconds. |

`byburst` |
logical. If |

`nrep` |
the number of randomisations of the test. |

### Details

The Schoener's ratio is a measure of time-autocorrelation in the data.
This ratio is computed as the squared mean distance between "neighbour"
relocations (t\^2) divided by the squared mean distance between the
relocations and their barycenter (r\^2). The theoretical value of this
ratio under the hypothesis of independance of the relocations is 2.

Swihart and Slade (1985) consider as neighbour two successive
relocations. However, the Schoener's ratio computed in this way makes
sense biologically only if the relocations are equally spaced in
time. However, as indicated by these authors, "such a data set
probably is the exception rather than the rule because many problems
may arise in taking a locational reading at a specified time".

In this function, we define as "neighbour" two relocations (not
necessarily successive relocations) separated by a time interval
comprised within the bounds specified in the vector `keep`

(in
seconds). For example, if `keep = c(60, 300)`

, all relocations
separated by a time interval comprised between 1 and 5 minutes are
considered in the computation. Thus, the total number of pairs of
relocations m taken into account in the computation may be larger than
the number of relocations n (m can be at most equal to n*(n-1)/2).

### Value

returns an object of class `schoener`

.

### Author(s)

Clement Calenge clement.calenge@oncfs.gouv.fr

### References

Schoener, T.W. (1981) An empirically based estimate of home
range. *Theoretical Population Biology*, **20**, 281–325.

Swihart, R.K. and Slade, N.A. (1985) Testing for independence of
observations in animal movements. *Ecology*, **66**,
1176–1184.

Solow, A.R. (1989) A randomization test for independence of animal
locations. *Ecology*, **70**, 1546–1549.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
data(puechcirc)
puechcirc <- ltraj2traj(puechcirc)
puechcirc$date[1:10]
## Relocations are taken every 10 minutes
## For example we consider relocations as
## neighbour when they are separated by a time
## interval comprised between 5 and 15 minutes
schoener(puechcirc, keep = c(5*60, 15*60))
## Not run:
schoener.rtest(puechcirc, keep = c(5*60, 15*60))
## End(Not run)
``` |