Computation of the First Passage Time From Trajectories

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Description

These functions compute the first passage time using trajectories of class "ltraj" of type II (time recorded).

Usage

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fpt(lt, radii, units = c("seconds", "hours", "days"))
varlogfpt(f, graph = TRUE)
meanfpt(f, graph = TRUE)
## S3 method for class 'fipati'
plot(x, scale, warn = TRUE, ...)

Arguments

lt

an object of class "ltraj" of type II (time recorded)

radii

a numeric vector giving the radii of the circles

units

The time units of the results

f,x

an object of class fipati returned by the function fpt

graph

logical. Whether the results should be plotted

scale

the value of the radius to be plotted

warn

logical. Whether the function should warn the user when the given scale does not correspond to possible radii available in the object of class fipati

...

additional arguments to be passed to the generic function plot

Details

The first passage time (FPT) is a parameter often used to describe the scale at which patterns occur in a trajectory. For a given scale r, it is defined as the time required by the animals to pass through a circle of radius r. Johnson et al. (1992) indicated that the mean first passage time scales proportionately to the square of the radius of the circle for an uncorrelated random walk. They used this property to differenciate facilitated diffusion and impeded diffusion, according to the value of the coefficient of the linear regression log(FPT) = a * log(radius) + b. Under the hypothesis of a random walk, a should be equal to 2 (higher for impeded diffusion, and lower for facilitated diffusion). Note however, that the value of a converges to 2 only for large values of radius.

Fauchald & Tveraa (2003) proposed another use of the FPT. Instead of computing the mean of FPT, they propose the use of the variance of the log(FPT). This variance should be high for scales at which patterns occur in the trajectory (e.g. area restricted search). This method is often used to determine the scale at which an animal seaches for food.

Value

fpt computes the FPT for each relocation and each radius, and for each animals. This function returns an object of class "fipati", i.e. a list with one component per animal. Each component is a data frame with each column corresponding to a value of radii and each row corresponding to a relocation. An object of class fipati has an attribute named "radii" corresponding to the argument radii of the function fpt.

meanfpt and varlogfpt return a data frame giving respectively the mean FPT and the variance of the log(FPT) for each animal (rows) and rach radius (column). These objects also have an attribute "radii".

Author(s)

Clement Calenge clement.calenge@oncfs.gouv.fr

References

Johnson, A. R., Milne, B.T., & Wiens, J.A. (1992) Diffusion in fractal landscapes: simulations and experimental studies of tenebrionid beetle movements. Ecology 73: 1968–1983.

Fauchald, P. & Tveraa, T. (2003) Using first passage time in the analysis of area restricted search and habitat selection. Ecology 84: 282–288.

See Also

ltraj for additional information on objects of class ltraj

Examples

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data(puechcirc)
i <- fpt(puechcirc, seq(300,1000, length=30))
plot(i, scale = 500, warn = FALSE)

toto <- meanfpt(i)
toto
attr(toto, "radii")


toto <- varlogfpt(i)
toto
attr(toto, "radii")

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