These functions compute the first passage time using trajectories of
class "ltraj" of type II (time recorded).
fpt(lt, radii, units = c("seconds", "hours", "days"))
varlogfpt(f, graph = TRUE)
meanfpt(f, graph = TRUE)
# S3 method for fipati
plot(x, scale, warn = TRUE, ...)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".
an object of class "ltraj" of type II (time
recorded)
a numeric vector giving the radii of the circles
The time units of the results
an object of class fipati returned by the function
fpt
logical. Whether the results should be plotted
the value of the radius to be plotted
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
Clement Calenge clement.calenge@ofb.gouv.fr
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.
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.
ltraj for additional information on objects of
class ltraj
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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