Random walks, Brownian motion, Brownian bridges and percolation

LatticeRandomWalk: simple random walks on the square lattice. CorrelatedRandomWalk: constant steps with von Mises turning angles (Best-Fisher rejection) and CrwMsd the Kareiva-Shigesada mean squared displacement. BrownianMotion: planar Brownian paths. BrownianBridgeUd: Brownian bridge movement model utilisation distribution (Horne et al. 2007). SitePercolation: site percolation clusters and spanning. Identical to the Python arm morie.fn.movement.

Usage

LatticeRandomWalk(steps, nwalk = 1L, seed = 1)

CrwMsd(steps, step_length = 1, kappa = 2)

CorrelatedRandomWalk(steps, step_length = 1, kappa = 2, nwalk = 1L, seed = 1)

BrownianMotion(n, dt, sigma = 1, nwalk = 1L, seed = 1)

BrownianBridgeUd(track, times, xs, ys, sig1, sig2, nalpha = 25L)

SitePercolation(nrow, ncol, p, seed = 1, nsim = 1L)

Arguments

steps, n

Number of steps.

nwalk

Number of walks.

seed

Philox seed.

step_length

Step length.

kappa

von Mises concentration.

dt

Time step.

sigma

Diffusion scale.

track

Two-column fixes.

times

Fix times.

xs, ys

Grid coordinates.

sig1, sig2

Motion variance scale and location error.

nalpha

Integration nodes per segment.

nrow, ncol

Grid size.

p

Site occupation probability.

nsim

Realisations.

Value

List (numeric vector for CrwMsd).

References

Kareiva, P. M. and Shigesada, N. (1983). Analyzing insect movement as a correlated random walk. Oecologia 56, 234-238.

Horne, J. S., Garton, E. O., Krone, S. M. and Lewis, J. S. (2007). Analyzing animal movements using Brownian bridges. Ecology 88, 2354-2363.

Stauffer, D. and Aharony, A. (1994). Introduction to Percolation Theory, 2nd edn. Taylor and Francis.

Examples

CrwMsd(3, kappa = 2)
#> [1] 0.000000 1.000000 3.395549 6.764878
SitePercolation(3, 3, 1)$spanning
#> [1] TRUE