gdistance (version 1.1-2)

pathInc: Incidence of paths from a common origin: overlap and non-overlap

Description

Calculate the overlap and non-overlap of two paths departing from a common origin. Two algorithms to are available: random walk and randomised shortest paths.

Usage

pathInc(transition, origin, fromCoords, toCoords, type, theta, weight)

Arguments

transition

transition matrix (class Transition)

origin

coordinates of the origin (one point location, SpatialPoints, matrix or numeric class)

fromCoords

coordinates of the destinations (SpatialPoints, matrix or numeric class)

toCoords

second set of coordinates of the destinations (only "missing" implemented)

type

a vector of one or two calculation types c("divergent","joint")

theta

value > 0 and < 20 (randomised shortest paths) or missing (random walk)

weight

weight matrix -- Reciprocals of the non-zero values are used as weights. If missing, reciprocals of the transition matrix are used.

Value

• dist object or list of dist objects

Details

This function calculates the overlap and non-overlap in the random walk trajectories or randomised shortest paths originating in a single point to sets of other locations. First, probabilities of passage are calculated for each cell-to-cell connection. The shared path is calculated as: Pjoint = Pi * Pj Divergence is calculated as: Pdivergent = max(0, max(Pi, Pj) * (1 - min(Pi, Pj)) - min(Pi, Pj)) Both are summed over all connections ij in the transition matrix.

References

McRae B.H., B.G. Dickson, and T. Keitt. 2008. Using circuit theory to model connectivity in ecology, evolution, and conservation. Ecology 89:2712-2724. Saerens M., L. Yen, F. Fouss, and Y. Achbany. 2009. Randomized shortest-path problems: two related models. Neural Computation, 21(8):2363-2404. van Etten, J., and R.J. Hijmans. 2010. A geospatial modelling approach integrating archaeobotany and genetics to trace the origin and dispersal of domesticated plants. PLoS ONE 5(8): e12060.

Examples

#Create TransitionLayer
r <- raster(ncol=36,nrow=18)
r <- setValues(r,rep(1,times=ncell(r)))
tr <- transition(r,mean,directions=4)

#Two different types of correction are required
trR <- geoCorrection(tr, type="r", multpl=FALSE)
trC <- geoCorrection(tr, type="c", multpl=FALSE)

#Create TransitionStack
ts <- stack(trR, trR)

#Points for origin and coordinates between which to calculate path (non)overlaps
sP0 <- SpatialPoints(cbind(0,0))
sP1 <- SpatialPoints(cbind(c(65,5,-65),c(-55,35,-35)))

#Randomised shortest paths
#rescaling is needed: exp(-theta * trC) should give reasonable values
trC <- trC / median(transitionMatrix(trC)@x) #divide by median of the non-zero values
pathInc(trC, origin=sP0, fromCoords=sP1, type=c("divergent","joint"), theta=2)

#Random walk
pathInc(trR, origin=sP0, fromCoords=sP1, type=c("divergent","joint"))

#TransitionStack as weights
pathInc(trR, origin=sP0, fromCoords=sP1, type=c("divergent","joint"), weight=ts)