spsample.prob: Estimate occurrence probabilities of a sampling plan (points)

Description

Estimates occurrence probabilities as an average between the kernel density estimation (spreading of points in geographical space) and MaxLike analysis (spreading of points in feature space). The output 'iprob' indicates whether the sampling plan has systematically missed some important locations / features, and can be used as an input for geostatistical modelling (e.g. as weights for regression modeling).

Usage

"spsample.prob"(observations, covariates,  quant.nndist=.95, n.sigma, ...)

Arguments

observations

object of class SpatialPoints; sampling locations

covariates

object of class SpatialPixelsDataFrame; list of covariates of interest

quant.nndist

numeric; threshold probability to determine the search radius (sigma)

n.sigma

numeric; size of sigma used for kernel density estimation (optional)

...

other optional arguments that can be passed to function spatstat::density

Value

Returns a list of objects where 'iprob' ("SpatialPixelsDataFrame") is the map showing the estimated occurrence probabilities.

References

Baddeley, A. (2008) Analysing spatial point patterns in R. Technical report, CSIRO Australia. Version 4.
Royle, J.A., Chandler, R.B., Yackulic, C. and J. D. Nichols. (2012) Likelihood analysis of species occurrence probability from presence-only data for modelling species distributions. Methods in Ecology and Evolution.

Examples

Run this code

library(plotKML)
library(maxlike)
library(spatstat)
library(maptools)

data(eberg)
data(eberg_grid)
## existing sampling plan:
sel <- runif(nrow(eberg)) < .2
eberg.xy <- eberg[sel,c("X","Y")]
coordinates(eberg.xy) <- ~X+Y
proj4string(eberg.xy) <- CRS("+init=epsg:31467")
## covariates:
gridded(eberg_grid) <- ~x+y
proj4string(eberg_grid) <- CRS("+init=epsg:31467")
## convert to continuous independent covariates:
formulaString <- ~ PRMGEO6+DEMSRT6+TWISRT6+TIRAST6
eberg_spc <- spc(eberg_grid, formulaString)

## derive occurrence probability:
covs <- eberg_spc@predicted[1:8]
iprob <- spsample.prob(eberg.xy, covs)
## Note: obvious omission areas:
hist(iprob[[1]]@data[,1])
## compare with random sampling:
rnd <- spsample(eberg_grid, type="random",
     n=length(iprob[["observations"]]))
iprob2 <- spsample.prob(rnd, covs)
## compare the two:
par(mfrow=c(1,2))
plot(raster(iprob[[1]]), zlim=c(0,1), col=SAGA_pal[[1]])
points(iprob[["observations"]])
plot(raster(iprob2[[1]]), zlim=c(0,1), col=SAGA_pal[[1]])
points(iprob2[["observations"]])

## fit a weighted lm:
eberg.xy <- eberg[sel,c("SNDMHT_A","X","Y")]
coordinates(eberg.xy) <- ~X+Y
proj4string(eberg.xy) <- CRS("+init=epsg:31467")
eberg.xy$iprob <- over(eberg.xy, iprob[[1]])$iprob
eberg.xy@data <- cbind(eberg.xy@data, over(eberg.xy, covs))
fs <- as.formula(paste("SNDMHT_A ~ ", 
    paste(names(covs), collapse="+")))
## the lower the occurrence probability, the higher the weight:
w <- 1/eberg.xy$iprob
m <- lm(fs, eberg.xy, weights=w)
summary(m)
## compare to standard lm:
m0 <- lm(fs, eberg.xy)
summary(m)$adj.r.squared
summary(m0)$adj.r.squared

## all at once:
gm <- fit.gstatModel(eberg.xy, fs, covs, weights=w)
plot(gm)