weeds: Dubbo weed data

In DSpat: Spatial Modelling for Distance Sampling Data

Description

Locations of devils claw in a farming paddock. Locations to all weeds are given and those observed along one of eight 150m wide transects (75m each side) are specified as Seen=1.

Usage

data(weeds)

Format

A data frame with 742 observations on the following 4 variables.

Transect

Label of the transect 1 to 8

SignedDistance

perpendicular distance in meters of weed from centerline; negative left and positive right

Distance

absolute perpendicular distance

Seen

weed was seen if 1 and 0 if missed

Details

These are the data that were provided by Melville and Welsh (see reference below) that were used in their Biometrics paper on distance sampling. In their paper they specified that the transects were laid out parallel in a north-south direction and presumably the transects were contiguous. This allows us to construct an x coordinate for each weed but no y coordinate was provided. In our use of these data we have created a y coordinate using runif and we have assumed the entire study area was 1200x1200 or 1.44 sq kilometers. They also stated that on transect 5-8 sheep ate the leafy part of the weed but there was no sheep grazing on transects 1-4. Presumably there was a fence between the sets of transects.

References

Melville, G. J., and A. H. Welsh. 2001. Line transect sampling in small regions. Biometrics 57:1130-1137.

Examples

###############################################################################
# Dubbo weed data
###############################################################################
#
# Example creates a function that you can run.  It is not run as
# part of the exampled to speed up package checking
# To run, code type do.weeds()
do.weeds=function()
{
  data(weeds.all)
  TrueAbundance=dim(weeds.all)[1]
  cat("\nTrue N= ",TrueAbundance,"\n")
  study.area=owin(xrange=c(0,1200),yrange=c(0,1200))
  data(weeds.lines)
  data(weeds.obs)
  data(weeds.covariates)
  study.area=owin(xrange=c(0,1200),yrange=c(0,1200))
#
# The entire study area is covered by the 8 N-S strips that are each 150m wide
# Sheep are absent on strips 1-4 and present on strips 5-8
# The following fits a model using all weeds whether they were seen or not
#
  weeds.dspat=dspat(int.formula=~factor(strip),det.formula=~-1,
                    study.area=study.area,
                    obs=weeds.all,lines=weeds.lines,covariates=weeds.covariates,
                    epsvu=c(100,1))
  mu.B <- integrate.intensity(weeds.dspat,dimyx=120,se=TRUE)
  cat('Abundance =       ', round(mu.B$abundance,0), "\n")
  pdf("TrueIntensity.pdf")
  plot(mu.B$lambda, main='True intensity by strip')
  plot(weeds.dspat$lines.psp,lty=2,add=TRUE)
  plot(owin(poly=weeds.dspat$transect),add=TRUE)
  plot(weeds.dspat$model$Q$data,add=TRUE,pch=20)
  dev.off()
# Compute distances for each weed
  obs.ppp=weeds.dspat$model$Q$data
  no.sheep.distances=NULL
  sheep.distances=NULL
  transects=weeds.dspat$transects
  for (i in 1:4)
    no.sheep.distances=c(no.sheep.distances,
      dist2line(obs.ppp[owin(poly=transects[i])],weeds.dspat$lines.psp$ends[i,])$distance)
  sheep.distances=NULL
  for (i in 5:8)
    sheep.distances=c(sheep.distances,
      dist2line(obs.ppp[owin(poly=transects[i])],weeds.dspat$lines.psp$ends[i,])$distance)
  pdf("True Distance Distribution.pdf")
  par(mfrow=c(2,1))
  hist(no.sheep.distances,breaks=(0:15)*5,main="Sheep absent",xlab="Perpendicular distance (m)")
  hist(sheep.distances,breaks=(0:15)*5,main="Sheep present",xlab="Perpendicular distance (m)")
  dev.off()
  no.sheep=hist(no.sheep.distances,breaks=(0:15)*5,plot=FALSE)$counts
  with.sheep=hist(sheep.distances,breaks=(0:15)*5,plot=FALSE)$counts
# summary of abundance per strip
  Est.N=by(mu.B$distribution$N,cut(mu.B$distribution$x,seq(0,1200,150)),sum)
  True.N=by(weeds.all$x,cut(weeds.all$x,seq(0,1200,150)),length)
  pdf("TrueAbundanceByStrip.pdf")
  barplot(rbind(True.N,Est.N),beside=TRUE,legend=TRUE,names.arg=1:8,main="All weeds")
  dev.off()
#  The following code will produce the true detection probability as a function of
#  distance for no sheep (lines 1-4) and sheep (lines 5-8) using all known weed locations
#  observed weed locations.
  sheep.labels.obs=cut(weeds.obs$label,c(1,4,8),include.lowest=TRUE)
  levels(sheep.labels.obs)=c("Sheep absent","Sheep present")
  sheep.labels=cut(weeds.all$label,c(1,4,8),include.lowest=TRUE)
  levels(sheep.labels)=c("Sheep absent","Sheep present")
  cat("\n All weeds \n")
  table(sheep.labels,cut(weeds.all$distance,(0:10)*7.5,include.lowest=TRUE))
  det=table(sheep.labels.obs,cut(weeds.obs$distance,(0:10)*7.5,include.lowest=TRUE))/
  table(sheep.labels,cut(weeds.all$distance,(0:10)*7.5,include.lowest=TRUE))
  cat("\n Detection \n")
  det
  pdf("TrueDetection.pdf")
  barplot(det,beside=TRUE,main="Dubbo weed detection probability",
             xlab="Perpendicular distance",legend=TRUE)
  dev.off()
#
# For the observed weeds with N-S transects:
#
# 6 different models were fit for each pairing of:
#  int.formula:
#  3 formulas for intensity: ~factor(sheep), ~factor(strip), ~s(x)
#  det.formula
#  2 formulas for detection: ~1 (constant sigma), ~factor(sheep) (sigma for sheep,no sheep)
#
# A half-normal detection function is assumed which is fitted with I(-distance^2/2)
#
# Fit model ~sheep, ~1
weeds.dspat.1=dspat(int.formula=~factor(sheep), study.area=study.area,
                     obs=weeds.obs,lines=weeds.lines,covariates=weeds.covariates,
                     epsvu=c(100,1))
AIC(weeds.dspat.1)
coef(weeds.dspat.1)
mu.B = integrate.intensity(weeds.dspat.1,dimyx=120,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat('Standard Error =  ', round(mu.B$precision$se,0), "\n",
    '95 Percent Conf. Int. =   (', round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ')', '\n')
pdf("NS_model_1_intensity.pdf")
plot(mu.B$lambda, main='Estimated Intensity')
plot(weeds.dspat.1$lines.psp,lty=2,add=TRUE)
plot(owin(poly=weeds.dspat.1$transect),add=TRUE)
plot(weeds.dspat.1$model$Q$data,add=TRUE,pch=20)
dev.off()
# Fit model ~sheep, ~sheep
weeds.dspat.2=dspat(int.formula=~factor(sheep),det.formula=~factor(sheep),
                   study.area=study.area,
                   obs=weeds.obs,lines=weeds.lines,covariates=weeds.covariates,
                   epsvu=c(100,1))
summary(weeds.dspat.2)
AIC(weeds.dspat.2)
coef(weeds.dspat.2)
mu.B = integrate.intensity(weeds.dspat.2,dimyx=120,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat('Standard Error =  ', round(mu.B$precision$se,0), "\n",
    '95 Percent Conf. Int. =   (', round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ')', '\n')
pdf("NS_model_2_intensity.pdf")
plot(mu.B$lambda, main='Estimated Intensity')
plot(weeds.dspat.2$lines.psp,lty=2,add=TRUE)
plot(owin(poly=weeds.dspat.2$transect),add=TRUE)
plot(weeds.dspat.2$model$Q$data,add=TRUE,pch=20)
dev.off()
# Fit model ~factor(strip), ~1
weeds.dspat.3=dspat(~factor(strip),study.area=study.area,
                  obs=weeds.obs,lines=weeds.lines,covariates=weeds.covariates,
                   epsvu=c(100,1))
summary(weeds.dspat.3)
AIC(weeds.dspat.3)
coef(weeds.dspat.3)
mu.B = integrate.intensity(weeds.dspat.3,dimyx=120,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat('Standard Error =  ', round(mu.B$precision$se,0), "\n",
    '95 Percent Conf. Int. =   (', round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ')', '\n')
pdf("NS_model_3_intensity.pdf")
plot(mu.B$lambda, main='Estimated Intensity')
plot(weeds.dspat.3$lines.psp,lty=2,add=TRUE)
plot(owin(poly=weeds.dspat.3$transect),add=TRUE)
plot(weeds.dspat.3$model$Q$data,add=TRUE,pch=20)
dev.off()
# Fit model ~factor(strip), ~factor(sheep)
weeds.dspat.4=dspat(int.formula=~factor(strip),det.formula=~factor(sheep),
                   study.area=study.area,
                   obs=weeds.obs,lines=weeds.lines,covariates=weeds.covariates,
                   epsvu=c(100,0.75),nclass=10)
summary(weeds.dspat.4)
AIC(weeds.dspat.4)
coef(weeds.dspat.4)
mu.B = integrate.intensity(weeds.dspat.4,dimyx=120,se=TRUE)
mu.B.4=mu.B
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat('Standard Error =  ', round(mu.B$precision$se,0), "\n",
    '95 Percent Conf. Int. =   (', round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ')', '\n')
pdf("NS_model_4_intensity.pdf")
plot(mu.B$lambda, main='Estimated Intensity')
plot(weeds.dspat.4$lines.psp,lty=2,add=TRUE)
plot(owin(poly=weeds.dspat.4$transect),add=TRUE)
plot(weeds.dspat.4$model$Q$data,add=TRUE,pch=20)
dev.off()
# Fit model ~s(x), ~1
weeds.dspat.5=dspat(int.formula=~s(x),
                    study.area=study.area,
                    obs=weeds.obs,lines=weeds.lines,covariates=weeds.covariates,
                    epsvu=c(100,1))
summary(weeds.dspat.5)
AIC(weeds.dspat.5)
coef(weeds.dspat.5)
mu.B = integrate.intensity(weeds.dspat.5,dimyx=120,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat('Standard Error =  ', round(mu.B$precision$se,0), "\n",
    '95 Percent Conf. Int. =   (', round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ')', '\n')
pdf("NS_model_5_intensity.pdf")
plot(mu.B$lambda, main='Estimated Intensity')
plot(weeds.dspat.5$lines.psp,lty=2,add=TRUE)
plot(owin(poly=weeds.dspat.5$transect),add=TRUE)
plot(weeds.dspat.5$model$Q$data,add=TRUE,pch=20)
dev.off()
# Fit model ~s(x), ~sheep
weeds.dspat.6=dspat(int.formula=~s(x),det.formula=~factor(sheep),
                    study.area=study.area,
                    obs=weeds.obs,lines=weeds.lines,covariates=weeds.covariates,
                    epsvu=c(100,1))

summary(weeds.dspat.6)
AIC(weeds.dspat.6)
coef(weeds.dspat.6)
mu.B = integrate.intensity(weeds.dspat.6,dimyx=120,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat('Standard Error =  ', round(mu.B$precision$se,0), "\n",
    '95 Percent Conf. Int. =   (', round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ')', '\n')
pdf("NS_model_6_intensity.pdf")
plot(mu.B$lambda, main='Estimated Intensity')
plot(weeds.dspat.6$lines.psp,lty=2,add=TRUE)
plot(owin(poly=weeds.dspat.6$transect),add=TRUE)
plot(weeds.dspat.6$model$Q$data,add=TRUE,pch=20)
dev.off()
# summary of abundance per strip using model 4
Est.N=by(mu.B.4$distribution$N,cut(mu.B.4$distribution$x,seq(0,1200,150)),sum)
True.N=by(weeds.all$x,cut(weeds.all$x,seq(0,1200,150)),length)
postscript("Figure3.ps",height=6,width=5,horizontal=FALSE)
barplot(rbind(True.N,Est.N),beside=TRUE,legend=TRUE,names.arg=1:8,main="N-S lines model 4")
dev.off()
# Show goodness of fit for sheep absent/present
postscript("Figure4.ps",height=6,width=5,horizontal=FALSE)
exp.nosheep=apply(weeds.dspat.4$exp.counts[1:4,],2,sum)
obs.nosheep=apply(weeds.dspat.4$obs.counts[1:4,],2,sum)
exp.sheep=apply(weeds.dspat.4$exp.counts[5:8,],2,sum)
obs.sheep=apply(weeds.dspat.4$obs.counts[5:8,],2,sum)
par(mfrow=c(2,1))
barplot(rbind(exp=exp.nosheep,obs=obs.nosheep),beside=TRUE,main="Sheep absent")
barplot(rbind(exp=exp.sheep,obs=obs.sheep),beside=TRUE,legend=FALSE,main="Sheep present")
dev.off()
# chi-square test for model 4
chisq=sum((exp.nosheep-obs.nosheep)^2/exp.nosheep)+
sum((exp.sheep-obs.sheep)^2/exp.sheep)
cat("Chi-square=",chisq," p= ",1-pchisq(chisq,2*10-length(weeds.dspat.4$par)),"\n")
# sigma for no sheep and sheep
sigmas=sqrt(1/coef(weeds.dspat.4)$detection)
cat("\n Sigma (no sheep) =",sigmas[1],"\n","Sigma (sheep)    =",sigmas[2],"\n")
###############################################################################
# Modify sampled vertical N-S strips to extend from 600 to 1200 and then
# add 4 E-W horizontal strips centered at 75,225,375,525. Using approximate
# detection functions for sheep/no sheep areas, a sample of observations from
# the points are randomly selected.
#
# NOTE: The following is random and will not produce the same results each time
# it is run because of the random observation process.
#
################################################################################
data(weeds.obs)
data(weeds.lines)
weeds.obs=weeds.obs[weeds.obs$y>600,]
xlines=data.frame(label=9:12,x0=rep(0,4),x1=rep(1200,4),y0=c(75,225,375,525),
                 y1=c(75,225,375,525),width=rep(149.999,4))
ls=lines_to_strips(xlines,study.area)
pts=ppp(x=weeds.all$x,y=weeds.all$y,window=study.area)
pdf("E-W_N-S samples.pdf")
plot(pts)
plot(ppp(x=weeds.obs$x,y=weeds.obs$y,window=study.area),add=TRUE,pch=19,col="red",cex=.5)
obs=sample.points(ls$transects,xlines,pts,detfct=hndetfct,
                det.par=c(3.637586,-.1466),det.formula=~factor(sheep),
                covariates=weeds.covariates)
weeds.obs=rbind(weeds.obs,obs)
plot(ppp(x=obs$x,y=obs$y,window=study.area),add=TRUE,pch=19,cex=.5)
dev.off()
weeds.lines[,"y0"]=600.0001
weeds.lines=rbind(weeds.lines,as.matrix(xlines))
weeds.dspat=dspat(int.formula=~factor(strip),det.formula=~factor(sheep),
                    study.area=study.area,
                    obs=weeds.obs,lines=weeds.lines,covariates=weeds.covariates,
                    epsvu=c(100,1),nclass=15)
coef(weeds.dspat)
# sigma for no sheep and sheep
sigmas=sqrt(1/coef(weeds.dspat)$detection)
cat("\n Sigma (no sheep) =",sigmas[1],"\n","Sigma (sheep)    =",sigmas[2],"\n")
mu.B <- integrate.intensity(weeds.dspat,dimyx=120,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat('Standard Error =  ', round(mu.B$precision$se,0), "\n",
    '95 Percent Conf. Int. =   (', round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ')', '\n')
pdf("E-W_N-S Estimated Intensity.pdf")
plot(mu.B$lambda, main='Estimated Intensity')
plot(weeds.dspat$lines.psp,lty=2,add=TRUE)
plot(owin(poly=weeds.dspat$transect),add=TRUE)
plot(weeds.dspat$model$Q$data,add=TRUE,pch=20)
dev.off()
# summary of abundance per strip
pdf("E-W_N-S AbundanceByStrip.pdf")
Est.N=by(mu.B$distribution$N,cut(mu.B$distribution$x,seq(0,1200,150)),sum)
True.N=by(weeds.all$x,cut(weeds.all$x,seq(0,1200,150)),length)
barplot(rbind(True.N,Est.N),beside=TRUE,legend=TRUE,names.arg=1:8,main="N-S and E-W lines")
dev.off()
# Show goodness of fit for sheep absent/present
pdf("GOF for NS_EW model.pdf")
exp.nosheep=apply(weeds.dspat$exp.counts[1:4,],2,sum)
obs.nosheep=apply(weeds.dspat$obs.counts[1:4,],2,sum)
exp.sheep=apply(weeds.dspat$exp.counts[5:8,],2,sum)
obs.sheep=apply(weeds.dspat$obs.counts[5:8,],2,sum)
par(mfrow=c(2,1))
barplot(rbind(exp=exp.nosheep,obs=obs.nosheep),beside=TRUE,legend=TRUE,main="Sheep absent")
barplot(rbind(exp=exp.sheep,obs=obs.sheep),beside=TRUE,legend=FALSE,main="Sheep present")
dev.off()
# chi-square test for model
chisq=sum((exp.nosheep-obs.nosheep)^2/exp.nosheep)+
sum((exp.sheep-obs.sheep)^2/exp.sheep)
cat("Chi-square=",chisq," p= ",1-pchisq(chisq,2*15-10),"\n")

###############################################################################
# Modify sampling such that all strips are E-W. Using approximate
# detection functions for sheep/no sheep areas derived from known data,
# a sample of observations from the points are randomly selected.
#
# NOTE: The following is random and will not produce the same results each time
# it is run because of the random observation process.
#
###############################################################################
xlines=data.frame(label=1:8,x0=rep(0,8),x1=rep(1200,8),y0=seq(75,1125,150),y1=seq(75,1125,150),
                       width=rep(149.999,8))
ls=lines_to_strips(xlines,study.area)
pts=ppp(x=weeds.all$x,y=weeds.all$y,window=study.area)
pdf("E-W samples.pdf")
plot(pts)
obs=sample.points(ls$transects,xlines,pts,detfct=hndetfct,
                det.par=c(3.637586,-.1466),det.formula=~factor(sheep),
                covariates=weeds.covariates)
plot(ppp(x=obs$x,y=obs$y,window=study.area),add=TRUE,pch=19,cex=.5)
dev.off()
weeds.dspat=dspat(int.formula=~factor(strip),det.formula=~factor(sheep),
                    study.area=study.area,
                    obs=obs,lines=xlines,covariates=weeds.covariates,
                    epsvu=c(100,1),nclass=15)
coef(weeds.dspat)
sigmas=sqrt(1/coef(weeds.dspat)$detection)
cat("\n Sigma (no sheep) =",sigmas[1],"\n","Sigma (sheep)    =",sigmas[2],"\n")
mu.B <- integrate.intensity(weeds.dspat,dimyx=120,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat('Standard Error =  ', round(mu.B$precision$se,0), "\n",
    '95 Percent Conf. Int. =   (', round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ')', '\n')
pdf("E-W Estimated Intensity.pdf")
plot(mu.B$lambda, main='Estimated Intensity')
plot(weeds.dspat$lines.psp,lty=2,add=TRUE)
plot(owin(poly=weeds.dspat$transect),add=TRUE)
plot(weeds.dspat$model$Q$data,add=TRUE,pch=20)
dev.off()
# summary of abundance per strip
Est.N=by(mu.B$distribution$N,cut(mu.B$distribution$x,seq(0,1200,150)),sum)
True.N=by(weeds.all$x,cut(weeds.all$x,seq(0,1200,150)),length)
pdf("E-W AbundanceByStrip.pdf")
barplot(rbind(True.N,Est.N),beside=TRUE,legend=TRUE,names.arg=1:8,main="E-W lines")
dev.off()
# Show goodness of fit for sheep absent/present
pdf("GOF for EW model.pdf")
exp.nosheep=apply(weeds.dspat$exp.counts[1:4,],2,sum)
obs.nosheep=apply(weeds.dspat$obs.counts[1:4,],2,sum)
exp.sheep=apply(weeds.dspat$exp.counts[5:8,],2,sum)
obs.sheep=apply(weeds.dspat$obs.counts[5:8,],2,sum)
par(mfrow=c(2,1))
barplot(rbind(exp=exp.nosheep,obs=obs.nosheep),beside=TRUE,legend=TRUE,main="Sheep absent")
barplot(rbind(exp=exp.sheep,obs=obs.sheep),beside=TRUE,legend=FALSE,main="Sheep present")
dev.off()
# chi-square test for model
chisq=sum((exp.nosheep-obs.nosheep)^2/exp.nosheep)+
sum((exp.sheep-obs.sheep)^2/exp.sheep)
cat("Chi-square=",chisq," p= ",1-pchisq(chisq,2*15-10),"\n")
}

DSpat documentation built on May 2, 2019, 11:10 a.m.