ctmcmove-package: Modeling Animal Movement with Continuous-Time Discrete-Space...

In ctmcmove: Modeling Animal Movement with Continuous-Time Discrete-Space Markov Chains

Description

Software to facilitates taking movement data in xyt format and pairing it with raster covariates within a continuous time Markov chain (CTMC) framework. As described in Hanks et al. (2015), this allows flexible modeling of movement in response to covariates (or covariate gradients) with model fitting possible within a Poisson GLM framework.

Details

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Typical work flow for analysis of telemetry / GPS movement data:

1. Fit a CTCRW movement model to telemetry xyt data using the "crawl" package.

2. Create or import raster layers (from package "raster") for each covariate.

3. Impute a quasi-continuous CTCRW path using the "get.crawl.path" command.

4. Turn the quasi-continuous CRAWL path into a CTMC discrete-space path using the "path2ctmc" command.

5. Turn discrete-space path into Poisson GLM format using the "ctmc2glm" command.

6. Repeat #3 - #5 multiple times (M times). Stack together the response "z", model matrix "X", and offset "tau" elements from each imputed path.

7. Fit a Poisson GLM model to the stacked data with response "z", model matrix "X", offset "tau", and weights for each row equal to "1/M".

Author(s)

Ephraim Hanks

Maintainer: Ephraim Hanks <[e-mail]>

References

Hanks, E. M.; Hooten, M. B. & Alldredge, M. W. Continuous-time Discrete-space Models for Animal Movement The Annals of Applied Statistics, 2015, 9, 145-165

Hanks, E.; Hooten, M.; Johnson, D. & Sterling, J. Velocity-Based Movement Modeling for Individual and Population Level Inference PLoS ONE, Public Library of Science, 2011, 6, e22795

Hooten, M. B.; Johnson, D. S.; Hanks, E. M. & Lowry, J. H. Agent-Based Inference for Animal Movement and Selection Journal of Agricultural, Biological, and Environmental Statistics, 2010, 15, 523-538

Examples

##
## Example of using a CTMC model for movement
##
## Steps:
##  1. Fit CRAWL to telemetry data (not done here)
##  2. Create covariate raster objects (the CTMC will be on the raster
##     grid cells)
##  3. Impute a CRAWL path
##  4. Turn quasi-continuous CRAWL path into a CTMC discrete-space path
##  5. Turn discrete-space path into latent Poisson GLM format
##  6. Fit a Poisson GLM model to the data
##

library(ctmcmove)

data(seal)
sim.obj=seal$sim.obj
cov.df=seal$cov.df
pred.times=seal$pred.times
xyt=seal$locs[,3:1]
head(xyt)
plot(xyt[,1:2],type="b")

##
## 2. Creating rasters
##

str(cov.df)

NN=sqrt(nrow(cov.df$X))
sst=matrix(seal$cov.df$X$sst,NN,byrow=TRUE)
sst=sst[NN:1,]
sst=raster(sst,xmn=min(seal$cov.df$X$x),xmx=max(seal$cov.df$X$x),
    ymn=min(seal$cov.df$X$y),ymx=max(seal$cov.df$X$y))


crs(sst)="+proj=longlat +datum=WGS84"
plot(sst)

chA=matrix(seal$cov.df$X$chA,NN,byrow=TRUE)
chA=chA[NN:1,]
chA=raster(chA,xmn=min(seal$cov.df$X$x),xmx=max(seal$cov.df$X$x),
    ymn=min(seal$cov.df$X$y),ymx=max(seal$cov.df$X$y))
crs(chA)="+proj=longlat +datum=WGS84"

pro=matrix(seal$cov.df$X$pro,NN,byrow=TRUE)
pro=pro[NN:1,]
npp=raster(pro,xmn=min(seal$cov.df$X$x),xmx=max(seal$cov.df$X$x),
    ymn=min(seal$cov.df$X$y),ymx=max(seal$cov.df$X$y))
crs(npp)="+proj=longlat +datum=WGS84"


int=sst
values(int) <- 1

d2r=int
rookery.cell=cellFromXY(int,xyt[1,1:2])
values(d2r)=NA
values(d2r)[rookery.cell]=0
d2r=distance(d2r)

grad.stack=stack(sst,chA,npp,d2r)
names(grad.stack) <- c("sst","cha","npp","d2r")

plot(sst)
points(xyt[,1:2],type="b")

plot(grad.stack)


##
## 3 Impute Quasi-Continuous Path Using Crawl
##

path=get.crawl.path(seal$sim.obj,int,
     mintime=min(sim.obj$datetime),maxtime=max(sim.obj$datetime))

str(path)
plot(sst)
points(path$xy,col=2,type="l")
points(xyt[,1:2],type="b",pch=2)


plot(sst)
for(i in 1:15){
    path=get.crawl.path(seal$sim.obj,int,
         mintime=min(sim.obj$datetime),maxtime=max(sim.obj$datetime))
    points(path$xy,col=i,type="l")
}
points(xyt[,1:2],type="b",pch=20,cex=2,lwd=2)

##
## 4. Turn continuous space path into a CTMC discrete space path
##

ctmc=path2ctmc(path$xy,path$t,int)

str(ctmc)

##
## 5. Turn CTMC discrete path into latent Poisson GLM data
##

loc.stack=stack(int,sst)
names(loc.stack) <- c("Intercept","sst.loc")

glm.data=ctmc2glm(ctmc,loc.stack,grad.stack)

str(glm.data)

## now repeat 3-5 for 10 imputations
for(i in 2:10){
    path=get.crawl.path(seal$sim.obj,int,
         mintime=min(sim.obj$datetime),maxtime=max(sim.obj$datetime))
    ctmc=path2ctmc(path$xy,path$t,int)
    glm.data=rbind(glm.data,ctmc2glm(ctmc,loc.stack,grad.stack))
}

str(glm.data)

## remove transitions that are nearly instantaneous

idx.0=which(glm.data$tau<10^-10)
idx.0
glm.data=glm.data[-idx.0,]

summary(glm.data)

##
## 6. Fit Poisson GLM and Poisson GAM with time-varying coefficients
##    (here we are fitting all "M" paths simultaneously,
##     giving each one a weight of "1/M")



fit=glm(z~cha+npp+sst+crw+d2r+sst.loc,
    weights=rep(1/10,nrow(glm.data)),family="poisson",offset=log(tau),data=glm.data)
summary(fit)

##
## 6. (Alternate) We can use any software which fits Poisson glm data.
##    The following uses "gam" in package "mgcv" to fit a time-varying
##    effect of "d2r" using penalized regression splines.  The result
##    is similar to that found in:
##
##    Hanks, E.; Hooten, M.; Johnson, D. & Sterling, J. Velocity-Based
##    Movement Modeling for Individual and Population Level Inference
##    PLoS ONE, Public Library of Science, 2011, 6, e22795
##

library(mgcv)

fit=gam(z~cha+npp+sst+crw++s(t,by=-d2r),
    weights=rep(1/10,nrow(glm.data)),family="poisson",offset=log(tau),data=glm.data)
summary(fit)
plot(fit)

ctmcmove documentation built on May 2, 2019, 5:25 p.m.