# Random Walk Covariance Models Code to facilitate simulation and inference of connectivity defined by random walks. package ## Details This package contains code to simulate (rGenWish) and evaluate the likelihood of (dGenWish) distance matrices from the Generalized Wishart distribution. It also contains helper functions to create and manage spatial covariance models created from landscape grids with resistance or conductance defined by landscape features. ## Author(s) Ephraim M. Hanks Maintainer: Ephraim M. Hanks ## References McCullagh 2009. Marginal likelihood for distance matrices. Statistica Sinica 19: 631-649. Hanks and Hooten 2013. Circuit theory and model-based inference for landscape connectivity. Journal of the American Statistical Association. 108(501), 22-33. Hanks 2017. Modeling spatial covariance using the limiting distribution of spatio-temporal random walks. Journal of the American Statistical Association. ## Examples ```r ## Not run: ## The following code conducts a simulation example by ## first simulating a heterogeneous landscape, then ## simulating pairwise distance data on the landscape ## and finally making inference on model parameters. library(rwc) library(MASS) ## source("GenWishFunctions_20170901.r") ## ## specify 2-d raster ## ras=raster(nrow=30,ncol=30) extent(ras) <- c(0,30,0,30) values(ras) <- 1 plot(ras,asp=1) ras int=ras cov.ras=ras ## simulate "resistance" raster TL.int=get.TL(int) Q.int=get.Q(TL.int,1) set.seed(1248) ## values(cov.ras) <- as.numeric(rnorm.Q(Q.int values(cov.ras) <- as.numeric(rnorm.Q(Q.int,zero.constraint=TRUE)) plot(cov.ras) stack=stack(int,cov.ras) plot(stack) TL=get.TL(stack) ## Create "barrier" raster which has no effect, to test model selection barrier=int values(barrier) <- 0 barrier[,10:11] <- 1 plot(barrier) TL.all=get.TL(stack(int,cov.ras,barrier)) ## ## sampling locations ## nsamps=150 set.seed(4567) samp.xy=cbind(runif(nsamps,0,30),runif(nsamps,0,30)) ## samp.xy=samp.xy[rep(1:nsamps,times=5),] samp.locs=cellFromXY(int,samp.xy) samp.cells=unique(samp.locs) nsamps=nrow(samp.xy) plot(cov.ras) points(samp.xy) K=matrix(0,nrow=nsamps,ncol=length(samp.cells)) for(i in 1:nsamps){ K[i,which(samp.cells==samp.locs[i])]=1 } image(K) ## ## beta values ## betas=c(-2,-1) tau=.01 Q=get.Q(TL,betas) Phi=get.Phi(Q,samp.cells) ## simulate from ibr model D.rand.ibr=rGenWish(df=20,Sigma=K%*%ginv(as.matrix(Phi))%*%t(K) + diag(nsamps)*tau) image(D.rand.ibr) ## crude plot of geographic distance vs genetic distance plot(as.numeric(as.matrix(dist(xyFromCell(ras,samp.locs)))),as.numeric(D.rand.ibr)) ################################### ## ## ## fitting using optim ## ## nll.gen.wish.icar <- function(theta,D,df,TL,obs.idx){ ## get K cells.idx=unique(obs.idx) n.cells=length(cells.idx) n.obs=length(obs.idx) K <- matrix(0, nrow = n.obs, ncol = n.cells) for (i in 1:n.obs){ K[i, which(cells.idx == obs.idx[i])] <- 1 } ## get precision matrix of whole graph tau=exp(theta[1]) beta=theta[-1] Q=get.Q(TL,beta) ## get precision matrix of observed nodes max.diag=max(diag(Q)) Q=Q/max.diag Phi=get.Phi(Q,cells.idx) ## get covariance matrix of observations Sigma.nodes=ginv(as.matrix(Phi)) Sigma.nodes=Sigma.nodes/max.diag Psi=K%*%Sigma.nodes%*%t(K)+tau*diag(nrow(K)) ## get nll nll=-dGenWish(D,Psi,df,log=TRUE) nll } fit=optim(c(log(tau),betas),nll.gen.wish.icar,D=D.rand.ibr,df=20,TL=TL, obs.idx=samp.locs,control=list(trace=10),hessian=TRUE) fit.all=optim(c(log(tau),betas,0),nll.gen.wish.icar,D=D.rand.ibr,df=20,TL=TL.all, obs.idx=samp.locs,control=list(trace=10),hessian=FALSE) fit.ibd=optim(c(log(tau),0),nll.gen.wish.icar,D=D.rand.ibr,df=20,TL=TL.int, obs.idx=samp.locs,control=list(trace=10),hessian=FALSE) ## model selection using AIC aic.ibr=2*fit$value + 2*length(fit$par) aic.all=2*fit.all$value + 2*length(fit.all$par) aic.ibd=2*fit.ibd$value + 2*length(fit.ibd$par) aic.ibr aic.all aic.ibd ## se's for best fit str(fit) ## get standard errors from optim H=fit$hessian S=solve(H) se=sqrt(diag(S)) se ## CI's for best fit CImat=matrix(NA,3,4) rownames(CImat) <- c("log(tau)","intercept","resistance") colnames(CImat) <- c("truth","estimate","lower95CI","upper95CI") CImat[,1]=c(log(tau),betas) CImat[,2]=fit$par CImat[,3]=fit$par-1.96*se CImat[,4]=fit$par+1.96*se CImat ## End(Not run) ```

rwc-package