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megsuscept.SCENARIO4.survred.R
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megsuscept.SCENARIO4.survred.R
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##########################################################################################################################################
## megafauna demographic susceptibility model
## AIM: construct plausible stochastic demographic models for main Sahul megafauna to determine relative demographic
## susceptibility to environmental change & novel predation (human) sources
##
## VOMBATIFORM HERBIVORES: ✓Diprotodon (†), ✓Palorchestes (†), ✓Zygomaturus (†), ✓Phascolonus (†), ✓Vombatus ursinus
## MACROPODIFORM HERBIVORES: ✓Protemnodon (†), ✓Osphranter rufus, ✓Sthenurus (†), ✓Simosthenurus (†), ✓Procoptodon (†), ✓Metasthenurus (†), ✓Notamacropus
## LARGE BIRDS: ✓Genyornis (†), ✓Dromaius novaehollandiae, ✓Alectura lathami
## CARNIVORES: ✓Sarcophilus, ✓Thylacinus (†), ✓Thylacoleo (†), ✓Dasyurus
## MONOTREMES: ✓Megalibgwilia (†), ✓Tachyglossus
##
## Corey Bradshaw
## Flinders University, August 2020
##########################################################################################################################################
###################################################################################
### *** run 'Sahul megafauna demographic susceptibility-base models.R' first *** ##
###################################################################################
#####################################################################
## SCENARIO 4: PROGRESSIVELY REDUCE SURVIVAL ACROSS ALL AGE GROUPS ##
#####################################################################
iter <- 10000
itdiv <- iter/10
Q.ext.thresh <- 100/2 # quasi-extinction threshold
surv.red.vec <- seq(0, 0.95, 0.025)
DP.Q.ext.pr <- PA.Q.ext.pr <- ZT.Q.ext.pr <- PH.Q.ext.pr <- VU.Q.ext.pr <- PG.Q.ext.pr <- SS.Q.ext.pr <- PT.Q.ext.pr <- SO.Q.ext.pr <- MN.Q.ext.pr <- OR.Q.ext.pr <- NR.Q.ext.pr <- GN.Q.ext.pr <- DN.Q.ext.pr <- AL.Q.ext.pr <- TC.Q.ext.pr <- TH.Q.ext.pr <- SH.Q.ext.pr <- DM.Q.ext.pr <- TA.Q.ext.pr <- MR.Q.ext.pr <- rep(NA,length(surv.red.vec))
for (k in 1:length(surv.red.vec)) {
## DIPROTODON (DP)
## set storage matrices & vectors
DP.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
DP.popmat <- DP.popmat.orig
DP.n.mat <- matrix(0, nrow=DP.age.max+1,ncol=(t+1))
DP.n.mat[,1] <- DP.init.vec
for (i in 1:t) {
# stochastic survival values
DP.s.alpha <- estBetaParams(DP.Sx, DP.s.sd.vec^2)$alpha
DP.s.beta <- estBetaParams(DP.Sx, DP.s.sd.vec^2)$beta
DP.s.stoch <- rbeta(length(DP.s.alpha), DP.s.alpha, DP.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/DP.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
DP.s.stoch <- DP.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
DP.fert.stch <- rnorm(length(DP.popmat[,1]), DP.pred.p.mm, DP.m.sd.vec)
DP.totN.i <- sum(DP.n.mat[,i], na.rm=T)
DP.pred.red <- DP.a.lp/(1+(DP.totN.i/DP.b.lp)^DP.c.lp)
diag(DP.popmat[2:(DP.age.max+1),]) <- (DP.s.stoch[-(DP.age.max+1)])*DP.pred.red
DP.popmat[DP.age.max+1,DP.age.max+1] <- (DP.s.stoch[DP.age.max+1])*DP.pred.red
DP.popmat[1,] <- ifelse(DP.fert.stch < 0, 0, DP.fert.stch)
DP.n.mat[,i+1] <- DP.popmat %*% DP.n.mat[,i]
} # end i loop
DP.n.sums.mat[e,] <- (as.vector(colSums(DP.n.mat)))
} # end e loop
# total N
DP.n.md <- apply(DP.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
DP.n.up <- apply(DP.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
DP.n.lo <- apply(DP.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
DP.Q.ext.mat <- ifelse(DP.n.sums.mat < Q.ext.thresh, 1, 0)
DP.Q.ext.sum <- apply(DP.Q.ext.mat[,ceiling(DP.gen.l):dim(DP.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
DP.Q.ext.pr[k] <- length(which(DP.Q.ext.sum > 0)) / iter
print("DIPROTODON")
## PALORCHESTES (PA)
## set storage matrices & vectors
PA.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
PA.popmat <- PA.popmat.orig
PA.n.mat <- matrix(0, nrow=PA.age.max+1,ncol=(t+1))
PA.n.mat[,1] <- PA.init.vec
for (i in 1:t) {
# stochastic survival values
PA.s.alpha <- estBetaParams(PA.Sx, PA.s.sd.vec^2)$alpha
PA.s.beta <- estBetaParams(PA.Sx, PA.s.sd.vec^2)$beta
PA.s.stoch <- rbeta(length(PA.s.alpha), PA.s.alpha, PA.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/PA.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
PA.s.stoch <- PA.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
PA.fert.stch <- rnorm(length(PA.popmat[,1]), PA.pred.p.mm, PA.m.sd.vec)
PA.totN.i <- sum(PA.n.mat[,i], na.rm=T)
PA.pred.red <- PA.a.lp/(1+(PA.totN.i/PA.b.lp)^PA.c.lp)
diag(PA.popmat[2:(PA.age.max+1),]) <- (PA.s.stoch[-(PA.age.max+1)])*PA.pred.red
PA.popmat[PA.age.max+1,PA.age.max+1] <- (PA.s.stoch[PA.age.max+1])*PA.pred.red
PA.popmat[1,] <- ifelse(PA.fert.stch < 0, 0, PA.fert.stch)
PA.n.mat[,i+1] <- PA.popmat %*% PA.n.mat[,i]
} # end i loop
PA.n.sums.mat[e,] <- (as.vector(colSums(PA.n.mat)))
} # end e loop
# total N
PA.n.md <- apply(PA.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
PA.n.up <- apply(PA.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
PA.n.lo <- apply(PA.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
PA.Q.ext.mat <- ifelse(PA.n.sums.mat < Q.ext.thresh, 1, 0)
PA.Q.ext.sum <- apply(PA.Q.ext.mat[,ceiling(PA.gen.l):dim(PA.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
PA.Q.ext.pr[k] <- length(which(PA.Q.ext.sum > 0)) / iter
print("PALORCHESTES")
## ZYGOMATURUS (ZT)
## set storage matrices & vectors
ZT.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
ZT.popmat <- ZT.popmat.orig
ZT.n.mat <- matrix(0, nrow=ZT.age.max+1,ncol=(t+1))
ZT.n.mat[,1] <- ZT.init.vec
for (i in 1:t) {
# stochastic survival values
ZT.s.alpha <- estBetaParams(ZT.Sx, ZT.s.sd.vec^2)$alpha
ZT.s.beta <- estBetaParams(ZT.Sx, ZT.s.sd.vec^2)$beta
ZT.s.stoch <- rbeta(length(ZT.s.alpha), ZT.s.alpha, ZT.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/ZT.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
ZT.s.stoch <- ZT.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
ZT.fert.stch <- rnorm(length(ZT.popmat[,1]), ZT.pred.p.mm, ZT.m.sd.vec)
ZT.totN.i <- sum(ZT.n.mat[,i], na.rm=T)
ZT.pred.red <- ZT.a.lp/(1+(ZT.totN.i/ZT.b.lp)^ZT.c.lp)
diag(ZT.popmat[2:(ZT.age.max+1),]) <- (ZT.s.stoch[-(ZT.age.max+1)])*ZT.pred.red
ZT.popmat[ZT.age.max+1,ZT.age.max+1] <- (ZT.s.stoch[ZT.age.max+1])*ZT.pred.red
ZT.popmat[1,] <- ifelse(ZT.fert.stch < 0, 0, ZT.fert.stch)
ZT.n.mat[,i+1] <- ZT.popmat %*% ZT.n.mat[,i]
} # end i loop
ZT.n.sums.mat[e,] <- (as.vector(colSums(ZT.n.mat)))
} # end e loop
# total N
ZT.n.md <- apply(ZT.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
ZT.n.up <- apply(ZT.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
ZT.n.lo <- apply(ZT.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
ZT.Q.ext.mat <- ifelse(ZT.n.sums.mat < Q.ext.thresh, 1, 0)
ZT.Q.ext.sum <- apply(ZT.Q.ext.mat[,ceiling(ZT.gen.l):dim(ZT.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
ZT.Q.ext.pr[k] <- length(which(ZT.Q.ext.sum > 0)) / iter
print("ZYGOMATURUS")
## PHASCOLONUS (PH)
## set storage matrices & vectors
PH.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
PH.popmat <- PH.popmat.orig
PH.n.mat <- matrix(0, nrow=PH.age.max+1,ncol=(t+1))
PH.n.mat[,1] <- PH.init.vec
for (i in 1:t) {
# stochastic survival values
PH.s.alpha <- estBetaParams(PH.Sx, PH.s.sd.vec^2)$alpha
PH.s.beta <- estBetaParams(PH.Sx, PH.s.sd.vec^2)$beta
PH.s.stoch <- rbeta(length(PH.s.alpha), PH.s.alpha, PH.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/PH.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
PH.s.stoch <- PH.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
PH.fert.stch <- rnorm(length(PH.popmat[,1]), PH.pred.p.mm, PH.m.sd.vec)
PH.totN.i <- sum(PH.n.mat[,i], na.rm=T)
PH.pred.red <- PH.a.lp/(1+(PH.totN.i/PH.b.lp)^PH.c.lp)
diag(PH.popmat[2:(PH.age.max+1),]) <- (PH.s.stoch[-(PH.age.max+1)])*PH.pred.red
PH.popmat[PH.age.max+1,PH.age.max+1] <- (PH.s.stoch[PH.age.max+1])*PH.pred.red
PH.popmat[1,] <- ifelse(PH.fert.stch < 0, 0, PH.fert.stch)
PH.n.mat[,i+1] <- PH.popmat %*% PH.n.mat[,i]
} # end i loop
PH.n.sums.mat[e,] <- (as.vector(colSums(PH.n.mat)))
} # end e loop
# total N
PH.n.md <- apply(PH.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
PH.n.up <- apply(PH.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
PH.n.lo <- apply(PH.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
PH.Q.ext.mat <- ifelse(PH.n.sums.mat < Q.ext.thresh, 1, 0)
PH.Q.ext.sum <- apply(PH.Q.ext.mat[,ceiling(PH.gen.l):dim(PH.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
PH.Q.ext.pr[k] <- length(which(PH.Q.ext.sum > 0)) / iter
print("PHASCOLONUS")
## VOMBATUS (VU)
## set storage matrices & vectors
VU.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
VU.popmat <- VU.popmat.orig
VU.n.mat <- matrix(0, nrow=VU.age.max+1,ncol=(t+1))
VU.n.mat[,1] <- VU.init.vec
for (i in 1:t) {
# stochastic survival values
VU.s.alpha <- estBetaParams(VU.Sx, VU.s.sd.vec^2)$alpha
VU.s.beta <- estBetaParams(VU.Sx, VU.s.sd.vec^2)$beta
VU.s.stoch <- rbeta(length(VU.s.alpha), VU.s.alpha, VU.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/VU.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
VU.s.stoch <- VU.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
VU.fert.stch <- rnorm(length(VU.popmat[,1]), VU.pred.p.mm, VU.m.sd.vec)
VU.totN.i <- sum(VU.n.mat[,i], na.rm=T)
VU.pred.red <- VU.a.lp/(1+(VU.totN.i/VU.b.lp)^VU.c.lp)
diag(VU.popmat[2:(VU.age.max+1),]) <- (VU.s.stoch[-(VU.age.max+1)])*VU.pred.red
VU.popmat[VU.age.max+1,VU.age.max+1] <- 0 # (VU.s.stoch[VU.age.max+1])*VU.pred.red
VU.popmat[1,] <- ifelse(VU.fert.stch < 0, 0, VU.fert.stch)
VU.n.mat[,i+1] <- VU.popmat %*% VU.n.mat[,i]
} # end i loop
VU.n.sums.mat[e,] <- (as.vector(colSums(VU.n.mat)))
} # end e loop
# total N
VU.n.md <- apply(VU.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
VU.n.up <- apply(VU.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
VU.n.lo <- apply(VU.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
VU.Q.ext.mat <- ifelse(VU.n.sums.mat < Q.ext.thresh, 1, 0)
VU.Q.ext.sum <- apply(VU.Q.ext.mat[,ceiling(VU.gen.l):dim(VU.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
VU.Q.ext.pr[k] <- length(which(VU.Q.ext.sum > 0)) / iter
print("VOMBATUS")
## PROCOPTODON (PG)
## set storage matrices & vectors
PG.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
PG.popmat <- PG.popmat.orig
PG.n.mat <- matrix(0, nrow=PG.age.max+1,ncol=(t+1))
PG.n.mat[,1] <- PG.init.vec
for (i in 1:t) {
# stochastic survival values
PG.s.alpha <- estBetaParams(PG.Sx, PG.s.sd.vec^2)$alpha
PG.s.beta <- estBetaParams(PG.Sx, PG.s.sd.vec^2)$beta
PG.s.stoch <- rbeta(length(PG.s.alpha), PG.s.alpha, PG.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/PG.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
PG.s.stoch <- PG.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
PG.fert.stch <- rnorm(length(PG.popmat[,1]), PG.pred.p.mm, PG.m.sd.vec)
PG.totN.i <- sum(PG.n.mat[,i], na.rm=T)
PG.pred.red <- PG.a.lp/(1+(PG.totN.i/PG.b.lp)^PG.c.lp)
diag(PG.popmat[2:(PG.age.max+1),]) <- (PG.s.stoch[-(PG.age.max+1)])*PG.pred.red
PG.popmat[PG.age.max+1,PG.age.max+1] <- (PG.s.stoch[PG.age.max+1])*PG.pred.red
PG.popmat[1,] <- ifelse(PG.fert.stch < 0, 0, PG.fert.stch)
PG.n.mat[,i+1] <- PG.popmat %*% PG.n.mat[,i]
} # end i loop
PG.n.sums.mat[e,] <- (as.vector(colSums(PG.n.mat)))
} # end e loop
# total N
PG.n.md <- apply(PG.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
PG.n.up <- apply(PG.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
PG.n.lo <- apply(PG.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
PG.Q.ext.mat <- ifelse(PG.n.sums.mat < Q.ext.thresh, 1, 0)
PG.Q.ext.sum <- apply(PG.Q.ext.mat[,ceiling(PG.gen.l):dim(PG.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
PG.Q.ext.pr[k] <- length(which(PG.Q.ext.sum > 0)) / iter
print("PROCOPTODON")
## STHENURUS (SS)
## set storage matrices & vectors
SS.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
SS.popmat <- SS.popmat.orig
SS.n.mat <- matrix(0, nrow=SS.age.max+1,ncol=(t+1))
SS.n.mat[,1] <- SS.init.vec
for (i in 1:t) {
# stochastic survival values
SS.s.alpha <- estBetaParams(SS.Sx, SS.s.sd.vec^2)$alpha
SS.s.beta <- estBetaParams(SS.Sx, SS.s.sd.vec^2)$beta
SS.s.stoch <- rbeta(length(SS.s.alpha), SS.s.alpha, SS.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/SS.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
SS.s.stoch <- SS.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
SS.fert.stch <- rnorm(length(SS.popmat[,1]), SS.pred.p.mm, SS.m.sd.vec)
SS.totN.i <- sum(SS.n.mat[,i], na.rm=T)
SS.pred.red <- SS.a.lp/(1+(SS.totN.i/SS.b.lp)^SS.c.lp)
diag(SS.popmat[2:(SS.age.max+1),]) <- (SS.s.stoch[-(SS.age.max+1)])*SS.pred.red
SS.popmat[SS.age.max+1,SS.age.max+1] <- (SS.s.stoch[SS.age.max+1])*SS.pred.red
SS.popmat[1,] <- ifelse(SS.fert.stch < 0, 0, SS.fert.stch)
SS.n.mat[,i+1] <- SS.popmat %*% SS.n.mat[,i]
} # end i loop
SS.n.sums.mat[e,] <- (as.vector(colSums(SS.n.mat)))
} # end e loop
# total N
SS.n.md <- apply(SS.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
SS.n.up <- apply(SS.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
SS.n.lo <- apply(SS.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
SS.Q.ext.mat <- ifelse(SS.n.sums.mat < Q.ext.thresh, 1, 0)
SS.Q.ext.sum <- apply(SS.Q.ext.mat[,ceiling(SS.gen.l):dim(SS.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
SS.Q.ext.pr[k] <- length(which(SS.Q.ext.sum > 0)) / iter
print("STHENURUS")
## PROTEMNODON (PT)
## set storage matrices & vectors
PT.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
PT.popmat <- PT.popmat.orig
PT.n.mat <- matrix(0, nrow=PT.age.max+1,ncol=(t+1))
PT.n.mat[,1] <- PT.init.vec
for (i in 1:t) {
# stochastic survival values
PT.s.alpha <- estBetaParams(PT.Sx, PT.s.sd.vec^2)$alpha
PT.s.beta <- estBetaParams(PT.Sx, PT.s.sd.vec^2)$beta
PT.s.stoch <- rbeta(length(PT.s.alpha), PT.s.alpha, PT.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/PT.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
PT.s.stoch <- PT.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
PT.fert.stch <- rnorm(length(PT.popmat[,1]), PT.pred.p.mm, PT.m.sd.vec)
PT.totN.i <- sum(PT.n.mat[,i], na.rm=T)
PT.pred.red <- PT.a.lp/(1+(PT.totN.i/PT.b.lp)^PT.c.lp)
diag(PT.popmat[2:(PT.age.max+1),]) <- (PT.s.stoch[-(PT.age.max+1)])*PT.pred.red
PT.popmat[PT.age.max+1,PT.age.max+1] <- (PT.s.stoch[PT.age.max+1])*PT.pred.red
PT.popmat[1,] <- ifelse(PT.fert.stch < 0, 0, PT.fert.stch)
PT.n.mat[,i+1] <- PT.popmat %*% PT.n.mat[,i]
} # end i loop
PT.n.sums.mat[e,] <- (as.vector(colSums(PT.n.mat)))
} # end e loop
# total N
PT.n.md <- apply(PT.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
PT.n.up <- apply(PT.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
PT.n.lo <- apply(PT.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
PT.Q.ext.mat <- ifelse(PT.n.sums.mat < Q.ext.thresh, 1, 0)
PT.Q.ext.sum <- apply(PT.Q.ext.mat[,ceiling(PT.gen.l):dim(PT.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
PT.Q.ext.pr[k] <- length(which(PT.Q.ext.sum > 0)) / iter
print("PROTEMNODON")
## SIMOSTHENURUS (SO)
## set storage matrices & vectors
SO.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
SO.popmat <- SO.popmat.orig
SO.n.mat <- matrix(0, nrow=SO.age.max+1,ncol=(t+1))
SO.n.mat[,1] <- SO.init.vec
for (i in 1:t) {
# stochastic survival values
SO.s.alpha <- estBetaParams(SO.Sx, SO.s.sd.vec^2)$alpha
SO.s.beta <- estBetaParams(SO.Sx, SO.s.sd.vec^2)$beta
SO.s.stoch <- rbeta(length(SO.s.alpha), SO.s.alpha, SO.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/SO.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
SO.s.stoch <- SO.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
SO.fert.stch <- rnorm(length(SO.popmat[,1]), SO.pred.p.mm, SO.m.sd.vec)
SO.totN.i <- sum(SO.n.mat[,i], na.rm=T)
SO.pred.red <- SO.a.lp/(1+(SO.totN.i/SO.b.lp)^SO.c.lp)
diag(SO.popmat[2:(SO.age.max+1),]) <- (SO.s.stoch[-(SO.age.max+1)])*SO.pred.red
SO.popmat[SO.age.max+1,SO.age.max+1] <- (SO.s.stoch[SO.age.max+1])*SO.pred.red
SO.popmat[1,] <- ifelse(SO.fert.stch < 0, 0, SO.fert.stch)
SO.n.mat[,i+1] <- SO.popmat %*% SO.n.mat[,i]
} # end i loop
SO.n.sums.mat[e,] <- (as.vector(colSums(SO.n.mat)))
} # end e loop
# total N
SO.n.md <- apply(SO.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
SO.n.up <- apply(SO.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
SO.n.lo <- apply(SO.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
SO.Q.ext.mat <- ifelse(SO.n.sums.mat < Q.ext.thresh, 1, 0)
SO.Q.ext.sum <- apply(SO.Q.ext.mat[,ceiling(SO.gen.l):dim(SO.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
SO.Q.ext.pr[k] <- length(which(SO.Q.ext.sum > 0)) / iter
print("SIMOSTHENURUS")
## METASTHENURUS (MN)
## set storage matrices & vectors
MN.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
MN.popmat <- MN.popmat.orig
MN.n.mat <- matrix(0, nrow=MN.age.max+1,ncol=(t+1))
MN.n.mat[,1] <- MN.init.vec
for (i in 1:t) {
# stochastic survival values
MN.s.alpha <- estBetaParams(MN.Sx, MN.s.sd.vec^2)$alpha
MN.s.beta <- estBetaParams(MN.Sx, MN.s.sd.vec^2)$beta
MN.s.stoch <- rbeta(length(MN.s.alpha), MN.s.alpha, MN.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/MN.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
MN.s.stoch <- MN.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
MN.fert.stch <- rnorm(length(MN.popmat[,1]), MN.pred.p.mm, MN.m.sd.vec)
MN.totN.i <- sum(MN.n.mat[,i], na.rm=T)
MN.pred.red <- MN.a.lp/(1+(MN.totN.i/MN.b.lp)^MN.c.lp)
diag(MN.popmat[2:(MN.age.max+1),]) <- (MN.s.stoch[-(MN.age.max+1)])*MN.pred.red
MN.popmat[MN.age.max+1,MN.age.max+1] <- (MN.s.stoch[MN.age.max+1])*MN.pred.red
MN.popmat[1,] <- ifelse(MN.fert.stch < 0, 0, MN.fert.stch)
MN.n.mat[,i+1] <- MN.popmat %*% MN.n.mat[,i]
} # end i loop
MN.n.sums.mat[e,] <- (as.vector(colSums(MN.n.mat)))
} # end e loop
# total N
MN.n.md <- apply(MN.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
MN.n.up <- apply(MN.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
MN.n.lo <- apply(MN.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
MN.Q.ext.mat <- ifelse(MN.n.sums.mat < Q.ext.thresh, 1, 0)
MN.Q.ext.sum <- apply(MN.Q.ext.mat[,ceiling(MN.gen.l):dim(MN.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
MN.Q.ext.pr[k] <- length(which(MN.Q.ext.sum > 0)) / iter
print("METASTHENURUS")
## OSPHRANTER (OR)
## set storage matrices & vectors
OR.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
OR.popmat <- OR.popmat.orig
OR.n.mat <- matrix(0, nrow=OR.age.max+1,ncol=(t+1))
OR.n.mat[,1] <- OR.init.vec
for (i in 1:t) {
# stochastic survival values
OR.s.alpha <- estBetaParams(OR.Sx, OR.s.sd.vec^2)$alpha
OR.s.beta <- estBetaParams(OR.Sx, OR.s.sd.vec^2)$beta
OR.s.stoch <- rbeta(length(OR.s.alpha), OR.s.alpha, OR.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/OR.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
OR.s.stoch <- OR.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
OR.fert.stch <- rnorm(length(OR.popmat[,1]), OR.pred.p.mm, OR.m.sd.vec)
OR.totN.i <- sum(OR.n.mat[,i], na.rm=T)
OR.pred.red <- OR.a.lp/(1+(OR.totN.i/OR.b.lp)^OR.c.lp)
diag(OR.popmat[2:(OR.age.max+1),]) <- (OR.s.stoch[-(OR.age.max+1)])*OR.pred.red
OR.popmat[OR.age.max+1,OR.age.max+1] <- (OR.s.stoch[OR.age.max+1])*OR.pred.red
OR.popmat[1,] <- ifelse(OR.fert.stch < 0, 0, OR.fert.stch)
OR.n.mat[,i+1] <- OR.popmat %*% OR.n.mat[,i]
} # end i loop
OR.n.sums.mat[e,] <- (as.vector(colSums(OR.n.mat)))
} # end e loop
# total N
OR.n.md <- apply(OR.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
OR.n.up <- apply(OR.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
OR.n.lo <- apply(OR.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
OR.Q.ext.mat <- ifelse(OR.n.sums.mat < Q.ext.thresh, 1, 0)
OR.Q.ext.sum <- apply(OR.Q.ext.mat[,ceiling(OR.gen.l):dim(OR.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
OR.Q.ext.pr[k] <- length(which(OR.Q.ext.sum > 0)) / iter
print("OSPHRANTER")
## NOTAMACROPUS rufogriseus (NR)
## set storage matrices & vectors
NR.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
NR.popmat <- NR.popmat.orig
NR.n.mat <- matrix(0, nrow=NR.age.max+1,ncol=(t+1))
NR.n.mat[,1] <- NR.init.vec
for (i in 1:t) {
# stochastic survival values
NR.s.alpha <- estBetaParams(NR.Sx, NR.s.sd.vec^2)$alpha
NR.s.beta <- estBetaParams(NR.Sx, NR.s.sd.vec^2)$beta
NR.s.stoch <- rbeta(length(NR.s.alpha), NR.s.alpha, NR.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/NR.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
NR.s.stoch <- NR.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
NR.fert.stch <- rnorm(length(NR.popmat[,1]), NR.pred.p.mm, NR.m.sd.vec)
NR.totN.i <- sum(NR.n.mat[,i], na.rm=T)
NR.pred.red <- NR.a.lp/(1+(NR.totN.i/NR.b.lp)^NR.c.lp)
diag(NR.popmat[2:(NR.age.max+1),]) <- (NR.s.stoch[-(NR.age.max+1)])*NR.pred.red
NR.popmat[NR.age.max+1,NR.age.max+1] <- (NR.s.stoch[NR.age.max+1])*NR.pred.red
NR.popmat[1,] <- ifelse(NR.fert.stch < 0, 0, NR.fert.stch)
NR.n.mat[,i+1] <- NR.popmat %*% NR.n.mat[,i]
} # end i loop
NR.n.sums.mat[e,] <- (as.vector(colSums(NR.n.mat)))
} # end e loop
# total N
NR.n.md <- apply(NR.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
NR.n.up <- apply(NR.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
NR.n.lo <- apply(NR.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
NR.Q.ext.mat <- ifelse(NR.n.sums.mat < Q.ext.thresh, 1, 0)
NR.Q.ext.sum <- apply(NR.Q.ext.mat[,ceiling(NR.gen.l):dim(NR.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
NR.Q.ext.pr[k] <- length(which(NR.Q.ext.sum > 0)) / iter
print("NOTAMACROPUS")
## GENYORNIS (GN)
## set storage matrices & vectors
GN.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
GN.popmat <- GN.popmat.orig
GN.n.mat <- matrix(0, nrow=GN.age.max+1,ncol=(t+1))
GN.n.mat[,1] <- GN.init.vec
for (i in 1:t) {
# stochastic survival values
GN.s.alpha <- estBetaParams(GN.Sx, GN.s.sd.vec^2)$alpha
GN.s.beta <- estBetaParams(GN.Sx, GN.s.sd.vec^2)$beta
GN.s.stoch <- rbeta(length(GN.s.alpha), GN.s.alpha, GN.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/GN.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
GN.s.stoch <- GN.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
GN.fert.stch <- rnorm(length(GN.popmat[,1]), GN.pred.p.mm, GN.m.sd.vec)
GN.totN.i <- sum(GN.n.mat[,i], na.rm=T)
GN.pred.red <- GN.a.lp/(1+(GN.totN.i/GN.b.lp)^GN.c.lp)
diag(GN.popmat[2:(GN.age.max+1),]) <- (GN.s.stoch[-(GN.age.max+1)])*GN.pred.red
GN.popmat[GN.age.max+1,GN.age.max+1] <- (GN.s.stoch[GN.age.max+1])*GN.pred.red
GN.popmat[1,] <- ifelse(GN.fert.stch < 0, 0, GN.fert.stch)
GN.n.mat[,i+1] <- GN.popmat %*% GN.n.mat[,i]
} # end i loop
GN.n.sums.mat[e,] <- (as.vector(colSums(GN.n.mat)))
} # end e loop
# total N
GN.n.md <- apply(GN.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
GN.n.up <- apply(GN.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
GN.n.lo <- apply(GN.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
GN.Q.ext.mat <- ifelse(GN.n.sums.mat < Q.ext.thresh, 1, 0)
GN.Q.ext.sum <- apply(GN.Q.ext.mat[,ceiling(GN.gen.l):dim(GN.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
GN.Q.ext.pr[k] <- length(which(GN.Q.ext.sum > 0)) / iter
print("GENYORNIS")
## DROMAIUS (GN)
## set storage matrices & vectors
DN.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
DN.popmat <- DN.popmat.orig
DN.n.mat <- matrix(0, nrow=DN.age.max+1,ncol=(t+1))
DN.n.mat[,1] <- DN.init.vec
for (i in 1:t) {
# stochastic survival values
DN.s.alpha <- estBetaParams(DN.Sx, DN.s.sd.vec^2)$alpha
DN.s.beta <- estBetaParams(DN.Sx, DN.s.sd.vec^2)$beta
DN.s.stoch <- rbeta(length(DN.s.alpha), DN.s.alpha, DN.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/DN.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
DN.s.stoch <- DN.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
DN.fert.stch <- rnorm(length(DN.popmat[,1]), DN.pred.p.mm, DN.m.sd.vec)
DN.totN.i <- sum(DN.n.mat[,i], na.rm=T)
DN.pred.red <- DN.a.lp/(1+(DN.totN.i/DN.b.lp)^DN.c.lp)
diag(DN.popmat[2:(DN.age.max+1),]) <- (DN.s.stoch[-(DN.age.max+1)])*DN.pred.red
DN.popmat[DN.age.max+1,DN.age.max+1] <- (DN.s.stoch[DN.age.max+1])*DN.pred.red
DN.popmat[1,] <- ifelse(DN.fert.stch < 0, 0, DN.fert.stch)
DN.n.mat[,i+1] <- DN.popmat %*% DN.n.mat[,i]
} # end i loop
DN.n.sums.mat[e,] <- (as.vector(colSums(DN.n.mat)))
} # end e loop
# total N
DN.n.md <- apply(DN.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
DN.n.up <- apply(DN.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
DN.n.lo <- apply(DN.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
DN.Q.ext.mat <- ifelse(DN.n.sums.mat < Q.ext.thresh, 1, 0)
DN.Q.ext.sum <- apply(DN.Q.ext.mat[,ceiling(DN.gen.l):dim(DN.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
DN.Q.ext.pr[k] <- length(which(DN.Q.ext.sum > 0)) / iter
print("DROMAIUS")
## ALECTURA (AL)
## set storage matrices & vectors
AL.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
AL.popmat <- AL.popmat.orig
AL.n.mat <- matrix(0, nrow=AL.age.max+1,ncol=(t+1))
AL.n.mat[,1] <- AL.init.vec
for (i in 1:t) {
# stochastic survival values
AL.s.alpha <- estBetaParams(AL.Sx, AL.s.sd.vec^2)$alpha
AL.s.beta <- estBetaParams(AL.Sx, AL.s.sd.vec^2)$beta
AL.s.stoch <- rbeta(length(AL.s.alpha), AL.s.alpha, AL.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/AL.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
AL.s.stoch <- AL.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
AL.fert.stch <- rnorm(length(AL.popmat[,1]), AL.pred.p.mm, AL.m.sd.vec)
AL.totN.i <- sum(AL.n.mat[,i], na.rm=T)
AL.pred.red <- AL.a.lp/(1+(AL.totN.i/AL.b.lp)^AL.c.lp)
diag(AL.popmat[2:(AL.age.max+1),]) <- (AL.s.stoch[-(AL.age.max+1)])*AL.pred.red
AL.popmat[AL.age.max+1,AL.age.max+1] <- (AL.s.stoch[AL.age.max+1])*AL.pred.red
AL.popmat[1,] <- ifelse(AL.fert.stch < 0, 0, AL.fert.stch)
AL.n.mat[,i+1] <- AL.popmat %*% AL.n.mat[,i]
} # end i loop
AL.n.sums.mat[e,] <- (as.vector(colSums(AL.n.mat)))
} # end e loop
# total N
AL.n.md <- apply(AL.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
AL.n.up <- apply(AL.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
AL.n.lo <- apply(AL.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
AL.Q.ext.mat <- ifelse(AL.n.sums.mat < Q.ext.thresh, 1, 0)
AL.Q.ext.sum <- apply(AL.Q.ext.mat[,ceiling(AL.gen.l):dim(AL.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
AL.Q.ext.pr[k] <- length(which(AL.Q.ext.sum > 0)) / iter
print("ALECTURA")
## THYLACOLEO (TC)
## set storage matrices & vectors
TC.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
TC.popmat <- TC.popmat.orig
TC.n.mat <- matrix(0, nrow=TC.age.max+1,ncol=(t+1))
TC.n.mat[,1] <- TC.init.vec
for (i in 1:t) {
# stochastic survival values
TC.s.alpha <- estBetaParams(TC.Sx, TC.s.sd.vec^2)$alpha
TC.s.beta <- estBetaParams(TC.Sx, TC.s.sd.vec^2)$beta
TC.s.stoch <- rbeta(length(TC.s.alpha), TC.s.alpha, TC.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/TC.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
TC.s.stoch <- TC.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
TC.fert.stch <- rnorm(length(TC.popmat[,1]), TC.pred.p.mm, TC.m.sd.vec)
TC.totN.i <- sum(TC.n.mat[,i], na.rm=T)
TC.pred.red <- TC.a.lp/(1+(TC.totN.i/TC.b.lp)^TC.c.lp)
diag(TC.popmat[2:(TC.age.max+1),]) <- (TC.s.stoch[-(TC.age.max+1)])*TC.pred.red
TC.popmat[TC.age.max+1,TC.age.max+1] <- (TC.s.stoch[TC.age.max+1])*TC.pred.red
TC.popmat[1,] <- ifelse(TC.fert.stch < 0, 0, TC.fert.stch)
TC.n.mat[,i+1] <- TC.popmat %*% TC.n.mat[,i]
} # end i loop
TC.n.sums.mat[e,] <- (as.vector(colSums(TC.n.mat)))
} # end e loop
# total N
TC.n.md <- apply(TC.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
TC.n.up <- apply(TC.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
TC.n.lo <- apply(TC.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
TC.Q.ext.mat <- ifelse(TC.n.sums.mat < Q.ext.thresh, 1, 0)
TC.Q.ext.sum <- apply(TC.Q.ext.mat[,ceiling(TC.gen.l):dim(TC.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
TC.Q.ext.pr[k] <- length(which(TC.Q.ext.sum > 0)) / iter
print("THYLACOLEO")
## THYLACINUS (TH)
## set storage matrices & vectors
TH.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
TH.popmat <- TH.popmat.orig
TH.n.mat <- matrix(0, nrow=TH.age.max+1,ncol=(t+1))
TH.n.mat[,1] <- TH.init.vec
for (i in 1:t) {
# stochastic survival values
TH.s.alpha <- estBetaParams(TH.Sx, TH.s.sd.vec^2)$alpha
TH.s.beta <- estBetaParams(TH.Sx, TH.s.sd.vec^2)$beta
TH.s.stoch <- rbeta(length(TH.s.alpha), TH.s.alpha, TH.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/TH.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
TH.s.stoch <- TH.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
TH.fert.stch <- rnorm(length(TH.popmat[,1]), TH.pred.p.mm, TH.m.sd.vec)
TH.totN.i <- sum(TH.n.mat[,i], na.rm=T)
TH.pred.red <- TH.a.lp/(1+(TH.totN.i/TH.b.lp)^TH.c.lp)
diag(TH.popmat[2:(TH.age.max+1),]) <- (TH.s.stoch[-(TH.age.max+1)])*TH.pred.red
TH.popmat[TH.age.max+1,TH.age.max+1] <- 0 # (TH.s.stoch[TH.age.max+1])*TH.pred.red
TH.popmat[1,] <- ifelse(TH.fert.stch < 0, 0, TH.fert.stch)
TH.n.mat[,i+1] <- TH.popmat %*% TH.n.mat[,i]
} # end i loop
TH.n.sums.mat[e,] <- (as.vector(colSums(TH.n.mat)))
} # end e loop
# total N
TH.n.md <- apply(TH.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
TH.n.up <- apply(TH.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
TH.n.lo <- apply(TH.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
TH.Q.ext.mat <- ifelse(TH.n.sums.mat < Q.ext.thresh, 1, 0)
TH.Q.ext.sum <- apply(TH.Q.ext.mat[,ceiling(TH.gen.l):dim(TH.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
TH.Q.ext.pr[k] <- length(which(TH.Q.ext.sum > 0)) / iter
print("THYLACINUS")
## SARCOPHILUS (SH)
## set storage matrices & vectors
SH.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
SH.popmat <- SH.popmat.orig
SH.n.mat <- matrix(0, nrow=SH.age.max+1,ncol=(t+1))
SH.n.mat[,1] <- SH.init.vec
for (i in 1:t) {
# stochastic survival values
SH.s.alpha <- estBetaParams(SH.Sx, SH.s.sd.vec^2)$alpha
SH.s.beta <- estBetaParams(SH.Sx, SH.s.sd.vec^2)$beta
SH.s.stoch <- rbeta(length(SH.s.alpha), SH.s.alpha, SH.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/SH.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
SH.s.stoch <- SH.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
SH.fert.stch <- rnorm(length(SH.popmat[,1]), SH.m.vec, SH.m.sd.vec)
SH.totN.i <- sum(SH.n.mat[,i], na.rm=T)
SH.pred.red <- SH.a.lp/(1+(SH.totN.i/SH.b.lp)^SH.c.lp)
diag(SH.popmat[2:(SH.age.max+1),]) <- (SH.s.stoch[-1])*SH.pred.red
SH.popmat[SH.age.max+1,SH.age.max+1] <- 0 # (SH.s.stoch[SH.age.max+1])*SH.pred.red
SH.popmat[1,] <- ifelse(SH.fert.stch < 0, 0, SH.fert.stch)
SH.n.mat[,i+1] <- SH.popmat %*% SH.n.mat[,i]
} # end i loop
SH.n.sums.mat[e,] <- (as.vector(colSums(SH.n.mat)))
} # end e loop
# total N
SH.n.md <- apply(SH.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
SH.n.up <- apply(SH.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
SH.n.lo <- apply(SH.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
SH.Q.ext.mat <- ifelse(SH.n.sums.mat < Q.ext.thresh, 1, 0)
SH.Q.ext.sum <- apply(SH.Q.ext.mat[,ceiling(SH.gen.l):dim(SH.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
SH.Q.ext.pr[k] <- length(which(SH.Q.ext.sum > 0)) / iter
print("SARCOPHILUS")
## DASYURUS (DM)
## set storage matrices & vectors
DM.n.sums.mat <- matrix(data=NA, nrow=iter, ncol=(t+1))
for (e in 1:iter) {
DM.popmat <- DM.popmat.orig
DM.n.mat <- matrix(0, nrow=DM.age.max+1,ncol=(t+1))
DM.n.mat[,1] <- DM.init.vec
for (i in 1:t) {
# stochastic survival values
DM.s.alpha <- estBetaParams(DM.Sx, DM.s.sd.vec^2)$alpha
DM.s.beta <- estBetaParams(DM.Sx, DM.s.sd.vec^2)$beta
DM.s.stoch <- rbeta(length(DM.s.alpha), DM.s.alpha, DM.s.beta) * (1 - surv.red.vec[k])
if (rbinom(1, 1, 0.14/DM.gen.l) == 1) { # catastrophe
cat.alpha <- estBetaParams(0.5, 0.05^2)$alpha
cat.beta <- estBetaParams(0.5, 0.05^2)$beta
DM.s.stoch <- DM.s.stoch * (rbeta(1, cat.alpha, cat.beta)) }
# stochastic fertilty sampler (gaussian)
DM.fert.stch <- rnorm(length(DM.popmat[,1]), DM.m.vec, DM.m.sd.vec)
DM.totN.i <- sum(DM.n.mat[,i], na.rm=T)
DM.pred.red <- DM.a.lp/(1+(DM.totN.i/DM.b.lp)^DM.c.lp)
diag(DM.popmat[2:(DM.age.max+1),]) <- (DM.s.stoch[-1])*DM.pred.red
DM.popmat[DM.age.max+1,DM.age.max+1] <- 0 # (DM.s.stoch[DM.age.max+1])*DM.pred.red
DM.popmat[1,] <- ifelse(DM.fert.stch < 0, 0, DM.fert.stch)
DM.n.mat[,i+1] <- DM.popmat %*% DM.n.mat[,i]
} # end i loop
DM.n.sums.mat[e,] <- (as.vector(colSums(DM.n.mat)))
} # end e loop
# total N
DM.n.md <- apply(DM.n.sums.mat, MARGIN=2, median, na.rm=T) # mean over all iterations
DM.n.up <- apply(DM.n.sums.mat, MARGIN=2, quantile, probs=0.975, na.rm=T) # upper over all iterations
DM.n.lo <- apply(DM.n.sums.mat, MARGIN=2, quantile, probs=0.025, na.rm=T) # lower over all iterations
# quasi-extinction probability
DM.Q.ext.mat <- ifelse(DM.n.sums.mat < Q.ext.thresh, 1, 0)
DM.Q.ext.sum <- apply(DM.Q.ext.mat[,ceiling(DM.gen.l):dim(DM.Q.ext.mat)[2]], MARGIN=1, sum, na.rm=T)
DM.Q.ext.pr[k] <- length(which(DM.Q.ext.sum > 0)) / iter
print("DASYURUS")