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banteng_harvest.R
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banteng_harvest.R
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## program for analysis of banteng population projection
## ----------------------------------------
## base model - rates from Choquenot (1993)
## giving stability
## ----------------------------------------
## Removes everything in memory
rm(list = ls())
## Add packages 'base'
library(base)
## define max age
age.max<-17
## define survival - fitted function (Choquenot 1993)
## s0<-0.7402 ## fitted from Choquenot (1993)
## s.vec <- c(0.55,0.9278,0.9346,0.9370,0.9382,0.9389,0.9394,0.9397,0.9400,0.9402,0.9403,0.9405,0.9406,0.9407,0.9408,0.9408,0.9409,0.9409)
## Mortality vector from Choquenot (1993)
q.vec <- c(0.26,0.08,0.075,0.07,0.075,0.06,0.06,0.06,0.06,0.05,0.05,0.05,0.07)
## Fit survival values
library(stats)
library(base)
## Create data frame
age.vec.q <- seq(-1,length(q.vec)-2)
age.vec.q[1] <- 0
age.vec.q[2:(length(age.vec.q))] <- age.vec.q[2:(length(age.vec.q))] + 0.5
q.fit.data <- data.frame(age.vec.q,q.vec)
## model formula (exponential rise to maximum): yhat = a*exp(b/(x+c))
fit.q.vec <- nls(q.fit.data$q.vec ~ a.coeff * exp(b.coeff/(q.fit.data$age.vec.q + c.coeff)),
data = q.fit.data,
start = list(a.coeff = 0.1, b.coeff = 1, c.coeff = 1),
trace = TRUE)
sum.fit.q.vec <- summary(fit.q.vec)
## Coefficients from fit
coeff.fit.q.vec <- as.numeric(sum.fit.q.vec$parameters)
## age vector
age.vec<-rep(0,age.max+1)
for (j in 1:(age.max)) {
age.vec[j+1] <- j
}
## Predict new q vector with integer age inputs
qf.new.vec <- coeff.fit.q.vec[1] * exp(coeff.fit.q.vec[2]/(coeff.fit.q.vec[3]+age.vec))
row <- 1
col <- 1
par(mfrow=c(row,col))
plot(age.vec.q,q.vec,xlab="age (years)",ylab="qx")
title(main="Fitted Survival")
lines(age.vec,qf.new.vec)
par(mfrow=c(1,2))
s.vec <- 1 - qf.new.vec
## change s0 in s.vec to give population stability
##s.vec[1] <- 0.62
## fitted fecundity parameters
## m.vec <- c(0.0000,0.0001,0.0133,0.0947,0.2303,0.3440,0.3964,0.3921,0.3525,0.2979,0.2414,0.1903,0.1471,0.1122,0.0849,0.0638,0.0478,0.0358)
m.vec.obs <- c(0,0,0,0,0.22,0.351,0.5,0.45,0.2,0.325,0.125,0.225) ## Choquenot (1993)
## Create data frame
age.vec.m <- seq(0,11)
m.fit.data <- data.frame(age.vec.m,m.vec.obs)
## model formula (log-normal): yhat=a*exp(-0.5*(ln(x/x0)/b)^2)
fit.m.vec <- nls(m.fit.data$m.vec.obs ~ a.coeff.m * exp(-0.5*(log(m.fit.data$age.vec.m/x0.coeff.m)/b.coeff.m)^2),
data = q.fit.data,
start = list(a.coeff.m = 0.4, x0.coeff.m = 6, b.coeff.m = 0.4),
trace = TRUE)
sum.fit.m.vec <- summary(fit.m.vec)
## Coefficients from fit
coeff.fit.m.vec <- as.numeric(sum.fit.m.vec$parameters)
## Predict new q vector with integer age inputs
mf.new.vec <- coeff.fit.m.vec[1] * exp(-0.5*(log(age.vec/coeff.fit.m.vec[2])/coeff.fit.m.vec[3])^2)
## re-scale m.vec.obs for plotting
m.vec.obs.rs <- rep(0,age.max+1)
m.vec.obs.rs[1:12] <- m.vec.obs
row <- 1
col <- 1
par(mfrow=c(row,col))
plot(age.vec,m.vec.obs.rs,xlab="age (years)",ylab="mx",xlim=range(c(0,age.max)),ylim=range(c(0,1)))
title(main="Fitted Fertility")
lines(age.vec,mf.new.vec)
par(mfrow=c(1,2))
m.vec <- mf.new.vec
primi<-4 ## age at first reproduction (females)
## initial population sizes
## Nmin<-4000 ## J. Christopherson (2004)
## Nmax<-5000 ## J. Christopherson (2004)
Nmin<-7000 ## K. Saalfeld (2004)
Nmax<-8000 ## K. Saalfeld (2004)
Navg <- mean(c(Nmin, Nmax))
## Use 2 scenarios - pop.init at 4000 and 8000
N1 <- 5000
N2 <- 9000
## Density estimates
Area.Cob <- 220000 ## Area of Cobourg Peninsula in hectares
D.avg1 <- N1/(Area.Cob*0.01)
D.avg2 <- N2/(Area.Cob*0.01)
## sex ratios
sr <- 0.5 ## overall sex ratio
x <- 0.5 ## foetal sex ratio (Choquenot 1993)
##total females in population
f1<-N1*sr
f2<-N2*sr
##total males in population
mal1<-N1*(1-sr)
mal2<-N2*(1-sr)
##Initial population size vector
N<-N1
## Matrix size
k <- 34
## Create matrix shell
a <- matrix(data<-0,nrow<-k,ncol<-k)
## Add survival vectors to matrix
diag(a[2:age.max,1:(age.max-1)]) <- s.vec[2:age.max] ## adds s.vec to female quadrant
diag(a[(age.max+2):k,(age.max+1):(k-1)]) <- s.vec[2:age.max] ## adds s.vec to male quadrant
a[1,1:(age.max)] <- s.vec[1] * m.vec[1:(age.max)] ## adds female fecundity
a[(age.max+1),1:(age.max)] <- s.vec[1] * m.vec[1:(age.max)] ## adds male fecundity
## Maximum lambda function
max.lambda <- function(x) Re((eigen(x)$values)[1]) ## where 'x' is a Leslie matrix
## Maximum r function
max.r <- function(x) log(Re((eigen(x)$values)[1])) ## where 'x' is a Leslie matrix
## Stable stage distribution
stable.stage.dist <- function(x) ((x %*% (Re((eigen(x)$vectors)[,1])))/(sum((x %*% (Re((eigen(x)$vectors)[,1]))))))[,1]
## Generation length function
R.val <- function(X,age.max) ## reproductive value (R0) where X = Leslie matrix; age.max = maximum age of females
{
## define the transition matrix
T <- X[1:age.max,1:age.max]
T[1,1:(age.max)] <- 0
## define the fertility matrix
F <- X[1:age.max,1:age.max]
diag(F[2:age.max,1:(age.max-1)]) <- 0
## define the identity matrix
I <- matrix(data<-0,nrow<-age.max,ncol<-age.max)
diag(I) <- 1
## define the fundamental matrix
library(MASS)
N.fund <- ginv(I-T)
## define the reproductive matrix
R <- F %*% N.fund
## define R0 (number of female offspring produced per female during lifetime)
R0 <- Re((eigen(R)$values)[1])
## output
print("number of female offspring produced per female during its lifetime")
print("_________________________________________________________________")
print(R0)
}
## Mean generation time function
G.val <- function (X,age.max) ## where X is a Leslie Matrix
{
G <- (log(R.val(X,age.max)))/(log(Re((eigen(X)$values)[1])))
print("mean generation time")
print("____________________")
print(G)
}
## max lambda
maxlambda<-max.lambda(a)
## r
r <- max.r(a)
## Reproductive value
R0 <- R.val(a,age.max)
## Generation time
G <- G.val(a,age.max)
## Stable stage distribution
ssd <- stable.stage.dist(a)
## ssd classes
## female
ssd.juvf <- sum(ssd[1:primi-1])
ssd.adf <- sum(ssd[primi:age.max])
## male
ssd.juvm <- sum(ssd[(age.max+1):(age.max+primi-1)])
ssd.adm <- sum(ssd[(age.max+primi):k])
## Average age of mothers at stability
G.age.mean <- weighted.mean(age.vec[2:(age.max+1)],ssd[1:age.max])
## pick initial vectors
n<-ssd*N
##Calculate Quasi-extinction times
thresh <- 50 ## Define quasi-exinction threshold
Q<-(log(thresh/sum(n)))/log(maxlambda)
if (Q < 0) {
Q <- "infinity"
}
Q <- Q
## do a simulation
## first specify the initial condition and length of simulation
tlimit <- 30
##set population size year step vector
pop.vec <- rep(1,tlimit+1)
pop.vec[1] <- sum(n)
##set year step vector
yr.vec <- rep(1,tlimit+1)
yr.vec[1] <- 0
for (j in 1:tlimit) {
yr.vec[j+1] <- j
}
##then iterate
for (ii in 1:tlimit) {
n <- a %*% n
pop.vec[ii+1] <- sum(n)
}
log.pop.vec <- log10(pop.vec)
##total population size after 'tlimit' years
pop.st <- N
pop.end <- sum(n)
tlimit
maxlambda
r
Q
R0
G
## continue displays
ssd.juv <- ssd.juvf + ssd.juvm
ssd.ad <- ssd.adf + ssd.adm
##Make density independent plots
row <- 2
col <- 2
par(mfrow=c(row,col))
plot(yr.vec,pop.vec,xlab="year",ylab="N",xlim=range(-0.5:(tlimit+1)),ylim=range(0:(max(pop.vec)+(0.25*(max(pop.vec))))),type='l')
plot(yr.vec,log.pop.vec,xlab="year",ylab="log N",xlim=range(-0.5:(tlimit+1)),ylim=range(0:(max(log.pop.vec)+(0.25*(max(log.pop.vec))))),type='l')
##Make survival and fecundity plots
plot(age.vec,s.vec,xlab="age (years)",ylab="P(survival)",xlim=range(0.5:(age.max+0.5)),ylim=range(0:1),type='l')
plot(age.vec,m.vec,xlab="age (years)",ylab="m (fertility)",xlim=range(0.5:(age.max+0.5)),ylim=range(0:1),type='l')
par(mfrow=c(1,2))
## *******************************************
## Density-dependence in survival & fertility
## Set kill rates
## *******************************************
## ***********************************************************************************************
##K population size vector
Nd <- 9000
## Set time limit for projection
tlimit <- 30
## Set kill type (2 = adult females (>2 years) only; 1 = adult males (>5 years) only; 0 = adults (fem >2, mal >3) only)
kill.type <- 0
if (kill.type == 0) scenario <- "adult kill"
if (kill.type == 1) scenario <- "adult male (>5 years) kill"
if (kill.type == 2) scenario <- "adult female (>2 years) kill"
## Set kill range
min.kill <- 2 ## Set minimum kill rate
max.kill <- 1000 ## Set maximum kill rate
## Set kill interval
kill.interval <- 50 ## (calculate kill in increments of x)
## Set target per cent reduction of original population size
thresh <- 0
## Stochasticity in rainfall
## 0 = deterministic; 1 = stochastic
stoch.select <- 1
rain.cv = 24 ## coefficient of variation in rainfall (Choquenot 1993)
## Set number of iterations to estimate mean & confidence interval for projections based on flooding stochasticity
perm <- 1000 ## number of permutations
if (stoch.select == 0) perm <- 1 else perm <- perm
## Tertiary sex ratio (0.83 = balanced in polygynous ungulates)
tsr.max <- 0.95 ## Tertiary sex ratio (breeding females:breeding adults)
######################################
## Economic analysis
######################################
## Exchange rate (AU$ to Euros); updated live from server
##exch.aud.euro <- 0.587673
exch.rates <- download.file("http://www.securetrading.net/download/currencyrates/curr-gbp-ns-today.txt","C:\\Documents and Settings\\c_bradshaw\\My Documents\\Biology\\Banteng\\R\\exch\\exch.txt", "internal", quiet = FALSE, mode="w")
exch.rat.dat <- scan(file="C:\\Documents and Settings\\c_bradshaw\\My Documents\\Biology\\Banteng\\R\\exch\\exch.txt",what="character",skip=3,nlines=1)
exch.scan.aud <- scan(file="C:\\Documents and Settings\\c_bradshaw\\My Documents\\Biology\\Banteng\\R\\exch\\exch.txt",what="character",skip=7,nlines=1)
##exch.rates <- download.file("http://www.securetrading.net/download/currencyrates/curr-gbp-ns-today.txt","F:\\Banteng\\R\\exch\\exch.txt", "internal", quiet = FALSE, mode="w")
##exch.rat.dat <- scan(file="F:\\Banteng\\R\\exch\\exch.txt",what="character",skip=3,nlines=1)
##exch.scan.aud <- scan(file="F:\\Banteng\\R\\exch\\exch.txt",what="character",skip=7,nlines=1)
aud.gbp <- 1/((as.numeric(as.character((strsplit(exch.scan.aud," ")[2]))))/10000000)
exch.scan.eur <- scan(file="C:\\Documents and Settings\\c_bradshaw\\My Documents\\Biology\\Banteng\\R\\exch\\exch.txt",what="character",skip=11,nlines=1)
##exch.scan.eur <- scan(file="F:\\Banteng\\R\\exch\\exch.txt",what="character",skip=11,nlines=1)
eur.gbp <- 1/((as.numeric(as.character((strsplit(exch.scan.eur," ")[2]))))/10000000)
print(aud.gbp); print(eur.gbp)
exch.aud.euro <- aud.gbp/eur.gbp
print(exch.aud.euro)
print(exch.rat.dat)
## Eastern Young Cattle Indicator (EYCI) market data (AU$/kilo meat)
eyci <- download.file("http://www.mla.com.au/content.cfm?sid=1173","C:\\Documents and Settings\\c_bradshaw\\My Documents\\Biology\\Banteng\\R\\eyci\\eyci.txt", "internal", quiet = FALSE, mode="w")
eyci.lat <- scan(file="C:\\Documents and Settings\\c_bradshaw\\My Documents\\Biology\\Banteng\\R\\eyci\\eyci.txt",what="character",skip=641,nlines=1)
##eyci <- download.file("http://www.mla.com.au/content.cfm?sid=1173","F:\\Banteng\\R\\eyci\\eyci.txt", "internal", quiet = FALSE, mode="w")
##eyci.lat <- scan(file="F:\\Banteng\\R\\eyci\\eyci.txt",what="character",skip=643,nlines=1)
eyci.now <- (as.numeric(substr((as.character(eyci.lat[2])),23,28)))/100
print(eyci.now)
## Read in full range of EYCI since 1996
eyci.dat <- read.table("C:\\Documents and Settings\\c_bradshaw\\My Documents\\Biology\\Banteng\\R\\eyci\\eycidat.csv", sep=",", header=TRUE)
##hist(eyci.dat$adjeyci)
##plot(eyci.dat$year,eyci.dat$adjeyci,type="l")
yrf.rnd <- factor(floor(eyci.dat$year))
yrn.rnd <- (floor(eyci.dat$year))
eycidat <- data.frame(eyci.dat$adjeyci,yrf.rnd,yrn.rnd)
## Summary table
attach(eycidat)
eyci.tab <- table(yrf.rnd)
eyci.xtab <- xtabs(eyci.dat$adjeyci ~ yrf.rnd)
detach(eycidat)
eyci.yr.mean <- eyci.xtab/eyci.tab/100
##plot(eyci.yr.mean,type="l")
## Min and max eyci (since 1996, set in 2004 AU$)
eyci.min <- min(eyci.dat$adjeyci)/100 ## 1.8596
eyci.max <- max(eyci.dat$adjeyci)/100 ## 4.3598
## Temporal autocorrelation
lag1 <- as.numeric(eyci.yr.mean[2:(nrow(eyci.yr.mean))])
base <- as.numeric(eyci.yr.mean[1:(nrow(eyci.yr.mean)-1)])
eyci.fit <- lm(lag1 ~ base)
##plot(base,lag1)
##abline(eyci.fit,col="red")
## Mean & SD
eyci.mean <- as.numeric(mean(eyci.yr.mean))
eyci.var <- as.numeric(var(eyci.yr.mean))
## User-defined values
ppkg.meat <- 10 ## (price in AU$ to obtain 1 kg banteng-equivalent meat); T. Griffiths, pers. comm.
## Meat eaten per day per person
adult.meat.day <- 67 ## g/day
adult.meat.yr <- (adult.meat.day*365)/1000 ## kg/year/adult
minjil.pop <- 254 ## 2001 census data
minjil.juv <- 39 + 53
minjil.ad <- 35 + 69 + 42 + 16
minjil.meat <- (adult.meat.yr*minjil.ad) + ((adult.meat.yr*minjil.juv)/2)
## Proportion of full animal producing marketable meat (dressing proportion)
meat.prop <- 0.526 ## for banteng (Kirby 1979)
## Price per mature male harvested passed to Traditional owners
safari.to <- 2500 ## AU$
## Costing
muster <- 10 ## per head
transport <- 10 ## per head (http://www.agric.nsw.gov.au/reader/an-transport/6980)
##cost.tot <- muster + transport ## set individually above OR,
cost.tot <- 150 ## set total cost in AU$ per head (Alister Trier, Proj. Mgr - NT Indigenous Pastoral Project
## Cost function
## Increasing costs as a function of a reduction in population size
cost.max <- 500 ## max cost (AU$) at 0.1*K
cost.min <- 150 ## min cost (AU$) at K
## Profit (http://www.abs.gov.au/websitedbs/c311215.NSF/0/641c9a7c2c02c6d9ca256d480012c608?OpenDocument)
profit <- 29 ## average % profit per $ invested (Australia average)
## Demand function
## Set the the probability (p.dem) of attracting max n safari hunters (n.saf) to kill trophy males
n.saf <- 40
p.dem <- 0.5
## *********************************************************************************
## ***************
## End user input
## ***************
## *********************************************************************************
## Calculate demand function (3-parameter Hill logistic decay)
## yhat = ((a * x^b)/(c^b + x^b))
## Create data.frame
p.dem.vec <- c(1,0.99,0.98,0.95,0.90,0.80,0.64,p.dem)
n.saf.vec <- c(1,n.saf/4,n.saf/2,n.saf*0.75,n.saf*0.85,n.saf*0.92,n.saf*0.95,n.saf)
dem.data <- data.frame(n.saf.vec,p.dem.vec)
fit.dem <- nls(dem.data$p.dem.vec ~ ((a.dem * ((dem.data$n.saf.vec)^b.dem))/((c.dem^b.dem)+(dem.data$n.saf.vec^b.dem))),
data = dem.data,
start = list(a.dem = 1, b.dem = -(n.saf/2), c.dem = n.saf),
trace = TRUE)
sum.fit.dem <- summary(fit.dem)
coeff.fit.dem <- as.numeric(sum.fit.dem$parameters)
dem.n.vec <- seq(1,n.saf*2,1)
dem.pred <- ((coeff.fit.dem[1] * ((dem.n.vec)^coeff.fit.dem[2]))/((coeff.fit.dem[3]^coeff.fit.dem[2])+(dem.n.vec^coeff.fit.dem[2])))
## Plot demand function
row <- 1
col <- 1
par(mfrow=c(row,col))
plot(dem.n.vec,dem.pred,xlab="number of male trophy tags",ylab="demand probability",ylim=range(c(0,1)),type="l")
title(main="Trophy Demand Function")
par(mfrow=c(1,2))
## Translate demand to numbers of harvest animals
demf.pred <- (1 - (0.97^dem.n.vec))
demf <- demf.pred*n.saf
row <- 1
col <- 1
par(mfrow=c(row,col))
plot(dem.n.vec,demf.pred,xlab="number of male trophy tags",ylab="demand n probability",type="l")
title(main="Trophy n Demand Function")
par(mfrow=c(1,2))
## Cost function
cost.dif <- cost.max - cost.min
kprop.vec <- (seq(0.1,1,0.1))*Nd
cost.vec <- c(cost.max,0.833*cost.max,(cost.min+cost.max)/2,0.66*cost.max,1.25*cost.min,1.2*cost.min,1.15*cost.min,1.1*cost.min,1.05*cost.min,cost.min)
## Fit function (exponential decay) f=y0+a*exp(-b*x)
cost.data <- data.frame(kprop.vec,cost.vec)
fit.cost <- nls(cost.data$cost.vec ~ y0.cost + a.cost*exp(-b.cost*cost.data$kprop.vec),
data = cost.data,
start = list(a.cost = (0.66*cost.max), b.cost = 0.0004, y0.cost = cost.min),
trace = TRUE)
sum.fit.cost <- summary(fit.cost)
coeff.fit.cost <- as.numeric(sum.fit.cost$parameters)
cost.n.vec <- seq(1,Nd,100)
cost.pred <- coeff.fit.cost[3] + coeff.fit.cost[1]*exp(-coeff.fit.cost[2]*cost.n.vec)
for (c in 1:(length(cost.n.vec))) {
if (cost.pred[c] > cost.max) cost.pred[c] <- cost.max
if (cost.pred[c] < cost.min) cost.pred[c] <- cost.min
}
## Plot cost function
row <- 1
col <- 1
par(mfrow=c(row,col))
plot(cost.n.vec,cost.pred,xlab="Population Size",ylab="Cost per head ($AU)",type="l")
title(main="Cost Function")
par(mfrow=c(1,2))
## Growth functions
f.wt.vec <- c(17,82,300); m.wt.vec <- c(17,100,600)
f.age.vec <- c(0,1,4); m.age.vec <- c(0,1,6)
## Create data frame
gr.data <- data.frame(f.wt.vec,f.age.vec,m.wt.vec,m.age.vec)
## model formula
## Von Bertalanffy growth function: M(t) = Mmax - (Mmax - M0) exp(-kt)
## M0 = mean birth mass
## Mmax = mean maximum mass
## k = rate constant per year
fit.gr.f <- nls(gr.data$f.wt.vec ~ gr.data$f.wt.vec[3] - (gr.data$f.wt.vec[3] - gr.data$f.wt.vec[1]) * exp(-k.coeff*gr.data$f.age.vec),
data = gr.data,
start = list(k.coeff = 0.2),
trace = TRUE)
sum.fit.gr.f <- summary(fit.gr.f)
fit.gr.m <- nls(gr.data$m.wt.vec ~ gr.data$m.wt.vec[3] - (gr.data$m.wt.vec[3] - gr.data$m.wt.vec[1]) * exp(-k.coeff*gr.data$m.age.vec),
data = gr.data,
start = list(k.coeff = 0.2),
trace = TRUE)
sum.fit.gr.m <- summary(fit.gr.m)
## Coefficients from fit
coeff.fit.gr.f <- as.numeric(sum.fit.gr.f$parameters)
coeff.fit.gr.m <- as.numeric(sum.fit.gr.m$parameters)
## Predict new q vector with integer age inputs
grf <- gr.data$f.wt.vec[3] - (gr.data$f.wt.vec[3] - gr.data$f.wt.vec[1]) * exp(-coeff.fit.gr.f[1]*age.vec)
grm <- gr.data$m.wt.vec[3] - (gr.data$m.wt.vec[3] - gr.data$m.wt.vec[1]) * exp(-coeff.fit.gr.m[1]*age.vec)
row <- 1
col <- 1
par(mfrow=c(row,col))
plot(age.vec,grf,xlab="age (years)",ylab="mass (kg)",ylim=range(c(0,max(m.wt.vec))),type="l")
lines(age.vec,grm,col="red")
title(main="von Bertalanffy Growth Functions",sub="(male vs. female)")
par(mfrow=c(1,2))
## Derivate growth expressions at "age.input"
vb.exp <- expression(Mmax - (Mmax - M0) * exp((-gr.k)*age))
## For a male
Mmax <- gr.data$m.wt.vec[3]
M0 <- gr.data$m.wt.vec[1]
gr.k <- coeff.fit.gr.m[1]
age1 <- 16/12
age2 <- age1 + (15/12)
age3 <- 10
age <- age1
dvb.exp1 <- D(vb.exp, c("age"))
m1.gr.yr <- eval(dvb.exp1)
m1.yr <- eval(vb.exp)
m1.gr.dy <- m1.gr.yr/365
age <- age2
dvb.exp2 <- D(vb.exp, c("age"))
m2.gr.yr <- eval(dvb.exp2)
m2.yr <- eval(vb.exp)
m2.gr.dy <- m2.gr.yr/365
age <- age3
dvb.exp3 <- D(vb.exp, c("age"))
m3.gr.yr <- eval(dvb.exp3)
m3.yr <- eval(vb.exp)
m3.gr.dy <- m3.gr.yr/365
## Average growth rate (per yr & per day) between
## the ages of 22 and 37 months (Moran 1973)
## Moran's value = 0.22 kg/day
m.sec.yr <- (m2.yr - m1.yr)/(age2 - age1)
m.sec.dy <- m.sec.yr/365 ## predicted kg/day
m.intcpt <- ((m1.yr + m2.yr) - ((age1+age2)*m.sec.yr))/2
row <- 1
col <- 1
par(mfrow=c(row,col))
plot(age.vec,grf,xlab="age (years)",ylab="mass (kg)",ylim=range(c(0,max(m.wt.vec))),type="l")
lines(age.vec,grm,col="red")
abline(v=age1,col="green")
abline(h=m1.yr,col="green")
abline(m.intcpt,m.sec.yr)
abline(v=age2,col="green")
abline(h=m2.yr,col="green")
##abline(v=age3,col="green")
##abline(h=m3.yr,col="green")
points(age1,m1.yr,col="black",pch=19)
points(age2,m2.yr,col="black",pch=19)
##points(age3,m3.yr,col="black",pch=19)
title(main="von Bertalanffy Growth Functions",sub="(male vs. female)")
par(mfrow=c(1,2))
## ************************************************************************************************
## Re-calculate logistic functions for survival & fecundity based on initial population vector
library(stats)
library(base)
pop.k <- Nd
pop.min <- 20
pop.step <- 50
xmid <- (Nd + pop.min)/2
num.vec <- seq(pop.min,pop.k,((pop.k-pop.min)/pop.step))
## Set up base logistic form
quant <- seq(0,1,(1/pop.step)) ## sets up quantile vector
## logistic.dens <- dlogis(quant, location = 0.01, scale = 10, log = FALSE) ## estimates logistic density function with long left tail
logistic.dens <- 0 + ((0.997)/(1+(quant/1.8217)^3.9151))
log.dens <- (logistic.dens - min(logistic.dens)) / max(logistic.dens - min(logistic.dens))
## Set min and max s0 values
s0.min <- 0.92
s0.max <- 0.62
## Calculate logistic function between min and max s0
s0.vec <- (seq(s0.min,s0.max,-((s0.min-s0.max)/pop.step)))
range.s0.vec <- range(s0.vec)[2] - range(s0.vec)[1]
s0.vec.logis <- (range.s0.vec * log.dens) + min(s0.vec)
## Set min and max s1+ values
s1p.min <- 0.99
s1p.max <- s0.min
## Calculate logistic function between min and max s1p
s1p.vec <- (seq(s1p.min,s1p.max,-((s1p.min-s1p.max)/pop.step)))
range.s1p.vec <- range(s1p.vec)[2] - range(s1p.vec)[1]
s1p.vec.logis <- (range.s1p.vec * log.dens) + min(s1p.vec)
## Set min and max fecundity a coefficient values
af.min <- 0.62
af.max <- coeff.fit.m.vec[1]
## Calculate logistic function between min and max
af.vec <- (seq(af.min,af.max,-((af.min-af.max)/pop.step)))
range.af.vec <- range(af.vec)[2] - range(af.vec)[1]
af.vec.logis <- (range.af.vec * log.dens) + min(af.vec)
## Plot dd functions
row <- 2
col <- 2
par(mfrow=c(row,col))
plot(num.vec,s0.vec.logis,xlab="N",ylab="s0",xlim=range(-0.5:((max(num.vec))+1)),ylim=range(c(0,1)),type='l')
title(main="Logistic DD Functions")
plot(num.vec,s1p.vec.logis,xlab="N",ylab="s1+",xlim=range(-0.5:((max(num.vec))+1)),ylim=range(c(0,1)),type='l')
plot(num.vec,af.vec.logis,xlab="N",ylab="a.f",xlim=range(-0.5:((max(num.vec))+1)),ylim=range(c(0,1)),type='l')
par(mfrow=c(1,2))
log.func <- data.frame(num.vec,s0.vec.logis,s1p.vec.logis,af.vec.logis) ## put new vectors into data.frame
## Estimate 4-parameter logistic model coefficients
s0.param <- getInitial(s0.vec.logis ~ SSfpl(num.vec, a.s0, b.s0, xmid.s0, scal.s0), data=log.func)
s1p.param <- getInitial(s1p.vec.logis ~ SSfpl(num.vec, a.s1p, b.s1p, xmid.s1p, scal.s1p), data=log.func)
af.param <- getInitial(af.vec.logis ~ SSfpl(num.vec, a.af, b.af, xmid.af, scal.af), data=log.func)
## ************************************************************************************************
## Stochastic catastrophe scenario modelled from 0.14G (Reed et al. 2004)
p.cat <- 0.147/G.age.mean
sev.cat.vec <- seq(0,100,10)
sev.cat.prob <- (2510*(0.9376^(sev.cat.vec)))/100
sev.cat.dat <- data.frame(sev.cat.vec,sev.cat.prob)
sev.cat.fit <- nls(sev.cat.vec ~ (a.cat*(sev.cat.prob^b.cat)),
data = sev.cat.dat,
start = list(a.cat = 50, b.cat = -0.2),
trace = TRUE)
sum.sev.cat.fit <- summary(sev.cat.fit)
sev.cat.coeff <- as.numeric(sum.sev.cat.fit$parameters)
karray <- seq(min.kill,max.kill,kill.interval) ## kill rate array
lkarray <- length(karray)
## Rainfall setup for stochastic projections
rain.sum.mean <- round(sum(c(275,240,300,140,20,5,2,0,5,20,120,230)),-1) ## mean monthly rainfall (1921-1978 - Choquenot 1993)
rain.var <- (rain.cv*rain.sum.mean)/100
rain.mult.sd <- (sqrt(rain.cv))/100
rain.mult.min <- 1-(2*rain.mult.sd)
rain.mult.max <- 1+(2*rain.mult.sd)
## Stochastic loop
## Set storage vectors for mean and confidence intervals for population sizes
min.popd.perm <- matrix(0,nrow=perm,ncol=lkarray)
minmal6p.perm <- matrix(0,nrow=perm,ncol=lkarray)
meat.dol.perm <- matrix(0,nrow=perm,ncol=lkarray)
cost.dol.perm <- matrix(0,nrow=perm,ncol=lkarray)
proft.dol.perm <- matrix(0,nrow=perm,ncol=lkarray)
profm.dol.perm <- matrix(0,nrow=perm,ncol=lkarray)
meat.mass.perm <- matrix(0,nrow=perm,ncol=lkarray)
safari.dol.perm <- matrix(0,nrow=perm,ncol=lkarray)
## Start stochastic loop
for (p in 1:perm) {
min.popd.vec <- rep(0,length(karray)) ## Minimum population size vector
mald.vec <- rep(0,length(karray)) ## Number of males vector
minmal6p.vec <- rep(0,length(karray)) ## Minimum male (>5 years) vector
minpmal6p.vec <- rep(0,length(karray)) ## Minimum proportion of males (>5 years) per males vector
minfem3p.vec <- rep(0,length(karray)) ## Minimum female (>2 years) vector
minpfem3p.vec <- rep(0,length(karray)) ## Minimum proportion of females (>2 years) per females vector
lambdad.vec <- rep(0,length(karray)) ## mean population rate of change (r)
mal6p.kill <- rep(0,length(karray)) ## mature males killed vector
## Economic vectors
meat.mass.tot <- rep(0,length(karray)) ## Total mass meat harvested
meat.dol.tot <- rep(0,length(karray)) ## total AU$ of harvested meat
safari.dol.tot <- rep(0,length(karray)) ## total AU$ of harvested meat
cost.dol.tot <- rep(0,length(karray)) ## total AU$ costs
meat.prop.worth <- rep(0,length(karray)) ## proportional worth of harvested meat
safari.prop.worth <- rep(0,length(karray)) ## proporational worth of safari
## Start simulation over kill vector
for (z in 1:lkarray) {
## Stochastic measure (variation in rainfall)
rain.mult <- runif(1,min=rain.mult.min,max=rain.mult.max)
## define start survival
s0.d <- rain.mult*(as.numeric((SSfpl(sum(Nd),s0.param[1],s0.param[2],s0.param[3],s0.param[4]))))
if (s0.d < s0.max) s0.d <- s0.max else s0.d <- s0.d
if (s0.d > s0.min) s0.d <- s0.min else s0.d <- s0.d
s1p.d <- rain.mult*(as.numeric((SSfpl(sum(Nd),s1p.param[1],s1p.param[2],s1p.param[3],s1p.param[4]))))
if (s1p.d < s1p.max) s1p.d <- s1p.max else s1p.d <- s1p.d
if (s1p.d > s1p.min) s1p.d <- s1p.min else s1p.d <- s1p.d
## define start fecundity
a.md <- as.numeric((SSfpl(sum(Nd),af.param[1],af.param[2],af.param[3],af.param[4])))
if (a.md < af.max) a.md <- af.max else a.md <- a.md
if (a.md > af.min) a.md <- af.min else a.md <- a.md
## Re-define fertility vector
md.vec <- rep(0,age.max); b.fert <- coeff.fit.m.vec[3]; x0.fert <- coeff.fit.m.vec[2]
for (j in (1:age.max)) {
md<-a.md*exp(-0.5*(log(j/x0.fert)/b.fert)^2)
md.vec[j] <- md
}
##total females in population
f<-Nd*sr
##total males in population
mal<-Nd*(1-sr)
## The normal matrix
ad <- matrix(data<-0,nrow<-k,ncol<-k)
## Fill matrix with survival & fecundity vectors
diag(ad[2:age.max,1:(age.max-1)]) <- s1p.d ## adds s1p.d to female quadrant
diag(ad[(age.max+2):k,(age.max+1):(k-1)]) <- s1p.d ## adds s1p.d to male quadrant
ad[1,2:(age.max)] <- s0.d * md.vec[1:(age.max-1)] ## adds female fecundity
ad[(age.max+1),2:(age.max)] <- s0.d * md.vec[1:(age.max-1)] ## adds male fecundity
## Stable stage distribution
ssdd <- stable.stage.dist(ad)
## pick initial vectors
nd<-ssdd*Nd
## max r
rd <- max.r(ad)
##set population size year step vector
popd.vec <- rep(1,tlimit+1)
popd.vec[1] <- sum(nd)
##set female population size year step vector
femd.vec<-rep(1,tlimit+1)
femd.vec[1]<-sum(nd[1:age.max])
femda.vec<-rep(1,tlimit+1)
femda.vec[1]<-sum(nd[3:age.max])
##set male population size year step vector
mald.vec<-rep(1,tlimit+1)
mald.vec[1]<-sum(nd[(age.max+1):k])
malda.vec<-rep(1,tlimit+1)
malda.vec[1]<-sum(nd[21:k])
## set large male year step vector
male6p.vec <- rep(0,tlimit+1)
male6p.vec[1]<-sum(nd[23:k])
##set year step vector
yrd.vec <- rep(1,tlimit+1)
yrd.vec[1] <- 0
for (j in 1:tlimit) {
yrd.vec[j+1] <- j
}
## Mature male kill vector
mal6p.kill.vec <- rep(0,tlimit+1)
## Economic vectors
meat.tot.vec <- rep(0,tlimit)
meat.dol.vec <- rep(0,tlimit)
cost.tot.vec <- rep(0,tlimit)
safari.tot.vec <- rep(0,tlimit)
meat.worth.vec <- rep(0,tlimit)
safari.worth.vec <- rep(0,tlimit)
meat.prop.vec <- rep(0,tlimit)
safari.prop.vec <- rep(0,tlimit)
eyci <- runif(1,eyci.min,eyci.max)
##then iterate
for (ii in 1:tlimit) {
nd <- ad %*% nd
## Calculate severity of a potential catastrophe
sev.cat.input <- runif(1,0,(max(sev.cat.prob)))
sev.cat <- ((sev.cat.coeff[1]*(sev.cat.input^sev.cat.coeff[2])))/100
##1-sev.cat
if (sev.cat > 1) sev.cat <- 0.99
## calculate whether a catastrophe occurs
if (runif(1,0,1) <= p.cat) nd <- nd*(1-sev.cat) else nd <- nd
## Set any negative values in nd to 0
zero.sub <- which(nd<0)
nd[zero.sub] <- 0
na.sub <- which(is.na(nd))
nd[na.sub] <- 0
if (sum(nd) == 0) next
## Stochastic measure (variation in rainfall)
rain.multp <- runif(1,min=rain.mult.min,max=rain.mult.max)
## rain.multp <- ifelse(stoch.select == 1, rain.multp <- rain.multp, rain.mult <- 1)
##rain.multp <- 1
## Set negative density feedback function for the matrix
## Redefine survival probabilities
s0.d <- rain.multp*(as.numeric((SSfpl(sum(nd),s0.param[1],s0.param[2],s0.param[3],s0.param[4]))))
if (s0.d < s0.max) s0.d <- s0.max else s0.d <- s0.d
if (s0.d > s0.min) s0.d <- s0.min else s0.d <- s0.d
s1p.d <- rain.multp*(as.numeric((SSfpl(sum(nd),s1p.param[1],s1p.param[2],s1p.param[3],s1p.param[4]))))
if (s1p.d < s1p.max) s1p.d <- s1p.max else s1p.d <- s1p.d
if (s1p.d > s1p.min) s1p.d <- s1p.min else s1p.d <- s1p.d
## re-define fecundity a coefficient
a.md <- as.numeric(SSfpl(sum(nd),af.param[1],af.param[2],af.param[3],af.param[4]))
if (a.md < af.max) a.md <- af.max else a.md <- a.md
if (a.md > af.min) a.md <- af.min else a.md <- a.md
## Re-define fertility vector
md.vec <- rep(0,age.max)
for (j in (1:age.max)) {
md <- a.md*exp(-0.5*(log(j/x0.fert)/b.fert)^2)
md.vec[j] <- md
}
## Adjust for demographic stochasticity (binomial & poisson resampling)
n.mf <- 2*md.vec[1:(age.max)]*nd[1:age.max]
n.f <- sum(nd[1:age.max])
sum.n.mf <- sum(n.mf)
if (sum.n.mf == 0) sum.n.mf <- 1
if ((is.na(sum.n.mf)) == TRUE) sum.n.mf <- 1
mds.vec <- sum(md.vec)*(rpois(age.max,(n.mf*n.f))/(sum.n.mf*n.f))
for (mm in 1:(length(md.vec))) {
if (md.vec[mm] > af.min) md.vec[mm] <- af.min else md.vec[mm] <- md.vec[mm]
} ## caps m at 0.62
## Tertiary sex ratio
if (sum(nd[1:age.max] / (1+sum(nd))) > tsr.max) md.vec <- rep(0,age.max) else md.vec <- md.vec
n.1 <- round(sum(nd))
if (n.1 == 0) n.1 <- 1
s1p.d <- rbinom(1,n.1,s1p.d)/n.1
if (s1p.d > s1p.min) s1p.d <- s1p.min else s1p.d <- s1p.d
n.0 <- round(sum(md.vec*n[1:age.max]))
if (n.0 == 0) n.0 <- 1
s0.d <- rbinom(1,n.0,s0.d)/n.0
## Fill matrix with adjusted survival & fecundity vectors
diag(ad[2:age.max,1:(age.max-1)]) <- s1p.d ## adds s1p.d to female quadrant
diag(ad[(age.max+2):k,(age.max+1):(k-1)]) <- s1p.d ## adds s1p.d to male quadrant
ad[1,2:(age.max)] <- s0.d * md.vec[1:(age.max-1)] ## adds female fecundity
ad[(age.max+1),2:(age.max)] <- s0.d * md.vec[1:(age.max-1)] ## adds male fecundity
## Fluctuating market values for beef sales (EYCI)
## random uniform distribution between 1996-2004 min and max EYCI (in 2004 AU$)
## Autocorrelated from last year
eyci <- as.numeric(eyci.fit$coefficients[1] + (eyci.fit$coefficients[2])*eyci)
eyci <- as.numeric(rnorm(1, mean=eyci,sd=(sqrt(eyci.var))))
## if (stoch.select == 0) eyci <- eyci.now else eyci <- eyci
##eyci <- ppkg.meat
##print(eyci)
## Cost function
cost.now <- coeff.fit.cost[3] + coeff.fit.cost[1]*exp(-coeff.fit.cost[2]*(sum(nd)))
if (cost.now > cost.max) cost.now <- cost.max
if (cost.now < cost.min) cost.now <- cost.min
##cost.now <- 0
## *****************************************************************
## Kill adult females (3-17 years)
## *****************************************************************
fem.kill <- ifelse(kill.type == 2, karray[z], 0)
nf.kill <- fem.kill/15 ## uniform distribution of kill in ages > 2
kill.f.vec <- rep(0,k)
kill.f.vec[3:age.max] <- nf.kill
if (sum(nd) < fem.kill) {
nd <- nd
}
nd <- nd - kill.f.vec ## Adjust nd vector for kill
f.mass.tot <- sum(kill.f.vec[3:age.max] * grf[4:(age.max+1)])
f.meat.tot <- f.mass.tot*meat.prop
f.cost.tot <- sum(kill.f.vec[3:age.max]) * cost.now
f.meat.dol <- f.meat.tot*eyci
## *****************************************************************
## *****************************************************************
## Kill large males (males 6-17 years)
## *****************************************************************
male.kill <- ifelse(kill.type == 1, karray[z], 0)
nm.kill <- male.kill/12 ## uniform distribution of kill in ages > 5
kill.m.vec <- rep(0,k)
kill.m.vec[23:k] <- nm.kill
if (sum(nd) < male.kill) {
nd <- nd
}
nd <- nd - kill.m.vec ## Adjust nd vector for kill
m.mal6p.kill <- sum(kill.m.vec[23:k])
m.mass.tot <- sum(kill.m.vec[23:k] * grm[7:(age.max+1)])
m.cost.tot <- sum(kill.m.vec[23:k]) * cost.now
m.meat.tot <- m.mass.tot*meat.prop
m.meat.dol <- m.meat.tot*eyci
m.m.kill <- m.mal6p.kill
dem.sub <- ifelse((m.mal6p.kill > length(dem.pred)), length(dem.pred), ceiling(m.mal6p.kill))
dem.kill <- (demf[dem.sub])
m.safari.tot <- dem.kill * safari.to
if (sum(kill.m.vec) == 0) m.safari.tot <- 0 else m.safari.tot <- m.safari.tot
## *****************************************************************
## *****************************************************************
## Kill adults (females >2 years; males >3)
## *****************************************************************
all.kill <- ifelse(kill.type == 0, karray[z], 0)
naf.kill <- (all.kill/2)/15 ## uniform distribution of females killed (> 2 years)
nam.kill <- (all.kill/2)/14 ## uniform distribution of males killed (> 3 years)
kill.all.vec <- rep(0,k)
kill.all.vec[3:age.max] <- naf.kill
kill.all.vec[21:k] <- nam.kill
if (sum(nd) < all.kill) {