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# program spuRs/resources/scripts/bp_grid.r
bp.sim <- function(gen, rv.sim, ...) {
# population of a branching process at generation gen
# rv.sim(n, ...) simulates n rv's from the offspring distribution
Z <- 1
for (i in 1:gen) {
if (Z > 0) {
Z <- sum(rv.sim(Z, ...))
}
}
return(Z)
}
# set parameter values
gen <- 50
size <- 2
prob <- seq(0.3, 0.6, by = 0.01)
n.reps <- 100 # sample size for estimating E Z
# estimate E Z for each value of prob
mu <- rep(0, length(prob))
Z.mean <- rep(0, length(prob))
for (i in 1:length(prob)) {
Z.sum <- 0
for (k in 1:n.reps) {
Z.sum <- Z.sum + bp.sim(gen, rbinom, size, prob[i])
}
mu[i] <- size*prob[i]
Z.mean[i] <- Z.sum/n.reps
}
# plot estimates
# note that values of log(0) (= -infinity) are not plotted
plot(mu, log(Z.mean), type = "o",
xlab = "E family size", ylab = paste("log pop at gen", gen))
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