Population models

Description

A package to run population simulations using an Individual-Based Model compiled in C. The population model is a discrete, age-structured model and follows the formalizing of a post-breeding Leslie matrix model.

Version 0.1 proposes functions to run and plot population projections and includes demographic and environmental stochasticities. There is also the option to parallelize simulations (except on Windows).

Version 0.2 fixes a bug that generated wrong results at very large population sizes.

Details

Author(s)

Guillaume Chapron <gchapron@carnivoreconservation.org>

Examples

# Initial number of individuals
n0 <- 10
n1 <- 20
n2 <- 15
n3 <- 10
n4 <- 5

# Age-specific survival rates
s0 <- 0.5
s1 <- 0.6
s2 <- 0.7
s3 <- 0.8
s4 <- 0.9

# Age-specific number of offspring
b1 <- 0.5
b2 <- 0.8
b3 <- 1.8
b4 <- 1.8
b5 <- 1.1

# Project 10 years ahead repeated 10000 times
years <- 10
runs <- 10000

results <- project(
	years = years,
	runs = runs,
	initial_population = c(n0, n1, n2, n3, n4),
	survival = cbind(c(s0, s1, s2, s3, s4), 0.0), # no environmental stochasticity
	litter = cbind(c(b1, b2, b3, b4, b5), 0.0) # no environmental stochasticity
)

# Plot projection
plot_projection(results, "mean")

# Equivalent model with a post-breeding Leslie matrix
postM <- matrix(nrow=5, ncol=5, byrow=TRUE, data = c(
	s0*b1, s1*b2, s2*b3, s3*b4, s4*b5,
	   s0,     0,     0,     0,     0,
	    0,    s1,     0,     0,     0,
	    0,     0,    s2,     0,     0,
	    0,     0,     0,    s3,     0
	))

popvector <- c(n0, n1, n2, n3, n4)
N <- numeric(years)
N[1] <- sum(popvector)

for (i in 2:years) {
	popvector <- postM 
	N[i] <- sum(popvector)
}

# Check we get similar results
lines(1:years, N, col="blue", lwd=2)

Get number of available cores

Description

Get number of available cores for parallel simulations. Non-Windows systems only.

Usage

get_cores(runs)

Arguments

Details

This function detects the number of cores (see 'detectCores' in package 'parallel') available and returns the largest possible number of cores being an integer divider of the number of runs. On multi-core machines at least one core is not used for the simulation.

Value

get_cores()

Examples

get_cores(2)
get_cores(1000)

Plot population projections

Description

Plot population projections.

Usage

plot_projection(projection, kind)

Arguments

Details

Plot all population projections or the median or mean with 95% confidence interval. Only total population sizes are displayed.

Value

No returned value, plot created

Examples

years <- 10
runs <- 100

init.pop <- c(30, 20, 15, 12, 10, 9, 8, 7, 6, 5)

surv.md <- c(0.5, 0.7, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9)
surv.sd <- c(0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1)
surv.msd <- cbind(surv.md, surv.sd)

litter.md <- c(0.2, 1.1, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 1.8, 0.2)
litter.sd <- c(0.1, 0.2, 0.15, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1)
litter.msd <- cbind(litter.md, litter.sd)

nclass <- 4 # vary number of classes

projection <- project(
	years = years,
	runs = runs,
	initial_population = init.pop[1:nclass],
	survival = surv.msd[1:nclass,],
	litter = litter.msd[1:nclass,]
	)

plot_projection(projection)
plot_projection(projection, kind="median")

Population projections

Description

Run stochastic population projections.

Usage

project(years, runs, initial_population, survival, litter, seed)

Arguments

Details

Run stochastic population projections with an Individual-Based Model (IBM) compiled in C.

Value

Examples

years <- 10
runs <- 100

init.pop <- c(30, 20, 15, 12, 10, 9, 8, 7, 6, 5)

surv.md <- c(0.5, 0.7, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9)
surv.sd <- c(0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1)
surv.msd <- cbind(surv.md, surv.sd)

litter.md <- c(0.2, 1.1, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 1.8, 0.2)
litter.sd <- c(0.1, 0.2, 0.15, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1)
litter.msd <- cbind(litter.md, litter.sd)

nclass <- 4 # vary number of classes

projection <- project(
	years = years,
	runs = runs,
	initial_population = init.pop[1:nclass],
	survival = surv.msd[1:nclass,],
	litter = litter.msd[1:nclass,]
	)

Parallel population projections

Description

Run parallel stochastic population projections. Non-Windows systems only.

Usage

project_parallel(years, runs, initial_population, survival, litter, cores)

Arguments

Details

Run parallel stochastic population projections with an Individual-Based Model (IBM) compiled in C.

Value

Examples

years <- 10
runs <- 100

init.pop <- c(30, 20, 15, 12, 10, 9, 8, 7, 6, 5)

surv.md <- c(0.5, 0.7, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9)
surv.sd <- c(0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1)
surv.msd <- cbind(surv.md, surv.sd)

litter.md <- c(0.2, 1.1, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 1.8, 0.2)
litter.sd <- c(0.1, 0.2, 0.15, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1)
litter.msd <- cbind(litter.md, litter.sd)

nclass <- 4 # vary number of classes

# with 2 cores
projection <- project_parallel(
	years = years,
	runs = runs,
	initial_population = init.pop[1:nclass],
	survival = surv.msd[1:nclass,],
	litter = litter.msd[1:nclass,],
	cores = 2
	)

# with all possible cores (not run)
# projection <- project_parallel(
# 	years = years,
# 	runs = runs,
# 	initial_population = init.pop[1:nclass],
# 	survival = surv.msd[1:nclass,],
# 	litter = litter.msd[1:nclass,]
# )