Define population dynamics for multiple populations of a single species linked by dispersal (a metapopulation).
metapopulation(structure, dynamics, dispersal)
is.metapopulation(x)binary or logical matrix denoting dispersal
links between populations. Columns move to rows, so a 1 or
TRUE in cell (a, b) denotes movement from population b
to population a
a dynamics object or list of dynamics objects
with one element for each population (each column/row of
structure). If a single dynamics object is
provided, it is recycled over all required populations
object created with
dispersal. dispersal objects
describe movements between populations and can include
class-specific movements and density-dependent movements.
dispersal objects must be a list with one element for each
link in structure. These links are interpreted in
column-major order, so that dispersal objects
must be ordered by links in column 1, then column 2, and so on
an object to pass to is.metapopulation
The metapopulation function connects multiple
populations through known dispersal probabilities, handling
standardisations of dispersal probabilities (if required) and
updating masks and functions for all processes defined within each
population. Further details on the definition of dispersal terms
are provided in dispersal.
Covariates can be included in metapopulation models. The default behaviour is for all populations to share a single set of covariates, with covariate associations and masks defined separately for each population. A workaround to the assumption of shared covariates is included in the examples, below. Including covariates on dispersal probabilities requires covariate associations and masks defined on the combined metapopulation model. This approach is possible but currently untested.
# define some populations, all with identical vital rates
nclass <- 5
popmat <- matrix(0, nrow = nclass, ncol = nclass)
popmat[reproduction(popmat, dims = 4:5)] <- c(10, 20)
popmat[transition(popmat)] <- c(0.25, 0.3, 0.5, 0.65)
# define a dynamics object
dyn <- lapply(
1:3,
function(i) dynamics(popmat)
)
# define metapopulation structure with populations
# 1 and 3 dispersing into population 2
pop_structure <- matrix(0, nrow = 3, ncol = 3)
pop_structure[1, 2] <- 1
pop_structure[3, 2] <- 1
# define dispersal between populations
dispersal_matrix <- matrix(0, nrow = nclass, ncol = nclass)
dispersal_matrix[survival(dispersal_matrix, dims = 20:25)] <- 0.2
pop_dispersal1 <- dispersal(dispersal_matrix, proportion = TRUE)
pop_dispersal2 <- dispersal(dispersal_matrix, proportion = FALSE)
pop_dispersal <- list(pop_dispersal1, pop_dispersal2)
# create metapopulation object
metapop <- metapopulation(pop_structure, dyn, pop_dispersal)
# simulate without covariates
sims <- simulate(metapop, nsim = 2)
# simulate with shared covariates
# define a covariates function
covar_fn <- function(mat, x) {
mat * (1 / (1 + exp(-0.5 * (x + 10))))
}
# and some covariates
xsim <- matrix(rnorm(20), ncol = 1)
# update the population dynamics objects with covariates
dyn <- lapply(
dyn,
update,
covariates(masks = transition(dyn[[1]]$matrix), funs = covar_fn)
)
# (re)create metapopulation object
metapop <- metapopulation(pop_structure, dyn, pop_dispersal)
sims <- simulate(
metapop,
nsim = 2,
args = list(covariates = format_covariates(xsim))
)
# simulate with separate covariates
# (requires re-definition of covariate functions)
new_fn <- function(i) {
force(i)
function(mat, x) {
mat * (1 / (1 + exp(-0.5 * (x[i] + 10))))
}
}
new_fn <- lapply(
1:3,
new_fn
)
# update the population dynamics objects with covariates
dyn <- lapply(
dyn,
update,
covariates(masks = transition(dyn[[1]]$matrix), funs = covar_fn)
)
# (re)create metapopulation object
metapop <- metapopulation(pop_structure, dyn, pop_dispersal)
# and simulate with one column of predictors for each population
xsim <- matrix(rnorm(60), ncol = 3)
sims <- simulate(
metapop,
nsim = 2,
args = list(covariates = format_covariates(xsim))
)
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