Specify density dependence in models of population dynamics

Specify density dependence in vital rates (density_dependence) and in total abundances (density_dependence_n).

density_dependence(masks, funs, nmask = NULL)

density_dependence_n(masks, funs)

Arguments

masks

a logical matrix or vector (or list of these) defining cells affected by funs. See Details and masks

funs

a function or list of functions with one element for each element of masks. See Details

nmask

logical vector or list of vectors defining elements of the population vector affected by each mask-function pair. Intended primarily for internal use when scaling up processes in metapopulation

Details

density_dependence specifies standard density dependence on vital rates, such as scramble or contest competition or allee effects.

density_dependence_n is an alternative parameterisation of density dependence that acts directly on population abundances.

Masks must be of the same dimension as the population dynamics matrix and specify cells influenced by density dependence according to funs. In the case of density_dependence_n, masks are logical vectors with one element for each class. Additional details on masks are provided in masks.

If using density_depenence, functions must take at least two arguments, a matrix x and a vector n, which represent the population dynamics matrix and the population abundances. Functions must return a matrix with the same dimensions as x, modified to reflect the effects of current abundances (n) on vital rates.

In the case of density_dependence_n, funs takes only one argument, the population abundances n following all other updates in a given iteration/generation. This allows rescaling of population abundances based on total abundance or through more complicated functions that depend on external arguments (e.g., mass mortality events or harvesting).

Additional arguments to functions are supported and can be passed to simulate with the args, args.dyn, or args.fn arguments.

Examples

# define a population matrix (columns move to rows)
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 <- dynamics(popmat)

# add some density dependence
dd <- density_dependence(
  masks = reproduction(popmat, dims = 4:5),
  funs = ricker(1000)
)

# update the dynamics object
dyn <- update(dyn, dd)

# simulate trajectories
sims <- simulate(dyn, nsim = 100, options = list(ntime = 50))

# and plot
plot(sims)