Author: Fallert, S. and Cabral, J.S.

# 07: Age structured populations

#### Fallert, S. and Cabral, J.S.

Many species have population dynamics that require more complex equations than the simple Ricker model, which describes overcompensatory scramble competition dynamics. A common abstraction to deal with this complexity is to partition a species into functional subgroups that undergo different processes, as for example juveniles who are dispersing and looking for a habitat, who then become adults who are stationary but have the ability to reproduce and generate the next generation of juveniles. The following illustrates a simple example on how one could model such a system with metaRange.

## Basic setup

    library(metaRange)
    library(terra)

Setup the basic simulation.

    raster_file <- system.file("ex/elev.tif", package = "terra")
    r <- rast(raster_file)
    habitat <- scale(r, center = FALSE, scale = TRUE)
    habitat <- rep(habitat, 10)
    landscape <- sds(habitat)
    names(landscape) <- c("habitat")
    sim <- create_simulation(landscape)
    sim$add_species("species_1")

## Traits

Now we add the traits for both the juveniles and adults.

    sim$add_traits(
        species = "species_1",
        n_juveniles = 100,
        n_adults = 100,
        mortality_juveniles = 0.1,
        mortality_adults = 0.7,
        reproduction_rate = 2
    )
    sim$add_traits(
        species = "species_1",
        population_level = FALSE,
        dispersal_kernel = calculate_dispersal_kernel(
            max_dispersal_dist = 8,
            kfun = negative_exponential_function,
            mean_dispersal_dist = 4
        )
    )

## Processes

Now we add some processes that manage the transition between the age classes. These processes could of course be of any desired complexity, but to make the example easier to follow, we will use simple functions:

    sim$add_process(
        species = "species_1",
        process_name = "reproduction",
        process_fun = function() {
            self$traits[["n_juveniles"]] <-
                self$traits[["n_adults"]] + (
                    self$traits[["n_adults"]] * self$traits[["reproduction_rate"]]
                ) * self$sim$environment$current$habitat
        },
        execution_priority = 1
    )
    sim$add_process(
        species = "species_1",
        process_name = "maturation",
        process_fun = function() {
            self$traits[["n_adults"]] <-
                self$traits[["n_adults"]] +
                self$traits[["n_juveniles"]] * (1 - self$traits[["mortality_juveniles"]])
        },
        execution_priority = 3
    )

## More processes

And some more for the dispersal and mortality. Note that we do not need to add an `mortality_of_juveniles` process, since their mortality is already included in the `maturation` process.

    sim$add_process(
        species = "species_1",
        process_name = "dispersal_of_juveniles",
        process_fun = function() {
            self$traits[["n_juveniles"]] <- dispersal(
                abundance = self$traits[["n_juveniles"]],
                dispersal_kernel = self$traits[["dispersal_kernel"]]
            )
        },
        execution_priority = 2
    )
    sim$add_process(
        species = "species_1",
        process_name = "mortality_of_adults",
        process_fun = function() {
            self$traits[["n_adults"]] <-
                self$traits[["n_adults"]] * (1 - self$traits[["mortality_adults"]])
        },
        execution_priority = 4
    )

## Result

Lastly, we add a process that reports the numbers of adults and juveniles over time, after which we can execute the simulation and plot the results.

    sim$add_globals(n_juveniles = c(), n_adults = c())
    sim$add_process(
        process_name = "logger",
        process_fun = function() {
            self$globals$n_juveniles <-
                c(self$globals$n_juveniles, sum(self$species_1$traits[["n_juveniles"]]))
            self$globals$n_adults <-
                c(self$globals$n_adults, sum(self$species_1$traits[["n_adults"]]))
        },
        execution_priority = 5
    )
    sim$begin()
    plot(
        1:10,
        sim$globals$n_juveniles,
        col = "darkred",
        type = "l",
        lwd = 2,
        ylim = c(0, max(sim$globals$n_juveniles, sim$globals$n_adults)),
        xlab = "Time",
        ylab = "Number of individuals",
        cex.lab = 0.7,
        cex.axis = 0.7
    )
    lines(1:10, sim$globals$n_adults, col = "darkblue", lwd = 2)
    legend(
        "topleft",
        legend = c("juveniles", "adults"),
        col = c("darkred", "darkblue"),
        lty = 1,
        lwd = 2,
        cex = 0.7
    )