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

# 05: Species interactions

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

To expand the example we have so far, we can introduce more processes around the interaction between the two species.

First we will generate the same setup.

Code

    library(metaRange)
    library(terra)
    set_verbosity(0)

    raster_file <- system.file("ex/elev.tif", package = "terra")
    r <- rast(raster_file)
    temperature <- scale(r, center = FALSE, scale = TRUE) * 10 + 273.15
    precipitation <- r * 2
    temperature <- rep(temperature, 10)
    precipitation <- rep(precipitation, 10)
    landscape <- sds(temperature, precipitation)
    names(landscape) <- c("temperature", "precipitation")

    sim <- create_simulation(landscape)
    sim$add_species(name = "species_1")
    sim$add_species(name = "species_2")

    sim$add_traits(
        species = c("species_1", "species_2"),
        population_level = TRUE,
        abundance = 900,
        climate_suitability = 1,
        reproduction_rate = 0.3,
        carrying_capacity = 1000
    )
    sim$add_traits(
        species = c("species_1", "species_2"),
        population_level = FALSE,
        dispersal_kernel = calculate_dispersal_kernel(
            max_dispersal_dist = 3,
            kfun = negative_exponential_function,
            mean_dispersal_dist = 1
        )
    )

## Competition

We are going to construct a simple model that simulates (asymmetric) competition between two species. First, we will give both species the same value for their optimal environmental niche values, but species 2 will be able to tolerate lower and higher values for both niches compared to species 1.

Code

    opt_temp <- 285
    min_temp_sp1 <- 270
    max_temp_sp1 <- 290
    min_temp_sp2 <- 260
    max_temp_sp2 <- 295

    opt_prec <- 700
    min_prec_sp1 <- 200
    max_prec_sp1 <- 1000
    min_prec_sp2 <- 0
    max_prec_sp2 <- 1200

    x <- seq(min_temp_sp2, max_temp_sp2, length.out = 100)
    y_sp1 <- calculate_suitability(max_temp_sp1, opt_temp, min_temp_sp1, x)
    y_sp2 <- calculate_suitability(max_temp_sp2, opt_temp, min_temp_sp2, x)
    plot(x, y_sp1, type = "l", xlab = "Temperature [K]", ylab = "Suitability", col = "darkred", lwd = 2)
    lines(x, y_sp2, col = "darkblue", lwd = 2)
    legend(
        "topleft",
        legend = c("species 1", "species 2"),
        col = c("darkred", "darkblue"),
        lty = 1,
        lwd = 2,
        cex = 0.7
    )

Figure 1: Suitability curve for the temperature niches of species 1 (blue) and species 2 (red).
Code

    x <- seq(min_prec_sp2, max_prec_sp2, length.out = 100)
    y_sp1 <- calculate_suitability(max_prec_sp1, opt_prec, min_prec_sp1, x)
    y_sp2 <- calculate_suitability(max_prec_sp2, opt_prec, min_prec_sp2, x)
    plot(x, y_sp1, type = "l", xlab = "precipitation [mm]", ylab = "Suitability", col = "darkred", lwd = 2)
    lines(x, y_sp2, col = "darkblue", lwd = 2)
    legend(
        "topleft",
        legend = c("species 1", "species 2"),
        col = c("darkred", "darkblue"),
        lty = 1,
        lwd = 2,
        cex = 0.7
    )

Figure 2: Suitability curve for the precipitation niches of species 1 (blue) and species 2 (red).

Now we can add these values as traits to the species and also add the other processes.

Code

    sim$add_traits(
        species = "species_1",
        population_level = FALSE,
        max_temperature = max_temp_sp1,
        optimal_temperature = opt_temp,
        min_temperature = min_temp_sp1,
        max_precipitation = max_prec_sp1,
        optimal_precipitation = opt_prec,
        min_precipitation = min_prec_sp1
    )
    sim$add_traits(
        species = "species_2",
        population_level = FALSE,
        max_temperature = max_temp_sp2,
        optimal_temperature = opt_temp,
        min_temperature = min_temp_sp2,
        max_precipitation = max_prec_sp2,
        optimal_precipitation = opt_prec,
        min_precipitation = min_prec_sp2
    )
    sim$add_process(
        species = c("species_1", "species_2"),
        process_name = "calculate_suitability",
        process_fun = function() {
            self$traits$climate_suitability <-
                calculate_suitability(
                    self$traits$max_temperature,
                    self$traits$optimal_temperature,
                    self$traits$min_temperature,
                    self$sim$environment$current$temperature
                ) *
                calculate_suitability(
                    self$traits$max_precipitation,
                    self$traits$optimal_precipitation,
                    self$traits$min_precipitation,
                    self$sim$environment$current$precipitation
                )
        },
        execution_priority = 1
    )

    sim$add_process(
        species = c("species_1", "species_2"),
        process_name = "reproduction",
        process_fun = function() {
            self$traits$abundance <-
                ricker_reproduction_model(
                    self$traits$abundance,
                    self$traits$reproduction_rate * self$traits$climate_suitability,
                    self$traits$carrying_capacity * self$traits$climate_suitability
                )
        },
        execution_priority = 2
    )
    sim$add_process(
        species = c("species_1", "species_2"),
        process_name = "dispersal_process",
        process_fun = function() {
            self$traits[["abundance"]] <- dispersal(
                abundance = self$traits[["abundance"]],
                dispersal_kernel = self$traits[["dispersal_kernel"]]
            )
        },
        execution_priority = 3
    )

The process that simulates competition between the two species will reduce the carrying capacity of one species based on the abundance of the other species. For simplicity, we will assume asymmetric competition, with species 1 being the superior competitor. Therefore, we will only reduce the carrying capacity of species 2 based on the abundance of species 1.

Code

    sim$add_process(
        species = "species_2",
        process_name = "competition",
        process_fun = function() {
            max_capacity <- max(self$traits$carrying_capacity)
            self$traits$carrying_capacity <-
                pmax(max_capacity - self$sim$species_1$traits$abundance, 0)
        },
        execution_priority = 4
    )

Note that this happens after the reproduction process, so the carrying capacity will be reduced for the next time step, not the current one. One could change this by changing the execution priority of the competition process.

Code

    sim$begin()
    plot_cols <- hcl.colors(100, "Purple-Yellow", rev = TRUE)
    plot(sim, "species_1", "abundance", main = "Sp: 1 abundance", col = plot_cols)
    plot(sim, "species_2", "abundance", main = "Sp: 2 abundance", col = plot_cols)

As you can see, species 2 is being pushed out of its preferred habitat, towards areas that are more unsuitable for species 1.

## Trophic interactions

We can also add a process that simulates trophic interactions in the form of predation. Assuming that species 2 is a predator and species 1 is its prey, this means that species 2 will reduce the abundance of species 1, but can only occur in the same areas as species 1. We will again use a similar setup as before, with slightly adjusted values:

Code

    sim <- create_simulation(landscape)
    sim$add_species(name = "species_1")
    sim$add_species(name = "species_2")

    sim$add_traits(
        species = "species_1",
        population_level = TRUE,
        abundance = 10000,
        climate_suitability = 1,
        reproduction_rate = 0.5,
        carrying_capacity = 10000
    )
    sim$add_traits(
        species = "species_2",
        population_level = TRUE,
        abundance = 500,
        climate_suitability = 1,
        reproduction_rate = 0.3,
        carrying_capacity = 1000
    )
    sim$add_traits(
        species = c("species_1", "species_2"),
        population_level = FALSE,
        dispersal_kernel = calculate_dispersal_kernel(
            max_dispersal_dist = 3,
            kfun = negative_exponential_function,
            mean_dispersal_dist = 1
        )
    )
    sim$add_traits(
        species = "species_1",
        population_level = FALSE,
        max_temperature = 300,
        optimal_temperature = 290,
        min_temperature = 270,
        max_precipitation = 1000,
        optimal_precipitation = 800,
        min_precipitation = 0
    )
    sim$add_traits(
        species = "species_2",
        population_level = FALSE,
        max_temperature = 300,
        optimal_temperature = 270,
        min_temperature = 260,
        max_precipitation = 1000,
        optimal_precipitation = 300,
        min_precipitation = 0
    )
    sim$add_process(
        species = c("species_1", "species_2"),
        process_name = "calculate_suitability",
        process_fun = function() {
            self$traits$climate_suitability <-
                calculate_suitability(
                    self$traits$max_temperature,
                    self$traits$optimal_temperature,
                    self$traits$min_temperature,
                    self$sim$environment$current$temperature
                ) *
                calculate_suitability(
                    self$traits$max_precipitation,
                    self$traits$optimal_precipitation,
                    self$traits$min_precipitation,
                    self$sim$environment$current$precipitation
                )
        },
        execution_priority = 1
    )
    sim$add_process(
        species = c("species_1", "species_2"),
        process_name = "reproduction",
        process_fun = function() {
            self$traits$abundance <-
                ricker_reproduction_model(
                    self$traits$abundance,
                    self$traits$reproduction_rate * self$traits$climate_suitability,
                    self$traits$carrying_capacity * self$traits$climate_suitability
                )
        },
        execution_priority = 2
    )
    sim$add_process(
        species = c("species_1", "species_2"),
        process_name = "dispersal_process",
        process_fun = function() {
            self$traits[["abundance"]] <- dispersal(
                abundance = self$traits[["abundance"]],
                dispersal_kernel = self$traits[["dispersal_kernel"]]
            )
        },
        execution_priority = 3
    )

Now we can add a process that simulates predation. Note that the predation effectiveness is dependent on the climate suitability of the predator.

Code

    sim$add_globals(trophic_conversion_factor = 0.5)
    sim$add_process(
        species = "species_2",
        process_name = "predation",
        process_fun = function() {
            self$traits$abundance <-
                self$sim$species_1$traits$abundance *
                self$traits$climate_suitability *
                self$sim$globals$trophic_conversion_factor

            self$sim$species_1$traits$abundance <-
                self$sim$species_1$traits$abundance -
                self$sim$species_1$traits$abundance *
                self$traits$climate_suitability
        },
        execution_priority = 4
    )

Code

    sim$begin()
    plot_cols <- hcl.colors(100, "Purple-Yellow", rev = TRUE)
    plot(sim, "species_1", "abundance", main = "Sp: 1 abundance", col = plot_cols)
    plot(sim, "species_2", "abundance", main = "Sp: 2 abundance", col = plot_cols)

We can see that species 2 occupies the same areas as species 1 despite having a vastly different climatic niche. Reminder:

species_1

Code

    max_temperature = 300
    optimal_temperature = 290
    min_temperature = 270
    max_precipitation = 1000
    optimal_precipitation = 800
    min_precipitation = 0

species_2

Code

    max_temperature = 300
    optimal_temperature = 270
    min_temperature = 260
    max_precipitation = 1000
    optimal_precipitation = 300
    min_precipitation = 0

## Final notes

This tutorial only shows the very basic options of species interactions that are possible with metaRange. One could also have a simulation that includes both competition and predation, or different (i.e. much more complex) forms of these two processes or other processes such as e.g. mutualism.