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