run_mutualism: Run model of mutualism with saturating functional response

In gauravsk/ecoevoapps: Simulate Dynamics of Ecology/Evolution Models

Run model of mutualism with saturating functional response

Description

Given a vector of time, initial values, and parameters, this function runs a phenomenological model of direct mutualism between two species as described by Holland (2012). This model features a saturating functional response for interspecific density dependence, which produces a stable equilibrium where both mutualist species can coexist above their respective population carrying capacities.

Usage

run_mutualism(
  time = 0:50,
  init = c(N1 = 20, N2 = 40),
  params = c(r1 = 0.5, r2 = 0.5, a12 = 0.8, a21 = 0.4, b1 = 10, b2 = 10, d1 = 0.02, d2 =
    0.01)
)

Arguments

time	Vector of time units over which to run the model, starting at 0. time can also be supplied as the total length of the simulation.
init	Named vector of initial population sizes. N1: Initial population size of species 1 N2: Initial population size of species 2
params	Named vector of model parameters. r1: Per capita growth rate of species 1 r2: Per capita growth rate of species 1 a12: Effect of species 2 on species 1 a21: Effect of species 1 on species 2 b1: Half-saturation constant for species 1 b2: Half-saturation constant for species 2 d1: Rate of self-limitation for species 1 d2: Rate of self-limitation for species 2

Value

A data frame of population sizes (N1, N2) simulated through time, produced by solving mutualism() with deSolve::ode() given time, init, and params. This data frame has additional attributes recording the model run (model), input parameter values (params) and population carrying capacities calculated from the parameter values (K).

Note

See the following for further context and details regarding this model: Holland, N.J. (2012). Population dynamics of mutualism. Nature Education Knowledge, 3, 2.

See Also

plot_mutualism_time(), plot_mutualism_portrait()

Examples

# Define full time series and run model with default parameter values
run_mutualism(time = 0:10)

# Define length of simulation and run model with default parameter values
run_mutualism(time = 10)

# Run model with custom input values
tmax <- 10
start <- c(N1 = 100, N2 = 50)
pars <- c(r1 = 1, r2 = 1, a12 = 1.2, a21 = 0.8, b1 = 20, b2 = 20, d1 = 0.04, d2 = 0.02)
run_mutualism(time = tmax, init = start, params = pars)

gauravsk/ecoevoapps documentation built on July 9, 2024, 9:37 p.m.