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Run the Tilman abiotic resource competition model

run_abiotic_comp_model.Rd

This function runs the abiotic resource model for two species competing for two essential resources. See page 42 onwards of Don Alstad's Populus guide for a thorough overview of the model: https://cbs.umn.edu/sites/cbs.umn.edu/files/public/downloads/PopulusHelp_e.pdf

Usage

run_abiotic_comp_model(
  time = seq(0, 100, 0.1),
  init = c(N1 = 10, N2 = 10, R1 = 20, R2 = 20),
  params = c(S1 = 12, S2 = 12, r1 = 1.6, r2 = 1, k11 = 18, k12 = 4, k21 = 2, k22 = 14, m1
    = 0.2, m2 = 0.2, c11 = 0.25, c12 = 0.08, c21 = 0.1, c22 = 0.2, a1 = 0.5, a2 = 0.5)
)

Arguments

time

vector of time units over which to run model, starting from 0. time can also be supplied as just the total length of the simulation (i.e. tmax)

init

vector of initial population sizes for both species, with names N1 and N2, AND initial resource pool sizes for both resources, with names R1 and R2

params

vector of model parameters (S1, S2, r1, r2, k11, k12, k21, k22, m1, m2, c11, c12, c21, c22, a1, a1)

See also

run_abiotic_comp_rstar() for calculating both species' R* values for both resource, plot_abiotic_comp_time() for plots of the population dynamics over time, and plot_abiotic_comp_portrait() for making portrait plots of Resources 1 and 2 over time (including visualizations of the ZNGIs)

Examples

# Define full time series, and run model in terms of carrying capacities
# and relative competitive effects
run_abiotic_comp_model(time = seq(0,10),
 init = c(N1 = 10, N2 = 10, R1 = 20, R2 = 20),
 params = c(S1 = 12, S2 = 12, r1 = 1.6, r2 = 1,
k11 = 18, k12 = 4, k21 = 2, k22 = 14,
m1 = .2, m2 = .2,c11 = .25, c12 = .08,
c21 = .1, c22 = .2, a1 = .5, a2 = .5))
#>    time       N1       N2        R1        R2
#> 1     0 10.00000 10.00000 20.000000 20.000000
#> 2     1 17.76430 14.23934 14.224707 15.123670
#> 3     2 27.49192 18.97057  9.886624 11.715800
#> 4     3 37.16125 23.81164  6.813571  9.367452
#> 5     4 44.87507 28.47318  4.941276  7.839348
#> 6     5 50.27519 32.85992  3.955379  6.877462
#> 7     6 54.00287 36.99158  3.459031  6.247831
#> 8     7 56.69429 40.89895  3.189335  5.799525
#> 9     8 58.71684 44.59145  3.021692  5.454483
#> 10    9 60.26154 48.06369  2.905057  5.175086
#> 11   10 61.43904 51.30650  2.818546  4.942415