# Run the Lotka-Volterra competition model

`run_lvcomp_model.Rd`

Given a vector of time, intiial values, and parameters, this function runs the Lotka-Volterra competition model. Note that the competition parameters can either be given as the relative effects of one species on the other (in terms of alpha (a) and beta (b)), or in terms of the absolute intraspecific and interspecific competition coefficients (a11, a12, a22, a21).

## 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

- params
vector of model parameters Note that carrying capacity for both species can be defined in

`params`

either as`K1`

and`K2`

, or in the inverse, as`a11`

and`a22`

. If carrying capacities are defined as`K1`

and`K2`

, interspecific competition should be defined as`a`

and`b`

; otherwise,`a12`

and`a21`

.

## See also

`plot_lvcomp_time()`

for making a plot of population dynamics over
time, and `plot_lvcomp_portrait()`

for making a phase portrait of the both
species (including the ZNGIs) the ZNGIs)

## Examples

```
# Define full time series, and run model in terms of carrying capacities
# and relative competitive effects
run_lvcomp_model(time = 0:5, init = c(N1 = 1, N2 = 5),
params = c(r1 = .15, r2 = .2, K1 = 1000, K2 = 800, a = 0.9, b = 1.05))
#> time N1 N2
#> 1 0 1.000000 5.000000
#> 2 1 1.160779 6.096851
#> 3 2 1.347153 7.431729
#> 4 3 1.563093 9.055053
#> 5 4 1.813144 11.027352
#> 6 5 2.102494 13.420985
# Run model in terms of absolute competition coefficients
# (i.e. a11, a12, a21, a22)
run_lvcomp_model(time = 0:5, init = c(N1 = 1, N2 = 5),
params = c(r1 = .15, r2 = .2, a11 = .001, a22 = 0.00125, a12 = .0005, a21 = .0007))
#> time N1 N2
#> 1 0 1.000000 5.000000
#> 2 1 1.161165 6.097656
#> 3 2 1.348145 7.433846
#> 4 3 1.565015 9.059236
#> 5 4 1.816463 11.034704
#> 6 5 2.107880 13.433107
# Give only the final time step rather than full time series
run_lvcomp_model(time = 0:5, init = c(N1 = 1, N2 = 5),
params = c(r1 = .15, r2 = .2, K1 = 1000, K2 = 800, a = 0.9, b = 1.05))
#> time N1 N2
#> 1 0 1.000000 5.000000
#> 2 1 1.160779 6.096851
#> 3 2 1.347153 7.431729
#> 4 3 1.563093 9.055053
#> 5 4 1.813144 11.027352
#> 6 5 2.102494 13.420985
run_lvcomp_model(time = 0:5, init = c(N1 = 1, N2 = 5),
params = c(r1 = .15, r2 = .2, a11 = .001, a22 = 0.00125, a12 = .0005, a21 = .0007))
#> time N1 N2
#> 1 0 1.000000 5.000000
#> 2 1 1.161165 6.097656
#> 3 2 1.348145 7.433846
#> 4 3 1.565015 9.059236
#> 5 4 1.816463 11.034704
#> 6 5 2.107880 13.433107
```