In this exercise, we will investigate successional models with disturbance. In the exercise about coexistence between two populations, we have simulated disturbance by using an extinction rate. Let's start with that model, and assess what happens to coexistence when the disturbance is amplified.
Let's first remember the model we used in the Metapopulation coexistence exercise. We were studying two species, one being the best competitor (which was able to colonize patches already occupied by the other species), and one that was only able to colonize empty patches. The variation in the patch occupancy is given by:
$$ (df_1)/dt = i_1f_1(1-f_1)-p_e f_1 $$ $$ (df_2)/dt = i_2f_2(1-f_1-f_2)-i_1f_1f_2-p_e f_2 $$
Where:
A necessary condition for the persistence of species 2 was:
$$ e/i_{(1)} > i_{(1)}/i_{(2)} $$
To proceed, you must have the R environment with the Ecovirtual package installed and loaded. If you do not have and do not know how to have them, see the Installation page.
To run the simulations we will use the function metaComp from the R package EcoVirtual.
Let's remember the parameters that can be changed:
| option | parameter | effect |
|---|---|---|
| data set | R object | stores the simulation results |
| Maximum time | $$t_(max) $$ | number of model iterations to be run |
| columns | $$n_(col)$$ | number of columns in the habitat |
| rows | $$n_(rows)$$ | number of rows in the habitat |
| Best Competitor | Parameters for the best competitor | |
| initial occupancy | $$fi_1 $$ | proportion of initial patch occupancy by species 1 |
| colonization coef. | $$i_1$$ | colonization coefficient for sp1 |
| Inferior Competitor | Parameters for the inferior competitor | |
| initial occupancy | $$fi_2 $$ | proportion of initial patch occupancy by species 2 |
| colonization coef. | $$i_2$$ | colonization coefficient for sp2 |
| Both Species | Parameters shared by both species | |
| prob. extinction | $$p_e$$ | extinction probability |
| Habitat Destruction | D | proportion of patches not available |
| Show simulation frames | anima=TRUE | should every step be graphically animated? |
Let's simulate an increase in the extinction probability, by keeping the following parameters fixed:
tmax=100; ncol=100; nrow=100; fi1=0.1; fi2=0.1; i1=0.4; i2=0.8; D=0; anima=FALSE
Now use the following extinction probabilities to simulate an increase in disturbance:
- pe = 0.1
- pe = 0.2
- pe = 0.25
- pe = 0.3
- pe = 0.4
- pe = 0.5
