## Simulation 8 Biological pest control with predator and parasitoid

In simulations 6 and 7 we simulated the effect of a predator and a parasitoid. Now we will combine the two into one model. We will en up with a model where we have three insect populations (pest, predator and parasitoid) developing side by side. You can change parameters for each of them and see how it affects the others.

For simulation the pest population the model uses the following parameters.

N1_{0 }= Population size
at the start of the simulation.

N1_{t }= Population size at time t (after
t days)

b1 = Birth factor

m1 = Mortality factor

r1 = b1-m1 = Reproduction
factor

K1 = Carrying capacity of the environment

For the predator population the model uses these parameters:

N2_{0 }= Population size
at the start of the simulation.

N2_{t }= Population size at time t (after
t days)

b2 = Birth factor

m2 = Mortality factor

r2 = b2-m2 = Reproduction factor

K2 = Carrying capacity of the environment

p2 = Predation factor

And for the parasitoid population the model uses these parameters:

N3_{0 }= Population size
at the start of the simulation.

N3_{t }= Population size at time t (after
t days)

b3 = Birth factor

m3 = Mortality factor

r5 = b2-m2 = Reproduction factor

K3 = Carrying capacity of the environment

p3 = Parasitization factor

For the predator we use formula [9] (see simulation 6):

[9] N2_{t+1} = N2_{t}
+ N2_{t} × r2 × (1 - N2_{t }/ K2)

For the parasitoid we use formula [12] (as in simulation 7):

[12] N3_{t+1} = N3_{t}
+ N3_{t} × r3 × (1 - N3_{t}/(K3 * N1_{t }/K1))

And the pest population is now affected by both the predator and parasitoid as follows;

[14] N1_{t+1} = N1_{t}
+ N1_{t} × r1 × (1 - N1_{t }/ K1)
- N1_{t} × p2 × (N1_{t }/K1)
× (N2_{t }/K2) -
N_{t} × p3 × (N1_{t }/K1) × (N3_{t }/K3)

Now try it with different parameters. You can change the default settings, then run the simulation.

### Simulation 8

This simulation shows maximum 300 days.

The simulation ends when the population size is above 10,000,000
or below 1.

So we have now a pest population which under ideal conditions (and without predators or parasitoids) would stabilize at capacity K1, but with the help of the predator and parasitoid population the pest is kept at a lower level. If this level is still causing damage a farmer may want to spray pesticide.

It's also interesting to see that the parasitoid cannot reach its maximum at K3. Both p2 (the effect of the predator) and p3 (effect of parasitoid) reduce the pest population, which in turn has its effect on the parasitoid.

The predator however is not influenced by the other two insects.

We will now make a model which includes pesticide spraying as we did in simulation 5. But now of course the pesticide will kill not only the pest, but also the natural enemies.

Go to Simulation 9: Biological pest control and chemical control.

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