## 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 end 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)

r1 = 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)

r2 = 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)

r3 = 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 × (N1_{t }/K1 – N3_{t}/K3)

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) – N1_{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

### Simulation settings

abc

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

It’s 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.

The scripts for these simulations are written in JavaScript. If you have any questions or comments, or if you discover any errors, please contact me.

- Introduction
- Simulation 1 - The development of an insect population
- Simulation 2 - A reproduction factor based on birth and mortality.
- Simulation 3 - Limiting population growth
- Simulation 4 - Simulate use of pesticides
- Simulation 5 - Pesticide applications at a threshold level
- Simulation 6 - Introducing biological pest control: a predator
- Simulation 7 - Introducing biological pest control: a parasitoid
- Simulation 8 - Biological pest control with predator and parasitoid
- Simulation 9 - Biological pest control and chemical control