# Simulating pest control

On these pages I will show step by step how to create a computer model to simulate pest control. We will first create a model to simulate the population growth of an insect population (the pest). Then we will make a model to control this pest population. First we will simulate pest control using pesticides (insecticides) to see what it takes to keep the pest under control. Then we introduce biological control in our model, simulating the effect of natural control agents (predators and parasitoids) to find out how they can regulate the size of the pest population.

Finally we will combine everything in a more complex model where pest and natural enemies interact with each other and where a pesticide is used to control the pest. The pesticide will not only kill the pest, but it also kills the natural enemies of the pest. In the end we will have a complex simulation model where you can try out a range of parameters to study how they affect the population development of pests and natural enemies.

I hope you are interested in biology (entomology), mathematics and computer models. Let's start.

## Simulation 1 The development of an insect population

Insect populations can multiply rapidly because female insects lay many eggs, often several hundred eggs per female. Let's see what happens if one female lays 250 eggs. If all eggs survice, and if 50% of the eggs is male and 50% female, this female would produce 125 new females. They would produce 125x250= 31,250 eggs to start the next population, of which 15,625 females grow up to produce 3,906,250 eggs.

Let's try to model this for the number of females in each generation:

F_{0} = Number of females at the start of
the simulation.

F_{1} = Number of females after 1 generation.

F_{g} = Number of females after g generations.

a = Number of eggs per female.

s = Fraction of female eggs (e.g. if 55% female then s =
0.55)

The number of females in each generation can be calculated based on the number of females in the previous generation. Multiply by the number of eggs, and multiply by the sex ratio. In a formula this would be:

[1] F_{g+1} = F_{g}
× a × s

In a simpler form this equation could be written as:

[2] F_{g+1} = F_{g}
× m

m = The multiple that determines the growth rate. It is also called the Malthusian factor, because this model was first developed by Thomas R. Malthus (1766-1834).

Now try it with some different parameters. You can change the default settings, then run the simulation. The results appear in a graph or table.

### Simulation 1

This simulation shows maximum 30 generations.

The simulation ends when the number of females is above 10,000,000
or below 1.

Try different values and you will see that the population grows very quickly, even when the number of eggs per female is low.

This is no surprise because we simulated an insect population in which all eggs survive and develop (via larva and pupa) to adult insects. This is not very realistic and we should find a way to also consider mortality. We should also find a way to simulate the population from day to day instead of just seeing the results per generation.

Go to Simulation 2: A reproduction factor based on birth and mortality.

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