## 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 insect lays 250 eggs.

If all 250 eggs survive, and if 50% of the eggs is male and 50% female, this female would produce 125 new females. They would produce 125 x 250 = 31,250 eggs to start the next population, of which 15,625 females grow up to produce 3,906,250 eggs. This is called exponential growth of a population.

Let’s try to make a model 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 different parameters. You can change the default settings, then run the simulation. The results appear in a graph and table.

## Simulation 1

### Simulation settings

abc

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.

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