Simulation 9: Combination of biological and chemical control
In simulation 8 we had already developed a rather complex model with three species (a pest, a predator and a parasitoid) interacting with each other. We have seen that the predator and parasitoid manage to keep pest populations at levels below the maximum capacity (K1). Now let’s assume that this level is still too high. A farmer would like to control the pest population to keep it at a lower level. So let’s reintroduce pesticides into our model.
In simulations 4 and 5 we already simulated pest control with a pesticide, but there we didn’t have natural control agents in the model. Now we will have to simulate the effect of the pesticide on the pest and also on its natural enemies. I will skip de "calendar spraying" (which we discussed in simulation 4) and go immediately for the threshold spraying as in simulation 5. The populations of pest and natural enemies grow as in simulation 8.
For the pest population the model we use:
N10 = Population size at the start of the simulation.
N1t = 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 we use:
N20 = Population size at the start of the simulation.
N2t = 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
For the parasitoid population we use these parameters:
N30 = Population size at the start of the simulation.
N3t = 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]
[9] N2t+1 = N2t + N2t × r2 × (1 – N2t / K2)
For the parasitoid we use formula [12]
[12] N3t+1 = N3t + N3t × r3 × (N1t /K1 – N3t/K3)
And for the pest population we use formula [14]
[14] N1t+1 = N1t + N1t × r1 × (1 – N1t / K1) – N1t × p2 × (N1t /K1) × (N2t /K2) – N1t × p3 × (N1t /K1) × (N3t /K3)
The decision to spray is set by a threshold level of the pest. If the pest population exceeds this level a pest control operation is executed. The effect of this spray could be different for pest, predator and parasitoid, so for this we will include three new parameters in the model.
Now try it with different settings. You can change the defaults, then run the simulation.
Simulation 9
Simulation settings
abc
Now you have plenty of parameters to play around with. Trying different settings you will find all kinds of interesting effects. Even if the parasitoid is not killed by the spray, its populations will still fluctuate when the spray kills the pest population.
Efficient predators and parasitoids can keep pest populations very low, and pesticide spray may not be needed. But even if they cannot keep the pest at a sufficient low level, they will delay the moment when spraying becomes necessary.
Ok, that’s it for the moment! Hope you enjoyed it and please send me some feedback.
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