What these collection of EBM’s (equation based models) don’t account for, is the population spread across space. A population will go ‘locally extinct’ before being ‘globally extinct’. Can we use agent-based modelling with its emphasis on local interactions, to see if a population can stay viable even if it does have a ‘rogue’ fittest type?
We outline our first model below, before using the software NetLogo to run an experiment. The assumptions behind the model are listed in Appendix 3.
First NetLogo model
We can choose our models to be in a space of dimensions of 1, 2, or 3. As the number of dimensions increases the model becomes more computationally intensive, so sometimes we restrict ourselves to just 1-dimension.
| ABM operations in order | Operation details |
|---|---|
| 1: Reproduction |  |
| 2: Calculate carrying-capacity locally |  where  |
| 3: Kill excess agents locally | excess agents are selected randomly |
| 4: Move agents a short distance | Turn by a small random angle (if 2 or 3 dimensions) and move forward by 0.2 of a ‘patch’ |
| 5: Repeat | repeat |
We choose three types in the population of replicators or agents. The type coloured red with the highest fertility but that impacts the nutrient income from the environment negatively. The type coloured blue with low fertility but that impacts the nutrient income positively. Finally the type coloured green with the same low fertility and that increases the nutrient income from the environment beyond what the blue type can do.
| Type no. | Type colour |  |  |
|---|---|---|---|
| 1 | Red | 2.0 | -9.0 |
| 2 | Blue | 1.0 | 6.0 |
| 3 | Green | 1.0 | 12.0 |
This model can be run at page (Note: the page is a large download at 5MB).
As hoped for the red agents quickly go extinct. Unexpectedly however, is that upon running the model for longer, the green agents force the blue agents to go extinct leaving just all green. Evidently the green agents are ‘fitter’ in this limited model even though they have the same fertility constant. The extra nutrient income from the environment generated is given equally to all agents existing on a patch whatever their ‘contribution’. For sake of argument we call the green agents fitness advantage ‘enrichment’.
This result holds true whether the space the agents inhabit is 1, 2, or 3 dimensions.