We extend the standard mathematical model of selection in a population, with the concept of co-evolving environment and population. This simple extended model shows how ‘survival of the fittest’ can drive the population to ‘extinction’.
In equation-based modelling this appears to be a fixed part of the theory of selection, but with agent-based modelling the picture changes substantially.
The agent based modelling is taken beyond solving this small theoretical problem to showing how competing types can work to increase the carrying capacity (this is a general conclusion and there are caveats).
This website is split into seven parts
- Introduction with some background information from Richard Lewontin
- Recap of selection from Martin Nowak’s book ‘Evolutionary Dynamics’
- Extension of the standard theory of selection to varying population size living on a nutrient income from its environment. Simplification of environment to a response of the different type frequencies. Show how this can lead to extinction in equation based modelling
- Present the simplest agent based model that allows local extinction but makes total extinction highly unlikely. Show a working example of that model on a page that a user can run.
- Present a similar ABM with random fertility and ‘enrichment’ changes to allow the user to gain a deeper understanding.
- Present reasons for population generally becoming larger under the influence of random ‘enrichment’ changes.
- List of assumptions behind the ABM with possible difficulties and future problems.