We introduce the concept of the population and its environment co-evolving within the established mathematical theory of selection in biology. It becomes apparent that competitive phenotypes neither contribute to nor impede population density and, at times, fail to even benefit themselves. It prompts us to contemplate whether organisms, or Life as a whole, can overcome this challenge.
As the title suggests, the research presented here uses agent-based modelling rather than the usual equation-based modelling. This research shows that the resulting picture changes substantially, with more competitive phenotypes increasing the population density (generally speaking – there are caveats).
Details
The research assumes the population is close to the carrying capacity of the environment everywhere. There are two phenotype properties in this simplified model, the first is the common fertility property. The second property affects the local environment to change the amount of nutrient income provided to itself and its neighbours.
An emergent dynamical behaviour arises when a large enough population interacts across a large enough territory, that makes replicators with larger 2nd property values more competitive. In other words, the population density increases in this ABM. Note that this is a general conclusion and that there are caveats.
This 2nd property we could call ‘enrichment’. Larger values of it give larger benefits to surrounding replicators whether they are the same phenotype or not. A phenotype with higher ‘enrichment’ can co-exist alongside a phenotype with higher fertility.
At present the author has not found a way to explain these theoretical phenomena using equation based modelling.
Why is this important?
From a simple Darwinian competition ABM, it can be shown that a population can optimise (approximately) the environment for themselves as well as evolving to suit the environment.
My thanks go to
Nigel Depledge PhD for helping to correct my biology mistakes. Any that remain are entirely my own.
The Santa Fe Institute for their online courses at https://www.complexityexplorer.org/ and course creators Melanie Mitchell and Bill Rand for their inspiring teaching.
Uri Wilensky for the software package NetLogo 6.3.0, an easy to learn tool for studying agent based models:
Wilensky, U. (1999). NetLogo. https://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.