  Single species population models and discrete stochastic gene frequency
models are two standards of mathematical biology important for the evolution of
populations. An agent based model is presented which reproduces these models
and then explores where these models agree and disagree under relaxed
specifications. For the population models, the requirement of homogeneous
mixing prevents prediction of extinctions due to local resource depletion.
These models also suggest equilibrium based on attainment of constant
population levels though underlying population characteristics may be nowhere
close to equilibrium. The discrete stochastic gene frequency models assume well
mixed populations at constant levels. The models' predictions for non-constant
populations in strongly oscillating and chaotic regimes are surprisingly good,
only diverging from the ABM at the most chaotic levels.
