Limits On The Information Acquired By An Evolving Population

The fitness landscape analogy, originally conceived in evolutionary genetics, has been a useful abstraction across several disciplines for modeling the evolution of populations of information parcels, or replicators. In this study, we use mutual information as a metric to ask a fundamental question: what does the time-varying population distribution tell us about the underlying landscape? We consider two scenarios: the mutual information between the landscape and a loss/stasis/growth step (the $\Delta-$channel), and that between the landscape and variant population at some time step $T$ (the $\mathcal{P}-$channel). Using a simple but extensible landscape model, we find that the information conveyed by these channels is dependent on the population distribution in that essentially no information is conveyed when the population is near extreme dominance by any one genotype. We also show how different the landscape possibilities must be so that various population measurements are good indicators of the underlying landscape. We close with reflections on the utility of information theoretic approaches in the study of evolving systems.