The evolution of fidelity in sensory systems.

We investigate the effect that noise has on the evolution of measurement strategies and competition in populations of organisms with sensory systems of differing fidelities. We address two questions motivated by experimental and theoretical work on sensory systems in noisy environments: (1) How complex must a sensory system be in order to face the need to develop adaptive measurement strategies that change depending on the noise level? (2) Does the principle of competitive exclusion for sensory systems force one population to win out over all others? We find that the answer to the first question is that even very simple sensory systems will need to change measurement strategies depending on the amount of noise in the environment. Interestingly, the answer to the second question is that, in general, at most two populations with different fidelity sensory systems may co-exist within a single environment.

Analysis of a certain class of replicator equations.

Motivated by a problem in the evolution of sensory systems where gains obtained by improvements in detection are offset by increased costs, we prove several results about the dynamics of replicator equations with an n x n game matrix of the form: A( ij ) = a( i )b( j ) - c( i ). First, we show that, generically, for this class of game matrix, all equilibria must be on the 1-skeleton of the simplex, and that all interior solutions must limit to the boundary. Second, for the particular ordering, a1b2> ... >bn, which is most natural in the study of the evolution of sensory systems, we show that topological restrictions require a unique local attractor in every face of the simplex. We conjecture that the unique local attractor for the full simplex is, in fact, a global attractor, and prove this for n < or = 5. In a separate argument supporting the conjecture, we show that there can be no chain recurrent invariant set entirely contained in the 1-skeleton of the simplex. Finally, we discuss the special, non-generic case and give a local description of the dynamics when there is an interior equilibrium.