Neutral stability, drift, and the diversification of languages

Dynamics in atomic signaling games

We study an atomic signaling game under stochastic evolutionary dynamics. There are a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with high probability or mutate with low probability. We analyze the long-run distribution of states and show that, for sufficiently small mutation probability, its support is limited to efficient communication systems. We find that this behavior is insensitive to the particular choice of evolutionary dynamic, a property that is due to the game having a potential structure with a potential function corresponding to average fitness. Consequently, the model supports conclusions similar to those found in the literature on language competition. That is, we show that efficient languages eventually predominate the society while reproducing the empirical phenomenon of linguistic drift. The emergence of efficiency in the atomic case can be contrasted with results for non-atomic signaling games that establish the non-negligible possibility of convergence, under replicator dynamics, to states of unbounded efficiency loss.

Evolution of communication protocols using an artificial regulatory network

I describe the Utrecht Machine (UM), a discrete artificial regulatory network designed for studying how evolution discovers biochemical computation mechanisms. The corresponding binary genome format is compatible with gene deletion, duplication, and recombination. In the simulation presented here, an agent consisting of two UMs, a sender and a receiver, must encode, transmit, and decode a binary word over time using the narrow communication channel between them. This communication problem has chicken-and-egg structure in that a sending mechanism is useless without a corresponding receiving mechanism. An in-depth case study reveals that a coincidence creates a minimal partial solution, from which a sequence of partial sending and receiving mechanisms evolve. Gene duplications contribute by enlarging the regulatory network. Analysis of 60,000 sample runs under a variety of parameter settings confirms that crossover accelerates evolution, that stronger selection tends to find clumsier solutions and finds them more slowly, and that there is implicit selection for robust mechanisms and genomes at the codon level. Typical solutions associate each input bit with an activation speed and combine them almost additively. The parents of breakthrough organisms sometimes have lower fitness scores than others in the population, indicating that populations can cross valleys in the fitness landscape via outlying members. The simulation exhibits back mutations and population-level memory effects not accounted for in traditional population genetics models. All together, these phenomena suggest that new evolutionary models are needed that incorporate regulatory network structure.