Evolved Codes Fall Short of Optimal Redundancy as Vocabularies Grow: A Drift Barrier on Keeping Good Codes and a Coordination Barrier on Finding Them

Codes that evolve under noise need redundancy: spare signals read as the intended meaning when a transmission is corrupted. This study asks how much of the best achievable redundancy evolution builds, and why it stops. In a spatial model, a source sends one of K meanings as a 6-bit codeword through a channel whose error rate grows with distance; listeners inherit decoding tables with mutation and survive only where they decode accurately enough. No table is designed. After 500,000 generations, evolved codes closed 98%, 82%, 62%, 33% and 22% of the gap between a code without synonyms and the best possible code for K = 2, 4, 8, 16 and 32. The shortfall was robust to the model’s settings, run length and a four-fold range of mutation rates. Interventions show two distinct limits. Keeping a good code is a drift barrier: the advantage of one synonym fell roughly as 1/K, and a best code placed by hand was eroded unless mutation was low or the population large. Finding a good code is a coordination barrier: with ideal listeners, step-by-step improvement reaches the best code, but evolving listeners cannot follow the source.