Polymorphic response patterns under frequency-dependent selection

Abstract

In a discrete-trials procedure, a frequency-dependent schedule shaped left-right choice proportion toward various equilibrium values between 0 and 1. At issue was (1) whether pigeons match when the overall reinforcement probabilities for two responses depend inversely on their recent frequency, and (2) how pigeons meet the schedule constraint in terms of local responding. That is, do they respond quasi-randomly (Bernoulli mode), or do they learn the stable pattern of the schedule (stable-pattern mode)? Molar choice behavior always tracked the equilibrium solution of the schedule, but the molecular response patterns varied substantially. Markov chains applied to the data revealed that responding was generally intermediate between the memoryless Bernoulli mode, and the perfect memory stable-pattern mode. The polymorphism of molecular patterns, despite molar regularities in behavior, suggests that (1) in order to engender the Bernoulli or stable-pattern modes, the reinforcement rule must strongly discourage competing response patterns (e.g., perseveration), and (2) under frequency-dependent schedules, molar matching is apparently not the outcome of momentary maximizing.