Concurrent performances: Reinforcement interaction and response independence.

Catania, A. C. (1963). Concurrent performances: Reinforcement interaction and response independence. Journal of the Experimental Analysis of Behavior, 6, 253-263.

When a pigeon's pecks on two keys were reinforced concurrently by two independent variable-interval (VI) schedules, one for each key, the response rate on either key was given by the equation: R1 = Kr1/[(r1 + r2)5/6], where R is response rate, r is reinforcement rate, and the subscripts 1 and 2 indicate keys 1 and 2. When the constant, K, was determined for a given pigeon in one schedule sequence, the equation predicted that pigeon's response rates in a second schedule sequence. The equation derived from two characteristics of the performance: the total response rate on the two keys was proportional to the one-sixth power of the total reinforcement rate provided by the two VI schedules; and, the pigeon matched the relative response rate on a key to the relative reinforcement rate for that key. The equation states that response rate on one key depends in part on reinforcement rate for the other key, but implies that it does not depend on response rate on the other key. This independence of response rates on the two keys was demonstrated by presenting a stimulus to the pigeon whenever one key's schedule programmed reinforcement. This maintained the reinforcement rate for that key, but reduced the response rate almost to zero. The response rate on the other key, nevertheless, continued to vary with reinforcement rates according to the equation.