A quantitative analysis of the behavior maintained by delayed reinforcers

Random-interval reinforcement was arranged for a sequence of pigeon first-key pecks followed by second-key pecks. First-key pecks, separated from reinforcers by delays that included number of second-key pecks and time, decreased in rate as delays increased. Delay functions, or gradients, were obtained in one experiment with reinforced sequences consisting of M first-key pecks followed by N second-key pecks (M + N = 16), in a second where required first-key pecks were held constant (M = 8), and in a third where minimum delay between most recent first-key pecks and reinforcers varied. In each, gradients were equally well fitted by exponential, hyperbolic and logarithmic functions. Performances were insensitive to reinforcer duration and functions were consistent across varied random-interval values. In one more experiment, time and number delays were independently varied using differential reinforcement of rate of second-key pecks. Delay gradients depended primarily on time rather than on number of second-key pecks. Thus, reinforcers have effects based on earlier responses, not just the ones that produced them, with the contribution of each response weighted by the time separating it from the reinforcer rather than by intervening behavior. Situations where unwanted responses (e.g., errors) often precede reinforced corrects can maintain them unless designed to avoid such effects of delay.