On the joint control of preference by time and reinforcer-ratio variation

Five pigeons were trained in a procedure in which, with a specified probability, food was either available on a fixed-interval schedule on the left key, or on a variable-interval schedule on the right key. In Phase 1, we arranged, with a probability of 0.5, either a left-key fixed-interval schedule or a right-key variable-interval 30s, and varied the value of the fixed-interval schedule from 5s to 50s across 5 conditions. In Phase 2, we arranged either a left-key fixed-interval 20-s schedule or a right-key variable-interval 30-s schedule, and varied the probability of the fixed-interval schedule from 0.05 to 1.0 across 8 conditions. Phase 3 always arranged a fixed-interval schedule on the left key, and its value was varied over the same range as in Phase 1. In Phase 1, overall preference was generally toward the variable-interval schedule, preference following reinforcers was initially toward the variable-interval schedule, and maximum preference for the fixed-interval schedule generally occurred close to the arranged fixed-interval time, becoming relatively constant thereafter. In Phase 2, overall left-key preference followed the probability of the fixed-interval schedule, and maximum fixed-interval choice again occurred close to the fixed-interval time, except when the fixed-interval probability was 0.1 or less. The pattern of choice following reinforcers was similar to that in Phase 1, but the peak fixed-interval choice became more peaked with higher probabilities of the fixed interval. Phase 3 produced typical fixed-interval schedule responding. The results are discussed in terms of reinforcement effects, timing in the context of alternative reinforcers, and generalized matching. These results can be described by a quantitative model in which reinforcer rates obtained at times since the last reinforcer are distributed across time according to a Gaussian distribution with constant coefficient of variation before the fixed-interval schedule time, changing to extended choice controlled by extended reinforcer ratios beyond the fixed-interval time. The same model provides a good description of response rates on single fixed-interval schedules.