Concurrent Fixed‐interval Variable‐ratio Schedules and the Matching Relation

Abstract

Five rats responded under concurrent fixed-interval variable-ratio schedules of food reinforcement. Fixed-interval values ranged from 50-seconds to 300-seconds and variable-ratio values ranged from 30 to 360; a five-second changeover delay was in effect throughout the experiment. The relations between reinforcement ratios obtained from the two schedules and the ratios of responses and time spent on the schedules were described by Baum's (1974) generalized matching equation. All subjects undermatched both response and time ratios to reinforcement ratios, and all subjects displayed systematic bias in favor of the variable-ratio schedules. Response ratios undermatched reinforcement ratios less than did time ratios, but response ratios produced greater bias than did time ratios for every subject and for the group as a whole. Local rates of responding were generally higher on the variable-ratio than on the fixed-interval schedules. When responding was maintained by both schedules, a period of no responding on either schedule immediately after fixedinterval reinforcement typically was followed by high-rate responding on the variableratio schedule. At short fixed-interval values, when a changeover to the fixed-interval schedule was made, responding usually continued until fixed-interval reinforcement was obtained; at longer values, a changeover back to the variable-ratio schedule usually occurred when fixed-interval reinforcement was not forthcoming within a few seconds, and responding then alternated between the two schedules every few seconds until fixedinterval reinforcement finally was obtained.

Herrnstein’s equation for the rates of responding during concurrent schedules

“…Second, Ro did not differ systematically for some differences in component schedules. There were no consistent differences in the size of R o between FR and VR or MR components (Rider, 1979), or between FI and VR components (Rider, 1981). Third, R, did not usually vary with the operanda used in the components.…”

“…The two studies that used two different operanda (Davison & Ferguson, 1978;McSweeney, 1978) and the two studies that used different reinforcers in the two components (Hollard & Davison, 1971;Matthews & Temple, 1979) fell into the intermediate or poor category. All studies that used two different simple schedules also fell into the intermediate or poor category (Herrnstein & Heyman, 1979;LaBounty & Reynolds, 1973;Nevin, 1971;Rider, 1979Rider, , 1981Trevett et al, 1972), except Lobb and Davison (1975). The results of Lobb and Davison's study fell into the best category, but were on the borderline.…”

“…It appears in the columns immediately to the right of the columns containing proportion of the variance in Table 1. The large standard deviations that occasionally occurred (Hollard & Davison, 1971;McSweeney, 1978;Nevin, 1971;Rider, 1981;Tustin & Davison, 1979;Wheatley & Engberg, 1978) are an artifact of extremely large point values of k or R o , produced by a rate of reinforcement or a rate of responding equal to zero for one or more schedules.…”

“…Second, k varied with the simple schedule used in the components. The value of k was usually larger for fixed-ratio (FR) than for VR or mixedratio (MR) components (Rider, 1979), for VR than for VI components (Rider, 1981), and for FI than for FR components (LaBounty & Reynolds, 1973).…”

Interreinforcement Time, Work Time, and the Postreinforcement Pause

“…Further, animals frequently alternate between FI and other concurrently available reinforcement schedules (see Catania, 1962;Ferster & Skinner, 1957, pp. 705-717;Nevin, 1971;Rider, 1981), and between FI responding and other measured activity that is not explicitly reinforced (Skinner & Morse, 1957), even after the first postreinforcement FI response. Similarly, lever holding in the present study did not always continue uninterrupted from the time lever holding began until the delivery of reinforcement, especially at long hold requirements.…”