Concurrent fixed-interval variable-ratio schedules and the matching relation

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 fixed-interval reinforcement typically was followed by high-rate responding on the variable-ratio 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 fixed-interval reinforcement finally was obtained.     

Effects of signaled and unsignaled shock on schedule-controlled lever pressing and schedule-induced licking: Shock intensity and body weight

Schedule-controlled lever pressing and schedule-induced licking were studied in rats under a multiple fixed-interval fixed-interval schedule of food reinforcement. Following acquisition of stable rates of pressing and licking, a multiple variable-time variable-time schedule of electric-shock delivery was superimposed upon the baseline schedule. In only one component of the multiple schedule, a 5-sec stimulus preceded each shock (signaled shock). In the other component shock was unsignaled. Several shock intensities (Experiment 1) and body weights (Experiment 2) were studied. Lever pressing and licking were affected similarly by experimental manipulations, although with parametric differences. Depending upon shock intensity and body weight, rates of lever pressing and licking were hardly suppressed, suppressed primarily in the unsignaled shock component (differential suppression), or markedly suppressed in both components. Differential suppression during components with signaled and unsignaled shock and conditioned suppression of responding during the preshock stimulus appeared not to be functionally related. Differential suppression depended more on the discriminability of shock-free time, and on shock intensity, body weight, and the type of response than on the “preparatory” behavior preceding shock.     

Preference for mixed versus constant delays of reinforcement: Effect of probability of the short, mixed delay

Preference for mixed versus constant delays of reinforcement was studied with a concurrent-chain procedure. Lever pressing by rats in concurrently available variable-interval 60-second initial links occasionally produced mutually exclusive terminal-link reinforcement delays. A constant delay of reinforcement (either 15 seconds or 30 seconds) composed one terminal link and mixed delays (.2 second and twice the value of the constant delay) were arranged in the other terminal link. The proportion of .2-second delays in the mixed-delay terminal link took on values of 0, .1, .25, .5, .75, .9, and 1.0 over experimental conditions. Based on relative rates of responding in the initial links, preference for the mixed delays was a negatively accelerated function of the proportion of short, mixed delays. Three of five rats preferred the mixed delays to the constant delays when the proportion of short, mixed delays was .1 or higher, and all five rats preferred the mixed delays when the proportion of short, mixed delays was .25 or higher. Neither Squires and Fantino's (1971) delay-reduction model of choice nor a model based on the harmonic mean reinforcement delay provided a close estimate of choice proportions over the range of short-delay proportions studied. The delay-reduction model underestimated choice for the mixed delays at low and intermediate proportions of short delays, and the harmonic-mean-delay model overestimated choice for the mixed delays at intermediate and high proportions of short delays.     

Choice as a function of local versus molar reinforcement contingencies.

Rats were trained on a discrete-trial probability learning task. In Experiment 1, the molar reinforcement probabilities for the two response alternatives were equal, and the local contingencies of reinforcement differentially reinforced a win-stay, lose-shift response pattern. The win-stay portion was learned substantially more easily and appeared from the outset of training, suggesting that its occurrence did not depend upon discrimination of the local contingencies but rather only upon simple strengthening effects of individual reinforcements. Control by both types of local contingencies decreased with increases in the intertrial interval, although some control remained with intertrial intervals as long as 30 s. In Experiment 2, the local contingencies always favored win-shift and lose-shift response patterns but were asymmetrical for the two responses, causing the molar reinforcement rates for the two responses to differ. Some learning of the alternation pattern occurred with short intertrial intervals, although win-stay behavior occurred for some subjects. The local reinforcement contingencies were discriminated poorly with longer intertrial intervals. In the absence of control by the local contingencies, choice proportion was determined by the molar contingencies, as indicated by high exponent values for the generalized matching law with long intertrial intervals, and lower values with short intertrial intervals. The results show that when molar contingencies of reinforcement and local contingencies are in opposition, both may have independent roles. Control by molar contingencies cannot generally be explained by local contingencies.     

Economic substitutability of electrical brain stimulation, food, and water.

Concurrent variable-ratio schedules of electrical brain stimulation, food, and water were paired in various combinations as reinforcement of rats' lever presses. Relative prices of the concurrent reinforcers were varied by changing the ratio of the response requirements on the two levers. Economic substitutability, measured by the sensitivity of response ratio to changes in relative price, was highest with brain stimulation reinforcement of presses on both levers and lowest with food reinforcement of presses on one lever and water reinforcement of presses on the other. Substitutability with brain stimulation reinforcement of presses on one lever and either food or water reinforcement for presses on the other was about as high as with brain stimulation for presses on both levers. Electrical brain stimulation for rats may thus serve as an economic substitute for two reinforcers, neither of which is substitutable for the other.     

Human performance on conjunctive fixed-interval fixed-ratio schedules

Eighteen young adults performed a lever-pulling task for money. Subjects were initially exposed to a fixed-interval 80-second schedule and subsequently to one of three conjunctive schedules in which the added fixed-ratio requirement was set at either 10, 80, or 120 responses. Three fixed-interval response patterns emerged: high constant rate, intermediate rate, or low rate, with most subjects displaying the last. Conjunctive performance was related to the subjects' prior fixed-interval patterns and the conjunctive ratio requirements. Low-rate subjects tended to optimize reinforcement (maximum reinforcers for minimum responses) on conjunctive schedules. Response rate was directly related to ratio requirements. Subjects' performance closely corresponded to their verbal statements of the contingencies.     

Schedule-induced locomotor activity in humans.

In two experiments, humans received tokens either on a fixed-interval schedule for plunger pulling or various response-nondependent fixed-time schedules ranging from 16 to 140 seconds. Locomotor activity such as walking, shifting weight, or pacing was recorded in quarters of the interreinforcement interval to examine the induced characteristics of that behavior in humans. While performance was variable, several characteristics were present that have counterparts in experiments with nonhumans during periodic schedules of food reinforcement: (a) first quarter rates, and sometimes overall rates, of locomotor activity were greater during intervals that terminated in a visual stimulus and token delivery than those without: (b) overall rates of locomotor activity were greater during fixed-time 16-second schedules than during fixed-time 80- or 140-second schedules; (c) rates of locomotor activity decreased during the interreinforcement intervals; (d) locomotor activity was induced by response-dependent and response-nondependent token delivery. These results showed that the rate and temporal pattern of locomotor activity can be schedule-induced in humans.     

Spaced food but not electrical brain stimulation induces polydipsia and air licking.

An attempt was made to induce polydipsia in rats whose lever pressing was reinforced with food pellets or electrical brain stimulation. Nine food-deprived, water-sated rats drank water excessively during sessions in which food pellets were delivered. When brain stimulation was substituted for food, drinking immediately ceased. Delivering brain stimulation according to a variety of schedules, pairing brain stimulation with food reinforcement, and substituting an air stream for water, each failed to produce polydipsic licking. These results show that polydipsia is not induced by all reinforcers.     

Demand for food on fixed-ratio schedules as a function of the quality of concurrently available reinforcement

Six rats lever pressed for food on concurrent fixed-ratio schedules, in a two-compartment chamber. In one compartment, mixed diet pellets were delivered on fixed-ratio schedules of 1, 6, 11, and 16; in the other, either no food was delivered, or sucrose or mixed diet pellets were delivered on fixed-ratio 8. The number of pellets obtained in the first compartment declined as a function of fixed-ratio size in that compartment in all three conditions, but the decline was greatest overall with mixed diet pellets concurrently available in the other compartment, and least with no food concurrently available. The result is discussed in terms of economic demand theory, and is consistent with the prediction that elasticity of demand for a commodity (defined in operant terms as the ratio of the proportionate change in number of reinforcements per session to the proportionate change in fixed-ratio size) is greater the more substitutable for that commodity are any concurrently available commodities.     

Effects of food deprivation and reinforcement magnitude on conditioned suppression

In Experiment I, the responding of rats lever pressing on a variable-interval schedule for sucrose solution was partially suppressed by a variable duration conditioned stimulus followed by shock. When food deprivation was increased, response rates during and before the conditioned stimulus increased monotonically. Varying the concentration of sucrose across blocks of sessions or from session to session in a semi-random sequence had little effect on response rates either before or during the conditioned stimulus. With a fixed sequence of increasing concentrations across a five-session block, increased concentration produced much more rapid increases in response rates before than during the conditioned stimulus. In Experiment II, rats were presented with the same sequence of increasing concentrations across a five-session block. When tested at 80% body weight, response rates increased rapidly as concentration increased, but at 100%, body-weight rates increased only slightly. The effect of a change in body weight in Experiment II thus mimicked the effect of the conditioned stimulus in the latter part of Experiment I. These findings support the view that the effect of a pre-aversive conditioned stimulus is similar to that of a change in food deprivation, but unlike that of a change in reinforcement magnitude.