A comparison of responding maintained under second-order schedules of intramuscular cocaine injection or food presentation in squirrel monkeys.

Key pressing by squirrel monkeys was maintained under second-order schedules of either intramuscular cocaine injection or food presentation. Under one schedule, each completion of a 10-response fixed-ratio unit produced a brief visual stimulus; the first fixed-ratio unit completed after 30 minutes elapsed produced the stimulus paired with either cocaine injection or food presentation. Generally, short pauses followed by high rates of responding were maintained within the fixed-ratio units, and responding was positively accelerated over the 30-minute interval. Under another schedule, each completion of a 3-minute fixed-interval unit produced the brief stimulus; completion of the 10th fixed-interval unit produced the stimulus paired with either cocaine injection or food presentation. Generally, short pauses followed by high rates of responding were maintained within the fixed-ratio units, and responding was positively accelerated over the 30-minute interval. Under another schedule, each completion of a 3-minute fixed-interval unit produced the brief stimulus; completion of the 10th fixed-interval unit produced the stimulus paired with either cocaine injection or food presentation. Rates of responding increased within the fixed-interval units, and to a greater extent over the entire 10 fixed-interval units. Patterns of responding depended more on the schedule of reinforcement than on whether cocaine or food maintained responding. Omitting the brief stimuli following all but the last fixed-ratio or fixed-interval units decreased average rates and altered the patterns of responding. Substituting a visual stimulus that was never paired with cocaine or food following all but the last fixed-ratio or fixed-interval units decreased response rates to a lesser extent and did not substantially alter patterns of responding. When the duration of the paired stimulus was varied from .3 to 30.0 seconds, the highest response rates occurred at intermediate durations (1.0 to 10.0 seconds). The manner in which the stimulus changes affected performances depended more on the schedule of reinforcement than on whether cocaine injection or food presentation maintained responding.     

Concurrent schedule assessment of food preference in cows

Six dairy cows (Bos taurus) were trained on several pairs of concurrent variable-interval schedules with different types of food available on each alternative. The required response was a plate press made by the animal's muzzle. Performance generally replicated that found with other species. The generalized matching law accounted for the preference data, showing that food preference could be quantitatively analyzed as a special case of response bias. The preference functions showed that the response- and time-allocation ratios were not as extreme as obtained reinforcement rate ratios (undermatching).     

Reinforcement magnitude and the inhibiting effect of reinforcement

In a two-key concurrent variable-interval schedule (using pigeons), if the reinforcement frequency for one response is held constant while that for the other is increased, the rate of response on the constant key decreases. The immediate reinforcement for key pecking can usually be conceptualized as the change from a condition in which the key light is on and the food hopper light is off to one in which the key light is off and the hopper light is on. The prechange condition is associated with a delay to food of one-half the average interreinforcement interval in effect during this condition. The postchange condition is associated with a delay to food of about .5 seconds. The programming of additional reinforcement results in a decrease in the delay to food associated with the prechange stimulus condition, and thus a decrease in the value of the improvement that results from the change. This would appear to be analogous to a decrease in the amount of reinforcement, and thus sufficient explanation for the decrease in the rate of the response.     

Concurrent schedules: undermatching and control by previous experimental conditions.

Five pigeons were trained on concurrent variable-interval schedules. A series of conditions in which the ratio of reinforcement rates on two keys was progressively increased and then decreased was arranged twice. The birds were then exposed to an irregular sequence of conditions. Each condition in which reinforcement was available on both keys lasted six sessions. Performance in the first, third, and sixth sessions after a condition change was analyzed. Following a condition change, preference was biased toward the preference in the last condition, but this effect largely disappeared before the sixth session of training. The birds' preferences also appeared less sensitive to reinforcement rates in early sessions after a transition. Preference in a session was a function of both the reinforcements in that session and the reinforcements obtained in as many as four or five previous sessions. The effects of reinforcements in previous sessions could be summarized by the performance in the immediately preceding session, giving a relatively simple relation between present performance and a combination of present reinforcement and prior session performance. While such hysteresis could cause undermatching when only a small number of sessions are arranged in a condition, undermatching in a stable-state performance probably arises elsewhere.     

Elimination of reinforced behavior: intermittent schedules of not-responding

Pigeons' key pecking resulted in food according to either a variable-ratio or a variable-interval schedule. At the same time, food was available for not pecking for a specified time. The required time of not-pecking was segmented into not-responding units, and these units were followed by food according to a fixed-ratio schedule. Both unit duration and the number required were varied. In general, the shorter the time unit or the smaller the ratio, the lower was response rate. When total required not-responding time was constant, but changes in unit duration and the number required altered how the total was achieved, shorter units produced lower rates. Other conditions involved substitution of food delivered independent of responding for the not-responding schedule. With low and moderate total times to food presentation, the not-responding schedule produced lower rates; with the longest times, the response-independent schedule generated less responding. When considered in terms of relative frequency of food presentation available from a source other than pecking, the not-responding schedule reduced rate more effectively than did the response-independent schedule. Comparisons with other research suggested that food presented dependent on not responding compared favorably with punishment as a procedure for reducing response rate. Transient effects differed. Although punishment temporarily depresses rate when first imposed and temporarily enhances it when first removed, food given for not responding quickly generated steady-state rates.     

Concurrent schedules: a quantitative relation between changeover behavior and its consequences

Data from several published experiments on concurrent variable-interval schedules were analyzed with respect to the effects of changeover delay on the time spent responding on a schedule before changing to an alternate schedule: i.e., the interchangeover time. Interchangeover time increases as the duration of the changeover delay increases, and the present analysis shows that a power function describes the relation. The power relation applied in spite of numerous differences in the experiments: different variable-interval schedules for the concurrent pairs; equal or unequal reinforcement rates for the schedules of the concurrent pairs; different durations of the changeover delay; response-dependent or response-independent reinforcers; pigeons or rats as subjects; different reinforcers. A power function also described the data in experiments where the changeover incurred a timeout, where a fixed ratio was required to changeover, and also when asymmetrical changeover delays were used.     

Fixed-interval responding under second-order schedules of food presentation or cocaine injection.

Squirrel monkeys operated a key under second-order schedules in which every tenth completion of a 5-minute fixed interval resulted in either presentation of food or intravenous injection of cocaine. When a 2-second light was presented at the completion of the component fixed-interval schedules, positively accelerated responding developed and was maintained in each component. Over a tenfold range of doses of cocaine(30 to 300 microgram/kg/injection) and amounts of food (0.75 to 7.5 g/presentation); the second-order schedule of cocaine injection maintained higher average rates of responding than the second-order schedule of food presentation. Substituting saline for cocaine or eliminating food presentation decreased average rates of responding. When no stimulus change occurred at the completion of the first nine component fixed-interval schedules, but the 2-second light and food presentation or cocaine injection still occurred after the tenth component, only low and relatively constant rates of responding were maintained in each component. Patterns of responding characteristic of 5-minute fixed-interval schedules were maintained by the 2-second light paired with either cocaine injection or food presentation, though the maximum frequency of cocaine injection or food presentation was less than once per 50 minutes.     

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.     

Duration and rate of reinforcement as determinants of concurrent responding

The duration and frequency of food presentation were varied in concurrent variable-interval variable-interval schedules of reinforcement. In the first experiment, in which pigeons were exposed to a succession of eight different schedules, neither relative duration nor relative frequency of reinforcement had as great an effect on response distribution as they have when they are manipulated separately. These results supported those previously reported by Todorov (1973) and Schneider (1973). In a second experiment, each of seven pigeons was exposed to only one concurrent schedule in which the frequency and/or duration of reinforcement differed on the two keys. Under these conditions, each pigeon's relative rate of response closely matched the relative total access to food that each schedule provided. This result suggests that previous failures to obtain matching may be due to factors such as an insufficient length of exposure to each schedule or to the pigeons' repeated exposure to different concurrent schedules.     

On Herrnstein's equation and related forms

In 1970, Herrnstein proposed a simple equation to describe the relation between response and reinforcement rates on interval schedules. Its empirical basis is firm, but its theoretical foundation is still uncertain. Two approaches to the derivation of Herrnstein's equation are discussed. It can be derived as the equilibrium solution to a process model equivalent to familiar linear-operator learning models. Modifications of this approach yield competing power-function formulations. The equation can also be derived from the assumption that response strength is proportional to reinforcement rate, given that there is a ceiling on response rate. The proportional relation can, in turn, be derived from a threshold assumption equivalent to Shimp's “momentary maximizing”. This derivation implies that the two parameters of Herrnstein's equation should be correlated, and may explain its special utility in application to internal schedules.