Inelastic supply: An economic approach to simple interval schedules

Economic theory predicts an inverse relationship between the quantity of a commodity supplied to the marketplace and the equilibrium market price of that commodity. This prediction was tested in three experiments. Pigeons responded on simple variable-interval schedules, and quantity of reinforcement supplied was varied in a different way in each experiment. In Experiment 1, quantity supplied was varied by manipulating reinforcement rate while keeping session length constant. In Experiment 2, quantity supplied was varied by manipulating reinforcement rate while keeping reinforcers per session constant. In Experiment 3, quantity supplied was varied by manipulating reinforcer magnitude while keeping number of reinforcers constant. As predicted by economic theory, the obtained behavioral cost (responses per reinforcer) increased as supply decreased. The results could not be explained by simple artifacts such as satiation and time available to respond. In addition, the function relating response rate to reinforcement rate was bitonic in 7 of 9 animals in Experiments 1 and 2, which supports economic and regulatory theories over more traditional reinforcement theories.     

The autoshaping procedure as a residual block clock

In the first experiment, 4 pigeons were each presented with a recurring sequence of four key colors followed by the delivery of grain (block clock). Once the rate of pecking had stabilized, three of the colors were replaced, during different series of sessions, by a darkening of the key. The rate of pecking was reduced within those segments of the interval between deliveries of food during which the key was dark; when the key was dark during the final portion of the interval, rates were reduced throughout the entire interval. In the second experiment, 3 new pigeons were exposed to a different sequence of colors, and the final stimulus was replaced in successive conditions by a novel color, a darkened key, and a restoration of the original color. The data indicated that darkening the key had a more severe, more extensive, and more persistent effect than did a mere change in color. These results suggest that it may be fruitful to conceptualize the autoshaping procedure as a special version of the block clock in which pecking is suppressed throughout the greater part of the interval by darkening the key. In the final condition, the same stimulus appeared in each of the last three portions of the interval. The rate of pecking was lower during the last two portions than when distinctive colors were presented, with the peak rate now appearing in the fifth of seven equal temporal components.     

Fixed-ratio pausing: Joint effects of past reinforcer magnitude and stimuli correlated with upcoming magnitude

Pigeons responded on fixed-ratio schedules ending in small or large reinforcers (grain presentations of different duration) interspersed within each session. In mixed-schedule conditions, the response key was lit with a single color throughout the session, and pausing was directly related to the past reinforcer (longer pauses after large reinforcers than after small ones). In multiple-schedule conditions, different colors accompanied the ratios ending in small and large reinforcers, and pausing was affected by the upcoming reinforcer as well as the past one. Pauses were shorter before large reinforcers than before small ones, but they continued to be longer after large reinforcers than after small ones. The influence of the past reinforcer was modulated by the magnitude of the upcoming reinforcer; in the presence of the stimulus before the small reinforcer, the effect of the past reinforcer was enhanced relative to its effect in the stimulus before the large reinforcer. These results show that pausing between ratios is jointly determined by two competing factors: past conditions of reinforcement and stimuli correlated with upcoming conditions.     

Discriminability between alternatives in a switching-key concurrent schedule

Six pigeons were trained to discriminate between two intensities of white light in a symbolic matching-to-sample procedure. These stimuli were then used to signal which schedule was available on the main key in a switching-key concurrent schedule. The concurrent schedules led to a symbolic matching-to-sample phase in which the subject identified the concurrent schedule to which it last responded before a reinforcer could be obtained. The concurrent schedules were varied across conditions. Discriminability, measured during the symbolic matching-to-sample performance, was high throughout and did not differ across the two procedures. Performance in the concurrent schedules was like that typically obtained using these schedules. Delays were then arranged between completion of the concurrent schedules and presentations of the symbolic matching-to-sample phase. A series of conditions with an intervening delay of 10 s showed that both concurrent-schedule performance and symbolic matching-to-sample performance were affected by the delay in a similar way; that is, choice responding was closer to indifference.     

Time-place learning by pigeons, Columba livia

In each of two experiments, 2 pigeons received discrimination training in which food reinforcement for key pecking was conditional upon both spatial and temporal cues. In Experiment 1, food was available for periods of 30 s at each of three locations (pecking keys) during trials that lasted 90 s. In Experiment 2, food was available for periods of 15 min at each of four locations (pecking keys) during a 60-min trial. In both experiments, pigeons' key pecking was jointly controlled by the spatial and temporal cues. These data, and other recent experiments, suggest that animals learn relationships between temporal and spatial cues that predict stable patterns of food availability.     

A quantitative analysis of chain-schedule performance

Six pigeons were trained with a chain variable-interval variable-interval schedule on the left key and with reinforcers available on the right key on a single variable-interval schedule arranged concurrently with both links of the chain. All three schedules were separately and systematically varied over a wide range of mean intervals. During these manipulations, the obtained reinforcer rates on constant arranged schedules also frequently changed systematically. Increasing reinforcer rates in Link 2 of the chain increased response rates in both links and decreased response rates in the variable-interval schedule concurrently available with Link 2. Increasing Link-1 reinforcer rates increased Link-1 response rates and decreased Link-2 response rates. Increasing reinforcer rates on the right-key schedule decreased response rates in Link 1 of the chain but did not affect the rate in Link 2. The results extend and amplify previous analyses of chain-schedule performance and help define the effects that a quantitative model must describe. However, the complexity of the results, and the fact that constant arranged reinforcer schedules did not necessarily lead to constant obtained reinforcer rates, precluded a quantitative analysis.     

Effects of relative reinforcer frequency on complex color detection

Pigeons were trained under a discrete-trials detection procedure in which one of a set of color stimuli was presented on the center key and a single response turned off the stimulus and illuminated two side keys. Single responses to one or the other side key produced occasional reinforcers depending on the value of the color stimulus. In Experiment 1, one color-stimulus set comprised 559, 564, 569, and 574 nm, and right-key pecks were occasionally reinforced following presentations of members of this set. The other stimulus set comprised 579, 584, 589, and 594 nm, and left-key pecks were occasionally reinforced following presentations of members of this set. Across seven experimental conditions, the left/(left + right) relative reinforcer frequency was varied from .1 to .9. In Experiment 2, one stimulus set contained only one member, 574 nm, and right-key responses were occasionally reinforced following its presentation. Over 12 experimental conditions, two manipulations were carried out. First, the number of stimuli comprising the other stimulus set was increased from one (579 nm) to two (579 and 584 nm) to three (579, 584, and 589 nm) and to four (579, 584, 589, and 594 nm), and left-key responses were reinforced occasionally following center-key presentations of members of this set. Second, for each stimulus combination, the left/(left + right) relative reinforcer frequency was varied from .1 to .5 to .9 across three experimental conditions. The principal finding of Experiments 1 and 2 was that reinforcers and stimuli interacted in their effects on behavior. In Experiment 3, pairs of adjacent stimuli (5 nm apart) in the range 559 to 594 nm were presented in each experimental condition, and the left/(left + right) relative reinforcer frequency was held constant at .5. The data from all three experiments were analyzed according to a detection model describing performance in multiple-stimulus two-response procedures. This model provided independent measures of stimulus discriminability, contingency discriminability, and bias. The analysis showed that (a) consistent with the color-naming function, pigeons were better able to discriminate between higher nanometer values than lower nanometer values; (b) their ability to discriminate between the stimuli was independent of the number of wavelengths comprising each stimulus set; (c) they allocated delivered reinforcers very accurately to the previously emitted response; and (d) no consistent biases emerged.     

Timing multimodal events in pigeons

The peak procedure was used in two experiments to study pigeons' ability to time multimodal events. In the first experiment, birds were trained to time a single event consisting of a 9-s tone or light followed by a 21-s fixed interval associated with a signal of light or tone (signal of the other modality). On occasional empty trials, different lengths of the first signal were followed by a long period of the second signal. Peak response times as a function of the duration of the first signal were linear and had a slope of close to one in all birds. This indicates that the birds were timing only the second signal. In a second experiment, two complex events were used in training. One consisted of a 9-s tone or light followed by a 21-s fixed interval associated with a light or tone. The other consisted of a 21-s tone or light followed by a 9-s fixed interval associated with a light or tone. Different durations of the first signal were again used on empty trials. Peak response times as a function of the duration of the first signal were again linear in all birds. The slope of the function was less than one but greater than zero for 3 birds. This indicates that these birds were partly timing the entire complex event of 30-s duration and partly timing only the second signal of the event. A model is proposed in which the bird takes as a criterion for timing a weighted average of different target criteria. Comparisons with the performance of rats are made.     

Probability and delay of reinforcement as factors in discrete-trial choice.

Pigeons chose between two alternatives that differed in the probability of reinforcement and the delay to reinforcement. A peck on the red key always produced a delay of 5 s and then a possible reinforcer. The probability of reinforcement for responding on this key varied from .05 to 1.0 in different conditions. A response on the green key produced a delay of adjustable duration and then a possible reinforcer, with the probability of reinforcement ranging from .25 to 1.0 in different conditions. The green-key delay was increased or decreased many times per session, depending on a subject's previous choices. The purpose of these adjustments was to estimate an indifference point, or a delay that resulted in a subject's choosing each alternative about equally often. In conditions where the probability of reinforcement was five times higher on the green key, the green-key delay averaged about 12 s at the indifference point. In conditions where the probability of reinforcement was twice as high on the green key, the green-key delay at the indifference point was about 8 s with high probabilities and about 6 s with low probabilities. An analysis based on these results and those from studies on delay of reinforcement suggests that pigeons' choices are relatively insensitive to variations in the probability of reinforcement between .2 and 1.0, but quite sensitive to variations in probability between .2 and 0.