Independence of sensitivity to relative reinforcement rate and discriminability in signal detection.

Six pigeons were trained to detect differences between two white stimuli, S1 and S2, differing in duration and arranged probabilistically on the center key of a three-key chamber. Detection performance was measured at two levels of discriminability. At one level, S1 was five seconds and S2 was thirty seconds. At the other level, S1 was twenty seconds and S2 was thirty seconds. The procedure was a standard signal-detection yes-no design in which stimulus-presentation probability was varied from .1 to .9 at both discriminability levels. On completion of the center-key stimulus, a peck on the center key darkened the center-key light and turned on the two red side keys. A left-key response was "correct" on S1 trials, and a right-key response was "correct" on S2 trials. Correct responses produced food reinforcement on a variable-ratio 1.3 schedule. Incorrect responses produced three second blackout. Discriminability was higher for the five-second versus thirty-second conditions than for the twenty-second versus thirty-second conditions, but there were no differences in sensitivity of behavior to reinforcement variation for the two stimulus pairs. Response bias was a function of the relative reinforcement rate for correct choice responses.     

On the discriminability of stimulus duration.

The performance of pigeons trained to detect differences in the duration of stimuli was analysed using a matching model of signal detection. Two white stimuli, S1 and S2, differing in duration, were arranged with equal probability on the center key of a three-key chamber. S1 was systematically varied from 5 seconds to 25 seconds while S2 remained constant at 30 seconds. On completion of the center-key stimulus, a peck on the center key turned on the two red side keys. A left-key response was "correct" when S1 had been in effect on the center key and a right-key response was "correct" on S2 trials. A correct response produced a 3-second magazine light accompanied intermittently by food. Incorrect responses produced 3-second blackouts. Detection performance was measured under two procedures. In the first, the obtained reinforcement ratio was uncontrolled by allowing the number of food reinforcements obtained for correct left- and right-key responses to vary as the stimuli were changed. In the second procedure, the presentation of food reinforcement was controlled by holding the obtained reinforcement ratio constant. Discriminability changed as a function of stimulus differences under both procedures. No such trend was found in response bias.     

Stimulus control and response bias in an analogue prey-detection procedure

The present study compared the performance of 6 pigeons trained to detect luminance differences in two different signal-detection procedures. Exposed to a three-key array, the pigeons were trained to peck the left key when the brighter of two light intensities had been presented on the center key and to peck the right key when the dimmer of two light intensities had been presented on the center key. Procedure A was a standard signal-detection procedure in which left/bright and right/dim responses produced food reinforcement and left/dim and right/bright responses produced periods of timeout. Procedure B was designed to simulate some of the contingencies operating in a prey-detection situation. Left-key responses produced reinforcement following the brighter center-key stimulus and a period of timeout following the dimmer center-key stimulus. Right-key responses always produced a short period of timeout irrespective of the stimulus. Within each procedure, the duration of timeout arranged for false alarms (left/dim responses) was varied between 3 s and 120 s. Measures of accuracy and response bias were compared between the two procedures. The timeout manipulation produced systematic, but relatively small, changes in these measures when right/dim responses (i.e., correct rejections) produced reinforcement (Procedure A). Arranging timeout for right/dim responses in Procedure B produced greater variability in accuracy and response bias than did arranging reinforcement, but this variability was not related to timeout duration. Overall, discrimination accuracy was considerably higher when right/dim responses produced timeout than when they resulted in reinforcement, and accuracy was accompanied by a large bias toward the response associated with reinforcement. These results are consistent with a recently proposed model of signal detection.     

Stimulus discriminability in free-operant and discrete-trial detection procedures.

Six pigeons were trained to discriminate different light intensities in four experimental procedures. Experiment 1 compared stimulus discriminability in a yes-no signal-detection task with discriminability measures obtained from two free-operant procedures. Discriminability estimates were significantly lower in the detection procedure. Experiment 2 showed this lowered discriminability to be a function of the delay between stimulus presentation and the availability of the choice-response keys in the standard detection task. In addition, reinforcement sensitivity was lowest when correct choice responses were intermittently, rather than continuously, reinforced.     

Concurrent schedules: Maximization versus reinforcement of changeover behaviour

Pigeons responded on concurrent variable-interval 180-sec variable-interval 36-sec schedules during Conditions 1 and 3 of Experiment 1. Condition 2 arranged variable-interval 60-sec schedules for both response alternatives. The schedule assigned to the alternative that was associated with the variable-interval 36-sec schedule in Conditions 1 and 3 operated only when the subject responded on that alternative. The proportion of time spent responding on the alternative with the conventional variable-interval 60-sec schedule increased during Condition 2, but exclusive choice of that alternative did not develop. This result is inconsistent with maximization of the overall reinforcement rate and with maximization of the momentary probability of reinforcement (momentary maximizing). Increasing time proportions were also found in Experiment 2, which arranged similar conditions, except that reinforcement was provided on a variable-time basis. The time proportions were close to the momentary maximizing prediction in Experiment 2. The results of both experiments can be explained if it is assumed that time allocation is controlled by delayed reinforcement of changeovers between alternatives.     

Stimulus control in a two-choice discrimination procedure

The relation between performance during discriminative training and subsequently obtained measures of stimulus control was investigated. Pigeons served as experimental subjects. In the discriminative training phase, a single peck on the center key, transilluminated by a bright or dim white light, resulted in the onset of the side keys, one red and one green. If the center key was brightly lighted, a response on the red side key was correct. A response on the green side key was correct if the center key was dimly lighted. Correct responses were reinforced on independently arranged variable-interval schedules. Following discriminative training, tests of stimulus control were administered during which white light of 11 intensities was projected on the center key and responses on the red and green side keys recorded. The proportion of correct responses in the presence of a bright or dim center-key stimulus decreased with decreases in the frequency of reinforcement of correct red or correct green responses, respectively. The slopes of the stimulus control gradients were related to the extent of response bias during training. The greater the bias to respond on the green key, the flatter the gradient showing the proportion of green-key responses to each stimulus and the steeper the corresponding gradient of red-key responses.     

How to teach a pigeon to maximize overall reinforcement rate

In two experiments deviations from matching earned higher overall reinforcement rates than did matching. In Experiment 1 response proportions were calculated over a 360-response moving average, updated with each response. Response proportions that differed from the nominal reinforcement proportions, by a criterion that was gradually increased, were eligible for reinforcement. Response proportions that did not differ from matching were not eligible for reinforcement. When the deviation requirement was relatively small, the contingency proved to be effective. However, there was a limit as to how far response proportions could be pushed from matching. Consequently, when the deviation requirement was large, overall reinforcement rate decreased and pecking was eventually extinguished. In Experiment 2 a discriminative stimulus was added to the procedure. The houselight was correlated with the relationship between response proportions and the nominal (programmed) reinforcement proportions. When the difference between response and reinforcement proportions met the deviation requirement, the light was white and responses were eligible for reinforcement. When the difference between response and reinforcement proportions failed to exceed the deviation requirement, the light was blue and responses were not eligible for reinforcement. With the addition of the light, it proved to be possible to shape deviations from matching without any apparent limit. Thus, in Experiment 2 overall reinforcement rate predicted choice proportions and relative reinforcement rate did not. In contrast, in previous experiments on the relationship between matching and overall reinforcement maximization, relative reinforcement rate was usually the better predictor of responding. The results show that whether overall or relative reinforcement rate better predicts choice proportions may in part be determined by stimulus conditions.     

Independence of stimulus discriminability from absolute rate of reinforcement in a signal-detection procedure.

Three experiments are reported in which two pigeons were trained to detect differences in stimulus duration under varying levels of absolute rate of reinforcement. Two red stimuli, differing in duration, were arranged probabilistically on the center key of a three-key chamber. On completion of the center-key duration, the center keylight was extinguished and the two side keys were illuminated white. Correct responses were left-key pecks following the shorter duration and right-key pecks following the longer duration. In Experiment 1, relative rate of reinforcement for correct responses was held constant and absolute rate of reinforcement was varied in seven conditions from continuous reinforcement to a variable-interval 90-second schedule. In Experiment 2, relative rate of reinforcement was manipulated across three different absolute rates of reinforcement (continuous reinforcement, variable-interval 15-second, and variable-interval 45-second). Stimulus discriminability was unaffected by changes in absolute or relative rates of reinforcement. Experiment 3 showed that discriminability was also unaffected by arranging the same consequences (three-second blackout) for unreinforced correct responses and errors.     

Response bias and the discrimination of stimulus duration

Pigeons discriminated stimulus duration in a psychophysical choice situation. Following presentation of any duration from a set of short duration (11 to 15 sec), responses on a red key were reinforced intermittently. Following presentation of any duration from a set of long durations (16 to 22 sec), responses on a green key were reinforced intermittently. Relative reinforcement rates were manipulated for choice responses across conditions. As relative reinforcement rates were varied, psychometric functions showed shifts in green-key responses at all durations. A signal-detection analysis showed that sensitivity remained roughly constant across conditions while response bias changed as a function of changes in relative reinforcement rate. Relative error rates tended to match relative reinforcement rates.     

Signal detection methods for measurement of utility in animals

Analytic methods of signal detection theory were employed to assess the utility of reinforcers. Four pigeons were trained to detect the presence or absence of a stimulus by pecking one of two side keys in a trial-by-trial choice paradigm. The relative rate of positive reinforcement for correct choices was varied to offset the biasing effects of electric shock for incorrect right side-key choices. The effects of relative rate of reinforcement on bias were similar at all shock intensities even though the subjects' sensitivity changed during the course of the experiment. The relative rate of reinforcement required to produce equal bias was calculated and plotted against shock intensity to generate utility functions. The relative rate of reinforcement necessary to offset the bias induced by shock was an increasing function of shock intensity.     

Interresponse-time sensitivity during discrete-trial and free-operant concurrent variable-interval schedules

Two experiments investigated the sensitivity of pigeons' choice to elapsed time since the last response (i.e., to inter-response time [IRT]) during concurrent variable-interval variable-interval schedules. Experiment 1 used a two-key discrete-trial procedure with variable intertrial intervals. Experiment 2 employed a three-key free-operant procedure. In both experiments choice was found to be a function of the active-schedule IRT, defined as the time since the most recent response. Monte Carlo simulations show how this finding permits the joining of several seemingly incompatible data sets held to both support and contradict a kind of choice strategy, termed momentary maximizing, which attempts to maximize momentary reinforcement probabilities. The studies suggest that only two variables are needed to describe the static molecular structure of concurrent variable-interval choice: active-schedule IRTs and "response states" consisting of the last one or two schedule choices.     

Effects of varying stimulus disparity and the reinforcer ratio in concurrent-schedule and signal-detection procedures.

The present study measured the effects of stimulus and reinforcer variations on pigeons' behavior in two different choice procedures. Two intensities of white light were presented as the stimuli on the main key in a switching-key concurrent schedule and as the sample stimuli in a signal-detection procedure. Under both procedures, the scheduled rate of reinforcement was varied across conditions to produce various ratios of obtained reinforcement. These ratios were obtained for seven pairs of light intensities. In the concurrent schedules, the effects of reinforcer-ratio variations were positively correlated with the physical disparity between the two light intensities. In the signal-detection procedure, changes in the reinforcer ratio produced greater effects on performance when stimulus disparity was very low or very high compared to those found at intermediate levels of stimulus disparity. This discrepancy creates a dilemma for existing behavioral models of signal-detection performance.     

Positive conditioned suppression: Transfer of performance between contingent and noncontingent reinforcement situations

Five homing pigeons were trained on concurrent variable-interval schedules. A fixed-duration stimulus was occasionally presented on one key; and, in various conditions, this stimulus terminated (a) without reinforcement, (b) in noncontingent reinforcement, (c) with reinforcement contingent on a response on the key on which the stimulus was presented, and (d) with reinforcement contingent on a response on the key on which the stimulus was not presented. Initially, a stimulus terminating in noncontingent reinforcement generally produced decreased response rates on both keys during the stimulus. Contingencies, however, reliably produced increased rates during the stimulus on the key on which the contingency was arranged, relative to the rate on the concurrently available key. Contingency conditions were followed by noncontingency conditions in which the separation of rates caused by contingencies was maintained. When rates during the stimulus were compared with response rates on the same keys in the absence of the stimulus, contingency-caused rate increases and decreases were again found, but only the rate decreases were maintained in subsequent noncontingency conditions. Further data suggested that the contingency-caused rate changes were not maintained when the stimulus terminated without reinforcement, and that they were unaffected by a threefold decrease in the reinforcement rate provided by the baseline schedules. The results support the suggestion that performance in the positive conditioned suppression procedure results from concurrent and multiple schedule interactions. They further suggest that the production of either acceleration or suppression is dependent on adventitious and historical contingencies.     

Evaluation of fixed momentary dro schedules under signaled and unsignaled arrangements

Fixed momentary schedules of differential reinforcement of other behavior (FM DRO) generally have been ineffective as treatment for problem behavior. Because most early research on FM DRO included presentation of a signal at the end of the DRO interval, it is unclear whether the limited effects of FM DRO were due to (a) the momentary response requirement of the schedule per se or (b) discrimination of the contingency made more salient by the signal. To separate these two potential influences, we compared the effects of signaled versus unsignaled FM DRO with 4 individuals with developmental disabilities whose problem behavior was maintained by social-positive reinforcement. During signaled FM DRO, the experimenter presented a visual stimulus 3 s prior to the end of the DRO interval and delivered reinforcement contingent on the absence of problem behavior at the second the interval elapsed. Unsignaled DRO was identical except that interval termination was not signaled. Results indicated that signaled FM DRO was effective in decreasing 2 subjects' problem behavior, whereas an unsignaled schedule was required for the remaining 2 subjects. These results suggest that the response requirement per se of FM DRO may not be problematic if it is not easily discriminated.     

Choice between response units: The rate constancy model

In a conjoint schedule, reinforcement is available simultaneously on two or more schedules for the same response. The present experiments provided food for key pecking on both a random-interval and a differential-reinforcement-of-low-rate (DRL) schedule. Experiment 1 involved ordinary DRL schedules; Experiment 2 added an external stimulus to indicate when the required interresponse time had elapsed. In both experiments, the potential reinforcer frequency from each component was varied by means of a second-order fixed-ratio schedule, and the DRL time parameter was changed as well. Response rates were described by a model stating that time allocation to each component matches the relative frequency of reinforcement for that component. When spending time in a given component, the subject is assumed to respond at the rate characteristic of baseline performance. This model appeared preferable to the absolute-rate version of the matching law. The model was shown to be applicable to multiple-response concurrent schedules as well as to conjoint schedules, and it described some of the necessary conditions for response matching, undermatching, and bias. In addition, the pigeons did not optimize reinforcer frequency.     

Behavioral and dimensional contrast in rats.

Rats pressed a nose key for brain stimulation reinforcement presented on a fixed-interval schedule. Stimuli were drawn at random from a continuum of 12 white noise intensities in the range 62-95 decibels, spaced in 3 decibel steps. Experiment 1 varied the number of stimuli and the reinforcement contingencies associated with them. In Condition I (baseline) all stimuli signaled reinforcement; in Conditions II and III stimuli from one half of the continuum signaled reinforcement and those from the other half, extinction. However, in Condition II the 6 stimuli from the middle of the continuum were omitted. Experiment 2 held constant the number of stimuli and varied their spacing. In Condition I, each of 6 sounds signaled reinforcement. In Conditions II and II, three stimuli from one half of the continuum signaled reinforcement and three from the other half, extinction. However, in Condition II the stimuli were near the extremes of the continuum (Stimuli 1, 3, 4, 9, 10, 12). Condition III replaced Stimulus 3 with Stimulus 6 and Stimulus 10 with Stimulus 7. Behavioral contrast was seen in an increase over baseline in response rate to the stimuli associated with the constant schedule component when the variable component was changed to extinction. Dimensional contrast was seen in a further elevation of rate to intermediate positive stimulus values when stimuli were added to the border region between positive and negative values.     

Stimulus and reinforcer relativity in multiple schedules: Local and dimensional effects on sensitivity to reinforcement

Pigeons' responses in two successive components of multiple schedules were reinforced according to variable-interval schedules of reinforcement that varied over five different conditions. Within each session of all conditions, line orientations of 0°, 30°, or 45° in Component 1 alternated with orientations of 45°, 60°, or 90° in Component 2. Response rates were recorded in three successive subintervals of each component. Ratios were taken between the response rate in each Component 1 line orientation and the response rate in each Component 2 orientation. These ratios were found to be power functions of the corresponding ratios of obtained reinforcement rates. Sensitivity of response ratios to changes in reinforcer ratios, given by the value of the exponent of the power function, increased systematically with increasing disparity between the dimensional values of orientation stimuli. In addition, sensitivity decreased systematically over successive subintervals of components, that is, with increasing time since component alternation. Dimensional and local (subinterval) effects interacted in that sensitivity increased with stimulus disparity to a far greater extent in the first subinterval than later in components. The data could be described by a combination of rectangular hyperbolae which attributed the interaction between local and dimensional effects to limits set by local effects on the extent that stimulus differences could affect sensitivity.     

Signal probability, reinforcement and signal detection.

Five pigeons were trained to detect differences in light intensity. Two stimuli, S1 and S2, differing in intensity, were arranged on the center key of a three-key chamber according to set probabilities. A peck on the center key turned on the two side keys. When S1 was presented on the center key, a peck on the left key was "correct" and when S2 was presented, a peck on the right key was "correct." Correct responses produced reinforcement and incorrect responses produced 3-second blackout. Detection performance was measured under three procedures. The first was a standard signal-detection design in which the probability of S1 was varied and the number of reinforcements obtained for correct responses to S1 was allowed to covary. In the second procedure, the probability of S1 was again varied but the distribution of reinforcements between the two choices was kept equal. In the third procedure, probability of S1 was held constant while the distribution of reinforcements was varied between the two choices. Changes in response bias were a function of variations in the relative reinforcement ratio for the choice responses and not a function of variations in the probability of stimulus presentation. Discriminability remained constant across the three procedures.     

Molar versus local reinforcement probability as determinants of stimulus value.

During one component of a multiple schedule, pigeons were trained on a discrete-trial concurrent variable-interval variable-interval schedule in which one alternative had a high scheduled rate of reinforcement and the other a low scheduled rate of reinforcement. When the choice proportion between the alternatives matched their respective relative reinforcement frequencies, the obtained probabilities of reinforcement (reinforcer per peck) were approximately equal. In alternate components of the multiple schedule, a single response alternative was presented with an intermediate scheduled rate of reinforcement. During probe trials, each alternative of the concurrent schedule was paired with the constant alternative. The stimulus correlated with the high reinforcement rate was preferred over that with the intermediate rate, whereas the stimulus correlated with the intermediate rate of reinforcement was preferred over that correlated with the low rate of reinforcement. Preference on probe tests was thus determined by the scheduled rate of reinforcement. Other subjects were presented all three alternatives individually, but with a distribution of trial frequency and reinforcement probability similar to that produced by the choice patterns of the original subjects. Here, preferences on probe tests were determined by the obtained probabilities of reinforcement. Comparison of the two sets of results indicates that the availability of a choice alternative, even when not responded to, affects the preference for that alternative. The results imply that models of choice that invoke only obtained probability of reinforcement as the controlling variable (e.g., melioration) are inadequate.     

Matching, maximizing, and hill-climbing

In simple situations, animals consistently choose the better of two alternatives. On concurrent variable-interval variable-interval and variable-interval variable-ratio schedules, they approximately match aggregate choice and reinforcement ratios. The matching law attempts to explain the latter result but does not address the former. Hill-climbing rules such as momentary maximizing can account for both. We show that momentary maximizing constrains molar choice to approximate matching; that molar choice covaries with pigeons' momentary-maximizing estimate; and that the “generalized matching law” follows from almost any hill-climbing rule.