Bayesian methods applied to the generalized matching law.

We demonstrate the usefulness of Bayesian methods in developing, evaluating, and using psychological models in the experimental analysis of behavior. We do this through a case study, involving new experimental data that measure the response count and time allocation behavior in pigeons under concurrent random-ratio random-interval schedules of reinforcement. To analyze these data, we implement a series of behavioral models, based on the generalized matching law, as graphical models, and use computational methods to perform fully Bayesian inference. We demonstrate how Bayesian methods, implemented in this way, make inferences about parameters representing psychological variables, how they test the descriptive adequacy of models as accounts of behavior, and how they compare multiple competing models. We also demonstrate how the Bayesian graphical modeling approach allows for more complicated modeling structures, including hierarchical, common cause, and latent mixture structures, to formalize more complicated behavioral models. As part of the case study, we demonstrate how the statistical properties of Bayesian methods allow them to provide more direct and intuitive tests of theories and hypotheses, and how they support the creative and exploratory development of new theories and models.

Temporal discounting of aversive consequences in rats.

Previous research has extensively evaluated the impact of delay on the value of positive reinforcers, but the study of its impact on the value of aversive consequences is scarce. The present study employed a modification of Evenden and Ryan's procedure (1996, Psychopharmacology, 128(2), 161-170) to obtain data on temporal discounting of an aversive consequence, with rats as experimental subjects. In the first phase of the procedure, rats chose between one-pellet and four-pellet alternatives; when subjects developed preference for the larger-amount alternative, a shock was added to it, resulting in a loss of preference. In the first experimental condition, the delay to shock was progressively increased within each session from zero to 40 s (ascending delays), which resulted in a recovery of the preference for the larger-amount + shock alternative as the delay to shock was increased. In a subsequent condition (descending delays) the delay to shock was progressively decreased within each session, from 40 to 0 s. In both conditions, the preference for the smaller-amount no-shock alternative was well described by a hyperbolic function. The order of presentation of the delays within the session, ascending or descending, did not alter the relationship between preference and delay to shock. The temporal discounting curve obtained in the present study could represent a baseline for analyzing the impact that diverse environmental and pharmacological variables have on the temporal discounting of aversive consequences.

Rats behave optimally in a sunk cost task.

The sunk cost effect has been defined as the tendency to persist in an alternative once an investment of effort, time or money has been made, even if better options are available. The goal of this study was to investigate in rats the relationship between sunk cost and the information about when it is optimal to leave the situation, which was studied by Navarro and Fantino (2005) with pigeons. They developed a procedure in which different fixed-ratio schedules were randomly presented, with the richest one being more likely; subjects could persist in the trial until they obtained the reinforcer, or start a new trial in which the most favorable option would be available with a high probability. The information about the expected number of responses needed to obtain the reinforcer was manipulated through the presence or absence of discriminative stimuli; also, they used different combinations of schedule values and their probabilities of presentation to generate escape-optimal and persistence- optimal conditions. They found optimal behavior in the conditions with presence of discriminative stimuli, but non-optimal behavior when they were absent. Unlike their results, we found optimal behavior in both conditions regardless of the absence of discriminative stimuli; rats seemed to use the number of responses already emitted in the trial as a criterion to escape. In contrast to pigeons, rats behaved optimally and the sunk cost effect was not observed.

Effect of streptozotocin-induced diabetes on performance on a progressive ratio schedule.

RATIONALE: It has been suggested that streptozotocin (STZ)-induced diabetes causes a motivational deficit in rodents. However, some of the evidence adduced in support of this suggestion may be interpreted in terms of a motor impairment rather than a motivational deficit. OBJECTIVE: This experiment examined the effect of STZ-induced diabetes on performance on a progressive ratio schedule. The data were analysed using a new model derived from Killeen's (Behav Brain Sci 17:105-172, 1994) Mathematical Principles of Reinforcement model which enables the effects of interventions on motivation or incentive value to be separated from effects on motor function. METHOD: Animals were trained under a progressive ratio schedule using food-pellet reinforcement. Then they received a single intraperitoneal injection of 50 mg/kg of STZ or the vehicle. Training continued for 30 sessions after treatment. Running and overall response rates in successive ratios were analysed using the new model, and estimates of the model's parameters were compared between groups. RESULTS: The parameter expressing incentive value was reduced in the group treated with STZ, whereas the parameters expressing motor capacity and post-reinforcement pausing were not affected by the treatment. Blood glucose concentration was significantly elevated in the STZ-treated group compared to the vehicle-treated group. CONCLUSIONS: The results are consistent with the suggestion that STZ-induced diabetes is associated with a reduction of the incentive value of food.

Coordinación en ratas: Ajuste a restricciones interdependientes / Coordenação em ratos: Ajuste a restrições interdependentes / Coordination in rats: Adjustment to interdependent restrictions

El estudio del ajuste conductual a entornos donde las interacciones entre los individuos y sus consecuencias son interdependientes ha derivado en procedimientos que limitan la interacción y restringen la operante a la simple simultaneidad de acciones sobre operandos individuales. En este estudio se evaluó una metodología alterna, en la que se expuso a pares de ratas a ir de un lugar a otro. El acceso al alimento fue contingente al trabajo individual o conjunto, en función de las posibilidades de interacción directa, determinadas por la ubicación de los sujetos. Se identificó coordinación únicamente en las diadas expuestas a interacción directa. El protocolo propuesto permite estudiar el ajuste a pagos interdependientes producto de patrones de acción conjunta.

The study of behavioral adjustment to environments in which interactions among individuals and their consequences are interdependent has resulted in procedures that limit interaction and restrict the operant to the simple simultaneity of actions on individuals' operands. This study evaluated an alternative methodology in which pairs of rats were made to go from one place to another. Access to food was contingent upon individual or joint work, depending on the possibilities of direct interaction determined by the location of the subjects. Coordination was identified only in the pairs that had direct interaction. The suggested protocol makes it possible to study the adjustment to interdependent payoffs resulting from joint action patterns.

O estudo do ajuste de conduta a ambientes nos quais as interações entre os indivíduos e suas consequências são interdependentes deriva em procedimentos que limitam a interação e restringem a operante à simples simultaneidade de ações sobre operandos individuais. Neste estudo, avaliou-se uma metodologia alterna, na qual se expôs a pares de ratos a ir de um lugar a outro. O acesso ao alimento foi contingente ao trabalho individual ou conjunto, em função das possibilidades de interação direta, determinadas pela localização dos sujeitos. Identificou-se coordenação unicamente nas díades expostas à interação direta. O protocolo proposto permite estudar o ajuste a pagamentos interdependentes produto de padrões de ação conjunta.

Sensitivity to delay is affected by magnitude of reinforcement in rats.

Previous research has provided discrepant results about how reinforcement delay and magnitude are combined to determine the value of the alternatives in concurrent-chains schedules. In the present experiment, we analyzed a possible interaction between these characteristics of reinforcement, employing a two component concurrent-chains schedule, with rats as experimental subjects. Non-independent VI schedules were presented in the initial links of each component. In the terminal links, the following pairs of delays to reinforcement were presented in 4 conditions: 2-28, 6-24, 24-6, 28-2s (fixed time schedules for a group, fixed interval schedules for the other). Magnitude of reinforcement was maintained constant within components: one pellet for one component, and four pellets for the other. The results indicated that in both groups, the sensitivity to delay - calculated according to the generalized matching law - was higher in the component with the larger reinforcer. This result is in contrast with those reported in the literature of temporal discounting with human participants.

Evaluation of rate-dependency and internal clock effects of D-amphetamine.

The impact of two doses of d-amphetamine on rats' peak-interval performance was evaluated at two different points of training: with minimum training, 20 sessions, and with extended training, 120 sessions. At both points of training, none of the doses changed the location of the peak time; however, both doses caused a significant increase in the standard deviation of the response distribution during peak trials. Both results are incompatible with some previous empirical results, and with timing accounts that assume that dopamine modulates the pacemaker rate, but are compatible with a rate-dependent effect.

Learning to stop or reset the internal clock.

In the present experiments, after training rats in a standard fixed interval (FI) 30s schedule, we induced a change in the strategy employed during gap trials, by presenting during FI with gaps training, 9-s interruptions of the FI discriminative stimulus in 40% of the trials; in one type of interruption, after the discriminative stimulus resumed, the FI was re-started; in the second type of interruption, the FI had to be completed considering the time before the interruption. The effect of these manipulations was tested in a peak-interval with gaps procedure. The main result was that the strategy employed during gap trials depended on the type of interruption experienced during the training phase, both in a comparison between subjects (experiment 1) and within subjects (experiment 2).

Timing behavior in streptozotocin-induced diabetic rats.

There is evidence of deterioration of spatial cognition in streptozotocin (STZ)-induced diabetic rats. Here, we evaluate a possible dissociation in the cognitive deficits due to diabetes by examining another crucial aspect of animal cognition: temporal perception. Timing behavior and temporal memory were evaluated in STZ-induced diabetic rats employing two timing tasks: the peak-interval procedure, with its Gap variant, and the interval bisection task. A spatial memory task, rewarded alternation in the T-maze, was also evaluated to explore spatial cognition. The two timing tasks employed coincide in the finding of a normal timing performance in STZ-induced diabetic rats. The peak-interval procedure provided results that suggest that the timing behavior is equally accurate and precise than in control subjects; in the Gap procedure, an equal change in peak time in both groups indicates that temporal working memory is also intact. In the interval bisection task, we analyzed the acquisition of a temporal discrimination and the sensitivity to changes in the duration of the stimulus; no differences were found in either the acquisition process or the sensitivity index. In contrast, in the rewarded alternation task, STZ-induced diabetic rats exhibited a significant deficit in spatial cognition. The cognitive processes involved in timing behavior and temporal memory are not deteriorated as a consequence of diabetes; the cognitive deficits associated to diabetes thus seem to be restricted to the spatial domain.

DRL performance of spontaneously hypertensive rats: dissociation of timing and inhibition of responses.

In this experiment, we used a differential reinforcement of low rates (DRL) schedule to evaluate the performance of spontaneously hypertensive rats (SHR), Wistar Kyoto (WKY) and Wistar (WIS) rats, with the goal of dissociating the processes of timing and inhibition of responses through the use of two quantitative models: the peak deviation analysis and the temporal regulation model. The subjects were divided in two groups; the first group was exposed to 70 sessions under a DRL 10s schedule. SHR rats showed an apparent temporary deficit in the inhibition of responses process; however, no differences among strains were observed in terms of the timing process. The second group of rats was exposed to 30 sessions in DRL 10s schedule, before receiving three doses (2 mg/kg, 4 mg/kg and 8 mg/kg) of methylphenidate. The results obtained through both models were consistent and indicated that at higher drug doses, the performance of all three strains of rats deteriorated. The impulsivity exhibited by SHR during acquisition supports the idea of these rats as an adequate animal model of ADHD. In contrast, evidence against this relies on the normal temporal processing found and in the worsening effect that methylphenidate produced in the process of inhibition of responses. These mixed results suggest the necessity of exploring timing behavior of other animal models in order to find a reliable animal model of ADHD.

Performance of spontaneously hypertensive rats in a peak-interval procedure with gaps.

The purpose of the present experiment was to evaluate timing behavior in spontaneously hypertensive rats (SHR), and compare it to the performance of Wistar Kyoto (WKY), and Wistar (WI) rats. In the first phase of the experiment, the subjects were exposed to a peak-interval procedure, in which fixed-interval 30s trials were alternated with nonreinforced and extended (peak) trials. After 60 sessions, an approximation to a Gaussian probability density function was fitted to the response rate during peak trials in order to estimate the peak time, the peak rate and the Weber fraction. The results showed no difference among the strains in the peak time and the Weber fraction, but a higher peak rate in SHR. In the second phase of the experiment, a gap procedure was introduced; in 80% of the peak trials the stimuli associated with the fixed interval and peak trials were turned off for 9s. Gap trials produced peak time shifts that were longer than those expected if the clock had stopped during the gap but shorter than those had the clock been reset, and no significant differences between the strains were found. Given the great importance that different theories give to temporal processing in the development of the main symptoms of attention deficit hyperactivity disorder (ADHD), and the existence of time perception deficits in humans with ADHD, the present results question the validity of SHR as an animal model of that disorder, and suggest the necessity of exploring the timing behavior of other animal models of ADHD.

Interval bisection in spontaneously hypertensive rats.

An interval bisection procedure was used to study time discrimination in spontaneously hypertensive rats (SHR), which have been proposed as an animal model for the attention deficit hyperactivity disorder (ADHD); Wistar Kyoto and Wistar rats were used as comparison groups. In this procedure, after subjects learn to make one response (S) following a short duration stimulus, and another (L) following a long duration stimulus, stimuli of intermediate durations are presented, and the percentage of L is calculated for each duration. A logistic function is fitted to these data, and different parameters that describe the time discrimination process are obtained. Four conditions, with different short and long durations (1-4, 2-8, 3-12, 4-16s) were used. The results indicate that time discrimination is not altered in SHR, given that no difference in any of the parameters obtained were significant. Given that temporal processing has been proposed as a fundamental factor in the development of the main symptoms of ADHD, and that deficits in time discrimination have been found in individuals with that disorder, the present results suggest the necessity of exploring time perception in SHR with other procedures and sensory modalities, in order to assess its validity as an animal model of ADHD.

Energy budget versus temporal discounting as determinants of preference in risky choice.

Four pigeons and three ringneck doves responded on an operant simulation of natural foraging. After satisfying a schedule of reinforcement associated with search time, subjects could "accept" or "reject" another schedule of reinforcement associated with handling time. Two schedules of reinforcement were available, a variable interval, and a fixed interval with the same mean value. Food available in the session (a variable related to the energy budget) was manipulated in the different conditions either by increases of the value of the search state schedule of reinforcement, or by increases in the mean value of the handling state schedules. The results indicate that the amount of food available in the session did not affect the preference for variable schedules of reinforcement, as would be predicted by an influential theory of risk sensitive foraging. Instead, the preference for variability depended on the relationship between the time spent in the search and the handling states, as is predicted by a family of models of choice that are based on the temporal proximity to the reinforcer.