A yoked-chamber comparison of concurrent and multiple schedules

Pigeons were exposed to alternative pairs of variable-interval schedules correlated with red and green lights on one key (the food key). In one experimental chamber, responses on a white key (the changeover key) changed the color of the food key and initiated a 2-sec changeover delay. Pigeons in a second chamber obtained food by pecking on a colored key whenever the pigeons in the first (concurrent) chamber had obtained food for a peck on that key color. There was no changeover key in the second (multiple) chamber: changeover responses in the first chamber alternated the schedules and colors in both chambers. The pigeons in both chambers emitted the same proportion of responses on each of the variable-interval schedules, and mastered discrimination reversals at the same rate. The pigeons differed only in their absolute response rates, which were greater under the concurrent schedules. In a second experiment, changes in key color occurred automatically, with different proportions of time allocated to the two variable-interval schedules. Matching of relative response frequency to relative reinforcement frequency was affected by the relative amounts of time in each component, by rate of changeovers, and by manipulations of the variable-interval scheduling.     

Unification of models for choice between delayed reinforcers.

Two models for choice between delayed reinforcers, Fantino's delay-reduction theory and Killeen's incentive theory, are reviewed. Incentive theory is amended to incorporate the effects of arousal on alternate types of behavior that might block the reinforcement of the target behavior. This amended version is shown to differ from the delay-reduction theory in a term that is an exponential in incentive theory and a difference in delay-reduction theory. A power series approximation to the exponential generates a model that is formally identical with delay-reduction theory. Correlations between delay-reduction theory and the amended incentive theory show excellent congruence over a range of experimental conditions. Although the assumptions that gave rise to delay-reduction theory and incentive theory remain different and testable, the models deriving from the theories are unlikely to be discriminable by parametric experimental tests. This congruence of the models is recognized by naming the common model the delayed reinforcement model, which is then compared with other models of choice such as Killeen and Fetterman's (1988) behavioral theory of timing, Mazur's (1984) equivalence rule, and Vaughan's (1985) melioration theory.     

A componential analysis of pacemaker-counter timing systems

Why does counting improve the accuracy of temporal judgments? Killeen and Weiss (1987) provided a formal answer to this question, and this article provides tests of their analysis. In Experiments 1 and 2, subjects responded on a telegraph key as they reproduced different intervals. Individual response rates remained constant for different target times, as predicted. The variance of reproductions was recovered from the weighted sum of the first and second moments of the component timing and counting processes. Variance in timing long intervals was mainly due to counting error, as predicted. In Experiments 3-5, unconstrained response rate was measured and subjects responded at (a) their unconstrained rate, (b) faster, or (c) slower. When subjects responded at the preferred rate, the accuracy of time judgment improved. Deviations in rates tended to increase the variability of temporal estimates. Implications for pacemaker-counter models of timing are discussed.     

Stability criteria

Three approaches to the determination of behavioral stability were examined. In the first, a learning curve was fit to acquisition data (from Cumming and Schoenfeld, 1960), and the “experiment” stopped when the data approached sufficiently close to the theoretical asymptote. In the second, the data were analyzed for variability and linear and quadratic trend. In the third, the experiment was stopped when the magnitude of the daily changes in the data fell below a criterion. Accuracy was measured as deviation between the average value of the dependent variable when the experiment was stopped, and the average value over the last 100 sessions. The first approach was most accurate, but at the cost of requiring the most sessions and being the most difficult to apply. Both the second and third approaches provided acceptable criteria with a reasonable cost-accuracy tradeoff. The second approach permits a continuous adjustment of the criteria to accommodate the variability intrinsic in the experimental paradigm. The third, nomothetic, approach also takes into account the decreasing marginal utility of extended training sessions.     

Temporal properties of responding during stimuli that precede response-independent food

Pigeons' keypecks were reinforced with grain on the average of once per minute by schedules that maintained low response rates and by schedules that maintained high response rates. During these schedules, a fixed-duration conditioned stimulus (CS) ranging from 7.5 to 120 sec in duration across conditions terminated with response-independent food. Response rates during the CS were inversely related to CS duration. The rates and the temporal patterns of responding during the shortest CS were similar whether the ongoing schedule maintained high response rates or low response rates. As CS duration increased, the rate and pattern of responding during the CS converged on the rate and pattern of responding maintained by the baseline schedule. These data indicate that changes in responding during stimuli that signal response-independent reinforcement are not homogeneous throughout the CS; that response measures, such as “suppression ratios”, which presume homogeneity may mislead us; and that conditioned suppression and conditioned enhancement may be better talked about in terms of species-specific approach and avoidance than in terms of emotional states.     

Molecular analyses of the principal components of response strength

Killeen and Hall (2001) showed that a common factor called strength underlies the key dependent variables of response probability, latency, and rate, and that overall response rate is a good predictor of strength. In a search for the mechanisms that underlie those correlations, this article shows that (a) the probability of responding on a trial is a two-state Markov process; (b) latency and rate of responding can be described in terms of the probability and period of stochastic machines called clocked Bernoulli modules, and (c) one such machine, the refractory Poisson process, provides a functional relation between the probability of observing a response during any epoch and the rate of responding. This relation is one of proportionality at low rates and curvilinearity at higher rates.     

Satiation, capacity, and within-session responding

Responding may change substantially over the course of a session (McSweeney, Hinson, & Cannon, 1996). The role of satiation in this effect was investigated in three experiments. Experiment 1 showed that the capacity of pigeons to consume milo over a 1-hr period was relatively stable across three different methods of measurement. In Experiment 2, pigeons were divided into two groups that differed in their capacity based on one of those measures. Key pecking was then reinforced under a variable-interval 30-s schedule with hopper durations of 2 or 5 s. According to the satiation hypothesis, subjects with small capacities should satiate faster and therefore show greater decreases in food-reinforced responding than would subjects with larger capacities. The results confirmed this prediction and showed that the magnitudes of within-session decreases were better predicted by the amount an animal consumed relative to its capacity than by absolute amount alone. In Experiment 3, each pigeon was prefed 0, 5, 15, or 25 g of milo prior to each session. Consistent with the satiation hypothesis, increases in prefeeding produced lower overall response rates in the smaller capacity subjects than in the larger capacity subjects at each level of prefeeding. These experiments demonstrate the importance of a new variable in the control of behavior, and provide a recommended technique for its measurement.