Research on animal metacognition has typically used choice discriminations whose difficulty can be varied. Animals are given some opportunity to escape the discrimination task by emitting a so-called uncertain response. The usual claim is that an animal possesses metacognition if (a) the probability of picking the uncertain response increases with task difficulty, and (b) animals are more accurate on "free-choice" trials -i.e., trials where the uncertain response was available but was not chosen-than on "forced-choice" trials, where the uncertain response is unavailable. We describe a simple behavioral economic model (BEM), based on familiar learning principles, and thus lacking any metacognition construct, which is able to meet both criteria in most of these tasks. We conclude that rather than designing ever more complex experiments to identify "metacognition," a necessarily ill-defined concept, knowledge might better be advanced not by further refining behavioral criteria for the concept, but by the development and testing of theoretical models for the clever behavior that many animals show in these experiments.

We propose a simple behavioral economic model (BEM) describing how reinforcement and interval timing interact. The model assumes a Weber-law-compliant logarithmic representation of time. Associated with each represented time value are the payoffs that have been obtained for each possible response. At a given real time, the response with the highest payoff is emitted. The model accounts for a wide range of data from procedures such as simple bisection, metacognition in animals, economic effects in free-operant psychophysical procedures and paradoxical choice in doublebisection procedures. Although it assumes logarithmic time representation, it can also account for data from the time-left procedure usually cited in support of linear time representation. It encounters some difficulties in complex free-operant choice procedures, such as concurrent mixed fixed-interval schedules as well as some of the data on double bisection, that may involve additional processes. Overall, BEM provides a theoretical framework for understanding how reinforcement and interval timing work together to determine choice between temporally differentiated reinforcers. Keywordsbehavioral economic model; choice; interval timing; reinforcement; Weber's law Choice and interval timing are two important areas of operant behavior that have remained relatively isolated from one another. Following the lead of B. F. Skinner, (Skinner, 1938;Ferster & Skinner, 1957), research on choice has focused on the role of "economic" variables (frequency and magnitude of reinforcement, etc.; see Williams, 1988 for a review) while research on timing was approached early on from a psychophysical point of view (Catania, 1970;Dews, 1970;Gibbon, 1977) which emphasized cognitively oriented questions such as the representation of time and the information-processing mechanisms governing temporal regulation of behavior (see Church, 2004;Staddon & Cerutti, 2003;Jozefowiez & Staddon, 2008, for some recent reviews). Choice researchers have ignored cognitive questions, while at the same time students of timing have underplayed the role of reinforcement. Yet it is clear that a complete theory of operant performance will require an integration of these two fields of research (see also Whitaker, Lowe, & Wearden, 2008 NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptInterval timing, the ability of animals to adapt to temporal relations ranging from seconds to minutes between two events, has been observed in a wide range of species, from fish to humans (Lejeune & Wearden, 1991). In pigeons at least, it has an automatic, almost reflex-like nature (Wynne & Staddon, 1988), suggesting strong selection pressure at an evolutionary level, hence a potentially key role in adaptive behavior. Indeed, according to some recent accounts (Gallistel & Gibbon, 2000;Staddon & Cerutti, 2003;Staddon & Ettinger, 1989;Cerutti & Staddon, 2004b;Grace, Berg, & Kyonka, 2006;Shapiro, Miller, & Kacelnik, 2008), interval timing may play an important role in choice. Moreover, s...

Pigeons were exposed to concurrent schedules for which reinforcement was alternately available at different times for each of two choices. In Experiment 1 (in which reinforcement times progressed arithmetically), overall, but not relative, response rate was timescale invariant. In Experiment 2 (in which reinforcement times progressed geometrically and were more spaced out), there was temporal control at all reinforcement times, but the amplitude of left-right response alternation decreased as time in the trial increased. These results indicate that the temporal regulation of both overall and relative response rates conforms to Weber's law although relative rate is heavily influenced by processes other than timing. It also adds support to the idea that overall and relative response rate reflects the operation of two independent processes.

To contrast the classic version of the Scalar Expectancy Theory (SET) with the Behavioral Economic Model (BEM), we examined the effects of trial frequency on human temporal judgments. Mathematical analysis showed that, in a temporal bisection task, SET predicts that participants should show almost exclusive preference for the response associated with the most frequent duration, whereas BEM predicts that, even though participants will be biased, they will still display temporal control. Participants learned to emit one response (R[S]) after a 1.0-s stimulus and another (R[L]) after a 1.5-s stimulus. Then the effects of varying the frequencies of the 1.0-s and 1.5-s stimuli were assessed. Results were more consistent with BEM than with SET. Overall, this research illustrates how the impact of non-temporal factors on temporal discrimination may help us to contrast associative models such as BEM with cognitive models such as SET. Deciding between these two classes of models has important implications regarding the relations between associative learning and timing.