Probabilistic numerical discrimination in mice

Previous studies showed that both human and non-human animals can discriminate between different quantities (i.e., time intervals, numerosities) with a limited level of precision due to their endogenous/representational uncertainty. In addition, other studies have shown that subjects can modulate their temporal categorization responses adaptively by incorporating information gathered regarding probabilistic contingencies into their time-based decisions. Despite the psychophysical similarities between the interval timing and nonverbal counting functions, the sensitivity of count-based decisions to probabilistic information remains an unanswered question. In the current study, we investigated whether exogenous probabilistic information can be integrated into numerosity-based judgments by mice. In the task employed in this study, reward was presented either after few (i.e., 10) or many (i.e., 20) lever presses, the last of which had to be emitted on the lever associated with the corresponding trial type. In order to investigate the effect of probabilistic information on performance in this task, we manipulated the relative frequency of different trial types across different experimental conditions. We evaluated the behavioral performance of the animals under models that differed in terms of their assumptions regarding the cost of responding (e.g., logarithmically increasing vs. no response cost). Our results showed for the first time that mice could adaptively modulate their count-based decisions based on the experienced probabilistic contingencies in directions predicted by optimality.     

Decision processes in temporal discrimination

The processing dynamics underlying temporal decisions and the response times they generate have received little attention in the study of interval timing. In contrast, models of other simple forms of decision making have been extensively investigated using response times, leading to a substantial disconnect between temporal and non-temporal decision theories. An overarching decision-theoretic framework that encompasses existing, non-temporal decision models may, however, account both for interval timing itself and for time-based decision-making. We sought evidence for this framework in the temporal discrimination performance of humans tested on the temporal bisection task. In this task, participants retrospectively categorized experienced stimulus durations as short or long based on their perceived similarity to two, remembered reference durations and were rewarded only for correct categorization of these references. Our analysis of choice proportions and response times suggests that a two-stage, sequential diffusion process, parameterized to maximize earned rewards, can account for salient patterns of bisection performance. The first diffusion stage times intervals by accumulating an endogenously noisy clock signal; the second stage makes decisions about the first-stage temporal representation by accumulating first-stage evidence corrupted by endogenous noise. Reward-maximization requires that the second-stage accumulation rate and starting point be based on the state of the first-stage timer at the end of the stimulus duration, and that estimates of non-decision-related delays should decrease as a function of stimulus duration. Results are in accord with these predictions and thus support an extension of the drift–diffusion model of static decision making to the domain of interval timing and temporal decisions.     

Mice optimize timed decisions about probabilistic outcomes under deadlines

Optimal performance in temporal decisions requires the integration of timing uncertainty with environmental statistics such as probability or cost functions. Reward maximization under response deadlines constitutes one of the most stringent examples of these problems. The current study investigated whether and how mice can optimize their timing behavior in a complex experimental setting under a response deadline in which reward maximization required the integration of timing uncertainty with a geometrically increasing probability/decreasing cost function. Mice optimized their performance under seconds-long response deadlines when the underlying function was reward probability but approached this level of performance when the underlying function was reward cost, only under the assumption of logarithmically scaled subjective costs. The same subjects were then tested in a timed response inhibition task characterized by response rules that conflicted with the initial task, not responding earlier than a schedule as opposed to not missing the deadline. Irrespective of original test groups, mice optimized the timing of their inhibitory control in the second experiment. These results provide strong support for the ubiquity of optimal temporal risk assessment in mice.     

Mice and rats fail to integrate exogenous timing noise into their time-based decisions

Endogenous timing uncertainty results in variability in time-based judgments. In many timing tasks, animals need to incorporate their level of endogenous timing uncertainty into their decisions in order to maximize the reward rate. Although animals have been shown to adopt such optimal behavioral strategies in time-based decisions, whether they can optimize their behavior under exogenous noise is an open question. In this study, we tested mice and rats in a task that required them to space their responses for a minimum duration (DRL task) in different task conditions. In one condition, the minimum wait time was fixed, whereas in other conditions minimum wait time was a Gaussian random variable. Although reward maximization entailed waiting longer with added exogenous timing variability, results indicated that both mice and rats became more impulsive and deviated from optimality with increasing levels of exogenous noise. We introduce a reward-rate-dependent sampling function to SET to account for optimal performance in noiseless and suboptimal performance in noisy environments.     

IS MATCHING INNATE?

Experimentally naive mice matched the proportions of their temporal investments (visit durations) in two feeding hoppers to the proportions of the food income (pellets per unit session time) derived from them in three experiments that varied the coupling between the behavioral investment and food income, from no coupling to strict coupling. Matching was observed from the outset; it did not improve with training. When the numbers of pellets received were proportional to time invested, investment was unstable, swinging abruptly from sustained, almost complete investment in one hopper, to sustained, almost complete investment in the other-in the absence of appropriate local fluctuations in returns (pellets obtained per time invested). The abruptness of the swings strongly constrains possible models. We suggest that matching reflects an innate (unconditioned) program that matches the ratio of expected visit durations to the ratio between the current estimates of expected incomes. A model that processes the income stream looking for changes in the income and generates discontinuous income estimates when a change is detected is shown to account for salient features of the data.     

Cross-domain transfer of quantitative discriminations: Is it all a matter of proportion?

Meck and Church (1983) estimated a 5:1 scale factor relating the mental magnitudes representing number to the mental magnitudes representing duration. We repeated their experiment with human subjects. We obtained transfer regardless of the objective scaling between the ranges; a 5:1 scaling for number versus duration (measured in seconds) was not necessary. We obtained transfer even when the proportions between the endpoints of the number range were different. We conclude that, at least in human subjects, transfer from a discrimination based on continuous quantity (duration) to a discrimination based on discrete quantity (number) is mediated by the cross-domain comparability of withindomain proportions. The results of our second and third experiments also suggest that the subjects compare a probe with a criterion determined by the range of stimuli tested rather than by trial-specific referents, in accordance with the pseudologistic model of Killeen, Fetterman, and Bizo (1997).     

Individual differences in long-range time representation

On the basis of experimental data, long-range time representation has been proposed to follow a highly compressed power function, which has been hypothesized to explain the time inconsistency found in financial discount rate preferences. The aim of this study was to evaluate how well linear and power function models explain empirical data from individual participants tested in different procedural settings. The line paradigm was used in five different procedural variations with 35 adult participants. Data aggregated over the participants showed that fitted linear functions explained more than 98% of the variance in all procedures. A linear regression fit also outperformed a power model fit for the aggregated data. An individual-participant-based analysis showed better fits of a linear model to the data of 14 participants; better fits of a power function with an exponent β?>?1 to the data of 12 participants; and better fits of a power function with β?<?1 to the data of the remaining nine participants. Of the 35 volunteers, the null hypothesis β?=?1 was rejected for 20. The dispersion of the individual β values was approximated well by a normal distribution. These results suggest that, on average, humans perceive long-range time intervals not in a highly compressed, biased manner, but rather in a linear pattern. However, individuals differ considerably in their subjective time scales. This contribution sheds new light on the average and individual psychophysical functions of long-range time representation, and suggests that any attribution of deviation from exponential discount rates in intertemporal choice to the compressed nature of subjective time must entail the characterization of subjective time on an individual-participant basis.