The pattern of responding in the peak-interval procedure with gaps: an individual-trials analysis.

Humans and lower animals time as if using an internal clock that can be “stopped” or “reset” on command (reviewed by Buhusi & Meck, 2005). The internal clock concept assumes that pulses emitted by a pacemaker are stored in an accumulator whose content represents the current subjective time (Fraisse, 1957; Francois, 1927; Hoagland, 1933; Treisman, 1963; Woodrow, 1930). A case in point that the internal clock can be used in discrete (stop/reset) modes is given by the response pattern in the peak-interval (PI) procedure with gaps, or PI-GAP procedure (Church, 1978; S. Roberts, 1981) (Figure 1). In the standard version of this procedure, during fixed-interval (FI) trials, the first response after a specified criterion, say 30 s, from the onset of a to-be-timed signal is reinforced (Figure 1A). In PI trials, the to-be-timed signal is presented but subject’s responses are not reinforced; typically, in PI trials the average response rate increases after the onset of the to-be-timed signal, reaches a peak about the time when subjects’ responses were (sometimes) reinforced, and declines afterwards (Catania, 1970; Church, 1978) (Figure 1A). During gap trials, a brief interruption (gap) of the to-be-timed signal prompts a delay in response relative to PI trials by about the duration of the gap, suggesting that on average subjects retain in working memory the pre-gap interval and resume timing after the gap where they left off before the gap, a response mode (alternative) called stop (e.g., Church, 1978; S. Roberts & Church, 1978) (Figure 1A). However, a quite different response pattern is observed in the reversed version of the PI procedure (Buhusi & Meck, 2000), in which subjects time the absence of a signal (e.g., in the dark) and their timing is interrupted by a signaled (e.g., illuminated) gap (Figure 1B): Subjects delay their response function after the gap for a duration that is approximately the sum of the gap and pre-gap intervals, suggesting that on average they restart the entire timing process after the gap, using a reset response (Buhusi & Meck, 2000). Figure 1 The peak-interval (PI) procedure with gaps Because the results presented in Figure 1 were obtained by averaging response rate over many trials, there is the possibility that the stop / reset modes represent averaging artifacts that do not readily reflect the behavior of the subjects in the experimental box. Indeed, while the average response function in PI trials is Gaussian-like (Figure 1), during individual PI trials both pigeons (Cheng & Westwood, 1993) and rats (Church, Meck, & Gibbon, 1994; Gibbon & Church, 1990) use a low-high-low pattern of response (Figure 2B). Similarly, during individual gap trials the pattern of response is relatively complex: Some gap trials follow a low-high-low-high-low pattern, while some lack pre-gap responses altogether, and have a pattern similar to that from PI trials, but delayed. Such complex response patterns challenge current interval timing theories, developed to address data averaged over many trials (e.g., Gibbon, Church, & Meck, 1984). To address the complex behavior in the PI-GAP procedure, two classes of theoretical interpretations have been proposed, attributing response variability to either the internal clock or to the interaction between the internal clock and other cognitive processes: Initial investigations indicated that on average rodents tend to stop (e.g., Church, 1978; S. Roberts & Church, 1978), while birds tend to reset (Bateson & Kacelnik, 1998; Brodbeck, Hampton, & Cheng, 1998; Cabeza de Vaca, Brown, & Hemmes, 1994; W. A. Roberts, Cheng, & Cohen, 1989), suggesting that the stop/reset response alternatives reflect discrete modes of the internal clock (Church, 1978), accounted for by a switch connecting the pacemaker and the accumulator, allowing or not pulse accumulation (Church, 1978; Gibbon et al., 1984). Figure 2 Example of singe-trial statistics distributions and for an individual subject In contrast, recent results indicate that rats reset their timing in PI trials upon presentation of reinforcement (Matell & Meck, 1999; Thorpe, Petrovic, & Wilkie, 2002), that both rats and pigeons stop or reset depending on gap content (Buhusi & Meck, 2000), gap discriminability (Buhusi, Perera, & Meck, 2005), gap/signal contrast (Buhusi & Cerutti, 2005; Buhusi, Sasaki, & Meck, 2002), and subjects’ visual acuity (Buhusi et al., 2005), and that similar delays are obtained when the procedure includes distracter events rather than gaps (Buhusi & Meck, 2006a, 2006b). These departures from the stop/reset modes support the alternative interpretation that the average response after a gap does not reflect discrete modes of the internal clock, but rather that working memory for time is sensitive to Resource Allocation (RA) (Buhusi, 2003), a process external to the clock, actively controlled by the perceived salience of events. This interpretation accounts not only for the discrete stop and reset responses, but also for a continuum of responses in between stop and reset. Here we evaluate whether the pattern of response in individual gap trials is consistent with either discrete modes of the internal clock (Gibbon et al., 1984) or a continuum of alternatives (Buhusi, 2003). To reconcile these views, Cabeza de Vaca et al. (1994) proposed a “stochastic” model, denoted here as the Probability-of-Reset hypothesis (PR), which assumes that during individual gap trials subjects use discrete alternatives (stop / reset) with a certain probability, such that the average response functions in gap trials is a mix of the “stop and “reset” responses, thus falling in between stop and reset, and giving the appearance of a continuous range of alternatives. This distinction is lost when analyzing average response functions, and requires special individual-trial analyses. Evidence for the PR hypothesis was previously sought by Cabeza de Vaca et al. (1994), by estimating the time of response initiation S1 (“start”) and the time of response termination S2 (“stop”) for each individual trial using Gibbon & Church’s (1990) algorithm (Figure 3A). Acknowledging that applying this algorithm to gap trials is problematic because they do not have a consistent start-stop pattern (Figure 2B), Cabeza de Vaca et al. focused on the stop time S2, which is reliably identified by the algorithm irrespective of trial type (PI or gap). Because the PR hypothesis assumes that subjects stochastically use stop and reset alternatives in gap trials, it predicts that the distributions of individual-trial statistics (e.g., S2) should be bi-modal in gap trials and wider in gap trials relative to PI trials (Cabeza de Vaca et al., 1994). However, analyses of pigeon’s responses failed to indicate bi-modality of S2 distribution in gap trials. Nevertheless, the S2 distribution was found to be wider for late gaps than for early gaps, thus providing partial support the PR hypothesis (Cabeza de Vaca et al., 1994). Figure 3 Single-trial analysis of the response pattern in the PI procedure with gaps The mixed results obtained Cabeza de Vaca et al. (1994) may be equally due to the algorithm used (Church et al., 1994; Gibbon & Church, 1990), since gap trials do not follow a consistent start-stop pattern, but also due to the species investigated, since pigeons have a known tendency to reset (W. A. Roberts et al., 1989) and are possibly less prone to stochastic variations in their responses. Therefore, here we extended the Church & Gibbon (1990) algorithm to gap trials with multiple start-stops (Figure 3B), and we applied this new algorithm to the analysis of rat’s response pattern in individual gap trials in the standard and reversed PI-GAP procedure (Buhusi & Meck, 2000) to evaluate the predictions of the PR hypothesis. Finally, we evaluated how well the PR and RA hypotheses fit the observed distributions of start and stop times in individual trials by computing an index of superposition (intra-class correlation, ICC) between observed and hypothetical distributions. By evaluating response variability as predicted by PR – an account relying on discrete modes of the internal clock – and by RA – an account based on the continuum of interactions between the internal clock and other cognitive processes, our study speaks more generally about the complex cognitive processes at work in behavioral tasks involving interval timing.