Implications For Theories Of Timing

Taken together, these results indicate that multiple local maxima in sensitivity to time are observed in the discrimination of time across several orders of magnitude (Figure 3.7; Crystal, 1999, 2001a, 2001b). The existence of a local maximum near a circadian oscillator (Figure 3.7, rightmost peak) and in the short-interval range (Figure 3.7, left side) is consistent with timing based on multiple oscillators (Church and Broadbent, 1990; Crystal, 1999, 2001a; Gallistel, 1990). The location of a local maximum may be used to identify an oscillator's period.

The continuity of timing across several orders of magnitude suggests that principles of short-interval timing may be useful in the analysis of circadian timing, as in the application of scalar variability (see Figures 3.2 and 3.4). Moreover, concepts and methodology from circadian research may be applied to interval timing. For example, documenting free-running behavioral rhythms and phase response curves are standard approaches in circadian research that may be applied to interval timing.

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Time/Interval

FIGURE 3.6 Rats anticipate intermeal intervals of 14, 18, and 19 h (filled symbols) with less precision (i.e., higher variability) than 24 h (unfilled symbols). Data from Bolles and Stokes (1965) and Boulos et al. (1980), in which meals were earned by pressing a lever, were obtained by enlarging published figures by 200% and measuring each datum at 0.5-mm resolution. (Adapted from Bolles, R.C. and Stokes, L.W., J. Comp. Physiol. Psychol., 60, 290-294, 1965; Boulos, Z. et al., Behav. Brain Res, 1, 39-65, 1980; and Crystal, J.D., J. Exp. Psychol. Anim. Behav. Process, 27, 68-78, 2001a.)

In addition, the identification of additional local maxima in sensitivity to time may be used to identify additional putative oscillators, such as in the temporal region in Figure 3.7 that has not been explored.

The existence of nonlinearities in the sensitivity to time provides constraints for the development of theories of timing. Four theories will be reviewed: scalar timing theory (Gibbon, 1977, 1991), multiple-oscillator theory of timing (Church and Broadbent, 1990), broadcast theory of timing (Rosenbaum, 1998), and stochastic counting cascades (Killeen, 2002; Killeen and Taylor, 2000).

3.5.1 Scalar Timing Theory

Scalar timing theory proposes that a pacemaker sends pulses to an accumulator; the amount accumulated in a currently elapsing interval is compared with a sample from memory of a previously stored reinforced duration, rendering a decision to respond or not to respond. A central feature of scalar timing theory is the prediction that sensitivity to time is constant across a broad range of intervals. The existence of

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