In scalar timing theory the decision subsystem is assumed to receive input from both working and reference memories and to compare these inputs, usually using a ratio rule, to produce a behavioral output. For the purposes of modeling fixed-interval timing performance, at the beginning of each trial the decision subsystem is assumed to receive a single input from reference memory and continuously compare this with the current value of elapsed time, m, in working memory. Importantly, the value of m* used in this comparison process is assumed to be a single random sample from the distribution of m* stored in reference memory. The rule used to compare the values of mt and m* is the discrimination ratio mt - m*

When this ratio becomes greater than or equal to a threshold value, b, a decision is made to start responding. The value of b can also vary between trials, but for fixed-interval schedules it is usually assumed to have a mean value of approximately zero. Variation between trials in either k* or b will induce the commonly observed relationship between the mean and variance of timing data known as the scalar property, whereby the coefficient of variation (i.e., the standard deviation or mean) is constant. Thus, the above scalar timing model is capable of producing the basic features of fixed-interval timing performance. The model is summarized in Figure 5.3.

One of the attractions of the scalar timing model is that the three components — clock, memory, and decision — are clearly modular, and the representation of information in memory is clearly separated from the way in which information is used in decisions. This modularity makes the scalar timing model very flexible and, as a result, particularly tractable for modeling a range of different foraging problems. The details of both the memory and decision components of the scalar timing model are altered depending on the specific task being modeled, as I shall demonstrate in the following section.

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