Animal Timing

Abstract

The importance of animal timing in the historical development of modern accounts of time perception cannot be overestimated, even if interest in animal timing per se has been declining for two decades or more. In this chapter, I attempt to trace some of the most interesting and influential research initially carried out in non-human animals, and to look at some ingenious and provocative theoretical models of animal performance on timing tasks, in particular competitors to SET. Animal learning, of which much of the work on animal timing is an offshoot, at one time occupied a central place in academic psychology, but now may be taught in only a cursory manner, if at all, in the undergraduate curriculum of many psychology departments, at least in the UK. This means that contemporary readers may be much less familiar with methods used and ideas derived from Pavlovian and operant conditioning. I cannot provide anything close to an in-depth course in animal learning in a volume on time perception, so a book like Domjan (1993, or later editions) should be consulted for background. I will, however, try to provide the reader with sufficient detail to enable an understanding of the results of the studies I describe. For simplicity of exposition, I have given myself licence to simplify, or even slightly misrepresent, the often complex techniques used in experiments with animals. In particular, some procedures require lengthy pre-training, with gradual approximations to the final method used. I will generally omit any mention of this pre-training, but I will sometimes present simplified versions of the techniques used.

Appendix: Correlations Between Performance Measures from the Peak Procedure

The aim of the arguments advanced in Gibbon and Church (1990) and Church et al. (1994) was to determine the contribution of different sources of variance to performance on individual peak procedure trials. In SET, there can be trial-to-trial variance in both memory/timing and the threshold for starting and stopping responding, as discussed in Chap. 3 and earlier in this chapter. A simplified outline of how these might contribute to performance is given here, but for full mathematical exposition, the reader should consult the articles mentioned immediately above.

In any attempt to assess the contribution of different variance sources, the data of interest are the correlations between the different performance measures (mainly start, stop, and spread). Gibbon and Church (1990) and Church et al. (1994; see their Table 2, p. 146) characterize the correlation pattern as follows, in which the values given are the means from Church et al.’s own study. Start and stop values are positively correlated (mean value 0.31), whereas start and spread (the length of the response period) are negatively correlated (mean −0.33).

Equation (9.1), the usual SET rule for judging the similarity of two time values, determines the start time and the stop time. Suppose that S is the standard FI value of the peak procedure task. The start of responding (ST) occurs when

$$ \left(S\hbox{--} ST\right)/S < b $$

Or, rearranging, ST = S − Sb

And the stop (SP) occurs when

$$ \left(SP\hbox{--} S\right)/S > b,\mathrm{or}SP = S + Sb $$

where b is the threshold.

We consider first the case where there is only trial-by-trial variability in S, and b remains constant. Suppose that the FI value in the peak procedure is 60 s, and the threshold is 0.25. Thus, ST = 45 s, SP = 75 s, and the spread is 75 − 45 = 30 s. The case just discussed assumes that the FI value is represented correctly, but SET proposes the existence of memory/timing variance, so on another trial, the value sampled from the memory might be “short,” 50 s. Now, SP = 48.5 s, ST = 62.5 s, and the spread is 24 s. On another trial, a “long” 70-s value might be sampled, so ST = 53.5 s, SP = 87.5 s, and the spread is 34 s. From these three examples, we can see that “early” starts lead to “early” stops, and “late” starts lead to “late” stops, so ST and SP are positively correlated. However, ST and the spread are also positively correlated: a “late” start gives rise to a longer response period than an “early” start. In data, ST and SP are positively correlated, but ST and the spread are negatively correlated. This shows that an account with memory/timing variance alone cannot produce the full pattern of correlations obtained.

Now, consider the effect of trial-by-trial variability only in the threshold, b, with S constant at 60 s on each trial. If b = 0.25, we have the case above with ST = 45 s, SP = 75 s, and spread = 30 s. If the threshold is more conservative (b = 0.2), then ST is 48 s, SP is 72 s, and the spread is 24 s. This is intuitively reasonable: if the decision to start and stop responding is more conservative, the response period should start later and finish earlier. In contrast, if b = 0.3, then ST = 42 s, SP = 78 s, and the spread is 36 s. Thus, when the threshold alone is varied, early starts lead to late stops, and late starts to early stops, so ST and SP are negatively correlated. However, the examples also show that early starts lead to longer response periods (spreads) than later starts: in other words, start and spread are negatively correlated. By itself, this model does not fit overall correlation patterns, as ST and SP are positively correlated in data.

The obvious suggestion that can be derived from the outline above is that an account with both memory/timing variance and threshold variance is needed to model the pattern of correlations in data, and this is exactly what Gibbon and Church (1990) and Church et al. (1994) propose. An additional issue is the number of samples of both memory and threshold used in a single trial. For example, the animal might sample the reference memory once and the threshold once, so the same threshold is used for start and stop decisions. Alternatively, the reference memory might be sampled twice (once for the start decision and once for the stop decision), and likewise, the threshold might be sampled twice for the same decisions. The arguments are too complex to illustrate here, but the articles cited above suggest that a single memory sample per trial is used, with either one threshold or different thresholds for start and stop.