0 1.0 2.0 Proportion of Peak Time

FIGURE 4.2 Typical results from the PI procedure. The animals are trained by rewarding them for the first lever press after a fixed time from the initiation of the signal (e.g., light or tone). Data are recorded on trials without reward. Peak response time is usually near the point of reward. The results here are normalized to the peak time, to show that the relative shape of the curve is conserved for different durations. (Adapted Roberts, S., J. Exp. Psychol. Anim. Behav. Process., 7, 242-268, 1981.)

FIGURE 4.3 Typical results from the temporal bisection procedure. Animals are trained by rewarding them for pressing the left or right lever following signals of short or long duration (e.g., 2 and 8 sec), respectively. Probe trials are then conducted in which intermediate times are tested for left or right responses. Animals are not rewarded on probe trials. The PSE is the point at which the animal shows equal proportions of long and short responses. (Adapted from Church, R.M. and Deluty, M.Z., J. Exp. Psychol. Anim. Behav. Process., 3, 216-228, 1977.)

Signal Duration (sec)

FIGURE 4.3 Typical results from the temporal bisection procedure. Animals are trained by rewarding them for pressing the left or right lever following signals of short or long duration (e.g., 2 and 8 sec), respectively. Probe trials are then conducted in which intermediate times are tested for left or right responses. Animals are not rewarded on probe trials. The PSE is the point at which the animal shows equal proportions of long and short responses. (Adapted from Church, R.M. and Deluty, M.Z., J. Exp. Psychol. Anim. Behav. Process., 3, 216-228, 1977.)

a linear relationship between the duration of a stimulus, I, and the measure of uncertainty associated with that stimulus, AI. The relationship

AI = kl describes the amount by which a second stimulus must be changed from I in order for the two to be discriminated. It also explains the proportionality between the timed interval and the mean and standard deviations associated with that interval. This relationship breaks down for very short intervals of several seconds (discussed in detail by Cantor, 1981). This relationship also breaks down as timed intervals approach the 24-h phase of the circadian clock (Crystal, 2001).

The results from the PI procedure resemble a Gaussian distribution, as illustrated in Figure 4.2. Longer intervals between the beginning of the signal (e.g., light or sound) and the reward lead to wider distributions (Church et al., 1994; Roberts, 1981). Regardless of the length of the duration, the shape of the curve is conserved, showing that the variance scales with the length of the duration. In the temporal bisection procedure, increasing the time between signals increases the accuracy, and longer duration signals require greater disparity in length in order to achieve the same levels of discrimination (e.g., Bizo and White, 1997; Roberts, 1998).

Weber's law applies in its general form to rats (Church and Gibbon, 1982), pigeons (Cheng and Roberts, 1991), and humans (Wearden, 1991). The ecological consequences of Weber's law are discussed more specifically by Bateson (this volume) and in Section 4.5 of this chapter.

4.2.2 The Clock Can Discriminate Based on Frequency of Reward

Animals can distinguish between the reward reliability of different temporal cues. This insures that animals have the temporal acuity to rate potential rewards based on their frequency. Ecologically, this means that animals can rank foraging sites based on their density of prey.

That rats can associate different cues with different frequencies of reward was shown with the PI procedure. Light was associated with an 80% probability of food, and a tone was associated with a 20% probability of food. Animals responded to the tone at about one quarter of the peak response rate for the light, showing that they can match the memory for two different intervals with the relevant external stimuli (Roberts, 1981). This same behavior has been observed using a different procedure in pigeons (Killeen et al., 1996). In fact, studies of risk-sensitive foraging have established that animals can make the same distinctions in the wild. I will discuss this in more detail in Section 4.5.5.

4.2.3 The Clock Can Be Paused

Pigeons and rats trained in the PI procedure will respond to a 10-sec signal blackout in the middle of a trial by moving their peak response rate back by 10 sec (see Buhusi, this volume; Buhusi and Meck, 2002; Buhusi et al., in press; Hopson, this volume; Roberts, 1981, 1998). This is true for a number of different blackout times, with the interesting caveat that longer blackout times can lead to a slower resetting of the clock (de Vaca et al., 1994).

The pausing of the clock suggests higher-order control in the nervous systems of animals capable of event timing. This kind of control is unlikely to be found in more primitive event timers (see Section 4.4 and the discussion of the decay timer) or in timers like the circadian protein oscillations described in Section 4.3.

4.2.4 Temperature Affects Clock Speed

The first evidence that a temporal sense was not temperature compensated was provided by Hoagland (1935), who made this discovery after subjecting his sick wife to various temporal acuity tests while measuring her temperature. At hotter internal temperatures her counting rate was faster than at lower temperatures. To exclude illness, he did the same for volunteers after short periods in a freezer. His data set exhibits an exquisite linear relationship between the inverse of temperature and the log speed of counting (see Wearden and Penton-Voak, 1995).

In perhaps the only ecological study of direct interval timing and temperature, the parasitoid wasp Trichogramma dendrolimi was demonstrated to lay eggs in its insect host based on the duration of its walk across the host's long axis (Schmidt and Pak, 1991). The hosts are eggs of larger insects, which vary greatly in size. This lends itself to an adaptive measure of host size. Too many or too few eggs laid on the host can lead to either starvation or underutilization of resources, providing a clear evolutionary force for optimal host size assessment. The host-crossing can take between 0.5 and 20 sec, depending on the host size, but for identically sized hosts, the speed is increased at higher ambient temperatures. At higher temperatures the wasp also lays its eggs faster. However, the wasp is able to compensate for this temperature adjustment and lays the same number of eggs in identically sized hosts regardless of the ambient temperature. The wasps may have a reduced estimate of elapsed time at lower ambient temperatures to compensate for their reduced speed (Schmidt and Pak, 1991).

In circadian studies of the courtship song of Drosophila melanogaster, the timing pattern of the behavior is temperature compensated and directly correlated with the duration of the free-running circadian clock (Iwasaki and Thomas, 1997). Under the assumption that the wasp's internal estimate of time is affected, in the same way that Hoagland's wife was, this is our first evidence that circadian clocks are unrelated to event timing. Circadian clocks are temperature compensated, while event timers are not. I pursue this argument further in Section 4.3.

The linearity of temperature effects is limited. Severe heat stress reduces response rates, and very severe heat stress changes the motivational state of the animal (e.g., they try to escape) (Richelle and Lejeune, 1980). The problem is that temperature changes could be affecting other physiological properties with little effect on the clock. An experiment by Rozin (1965) looked at temperature effect in the goldfish Carassius auratus. In FI trials, goldfish at different temperatures showed similar scalloped response curves that were different in absolute, but not relative response rates over the trial interval. This suggests that effects of temperature may be operating downstream of the clock, to modify the absolute rate of behavioral processes.

4.2.5 The Clock Rate Changes with Reinforcement Rate

Increased rates of reinforcement increase the relative temporal rate such that, in the temporal bisection procedure, the PSE is moved toward the long response. This is supported by several studies that show altered PSEs for different between-trial durations (Bizo and White, 1997; Fetterman and Killeen, 1991; Morgan et al., 1993).

The consequences of reinforcement rate on the subjective perception of time are quite significant. To the extent that this phenomenon is real in the wild, it complicates the possibility of optimal foraging in the sense of Charnov's marginal value theorem (Charnov, 1976). In this and many optimal foraging models, the ability of the animal to measure absolute time is directly responsible for its preference for certain food types and times of patch departure. If animals are incapable of measuring absolute time, then the ability to forage optimally should be predictably changed. The consequences of rate-biased time perception have been worked out in detail for the marginal value theorem (Hills and Adler, 2002). One of the conclusions of this work is that because of the costs associated with running the nervous system, animals have probably evolved to tune their arousal (and therefore temporal accuracy) to meet the requirements of specific environments. So they pay the price of rate-biased optimal foraging to avoid the price of inappropriately tuned perceptual timing.

4.2.6 Species Comparisons

Animals show different capacities for learning and different sensory biases (e.g., Bitterman, 1975; Dukas, 1998). The capacity for learning temporal intervals has evolved in vertebrates and is supported in at least one parasitoid wasp. Many vertebrates show scalloped responses (Richelle and Lejeune, 1980). The consensus among fish studies is that some do and some do not (Eskin and Bitterman, 1960; Richelle and Lejeune, 1980; Talton et al., 1999). The African mouthbreeder (Tilapia macrocephala) apparently fails to show a scalloped response, whereas goldfish (Carassius auratus) appear to have no problem with it (Rozin, 1965). Pigeons can show varying responses under a wide range of different reinforcement regimes (Ferster and Skinner, 1957). Surprisingly (see Section 4.5.2), honeybees (Apis mel-lifera) show break-and-run behavior in pseudonaturalistic environments with delays of 20 or 90 sec (Grossman, 1973).

Are insects in general capable of timing short intervals? It is certainly possible that we have not yet asked the question in the appropriate way. It is equally possible that the genesis of certain brain structures coincident with vertebrate evolution mark a significant dichotomy in the evolutionary history of event timing. The evolution of the vertebrate forebrain facilitates the possibility of a homologous structure with the hippocampus in all vertebrates (Colombo et al., 2001; Portavella et al., 2002). The role of the hippocampus in spatial and temporal learning and memory is widely demonstrated (Jackson et al., 1998; Ono et al., 1995; Thompson, et al., 1982). Given their capacities for spatial learning in navigation, the possibility of an analogous structure in insects should not be ruled out (Dyer, 1998). I address this relationship in more detail in Section 4.4.

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