Scalar Timing and Response to Risk

There have been several experimental investigations of how foraging animals respond to variability in both delay to reward and amount of reward. For example, Bateson and Kacelnik (1995b) used an operant paradigm to study risk sensitivity in starlings. The starlings' preferences were tested in two treatments, one with variability in amount of reward and one with variability in delay to reward, and the energy budgets of the birds were maintained unchanged throughout the experiment. In the variable-amount treatment, the starlings were initially trained that a flashing red light indicated the availability of a fixed interval of 20 sec that culminated with a reward of 5 units of food, and that a flashing green light signaled the availability of a fixed interval of 20 sec culminating in a reward that was either 3 or 7 units of food with equal probability. In the variable-delay treatment, the fixed option was identical to the variable-amount treatment, but the other color signaled the availability of a variable interval of either 2.5 or 60.5 sec with equal probability, culminating in 5 units of reward. The assignment of colors to options was balanced across birds. The birds initially learned about the two options available in a treatment in forced trials in which only one option was presented. Following this training, the birds' choices were tested in trials in which both options were presented simultaneously, and the bird was required to commit to one of the options by choosing to peck one of the two flashing lights.

Bateson and Kacelnik (1995b) recorded two measures of preference in both treatments: the latency to peck the flashing lights in the training trials, and the option chosen by the birds in the choice trials. The choice data revealed that the birds were indifferent to risk in the variable-amount treatment, but strongly risk prone in the variable-delay treatment. The latency results showed that the birds had a shorter latency to begin a fixed-amount trial in the variable-amount treatment and a shorter latency to begin a variable-delay trial in the variable-delay treatment. Thus the results provide support for the general finding that animals tend to be risk averse to variability in amount, but strongly risk prone to variability in delay (Kacelnik and Bateson, 1996), because the birds preferred the variable-delay option even though the fixed delay of 20 sec was well below the mean delay of 31.5 sec in the variable-delay option.

The above results are not predicted by any purely evolutionary model; however, Reboreda and Kacelnik (1991) proposed that this pattern of preference could be explained by a modification of a version of scalar timing theory first proposed by Gibbon et al. (1988) to explain the preferences for delayed rewards seen in concurrent schedules. Gibbon et al. proposed that when animals are subjected to two alternative options between which they are required to choose, they build up a separate reference memory representation for each option. Thus, in Bateson and Kacelnik's experiment, the starlings in the variable-delay treatment would build up one reference memory for the fixed option and one for the variable option. As explained previously, the memory representation for the fixed interval would be a symmetrical distribution centered on the experienced interval, whereas the memory representation for the variable interval would be an asymmetrical distribution resulting from the sum of a symmetrical low variance distribution with a mean of 2.5 and a symmetrical high variance distribution with a mean of 60.5. The starling is assumed to choose between the two options by taking one random sample from each reference memory distribution, comparing these two samples, and choosing the option that yielded the lower sample (see Figure 5.5). Due to the skew in the representation of the variable delay (see Figure 5.2), this distribution will on average yield smaller samples than the

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