## Decision

Choose FI

### Choose VI

FIGURE 5.5 Diagrammatic representation of the scalar timing model applied to a choice scenario. In this case, the model is applied to the choice between a fixed interval and a variable interval (composed of two different intervals), as is found in many risk-sensitive foraging experiments.

Choose FI

### Choose VI

FIGURE 5.5 Diagrammatic representation of the scalar timing model applied to a choice scenario. In this case, the model is applied to the choice between a fixed interval and a variable interval (composed of two different intervals), as is found in many risk-sensitive foraging experiments.

symmetrical distribution representing the fixed option. This model can therefore explain why animals might be risk prone to variance in delay to reward. Reboreda and Kacelnik's (1991) innovation was to realize that the same argument could explain risk aversion to variance in amount. They suggested that if the birds form memory representations similar to those amounts assumed for delays, then the variable-amount option will be represented by an asymmetrical distribution formed from the sum of a symmetrical low variance distribution with a mean of 3 and a symmetrical higher variance distribution with a mean of 7. This is not an unreasonable assumption because in most experiments manipulating the amount of reward, the size of a reward is positively correlated with the time taken to consume it; thus consumption time could be used as a mechanism for measuring amount. A random sample drawn from the asymmetric distribution representing the variable-amount option will, as for the variable-delay option, on average be smaller than a random sample drawn from a symmetrical distribution with a mean of 5. However, in the case of amounts, the bird prefers the option yielding the larger sample, because although short delays to food are preferable to long delays, large amounts of food are preferable to small amounts.

One of the attractive features of the scalar timing theory account of choice is that the model not only makes predictions about the direction of preference, but also makes quantitative predictions about the exact magnitude of preference. Bate-son and Kacelnik (1995b) proved that if a fixed-delay option is compared with a variable-delay option in which the delay is either short or long with equal probability, scalar timing theory predicts that the two options will become subjectively equivalent when the delay in the fixed option is equal to the geometric mean (i.e., Vshort delay x long delay) of the two delays in the variable option. Bateson and Kacelnik (1996) tested this prediction in a subsequent starling experiment. They used a titration procedure to find the fixed delay equal to the variable mixture of 2.5- and 60.5-sec delays used in their previous experiment, and showed that indifference occurred when the fixed delay was equal to 5.61 sec, which is significantly below the geometric mean of 2.5 and 60.6 that equals 12.30 sec. Therefore, although scalar timing theory predicts the qualitative features of choice for variable delays, in this instance it failed to predict the quantitative detail of the results.

In the case of risk-sensitive foraging, the main outcome of considering the mechanistic account provided by scalar timing theory is that behavioral phenomena previously interpreted by behavioral ecologists as adaptive (e.g., Caraco et al., 1990) potentially now emerge as nonadaptive artifacts of the mechanisms by which animals maximize their rate of energy intake.

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