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Kacelnik, A., & Todd, I. A. (1992). Psychological mechanisms and the Marginal Value Theorem: effect of variability in travel time on patch exploitation. Anim. Behav., 43(2), 313–322.
Abstract: The Marginal Value Theorem (MVT) describes the behaviour that maximizes the ratio of expected gain over expected foraging time in a patchy environment. When travel time is variable, the MVT rationale and its predictions are sensitive only to the mean travel time and not to the spread or skew of the distribution. Two mechanistic arguments contradict these predictions. First, tests of the MVT have previously shown that there is a disproportionate influence of the last travel time, and second, psychological models of information processing suggest that memory for time intervals is strongly dependent on the scatter of the distribution experienced. These mechanistic concepts, combined with Jensen's inequality, suggest that patch exploitation should decrease as the scatter of the travel distribution increases. In a Skinner box experiment with pigeons, Columba livia, the problem was examined by simulating three environments with identical patches and the same mean travel time, but different travel time variability. Patch exploitation decreased with increasing variance in travel time. The results are used to argue in favour of the inclusion of realistic psychological properties as constraints in functional models of behaviour. Although both the MVT and the mechanistic models account for some features of the results, none of them can explain all the findings.
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Todd, I. A., & Kacelnik, A. (1993). Psychological mechanisms and the Marginal Value Theorem: dynamics of scalar memory for travel time. Anim. Behav., 46(4), 765–775.
Abstract: Abstract. The relation between memory for travel time and foraging decisions was studied experimentally. The temporal properties of two environments with patchily distributed food were simulated in the laboratory using pigeons, Columba livia, as subjects. The two environments differed in mean travel time, while the coefficient of variation of travel time and the decelerated function relating cumulative food gain to time in the patch were held constant within and between environments. Each environment contained a uniform mixture of five travel times experienced in a random order. Two of the five travel times were common in both environments. Effects of travel time were studied by comparing prey collected per patch visit (PPV) after various travel times within each environment, and by comparing patch exploitation after equal travel times between environments. Within the environment with long mean travel time (LMT) PPV was positively correlated with the last and the penultimate travel times but not with travel times before that. The increase in PPV per second of last travel time was six times greater than the increase per second of penultimate travel time, implying very steep memory discounting. In the environment with short mean travel time (SMT), there was no correlation between PPV and previous travel times. However, comparisons between environments of visits following travel times common to both environments (thus removing the effect of the last travel time) showed that substantially more prey were taken after equal travel times in the LMT than in the SMT environment. This difference cannot be accounted for by the within-environment effect of penultimate travel time, implying that there is a different, less steeply devalued, effect of the mixture of travel times. A model of information processing based on combining Scalar Expectancy Theory with the predictions of rate maximization under the Marginal Value Theorem is presented. The model can approximate the results obtained in this and previous experiments and provides a framework for further analysis of memory mechanisms of foraging behaviour.
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