Anita. Behav., 1992, 43, 313-322 Psychological mechanisms and the Marginal Value Theorem: effect of variability in travel time on patch exploitation ALEJANDRO KACELNIK* & IAN A. TODD* King's College and Department of Experimental Psychology, University of Cambridge, Cambridge, U.K. (Received 11 January 1991;initial acceptance21 February 1991; final acceptance 19 June 1991; MS. number: 3707) 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, psychologi- cal 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. The marginal value theorem (MVT; Charnov 1976) describes the behaviour that maximizes the long-term rate of return for patchily distributed resources. Long-term return rate is maximized if the forager stays in each patch as long as the instan- taneous rate in that patch is not lower than the expected overall rate in the background environ- ment. This rate is in turn a function of environmental variables such as the type of patches composing the environment and the travel time between these patches. In this study we examine only the case when all patches are identical, but the travel time between them is a random variable. The patches considered provide successive food items at discrete, increasing intervals. Although the instantaneous rate rule cannot be used in discrete interval patches, the optimal number of prey per visit to patch (PPV) can be calculated following the same principles (Pyke 1979; Stephens & Krebs 1986). The background rate of return may vary depend- ing on mean travel time. When such changes occur, the number of prey captured per patch under the *Present address: Department of Zoology, South Parks Road, Oxford OX1 3PS, U.K. rate-maximizing policy decreases when the overall rate in the environment increases. This prediction has been upheld in a variety of studies (Hodos & Trumbule 1967; Cowie 1977; Kramer & Nowell 1980; Carlson & Moreno 1981; Tinbergen 1981; Kacelnik 1984; Cassini et al. 1990; review in Stephens & Krebs 1986). Tests of quantitative predictions based on the MVT, however, require specific assumptions about the time window over which the estimates of patch 'instantaneous' rate and background rate are formed. The literature related to this issue (Templeton & Lawlor 1981; Gilliam et al. 1982; Turelli et al. 1982; Stephens & Krebs 1986; CuthiU et al. 1990) has clearly established that the rationale of the MVT is based on maximizing the ratio of the expected intake over the expected total time spent over long periods, rather than maximizing the expected ratio of intake over time over single patch cycles. Since the expected total time is a function of the arithmetic mean of travel time but is not depen- dent on its distribution around the mean, it follows that the MVT makes the negative prediction that variations in the distribution of travel times that preserve the mean should not have any effect over 0003-3472/92/020313 + 10 $03.00/0 9 1992 The Association for the Study of Animal Behaviour 313