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In this article scalar expectancy theory is applied to variable and fixed delays to reward. It is assumed that all delays are represented in memory with scalar variance and that subjects choose between alternatives by sampling from the memory distributions associated with each and choosing the smaller delay. This simple scheme is shown to entail four common findings in the choice literature: (a) approximate matching of choice ratios to reward ratios (the matching law) when both alternatives are associated with variable delays scheduled with constant probability; (b) undermatching, in which choice is closer to indifference than matching, when both alternatives are variable but scheduled with uniform distributions; (c) overmatching, in which choice is more extreme than matching, when both alternatives are fixed delays; and (d) preference for variable delays scheduled with a constant probability over fixed delays. Overmatching and Weber's law are illustrated in experiments using the time-left procedure (Gibbon & Church, 1981). The preference for variable delay is demonstrated in this procedure, followed by study of a unique variable schedule of delays for which the theoretical account predicts, and the data confirm, the elimination of the preference for variability.A continuing controversy in psychological research addresses the question of whether animals choose the more valuable of two or more alternatives when these consist of food or other goods delivered under differing delays or schedules (e.g., Rachlin, Battallio, Kagel, & Green, 1981). The question arises from a fundamental and very well-documented empirical finding in the operant conditioning literature, the matching law, which asserts that subjects match choice responses to the relative frequency of rewards associated with the alternatives. A voluminous literature, beginning with Herrnstein's (1970) analysis, is ably summarized from several different perspectives by Baum (1979), de Villiers (1977, Vaughan (1980), andNevin(1984).An omniscient subject that knows the choices and their consequences exhaustively might be expected, according to economic or optimality considerations, to maximize net energy intake (Rachlin et al., 1981;Staddon,Hinson, &Kram, 1981)by concentrating on the better alternative. Indeed, at one level, one might argue that animals that must forage for food would be ill advised by evolution to adopt a matching strategy if the availability of prey in alternative patches remained constant in the mean (although perhaps variable from moment to moment). Specializing on the higher density patch or the more profitable prey item should maximize fitness (e.g.,

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. British Ecological Society is collaborating with JSTOR to digitize, preserve and extend access to Journal of Animal Ecology. SUMMARY (1) We investigate properties of a model of predator distribution in relation to prey abundance, when the predation process is subject to:(i) non-negligible handling time and mutual interference; (ii) predator learning; (iii) intake rate maximization by individual predators. The model is a development of that of Bernstein, Kacelnik & Krebs (1988).(2) The independent variables are between-patch travel cost and structure of the environment. The outcome of the model is described in relation to the predictions of the ideal free distribution (IFD). We consider both the numerical distribution of predators and the mortality rate imposed on the prey population.(3) When travel cost is small, prey depletion is slow and interference is moderate, predators conform to the predictions of the IFD and prey mortality is densitydependent.(4) As travel cost is increased, rate-maximizing predators become more sedentary and the population settles at distributions far from the IFD. In common with all other disturbances of the predation process that impair the correlation between prey and predator densities, this causes mortality to approach density independence and later negative density dependence.(5) In semi-continuous environments where prey density is correlated between neighbouring patches, the slower the spatial rate of variation in prey density (the coarser the environmental grain), the poorer is the adjustment to the IFD. This effect is due to the predators' need for learning: when the environmental sample experienced within the reach of each individual predator is unrepresentative of the global average prey density (as it happens when the environmental grain is very coarse relative to migration range of predators), the predators cannot learn the ? Present address:

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. British Ecological Society is collaborating with JSTOR to digitize, preserve and extend access to Journal of Animal Ecology. Summary 1. On the basis of his study of patch time allocation by Venturia canescens, a larval parasitoid of phycitid flour moths (Lepidoptera: Pyralidae), J. K. Waage proposed a decision mechanism for patch exploitation. This putative mechanism would be efficient in habitats, such as granaries, consisting of patches with heterogeneous host densities. However, the distribution of hosts in mummified fallen fruits, a common natural substrate, differs from their distribution in granary stores, tending to be rather uniform with patches containing a few, mostly one, host larva. This discrepancy led us to re-examine Waage's mechanism. 2. We investigated V. canescens's decision mechanism in small patches containing low host densities. Following the previous study, we tested the relation between the probability per unit time to abandon a patch and the following variables: the concentration of the contact kairomone produced by host larvae, the time elapsed since the first patch entry and the occurrence of ovipositions. A major component of Waage's model is an increase in the tendency to remain in a patch after an oviposition. In habitats where hosts are uniformly distributed, andparticularly when patches contain a single host, this behaviour would not be adaptive. 4. Our results confirm that V. canescens spends more time on patches with higher concentrations of contact kairomone and that the probability per unit time of leaving the patch increases with patch residence time. Ovipositions, however, decrease the amount of time subsequently spent by the parasitoid on the patch. 5. Based on these results we formulate apost-hoc 'count-down' model for the decision rule for patch leaving in V. canescens in habitats with uniform host distributions. 6. There is no evidence for or against the possibility that this parasitoid may be capable of facultative changes in its patch exploitation rule as a function of host distribution. 7. Although increases in patch time after oviposition have been found in several other parasitoid species, re-examination of Waage's experiments shows that his results do not unambiguously support the existence of such a mechanism in Venturia. the rate at which hosts are found exceeds the rate at which new hosts develop. The time spent in each patch Parasitoids searching for patchily distributed hosts increases the number of offspring realized there, but experience diminishing returns within patches when reduces the search time that can be spent on other patches. In consequence, the mechanisms determining