## Introduction

The classical model of prey choice (named the ‘contingency model’ (CM) by Belovsky 1984) describes the diet that would maximize the long-term intake rate of a mobile predator whose foraging time is divided between two alternative activities: searching for and handling prey items (MacArthur & Pianka 1966; Charnov 1976). Handling time is defined as the time taken for an animal to pursue, capture and consume its prey. This use of carnivore-centric language is merely historical and the foraging terminology throughout this paper is meant to apply equally to herbivory. The contingency model has been progressed in a number of ways (reviewed by Stephens & Krebs 1986), by changing the assumptions about the constraints under which the forager operates, for example that the forager has complete information, encounters prey sequentially and recognizes them at once. The assumption that searching and handling are mutually exclusive and competing activities originated with the use of Holling's disc equation (an economic model of diminishing returns) to describe multispecies functional responses (relationships between food abundance and intake rate; Holling 1959), and has persisted in standard descriptions of the prey model (e.g. Krebs & Davies 1991). The CM continues to be the most frequently used model of diet selection.

There are many foraging circumstances when exclusivity of searching and handling will not necessarily hold. Vertebrate herbivory offers an important example where certain aspects of feeding do not exclude searching for food, others include the short-term feeding of Baleen Whales on zooplankton and birds and bats that feed by flying through clusters of insects (Stephens & Krebs 1986). Recent empirical studies have supported the view that the handling time of large grazers is partly exclusive to searching and partly inclusive (Spalinger, Hanley & Robbins 1988; Gross *et al.* 1993; Laca, Ungar & Demment 1994; Ginnett & Demment 1995).

Vertebrate herbivores are frequently generalists, but feed selectively. The way the vertebrate herbivore's functional response varies with prey characteristics and foraging circumstances is important to optimal diet choice (Lundberg, Åström & Danell 1990; Spalinger & Hobbs 1992). The contingency model of optimal diet choice has been used in an attempt to explain the proportions of food types in the diet of large herbivores (e.g. Owen-Smith & Novellie 1982). It has been contrasted with linear programming models (Belovsky 1978, 1984, 1986) in Belovsky (1981) and Belovsky (1984) and nutritional wisdom models (Westoby 1974; Rapport 1980) in Dearing & Schall (1992) and in both cases, the classical CM matched observed diet choice less closely. In the above studies, herbivore searching and handling were assumed to be mutually exclusive in the CM.

Spalinger & Hobbs (1992) derived functional responses that explicitly account for the overlap in handling and searching times that mammalian herbivores can exhibit (following the observations of Spalinger *et al.* 1988). Recently, Farnsworth & Illius (1996) extended Holling's disc equation to include overlapping of searching and handling, and showed that grazing by mammalian herbivores is consistent with it. Overlapping searching and handling undoubtedly affects the functional response of predators and will have an impact on the make-up of optimal diets (Spalinger & Hobbs 1992) and hence on diet breadth.

In this paper we will derive optimal prey choice rules from the more general foraging model of Farnsworth & Illius (1996) which allows searching and handling to overlap, building on the theoretical developments of Spalinger & Hobbs (1992). We will go on to enumerate the effect of competition between the searching and the prehension and mastication components of handling on diet choice in grazing and browsing herbivores using an extended contingency model. We shall conclude that this has significance for plant–herbivore interactions. It is important to note that our theory refers to within-patch foraging, rather than issues of choices between patches, thus we are considering situations in which different prey types are encountered at random during simultaneous searching. Also, in common with other models of this type, the values of foraging variable referred to in our analysis are the expected values of random variables whose time series is assumed to be stationary so that there is no change in expected values as foraging progresses (thus we do not consider patch depletion, for example).