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Search Tactics and Frequency-Dependent Prey Detection

Frequency-dependent (or apostatic) predation can have important evolutionary and ecological consequences related to genotypic and phenotypic diversity. The maintenance of balanced polymorphisms within species and the regulation of cryptic and mimetic prey populations within communities are of particular interest (Greenwood 1984; Allen 1988; Guilford 1989; Endler 1991). Many different kinds of processes can create frequency dependence. Within mixtures of cryptic prey the possibilities include variable perceptual sensitivity (search image formation) and variable search tactics (Gendron and Staddon 1983; Guilford and Dawkins 1987; Endler 1991). There is much debate about the importance of these alternatives because the distinction seems to matter, but both processes are conceptually loose and empirically challenging. The distinction seems to matter because of the widespread belief that search images can generate potentially stabilizing, positive frequency-dependent (or proapostatic) encounter rates with a relatively cryptic prey type but variable search tactics cannot (Allen 1989; Guilford 1989). This note examines the consequences of variable tactics within the context of a common foraging mode known as pause-travel search and shows that, contrary to analyses based on a continuous swept-path conceptualization, variable tactics can generate positive frequency-dependent encounter rates. Pause-travel search tactics are described in detail in Andersson's (1981) work with birds and O'Brien's work with fish (e.g., O'Brien et al. 1990). Apparently, pause-travel searchers cannot detect cryptic prey while moving, or at least not very well. A casual look at a sparrow searching for seeds may give the impression that it just walks along sweeping out a continuous path, but closer inspection shows that it moves in a series of cycles: it pauses briefly to scan the area around itself, and if it fails to detect a seed after some amount of effort it runs quickly to a new spot, plants its feet, and renews scanning. The primary tactics in this search mode are variations of pause (giving up) time and travel (run) length between pauses. Secondary tactics, like the distribution of attention within pauses (Guilford and Dawkins 1987; Getty and Pulliam 1991), cannot be addressed here, but they should not invalidate the general conclusions. In an earlier article, H. R. Pulliam and I analyzed a spatially explicit, stochastic model of pause-travel search and detection and concluded that density-dependent detection rates are almost inevitable, even in the absence of search image formation or variable search tactics (Getty and Pulliam 1991). We gave brief consideration to frequency dependence between types and concluded that it is less likely. This note presents a more comprehensive analysis, showing how variable pausetravel tactics can create frequency-dependent detection rates, what parameters