Notes 1635 Ecology, 84(6), 2003, pp. 1635–1639 q 2003 by the Ecological Society of America USE OF SELECTION INDICES TO MODEL THE FUNCTIONAL RESPONSE OF PREDATORS DAMIEN O. JOLY 1,3 AND BRENT R. PATTERSON 2 1 Wisconsin Cooperative Wildlife Research Unit, Department of Wildlife Ecology, University of Wisconsin, 218 Russell Labs, 1630 Linden Drive, Madison, Wisconsin 53706 USA 2 Ontario Ministry of Natural Resources, Wildlife Research and Development Section, 300 Water Street, 3rd Floor N., Peterborough, Ontario, Canada K9J 8M5 Abstract. The functional response of a predator to changing prey density is an important determinant of stability of predator–prey systems. We show how Manly’s selection indices can be used to distinguish between hyperbolic and sigmoidal models of a predator functional response to primary prey density in the presence of alternative prey. Specifically, an inverse relationship between prey density and preference for that prey results in a hyperbolic func- tional response while a positive relationship can yield either a hyperbolic or sigmoidal func- tional response, depending on the form and relative magnitudes of the density-dependent preference model, attack rate, and handling time. As an example, we examine wolf (Canis lupus) functional response to moose (Alces alces) density in the presence of caribou (Rangifer tarandus). The use of selection indices to evaluate the form of the functional response has significant advantages over previous attempts to fit Holling’s functional response curves to killing-rate data directly, including increased sensitivity, use of relatively easily collected data, and consideration of other explanatory factors (e.g., weather, seasons, productivity). Key words: Alces alces; Canis lupus; density dependence; disc equation; functional response; predation; prey, multiple; prey selection; Rangifer tarandus; selection indices; wolf prey preference. INTRODUCTION An important component of predicting the regulatory role of a predator is describing the relationship between prey density and number of prey killed per predator in a given unit of time (i.e., the ‘‘functional response,’’ Holling 1959a, b). Typically, research on this relation- ship focusses on whether a type II (hyperbolic) or type III (sigmoidal) curve best describes the functional re- sponse (e.g., Trexler et al. 1988, Marshal and Boutin 1999), as the combination of functional and numerical responses of a predator to prey density determines the potential for predator regulation of prey (reviewed by Messier [1995]). However, the available data are often insufficient to determine which curve best fits killing- rate data for large-mammal predator–prey systems. For example, Marshal and Boutin (1999) convincingly demonstrated that killing-rate data would only be suf- ficient to detect a sigmoidal functional response when the curve was extreme in its curvature. Manuscript received 13 May 2002; revised 10 October 2002; accepted 6 November 2002; final version received 4 December 2002. Corresponding Editor: J. M. Ver Hoef. 3 E-mail: dojoly@wisc.edu A common explanation for a sigmoidal functional response is prey switching (Murdoch and Oaten 1975). For example, a density-dependent preference for a par- ticular prey type would result in a sigmoidal functional response (e.g., Hassell 1978, Chesson 1983). Herein we derive a functional-response model that can gen- erate either a hyperbolic or a sigmoidal functional re- sponse, depending on how a predator’s preference for prey changes with prey density. A hyperbolic func- tional response is generated if preference is a negative function of prey density, whereas a positive function yields either a hyperbolic or a sigmoidal response de- pending on the strength of this density relationship. We illustrate the approach by testing for a density-depen- dent relationship between moose (Alces alces L.) den- sity and wolf (Canis lupus L.) preference for moose over caribou (Rangifer tarandus L.), assuming that moose are the primary prey (Messier 1994, Hayes et al. 2000). We also discuss implications of linking the functional response to prey preference for the stability of predator–prey systems. DENSITY-DEPENDENT PREY SELECTION A simple index of prey preference is given by Manly et al. (1972) and Chesson (1978):