Prey Preference By A Top Predator And The Stability Of Linked Food Chains

Ecology, Jan, 2000 by David M. Post, M. Elizabeth Conners, Debra S. Goldberg

DAVID M. POST [1,2,5]

M. ELIZABETH CONNERS [3]

DEBRA S. GOLDBERG [4]

Abstract. Recent theoretical studies have shown the potential for chaotic dynamics in simple three-species food chains. Most of these studies have focused on linear food chains, although natural food chains are seldom isolated from the surrounding food web. There is a growing awareness that food web dynamics can be strongly influenced by the behavior and movement of predators, energy, and nutrients across ecosystem and subecosystem boundaries. Motivated by observations from lakes, where the pelagic food web is often linked to the littoral food web by mobile predators, we constructed a simple model to evaluate the dynamics of two food chains linked by a top predator with prey preference. Linking the two food chains had no qualitative effect on model dynamics, although it did increase the density of the top predator. Instead, the prey preference of the top predator changed the system dynamics. We found a range of prey preferences that could eliminate chaos, dampen oscillations, and even produce point stability in a previously oscillatory system. The strength of prey preference required to produce a point attractor in a previously chaotic system was positively related to the dimension of chaos (a measure of the complexity of chaos). Our results suggest that, although chaos is possible in food webs, common processes like prey preference reduce the potential for chaos.

Key words: chaos; food chain; food web, functional response; predation; prey preference.

INTRODUCTION

Simple mathematical models can produce surprisingly complex population dynamics (e.g., May 1974, 1976). Recently, much attention has focused on complex dynamics in three-species continuous-time food chain models (modeling three trophic levels; Hastings and Powell 1991, McCann and Yodzis 1994, Ruxton 1996, and others). These models have paralleled work on complex interactions in multilevel trophic food webs in terrestrial (Price et al. 1980, McLaren and Peterson 1994), marine (Paine 1980), and fresh water aquatic communities (Carpenter and Kitchell 1984, 1993, Power 1990). Previous models have addressed simple three-species food chains (Hastings and Powell 1991) and the effects of enrichment, prey refuges, and omnivory on three-species food chains (Abrams and Roth 1994, Ruxton 1996, McCann and Hastings 1997). No study has yet evaluated the dynamics of two three-species food chains linked by a top predator with prey preference. Prey preference is common in natural food webs and is likely to be important to foo d web dynamics.

Although many food web studies have focused on effectively linear food chains, even largely isolated food chains are linked to surrounding food webs (Hairston and Hairston 1993, Polis and Strong 1996), and their dynamics may be strongly influenced by the flow of energy and nutrients across ecosystem and subecosystem boundaries. A good example is in lakes, where pelagic food webs (open water) are linked to littoral food webs (near shore) through predation and nutrient translocation by mobile predators (Schindler et al. 1996, Vanni 1996). While many aquatic food web studies have focused on pelagic food webs (e.g., Mills et al. 1987, Carpenter and Kitchell 1993), there is an acute awareness that littoral-pelagic coupling is critical to the food web dynamics of lakes (Lodge et al. 1988). The same is true for marine systems, where benthic--pelagic coupling is important to the flow of nutrients, propagules, and predators (Meyer et al. 1983, Boero et al. 1996); and terrestrial systems, where allochthonous inputs fr om marine systems can subsidize terrestrial food webs (Polis and Hurd 1996).

Here, we test the dynamics of two food chains linked by a mobile top predator with differing prey preferences. The model food web (Fig. 1) is motivated by observations from freshwater lakes, where the pelagic food web is often linked to the littoral food web by mobile predators (e.g., planktivorous and piscivorous fishes), but it is analogous to many other spatially linked food webs (see Polis et al. [1997] for a review). We first establish the dynamic behavior of an isolated food chain, then we test the effect of linking two identical food chains through a mobile top predator. Finally, we address the effect of different prey preferences on the dynamics of this food web. We are particularly interested in the hypothesis that prey preference may reduce the variability of a previously oscillatory system. We demonstrate that linking two food chains generally bounds the system away from zero and, for a range of prey preference values, can dampen oscillations and impart point stability.

MODEL

We constructed two food chains linked by a mobile top predator (Fig. 1). In this food web, a consumer ([C.sub.i]) preys on a resource ([R.sub.1]), and the mobile top predator (P) preys on both [C.sub.1] and [C.sub.2]. Our model is based on the three-species food chain of McCann and Yodzis (1994, 1995), which expanded the Hastings and Powell (1991) model by using the energetic arguments of Yodzis and Innes (1992). We further expanded the model by incorporating a prey preference function [[delta].sub.i], to link the two food chains through a top predator. The population dynamics of [R.sub.i], [C.sub.i], and P are described by the following system of coupled equations: