Positive indirect effects between prey species that share predators

Ecology, March, 1996 by Peter A. Abrams, Hiroyuki Matsuda

INTRODUCTION

The indirect interaction between two prey that share a predator often represents the sum of effects transmitted by the predator's numerical and functional responses. Increases in the numbers of one prey often decrease the predator's functional response to other prey, either due to satiation or switching (Murdoch 1969, Murdoch and Oaten 1975); this tends to increase the numbers of the other prey. Alternatively or additionally, increases in the density of one prey increase predator numbers (a numerical response), which tends to reduce the numbers of the second prey species (Holt 1977, Holt and Lawton 1994). This potential conflict between the indirect effects due to functional and numerical responses has been noted by Holt (1977, 1984, 1987, Holt and Kotler 1987), Noy-Meir (1981), and Abrams (1983, 1987a, b, 1990a), among others. However, the balance between the two opposing indirect effects has not been explored quantitatively. This article analyzes some simple models to determine when mutually beneficial effects between prey are likely to occur via their shared predators.

As Holt (1977) has noted, there will always be mutually negative effects between prey via their shared predator if the predator's per capita growth rate is independent of predator density, given that all three species reach stable equilibrium densities. Under these conditions the numerical response will always outweigh the opposing functional response. However, this need not be true when the predator's per capita growth rate decreases with predator density for reasons other than prey depletion (Holt 1977, Noy-Meir 1981, Abrams 1987a). All of the models we consider have such predator density dependence.

DEFINITIONS AND METHODS

We will measure interactions by the change in the equilibrium density of one prey species caused by a change in the per capita death (harvest) rate of another prey species. Measuring indirect effects this way facilitates experimental studies because harvest rates may be changed in a continuous manner in most systems. If increasing the per capita death rate of one prey species increases the density of the other prey species, the interaction is negative (apparent competition if this is true for both species). If increasing the per capita death rate of the first prey species decreases the density of the other prey, then the first prey has a positive effect on the second; when this is true for both members of the pair, the interaction is apparent mutualism. Removal of one prey species corresponds to an increase in its per capita death rate large enough to cause extinction.

An increase in the density of one prey reduces the functional response to the other prey under (at least) two circumstances: (1) the predator reduces its general intensity of foraging when total prey density increases (saturation or satiation); or (2) the predator cannot hunt equally effectively for all prey simultaneously, and devotes more attention to a given prey type, the more abundant it becomes (switching). Saturation can arise because of constraints on the predator's food processing capacity or because of adaptive reduction in the amount of costly foraging activities with increasing prey density (Abrams 1990b). Switching can arise because of adaptive habitat choice by the predator or because of adaptive search strategies within habitats (Murdoch and Oaten 1975, Abrams 1987b).

Our models assume that there is density dependence in the predator growth rate. Mechanisms for such density effects include: (1) predators compete for other resources required for population growth, such as shelter, nesting sites, water, etc.; (2) predators have their own parasites, diseases, and predators, which may increase in numbers or activity with increased predator density; (3) predator social behaviors such as aggression or grouping patterns may change with increased density in ways that reduce fitness; (4) antipredator behavior by the prey generally increases with predator density. Given that most predators in a food web are not top predators (Cohen et al. 1990), it is likely that a subset of point (2) is sufficient to lead to density dependence in most predator populations.

MODELS

The analyses address two questions: (1) If there is a single resident prey and a predator, how does the predation pressure on an invading prey species change as the per capita death rate of the resident prey is increased? (2) When two or more prey species are present at equilibrium with a common predator, how does an increased death rate of one prey affect the density of the other? In all of the analyses, parameters are chosen so that the equilibrium point is stable. When the equilibrium is unstable, the average density may change in a manner very different from the equilibrium density as harvest rates are changed (Abrams and Roth 1994). After deriving some general results, we illustrate them using two specific examples. Two types of predator density dependence affecting the predator's per capita death rate or its functional response are considered.