Buzz Holling and the Functional Response

Abstract

Beginning in the late 1950s, C. S. (Buzz) Holling conducted experiments to investigate how a predator's rate of prey capture is related to prey density, a relationship that had previously been dubbed the functional response (Solomon 1949). In the resulting series of seminal articles (Holling 1959a, b, 1965), Holling identified three general categories of functional response that he called Types 1, 2, and 3 (Fig. 1). Type 1 is the simplest: capture rate increases in direct proportion to prey density until it abruptly saturates. Type 2 is similar in that the rate of capture increases with increasing prey density, but in contrast to the linear increase of Type 1, Type 2 approaches saturation gradually. Type 3 is similar to Type 2 except at low prey density, where the rate of prey capture accelerates. Holling's work struck a deep chord among ecologists. Over the 55 years since it was proposed, his classification of functional responses has been woven into the fabric of ecology, where it has acquired the aura of received knowledge. Now designated by roman numerals, Holling's functional responses appear in every introductory ecology text, usually with illustrative examples (e.g., filter feeders are Type I; insects and parasitoids, Type II; vertebrates, Type III), and his classification is commonly employed by theoretical ecologists when incorporating predation into models of population and community dynamics. Holling's classic papers have been cited nearly 4000 times, 222 times in 2012 alone. However, as with any well-established scientific dogma, it is useful to revisit its roots, and it was with great interest that I dug out my copies of Holling's work. Three messages emerged from this trip into ecological history: 1. Holling's categories serve as a reminder of the utility of mechanistic approaches in ecology. The complexity of ecological interactions can be overwhelming, at times leading ecologists to wonder whether they will ever be able to delineate general laws (e.g., Lawton 1999). In a field where contingency is king, many ecologists doubt the viability of a reductionist approach in which community dynamics can be explained by quantifying the physical environment and understanding the physiology and behavior of individuals. It is therefore worth remembering that Holling's classification of functional responses—so broadly accepted, taught, and used—was developed in a reductionist context. Holling's primary purpose in his articles was not to promote the classification of functional responses, but rather to outline the experimental and computational methods necessary to account for predation in terms of its basic components. For instance, the core value of his work on the Type II functional response lies in his demonstration that observed capture rates can be explained by taking into account the time required for a predator to handle its prey. Similarly, his work on the Type III response is notable because it develops the idea that predators increase their capture efficiency by learning as they hunt. By accounting for the basic functional components of predation, Holling was attempting to move beyond the phenomenological description of predation. By examining the mechanisms underlying his three types of functional response, he hoped to enhance the value of his classification. Whenever one sees Holling's categories put to use in ecology, it should serve as a reminder that predation is open to mechanistic explanation (e.g., Smout et al. 2010) and that a reductionist perspective can indeed be useful in ecology. 2. Despite its stature in ecology, the division of functional responses into three distinct categories has limited practical value. I reached this conclusion while tracing the lineage of the math behind Types I, II, and III. The Type I functional response is characterized by a linear relationship between capture rate C and prey density N (1) where α is a proportionality constant set by the rate at which predators encounter prey. This was the functional response assumed by Lotka and Volterra in their classic theoretical work on predator–prey interactions (Lotka 1925, Volterra 1926). (Unlike Lotka and Volterra, Holling supposed that this linear relationship obtained only up to a critical value of N, but this constraint is now commonly ignored.) In the second of his classic articles (Holling 1959b), Holling derived a mathematical expression for C in which handling time t is taken into account (t is assumed to be greater than zero). Expressed in its currently accepted form, Holling's Type II relationship is (2)