Coupling in predator-prey dynamics: Ratio-Dependence

Predator-prey theory is traced from its origins in the Malthus-Verhulst lo- gistic equation, through the Lotka-Volterra equations, logistic modifications to both prey and predator equations, incorporation of the Michaelis-Menten-Holling functional response into the predator and prey equations, and the recent development of ratio-dependent functional responses and per-capita rate of change functions. Some of the problems of classical predator-prey theory, including the paradoxes of enrichment and biological con- trol, seem to have been caused by the application of the principle of mass action to predator- prey interactions. Predator-prey models that evolved from logistic theory or that incor- porate ratio-dependent functional responses do not have these problems and also seem to be more biologically plausible.

The Orgins and Evolution of Predator‐Prey Theory

To describe a predator-prey relationship, it is necessary to specify the rate of prey consumption by an average predator. This functional response largely determines dynamic stability, responses to environmental influences and the nature of indirect effects in the food web containing the predator-prey pair. Nevertheless, measurements of functional responses in nature are quite rare. Recently, much work has been devoted to comparing two idealized forms of the functional response: prey dependent and ratio dependent. Although we agree that predator abundance often affects the consumption rate of individual predators, this phenomenon requires more attention. Disagreement remains over which of the two idealized responses serves as a better starting point in building models when data on predator dependence are absent.

The nature of predation: prey dependent, ratio dependent or neither?

A predator's per capita feeding rate on prey, or its functional response, provides a foundation for predator-prey theory. Since 1959, Holling's prey-dependent Type II functional response, a model that is a function of prey abundance only, has served as the basis for a large literature on predator-prey theory. We present statistical evidence from 19 predator-prey systems that three predator-dependent functional responses (Beddington- DeAngelis, Crowley-Martin, and Hassell-Varley), i.e., models that are functions of both prey and predator abundance because of predator interference, can provide better descrip- tions of predator feeding over a range of predator-prey abundances. No single functional response best describes all of the data sets. Given these functional forms, we suggest use of the Beddington-DeAngelis or Hassell-Varley model when predator feeding rate becomes independent of predator density at high prey density and use of the Crowley-Martin model when predator feeding rate is decreased by higher predator density even when prey density is high.

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Functional responses with predator interference: viable alternatives to the holling type ii model

We present a handy mechanistic functional response model that realistically incorporates handling (i.e., attacking and eating) and digesting prey. We briefly review current functional response theory and thereby demonstrate that such a model has been lacking so far. In our model, we treat digestion as a background process that does not prevent further foraging activities (i.e., searching and handling). Instead, we let the hunger level determine the probability that the predator searches for new prey. Additionally, our model takes into account time wasted through unsuccessful attacks. Since a main assumption of our model is that the predator's hunger is in a steady state, we term it the steady-state satiation (SSS) equation. The SSS equation yields a new formula for the asymptotic maximum predation rate (i.e., asymptotic maximum number of prey eaten per unit time, for prey density approaching infinity). According to this formula, maximum predation rate is determined not by the sum of the time spent for handling and digesting prey, but solely by the larger of these two terms. As a consequence, predators can be categorized into two types: handling-limited predators (where maximum predation rate is limited by handling time) and digestion-limited predators (where maximum predation rate is limited by digestion time). We give examples of both predator types. Based on available data, we suggest that most predators are digestion limited. The SSS equation is a conceptual mechanistic model. Two possible applications of this model are that (1) it can be used to calculate the effects of changing predator or prey characteristics (e.g., defenses) on predation rate and (2) optimal foraging models based on the SSS equation are testable alternatives to other approaches. This may improve optimal foraging theory, since one of its major problems has been the lack of alternative models.

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Predator functional responses: discriminating between handling and digesting prey

A nonlinear function general enough to include the effects of feeding saturation and intraspecific consumer interference is used to represent the transfer of material or energy from one trophic level to another. The function agrees with some recent experimental data on feeding rates. A model using this feeding rate function is subjected to equilibrium and stability analyses to ascertain its mathematical implications. The anaylses lead to several observations; for example, increases in maximum feeding rate may, under certain circumstances; result in decreases in consumer population and mutal interference between consumers is a major stabilizing factor in a nonlinear system. The analyses also suggest that realistic classes of consumer—resource models exist which do not obey Kolmogorov's Criteria but are nevertheless globally stable. See full-text article at JSTOR

R. V. O'Neill

Papers

A Model for Tropic Interaction