Abstract
The functional response (trophic function or individual ration) quantifies the average amount of prey consumed per unit of time by a single predator. Since the seminal Lotka-Volterra model, it is a key element of the predation theory. Holling has enhanced the theory by classifying prey-dependent functional responses into three types that long remained a generally accepted basis of modeling predator-prey interactions. However, contradictions between the observed dynamics of natural ecosystems and the properties of predator-prey models with Holling-type trophic functions, such as the paradox of enrichment, the paradox of biological control, and the paradoxical enrichment response mediated by trophic cascades, required further improvement of the theory. This led to the idea of the inclusion of predator interference into the trophic function. Various functional responses depending on both prey and predator densities have been suggested and compared in their performance to fit observed data. At the end of the 1980s, Arditi and Ginzburg stimulated a lively debate having a strong impact on predation theory. They proposed the concept of a spectrum of predator-dependent trophic functions, with two opposite edges being the prey-dependent and the ratio-dependent cases, and they suggested revising the theory by using the ratio-dependent edge of the spectrum as a null model of predator interference. Ratio-dependence offers the simplest way of accounting for mutual interference in predator-prey models, resolving the abovementioned contradictions between theory and natural observations. Depending on the practical needs and the availability of observations, the more detailed models can be built on this theoretical basis.
Highlights
Since the first predator-prey model (Lotka, 1925; Volterra, 1926), classical trophic functions ignored interactions among predators, depending only on prey density, g(N)
The first trophic function taking into account the mutual interference of predators was ratio-dependent
While predator interference can be overestimated due to systematic bias arising at a low sample size (Novak and Stouffer, 2021a), the parsimonious ratio-dependent model could satisfactorily describe the predation process, providing a reasonable trade-off between complexity and performance, in such cases of scarce data (Ginzburg and Colyvan, 2004; Weijs and Ruddell, 2020)
Summary
Having highlighted the contradictions between the observed dynamics of natural ecosystems and the qualitative properties of predator-prey models with prey-dependent trophic functions, Arditi and Ginzburg (1989) suggested revising theoretical models by means of ratio-dependent functions providing the most parsimonious way of accounting for predator interference (Arditi et al, 1992). Their ideas inspired a lively debate stimulating great interest in justifying criteria for realistic functional response.
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