A limitation of early models was that the reproductive rate of predators was not constrained. This is clearly a biological nonsense and led to attempts to understand and incorporate into models the response of predators to changes in prey density. It is now recognized that predators (agents in the terminology of biological control) may exhibit a response at the population level termed the numerical response and a behavioral response at the individual level termed the functional response. The numerical response is intuitive in nature, being based on
(1) the aggregation of predator individuals in patches of dense prey and (2) a reproductive response reflecting greater fitness of predators when well nourished. The latter is most commonly incorporated in models of invertebrates with short generation times.
The nature of the response at the individual level is less obvious. Three types of functional responses are generally accepted. The type I response consists of a linear increase in attack rate as prey density rises until the density at which attack rate matches satiation is reached. This is observed for predators such as daphnia and sedentary filter feeders, so is generally of little relevance to biological control. In contrast, the type II functional response is common in specialist insect para-sitoids (which are among the most widely used biological control agents against insect targets). In this C-shaped relationship, attack rate increases at a decreasing rate with rising prey (or host) density. The type III response is S-shaped such that attack rate initially increases with rising prey density, then decreases as the asymptote is reached. This relationship is associated with generalist predators including vertebrate predators that (1) exhibit 'switching' from one prey to another in response to availability or (2) that aggregate in patches of dense prey.
The incorporation of predator response into models has, however, led to debate over whether 'ratio-dependent models' that consider the ratio of prey to predators are superior to the Lotka-Volterra and Nicholson Bailey ('prey-dependent') models that use prey density alone. Functional responses were important in the development of population models more generally, because they led to the incorporation of model components that represent real-world variables such as the degree of hunger, time available for searching, rate of successful search, and the time it takes a predator to capture and consume a prey item (handling time). The concept of functional responses is also intellectually satisfying in relation to the notion of density-dependent regulation, that is, natural enemies kill more prey when prey are common and proportionally fewer prey when prey are scarce. Such a mechanism allows models to reflect the popularly held notion of the balance of nature whereby the numbers of a given species are kept in check but it is not forced into extinction. Despite the intuitive appeal of this concept, both modeling and empirical work suggest limitations to the density-dependence notion.
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