Predatorprey cycles in nature or are they

The inherent tendency for predator-prey interactions to generate coupled oscillations in abundance might suggest an expectation of such oscillations in real populations. However, there are many important aspects of predator and prey ecology that have not been considered in the models derived so far; and as subsequent sections will show, these can greatly modify our expectations. Certainly, even if a population exhibits regular oscillations, this does not necessarily provide support for the Lotka-Volterra, Nicholson-Bailey or any other simple model. We saw cycles generated by intraspecific competition in Section 5.8, and we shall see several other routes to cycles in subsequent chapters (see also Kendall et al., 1999). At this point, though, it is worth simply making the point that even when predators or prey exhibit regular cycles in abundance, it is never easy to demonstrate that these are predator-prey cycles.

... giving rise to (unstable) coupled oscillations

This is the basic Nicholson-Bailey model of a host-parasitoid interaction. Its behavior is reminiscent of the Lotka-Volterra model but it is even less stable. An equilibrium combination a model based on random encounters . . .

This is the basic Nicholson-Bailey model of a host-parasitoid interaction. Its behavior is reminiscent of the Lotka-Volterra model but it is even less stable. An equilibrium combination hare and lynx: not the simple predator and prey they appear to be

Figure 10.4 Schematic illustration of how a parasitoid or pathogen may generate coupled cycles in abundance in the host and itself that are approximately one host generation in length. For this, the parasitoid or pathogen must have a generation length approximately half that of the host. Any chance increase in host abundance (A) will first give rise to an increase in parasitoid abundance one parasitoid generation later (B), and also to an increase in host abundance one host generation later (C). But the parasitoid peak at B will also give rise to a coincident host trough, which will give rise to a parasitoid trough at C, reinforcing the host peak at that point. This mutual reinforcement will continue until by, say, D, persistent host generation-length cycles have become established. (After Knell, 1998; from Godfray & Hassell, 1989.)

Figure 10.4 Schematic illustration of how a parasitoid or pathogen may generate coupled cycles in abundance in the host and itself that are approximately one host generation in length. For this, the parasitoid or pathogen must have a generation length approximately half that of the host. Any chance increase in host abundance (A) will first give rise to an increase in parasitoid abundance one parasitoid generation later (B), and also to an increase in host abundance one host generation later (C). But the parasitoid peak at B will also give rise to a coincident host trough, which will give rise to a parasitoid trough at C, reinforcing the host peak at that point. This mutual reinforcement will continue until by, say, D, persistent host generation-length cycles have become established. (After Knell, 1998; from Godfray & Hassell, 1989.)

The regular oscillations in the abundance of the snowshoe hare and the Canadian lynx shown in Figure 10.1a have often been held to epitomize predator-prey cycles. Recently, however, evidence has increasingly indicated that even this apparent exemplar is not as straightforward as it has seemed. Experimental manipulations carried out in the field are one powerful means of suggesting what forces are normally acting: if those forces are removed or exaggerated, is the cycle eliminated or enhanced? A whole series of coordinated field experiments has indicated that the cyclic hare is not simply a prey of the lynx (and other predators in the community), nor simply a predator of its plant food resources: the cycle can be understood only by taking account of its interactions both as a prey and as a predator (Krebs et al., 2001). Furthermore, modern statistical analysis of the time series of abundances has tended to confirm this: the hare series carries a relatively complex 'signature', suggesting the influence of both its predators and its food, whereas the lynx series has a simpler signature, suggesting only the influence of its (hare) prey (Stenseth et al., 1997; see also Section 14.5.2). What has so often been described as a predator-prey cycle seems rather to comprise one predator linked to a species that is both predator and prey.

Apparently coupled one-generation cycles linking a moth host (Plodia inter-punctella) and its parasitoid Venturia canescens were shown in Figure 10.1c. In this case, the dangers ofjumping too readily to the conclusion that these are predator-prey cycles are highlighted by the fact that the host also exhibits generation-length cycles when maintained alone, without any natural enemies, and also when maintained with another enemy, a granulovirus (Figure 10.5). It has been possible, however, to confirm that the cycles in Figure 10.1c are indeed coupled oscillations, using methods similar to those applied to the hare-lynx time series (Bjornstad et al., 2001). The host-alone cycles have within them the signature simply of intraspecific competition, and the virus seems to modulate this pattern but does not alter its basic structure (i.e. the patterns in Figure 10.5 are not predator-prey cycles). However, the host and parasitoid cycles in Figure 10.1c both carry the same, more complex signature that indicates a tightly coupled prey-predator interaction (see also Section 12.7.1).

We return to the question of cycles - indeed, some of the same cycles discussed above - in Section 14.6, as part of a more general exploration of how the whole range of biotic and abiotic factors come together to determine the level and pattern of a population's abundance.

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