Onegeneration cycles

The coupled oscillations generated by the basic Lotka-Volterra and Nicholson-Bailey models are multigeneration cycles, i.e. there are several generations between successive peaks (or troughs), and such oscillations have lain at the heart of most attempts to understand cyclic predator-prey dynamics. However, other models of host-parasitoid (and host-pathogen) systems are able to generate coupled oscillations just one host generation in length (Knell, 1998; see, for example, Figure 10.1c). On the other hand, such 'generation cycles' can also occur in a population for reasons other than a predator-prey interaction - specifically as a result of competition between age classes within a population (Knell, 1998).

Predator-prey generation cycles occur essentially when the generation length of the consumer is roughly half that of its host - as it often is. Any small, chance peak in host abundance tends to generate a further peak in host abundance one host generation later. But any associated peak in consumer abundance occurs half a host generation length later, creating a trough in host abundance between the twin peaks. And this host trough creates a further host trough one generation later, but a consumer trough coinciding with the next host peak. Thus, the consumers have alternate 'feasts' and 'famines' that accentuate the originally small peaks and troughs in host abundance, and hence promote one-generation cycles (Figure 10.4).

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