Multiple attacks may provide a different kind of refuge

Solitary parasitoids lay only a single egg in a host, but often they do not perfectly discriminate when laying eggs (Figure 4.8). When that happens, there will be larval competition with the host (Taylor 1988a, b,

Figure 4.8. The parasitoid Nasionia vitrepennis is solitary and attacks a variety of hosts (shown here are pupae of Phormia regina). However, sometimes more than one egg is laid in a host, in which case larval competition of the parasitoids occurs. Photographs compliments of Robert Lalonde, University of British Columbia, Okanagan Campus.

Figure 4.8. The parasitoid Nasionia vitrepennis is solitary and attacks a variety of hosts (shown here are pupae of Phormia regina). However, sometimes more than one egg is laid in a host, in which case larval competition of the parasitoids occurs. Photographs compliments of Robert Lalonde, University of British Columbia, Okanagan Campus.

1993) and this competition may have profound effects on the dynamics of the parasitoids, with associated effects on the dynamics of the host. Taylor (1988a, b, 1993) provides a general treatment of the effects of within-host competition; here we will consider a simplification that Bob Lalonde (University of British Columbia, Okanagan Campus) taught me.

Let us suppose that a host that is attacked and receives only one parasitoid egg produces a parasitoid in the next generation with certainty, but that hosts that receive more than one egg fail to produce a parasitoid because of competition between the parasitoid larvae within the host (that is, they fight each other to the point of being unable to complete development but kill the host too). Now the standard Nicholson-Bailey dynamics correspond to random search, so that the probability that a host receives exactly one egg is a aP(t) exp(—aP(t)). Thus, the original Nicholson-Bailey dynamics become

H (t + 1) = RH (t)e-aP(t) P(t + 1) =H (t)aP(t)e~aP(i)

The first line in Eq. (4.16) corresponds to hosts that escape parasitism entirely (the zero term of the Poisson distribution); the second line

Figure 4.9. If multiple attacks on a host lead to no emergent parasitoids, the Nicholson-Bailey dynamics are stabilized.

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