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rowth parameter Figure 5.9. Optimal virulence

1 0.48 0.24 0.11 0.03 of the parasites when hosts

'-1-1- mature at age t (reprinted from

Koella and Restif (2001) with rowth parameter Figure 5.9. Optimal virulence

1 0.48 0.24 0.11 0.03 of the parasites when hosts

'-1-1- mature at age t (reprinted from

Koella and Restif (2001) with

ge at reproduction

ge at reproduction

S(t) uninfected individuals and I(t) infected individuals (with S(0) = N and 1(0) = 0). Recall that we assumed that hosts become infected at rate l, independent of the density of infected individuals. Consequently, the dynamics for susceptible and infected individuals is slightly different than before:

We now solve these equations subject to the initial conditions. The first equation can be solved by inspection, so that S(t) = Ne-(1+/)t. The solution of the second equation is slightly more complicated. We separate the case in which l = a*(tm) and the case in which they are not equal. In the latter case, we solve the equation for infected individuals by the use of an integrating factor and we obtain

For the case in which l = a*(tm) show that I(t) = 1tmNe"(1+^)tm.

Given S(t) and I(t), we next compute the probability that an individual survives to age t as jp(t) = [S(t) + I(t)]/N and thus the expected lifetime reproductive success is F(tm) / jp(tm)(1 - e" "k'm. We may then assume that natural selection acts to maximize this expression through the choice of age at maturity, which you should now be able to find. This approach differs somewhat from that of Koella and Restif (2001) and I encourage you to read their paper, both for the approach and the discussion of the advantages and limitations of this model in the study of the evolution of virulence.

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