+ l maxc{f (c) + e-mchF(x - c, t + ch\h, T)} (4 . 43)

and identify the other assumptions that are implicitly included in this equation. (As you might imagine, the results obtained using Eq. (4.43) are similar, but not identical, to those obtained using Eq. (4.42).)

Let us close by considering how all this might be modified for a synovigenic parasitoid. In such a case, we require two state variables to describe the parasitoid: mature eggs (denoted by x) and oocytes (denoted by y) and also need to specify the egg maturation time r, in the sense that oocytes mature into eggs at rate 1/r. A very simple example is one in which in a single period of time the parasitoid either encounters food (understood to be both protein and carbohydrate) or a host, with probabilities lf and lh respectively. If she encounters food, her oocyte reserve is incremented by an amount S and if she encounters a host, her lifetime fitness is incremented by 1 offspring and eggs are decremented by 1 egg. In such a case, the dynamic programming equation is (with the dependence on h and T suppressed)

F(x,y, t) = (1 - 4 - lf)e-mF(x + ^,y - y, t + l) + 2fe-mF(x + y,y - ^ + S, t + 1)

and we can now think about time limitation in two contexts: handling time and egg maturation time. That would be a pretty interesting project.

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