## The Nicholson Bailey model and its generalizations

The starting point for our (and most other) analysis of host-parasitoid dynamics is the Nicholson-Bailey model (Nicholson 1933, Nicholson and Bailey 1935) for a solitary univoltine parasitoid. We envision that hosts are also univoltine, in a season of unit length, in which time is measured discretely and in which H(t) and P(t) denote the host and parasitoid populations at the start of season t. Each host that survives to the end of the season produces R hosts next year. The parasitoids search randomly for hosts, with search parameter a, so that the probability that a single host escapes parasitism from a single parasitoid is e~a. Thus, the probability that a host escapes parasitism when there are P(t) parasitoids present at the start of the season is e-ap(t). These absolutely sensible assumptions lead to the dynamical system

Note that in this case the only regulation of the host population is by the parasitoid. Hassell (2000a, Table 2.1) gives a list of 11 other sensible assumptions that lead to different formulations of the dynamics.

The first question we might ask concerns the steady state of Eq. (4.1), obtained by assuming that H(t + 1) = H(t) and P(t + 1) = P(t). These are easy to find.

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