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whichever is closer. Thus, for example, for the situation in Figure 4.5 we must have 1 — |3/2| > \/32 — 47/2; if we square both sides of this expression the condition becomes 1 — |3| + (32/4) > (32/4) — 7 and this simplifies to 1 + 7 > |3|. Our first condition was 32 > 47 and we have agreed that |3| < 2 so that 32 < 4. Therefore, 4 > 32 > 47, so that 1 > 7 or 2 > 1 + 7. When we combine the two conditions, we obtain the criterion for stability that (Edelstein-Keshet 1988)

Hassell (2000a) gives (his Eqs. (2.2), (2.3)) the application of this condition to the general Eqs. (4.6).

In the case of Nicholson-Bailey dynamics, f (H, P) = exp(—aP), so that fH = 0 and fP =— aexp(—aP); these need to be evaluated at the steady states and the coefficients a, b, c, and d in Eq. (4.9) evaluated so that we can then determine 3 and 7.

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