The effect of small, plausible changes in parameters on stability and period. One parameter was varied at a time, while others were held at values for the system that generated realistic dynamics (figure 1c): parasite-induced hare mortality (α) was varied from its point estimate to upper plausible limit; hare intrinsic fecundity (a), hare intrinsic mortality (b) and adult parasite mortality (μ) were varied from lower to upper plausible limits; degree of overdispersion (k) values 0.5, 1, 2; δ was varied from its point estimate to 0.001 hare parasite−1 and follows the opposite path to α. The dashed line marks the boundary between a stable (negative) and an unstable (positive) equilibrium.