(5.8, 10.7) (0.1, 0.22) (0.01, 0.012) (0.012, 0.015) (0.0039, 0.0048) (0.0032, 0.0052)

( 0.567 -0.145 0.00247 \ (-0.49) 0.157 0.00155 (0.28) (0.31) 0.000154

0.828 -0.0845 -0.00297^ (-0.22) 0.175 -0.0202 \(-0.02) (-0.33) 0.0206

In Tables 3.1 and 3.2 appear the results of using the Nelder-Mead simplex algorithm [148] to maximize numerically the log-likelihood function for each strain separately. The calculations were numerically well-behaved, and repeated maximizations from many different starting points converged to the same parameter values. Confidence intervals for each unknown parameter also appear in these tables (as calculated from the deterministic skeleton (3.1) using the profile likelihood method as described in Section 2.5).

The estimated parameters appearing in Tables 3.1 and 3.2 for the SS and RR genetic strains differ somewhat from the estimates in Table 2.1 for the cos strain of T. castaneum obtained in Chapter 2. These new parameteri-zations (provided by the "estimation" subset of the data) yield two modified bifurcation diagrams, one for each experiment. As Figs. 3.2 and 3.3 show, however, the new model predicted bifurcations are qualitatively and quantitatively similar to those in Fig. 3.1 on which we based the original experimental design. Both bifurcation diagrams in Figs. 3.2 and 3.3 have, at intermediate values of the adult death rate pLa, the "2-cycle bubble" that results from two period-doubling bifurcations. A notable

FIGURE 3.2 I The top graph shows the equilibrium stability boundaries in the \ia and cpa parameter plane for the LPA model (3.1) when the remaining model parameters are set at the estimated values for the SS strain in Table 3.1. The horizontal line is the path followed in the bifurcation diagram and the solid circles indicate the control and adult mortality treatments enforced in the bifurcation experiment (with cpa confidence intervals). The bottom graph shows the resulting bifurcation diagram. Reprinted from [44], f c-^

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