Appendix A. “Calculated” priors and posterior distributions for natural demographic rates.

FIG. A1. One-hundred survivorship and mortality curves, calculated from 100 random samples of Siler parameters (a1, a2, a3, b1, b3) and fertility rates [m(4) and m(5+)] that were drawn from their prior distributions (see Table 1) and that satisfied model constraints (r_{nat} > 0, l_{nat}(24) < 0.01). |

FIG. A2. Median (solid) and 95% Bayesian credible limits (dotted) for age-specific natural survivorship and mortality, calculated from Siler parameters. Red lines illustrate the “calculated” or “actual” prior distribution for survivorship and mortality, based on 4814 random samples of parameter sets. These samples were obtained by drawing 10 million samples from the prior distributions for each Siler and fertility parameter (see Table 1 in text) and keeping those that satisfied constraints of r_{nat} > 0 and l_{nat}(24) < 0.01. This exercise was performed in R, solely for the purpose of illustrating the shape of the actual prior distributions. Black lines depict the posterior distribution, based on 10,000 MCMC samples from estimation conducted in WinBUGS. |

FIG. A3. “Calculated” prior (red) and posterior (black) densities for selected natural rate parameters. Prior densities for r_{nat} and Siler parameters were generated from 4814 random samples. These samples were obtained by drawing 10 million samples from the prior distributions for each Siler and fertility parameter (see Table 1 in text) and keeping those that satisfied constraints of r_{nat} > 0 and l_{nat}(24) < 0.01. This exercise was performed in R, solely for the purpose of illustrating the shape of the calculated (or “actual”) prior distributions. Age-0 natural mortality [q(0)] was calculated from the Siler parameters and is shown to exemplify difference between prior and posterior mortality estimates. The posterior density is based on 10,000 MCMC samples from estimation in WinBUGS. |