Kevin Gross, Anthony R. Ives, and Erik V. Nordheim. 2005. Estimating fluctuating vital rates from time-series data: a case study of aphid biocontrol. Ecology 86:740–752.

Appendix F. Posterior distributions for and . See Appendix H for references cited.

The posterior for (proportion of attacks on adults) suggest that the data do not contain enough information to override our prior information from Ives et al. (1999) that wasps preferentially attack juvenile aphids (Fig. F1). The posterior for (fecundity reduction for parasitized aphids) suggests that parasitized adult aphids are much less fecund on average than unparasitized adult aphids. The aggregation parameters for aphids and mummies, k_A and k_M, suggest that both are clumped among stems. The small posterior values of the overdispersion parameters for dissections and hyperparasitism (_W and _H) suggest that variation in aphid dissection and mummy emergence is not much more than binomial or trinomial variation. The parameters that convert sweeps and time counts to a per-stem basis are not at odds with our empirical expectations. Finally, the mummy emergence parameters, _W and _H, suggest that most of the unemerged mummies were hyperparasitized. This is consistent with previous field work, where a great majority of unemerged mummies showed evidence of being hyperparasitized (Schooler et al. 1996, and unpublished data). However, it could also be a way for the model to reconcile a fitted trajectory that anticipated more hyperparasitized mummies than we actually observed.

FIG. F1.  Prior (dotted lines) and posterior (solid lines) densities for parameters in  and .  Posterior densities are smoothed kernel density estimates from the MCMC output.