Appendix D. Priors. See Appendix H for references cited.
Here, we describe the prior distributions on all the parameters except for the time-varying vital rates, which are discussed in the main text.
To facilitate MCMC mixing, the initial state vector X1 is re-parameterized into the following six components: total aphid density, fraction of aphids that are juveniles, fraction of juveniles parasitized, fraction of adults parasitized, total mummy density, and fraction of mummies hyperparasitized. Priors for each of the fractional components are Uniform(0,1). The prior for the total aphid density is Uniform(0,50) and for the total mummy density is Uniform(0,10).
Process model parameters that do not depend on cutting cycle
Ives et al. (1999) showed that parasitoids
preferentially attack juvenile aphids. We assume that the ratio of attacks on
adults to attacks on juveniles is a constant
, and use the data in Ives et al. to build an informative Beta prior for , with prior mode 0.064 and prior standard deviation 0.025. For the reduction in aphid fecundity due to parasitism, , we use a vague prior, Uniform on (0,1).
Parameters in the observation model
There are 8 parameters in , and the priors for all are mutually independent. For the overdispersion parameters in the negative binomial distributions, kA and kM, stem count data from 1996 were used to calculate the priors, with prior modes set equal to their MLEs from 1996, and prior variances inflated substantially compared to the sampling variances of the MLEs. Both priors were Gamma distributions, for kA with mean 7.63 and standard deviation 7.07, and for kM with mean 29.60 and standard deviation 22.36.
For the conversion parameters, s
priors were modified triangular distributions, with uniform prior density on
a range covering all reasonable values, and tapering prior density at the boundaries
of the prior support (Fig. F1, Appendix F). The
prior support for s
is informed by 1996 data, and the prior support for
tc is based on empirical observation.
Priors for the overdispersion parameters W and H are triangular priors on (0,1), with prior modes at 0 (Fig. F1). Priors for the emergence parameters W and H are Uniform(0,1).