A hierarchical Bayesian model to estimate the unobservable predation rate on sawfly cocoons by small mammals

Predation by small mammals has been reported as an important mortality factor for the cocoons of sawfly species. However, it is difficult to provide an accurate estimate of newly spun cocoons and subsequent predation rates by small mammals for several reasons. First, all larvae do not spin cocoons at the same time. Second, cocoons are exposed to small mammal predation immediately after being spun. Third, the cocoons of the current generation are indistinguishable from those of the previous generation. We developed a hierarchical Bayesian model to estimate these values from annual one-time soil sampling datasets. To apply this model to an actual data set, field surveys were conducted in eight stands of larch plantations in central Hokkaido (Japan) from 2009 to 2012. Ten 0.04-m(2) soil samples were annually collected from each site in mid-October. The abundance of unopened cocoons (I), cocoons emptied by small-mammal predation (M), and empty cocoons caused by something other than small-mammal predation (H) were determined. The abundance of newly spun cocoons, the predation rate by small mammals before and after cocoon sampling, and the annual rate of empty cocoons that remained were estimated. A posterior predictive check yielded Bayesian P-values of 0.54, 0.48, and 0.07 for I, M, and H, respectively. Estimated predation rates showed a significant positive correlation with the number of trap captures of small mammals. Estimates of the number of newly spun cocoons had a significant positive correlation with defoliation intensity. These results indicate that our model showed an acceptable fit, with reasonable estimates. Our model is expected to be widely applicable to all hymenopteran and lepidopteran insects that spin cocoons in soil.