A Bayesian approach to estimating copepod development times from stage frequency data

Abstract

We developed Bayesian hierarchical models to estimate life stage durations of copepods from data on life stage frequencies over time in laboratory cohorts. This approach can determine stage duration or development rate, as well as other parameters of the development process, with probability distributions for each parameter. Uncertainty arising from sources such as experimental replication and the variability inherent in count data can easily be incorporated. Prior probability distributions can be uninformative, or they can apply constraints (e.g., stage durations > 0), general knowledge of development, or results of previous experiments. The approach is flexible, with the capability to model any number of life stages from experiments using replicated or unreplicated designs. We verified the model by accurately recovering the life stage distributions used to produce data in a simulation. We then applied the method to laboratory data on the development of two calanoid copepods and one cyclopoid copepod from the San Francisco Estuary. With replication (3 or 4 replicates), the method can determine stage durations with ~30 copepods per sample, although the uncertainty around estimates of stage duration increases as the number of copepods per sample decreases or the sampling interval increases.