Combining multiple data sources with different biases in state-space models for population dynamics

The resolution at which animal populations can be modeled can be increased when multiple datasets corresponding to different life stages are available, allowing, for example, seasonal instead of annual descriptions of dynamics. However, the abundance estimates used for model fitting can have multiple sources of error, both random and systematic, namely bias. We focus here on the consequences of, and how to address, differing and unknown observation biases when fitting models.State-space models (SSMs) separate process variation and observation error, thus providing a framework to account for different and unknown estimate biases across multiple datasets. Here we study the effects on the inference of including or excluding bias parameters for a sequential life stage population dynamics SSM using a combination of theory, simulation experiments, and an empirical example.When the data, that is, abundance estimates, are unbiased, including bias parameters leads to increased imprecision compared to a model that correctly excludes bias parameters. But when observations are biased and no bias parameters are estimated, recruitment and survival processes are inaccurately estimated and estimates of process variance become biased high. These problems are substantially reduced by including bias parameters and fixing one of them at even an incorrect value. The primary inferential challenge is that models with bias parameters can show properties of being parameter redundant even when they are not in theory.Combining multiple datasets into a single analysis by using bias parameters to rescale data can offer significant improvements to inference and model diagnostics. Because their estimability in practice is dataset specific and will likely require more precise estimates than might be expected from ecological datasets, we outline some strategies for characterizing process uncertainty when it is confounded by bias parameters.