On the use of conditional age at length data as a likelihood component in integrated population dynamics models

Integrated population dynamics models use a variety of data types, and all the data used impact modeled processes and estimated dynamics. Paired age-length data treated as conditional age-at-length (CAAL) data are increasingly being used as a data component in stock assessment models. The original intent of the use of CAAL data was to directly estimate the length-at-age process, including the associated variability in length-at-age. However, we show that introduction of CAAL data that are not representative of the age-structure of the population can cause bias and imprecision in estimates of not only growth, but also dynamics and management quantities. Estimation of an appropriate age-based observations-modeled process may improve model performance. We also show that even the use of representative CAAL data in a model with misspecified age-based systems-modeled processes (natural mortality and time-varying growth) can lead to bias and imprecision in growth, dynamics, and management quantities. In these cases, estimation of an age-based observations-modeled process magnified the bias and imprecision. Greater consideration of this type of data is needed.