Most, if not all, population dynamics (recruitment, growth, natural mortality, movement) or fisheries process (selectivity, index catchability) vary over time. However, few stock assessment models deal with this temporal variation comprehensively. Most will model temporal variation in recruitment and treat it as a random effect is some way. This means that recruitment is assumed to come from a distribution so that recruitment for time periods where there is incomplete information is informed by time periods where there is information. Traditionally, this has be implemented within a penalized likelihood context and the standard deviation of the distribution is assumed (e.g., 0.6) due to difficulties estimating the standard deviation within the assessment without integration across the random effect. Notoriously, this has caused complications due to the use of the lognormal bias correction factor. Bayesian stock assessments did not have this complication and iterative approximations are available. The introduction of La Place approximation in ADMB and the consequent development of TMB has facilitated integration across the random effects. Stock Synthesis and MULTIFAN-CL, which are used for many tuna assessments, are not based these software.
The introduction of La Place approximation has facilitated the development of more comprehensive state-space models (e.g., SAM and WHAM). State-space models and random effects for temporal variation in population and fishing processes are the same thing, although the term state-space model is generally used for more comprehensive use of random effects. A typical state-space models includes temporal variation in recruitment and survival (combined fishing and natural mortality or directly in natural mortality). Temporal variation in selectivity is often modelled and is an integral characteristic of SAM.
Clearly, random effects are a vital part of any contemporary stock assessment model. However, as more processes are allowed to vary and the standard deviations of the distributional assumptions for this variation are estimated, the computational demands will increase, parameter estimability will become more difficult, and data requirements will increase.