Recent highly detailed catch-age models are sometimes termed statistical catch-age (SCA) models. Here, we use that term to refer to generalizations of VPA that use a forward solution of the catch equation. Most such models also differ from basic VPA in assuming that catch at age is subject to sampling error.
The major advantage of using a forward solution of model equations is the ease with which stock-specific detail can be added to the model structure. In SCA models, initial abundance of each cohort is typically estimated using a spawner-recruit model, and subsequent abundances are estimated using an age-structured population model, usually eqn . The Baranov catch equation provides estimates of catch at age.
Growth in computing power and the advent of specialized software packages have fostered increased detail in SCA models. A typical stock-specific model includes some of the following extensions: migration, changing selectivity or catchability over time, simultaneous estimation of growth from data on length and age composition, distinct modeling of many different gears, explicit treatment of discarded fish, and sex-specific submodels. Some SCA models estimate hundreds of parameters.
The complexity of the models described in the preceding two sections typically requires use of a compound objective function, in which appropriate objective functions for each type of data are weighted and added together. Objective functions have usually used least-squares or maximum likelihood, with either being conditional on the weights chosen. Estimates can be sensitive to the choice of weights, and this is an important research topic.
Although fishery models have become much more detailed and optimization techniques have improved, the basic equations of population dynamics have changed very little since VPA was introduced in the mid-1960s. In many cases, the limiting factor is uncertainty in the data. Even in well-studied species, surprises occur as aging and other biometric techniques improve.
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