Many developments in catch-age analysis beyond basic VPA have aimed at reducing the number of estimated parameters and thus allowing a reasonable error structure. A common approach has been to consider Fa, as the product of a time factor and an age factor. The age factor is often parametrized by use of a selectivity curve (e.g., eqn ). This approach has been called 'separable VPA', for the separation of F into components due to selectivity (age or length) and time. The separability assumption is also found in many more detailed catch-age models.
A second common extension is use of auxiliary data, such as indices of abundance, to help shape the estimates. This can, to some degree, resolve the indeterminacy of VPA in estimating current population status.
Other common extensions include conditioning estimates on a spawner-recruitment function; modeling error in the catch-at-age data; and partitioning selectivity, catch, and fishing mortality by fleet. Standard errors of estimates are derived through analytical approximations or resampling procedures, including the bootstrap.
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