A general theory of age-length keys: combining the forward and inverse keys to estimate age composition from incomplete data

There are two approaches to estimating age composition from a large number of length observations and a limited number of age determinations: the forward and the inverse age-length keys. The forward key looks at the distribution of age within each length bin while the inverse key looks at the distribution of length at each age. The former is more precise but has stringent requirements for the way data are collected. The latter approach is more widely applicable. We review the theory of the two keys with particular attention to necessary assumptions and the restrictions on when the methods are applicable. We show it is possible to combine the two approaches into a combined forward-inverse age-length key. This approach can be used to estimate age composition in several years simultaneously. It takes advantage of the efficiency of the forward key in years when that is appropriate, applies the inverse key to years with no age data, and uses a blending of the two approaches for years with moderate amounts of age data.