Efficient statistical estimators and sampling strategies for estimating the age composition of fish

Estimates of age compositions of fish populations or catches that are fundamental inputs to analytical stock assessment models are generally obtained from sample surveys, and multistage cluster sampling of fish is the norm. We use simulations and extensive empirical survey data for Northeast Arctic cod (Gadus morhua) to compare the efficiency of estimators that use age-length keys (ALKs) with design-based estimators for estimating age compositions of fish. The design-based weighted ratio estimator produces the most accurate estimates for cluster-correlated data, and an alternative estimator based on a weighted ALK is equivalent under certain constraints. Using simulations to evaluate subsampling strategies, we show that otolith collections from a length-stratified subsample of one fish per 5 cm length bin (similar to 10 fish total) per haul or trip is sufficient and nearly as efficient as a random subsample of 20 fish. Our study also indicates that the common practice of applying fixed ALKs to length composition data can severely underestimate the variance in estimates of age compositions and that borrowing of ALKs developed for other gears, areas, or time periods can cause serious bias.