Using adaptive area stratification to standardize catch rates with application to North Pacific swordfish ( Xiphias gladius)

Abstract

This paper develops a new method to objectively construct an area stratification for standardizing catch-per-unit effort (CPUE) with generalized linear models (GLMs). This algorithm incorporates the advantages of binary recursion as used in regression trees to minimize a chosen objective function, and extends the concept of stepwise model selection to minimize an appropriate goodness-of-fit criterion for a chosen statistical model, such as GLM. The algorithm can adaptively search for area stratifications that achieved better GLM fits to the CPUE data. The new algorithm, which we call ‘GLM-tree’, is applied to swordfish CPUE data from Japanese longline vessels in the North Pacific as a case study. The GLM-tree algorithm was conducted with the fishery CPUE data under alternative assumptions about the structural complexity of the GLMs and alternative choices of goodness-of-fit criteria, e.g., Akaike or Bayesian information criteria. Results show that the GLM-tree algorithm created area stratifications more effectively than area stratification determined in an ad hoc manner, and made area stratifications with better fits to swordfish CPUE data until a goodness-of-fit criteria achieved minimum. The algorithm produced many alternative models under different model complexity and area stratifications, which could explain the swordfish CPUE data equally well, because the structural complexity of the GLMs can be compensated by increasing the number of areas. Effects of area stratifications on the estimates of standardized CPUE are also shown to indicate that estimates of the abundance indices tend to converge after a sufficient number of areas have been added.