Estimation of the two-stanza growth curves with age determination uncertainty for Pacific blue marlin (<i>Makaira nigricans</i>) in the western and central North Pacific Ocean

Abstract The Pacific blue marlin (Makaira nigricans) is a highly migratory apex predator of ecological and economic importance. However, uncertainties in age and growth estimates remain a challenge for stock assessments. This study aims to refine these estimates by integrating otolith micro-increment counts from 13 juveniles (115–152 cm eye-to-fork length, EFL) and sectioned dorsal fin spines from 504 juveniles and adults (115–269.4 cm EFL) collected off Taiwan waters, together with historical length-at-age data compiled by the ISC International Billfish Biological Sampling Program using fin spine- (n = 591, 118–321.9 cm EFL) and otolith-based (n = 27, 17.2–159.7 cm EFL) methods and bomb radiocarbon dating (n = 1, 330.5 cm EFL) on specimens sampled across the western and central North Pacific Ocean (WCNPO). The combined otolith dataset (n = 40) yielded daily age estimates ranging from 26 to 349 days, with the Gompertz model predicting an EFL of 146.92 cm at age one. Port-sampled blue marlin from Taiwan showed similar observed age ranges for both sexes: females aged 1.5–11 years (142.8–269.4 cm EFL) and males 1–10.5 years (133–208 cm EFL). Across the WCNPO, the combined spine and bomb radiocarbon dataset showed age ranges of 1–27 years for females (136–330.5 cm EFL) and 1–18 years for males (118–232.1 cm EFL). Growth was sexually dimorphic, with females growing faster and consistently attaining greater mean lengths-at-age than males from age one onward. Mean marginal increment ratio analysis indicated annual growth band formation primarily in Sep–Oct. Sex-specific von Bertalanffy and two-stanza growth models (TSGM) were fitted using a Bayesian errors-in-variables approach to account for age determination uncertainty. The TSGM better described growth patterns, capturing a transition near age one and providing an improved fit, particularly for older individuals, as indicated by lower Deviance Information Criterion values. This is the first study on blue marlin growth to cover a broader size range and spatial distribution in the WCNPO, enhancing the accuracy of growth parameter estimates for stock assessment models. The study also addresses limitations and outlines potential directions for future research.