Estimating Patagonian toothfish ( <i>Dissostichus eleginoides</i> ) length at first maturity from their age, sex and temperature experience around South Georgia

Patagonian toothfish (Dissostichus eleginoides) are a long-lived, slow-growing deep-sea species endemic to the Southern Hemisphere and the focus of longline fisheries managed to ensure sustainable exploitation. Managing the fisheries relies on accurate stock assessments that include pertinent biological and exploitation processes. Length and age at first maturity are key biological parameters used in the stock assessments for Patagonian toothfish in South Georgia (Subarea 48.3). The conventional approach to estimating length and age at first maturity relies on macroscopic gonadal staging, but this may be confounded by the difficulty in distinguishing immature and mature resting (i.e., skipped spawning) individuals. Here, we extend existing length-at-age breakpoint models to incorporate sex and individual temperature experience, while accounting for increasing variation in length with age. We fit and compare a set of candidate models to assess the empirical evidence for temperature experience effect on sex-specific length at first maturity estimates using data from 3683 Patagonian toothfish sampled by both commercial longline fisheries and scientific surveys around South Georgia between 2010 and 2023. Our analysis supports an expected non-linear effect of age on length, with a higher age at first maturity for females compared to males, and demonstrates that temperature experience explains significant variation unaccounted for by age and sex alone, showing an inverse relationship between the temperature experienced by Patagonian toothfish and their length-at-age. These findings have direct implications for improving the biological realism and predictive accuracy of stock assessment models, particularly under climate change.