A mixture model approach to derive within-season, cohort-specific CPUE for arrow squid (Nototodarus sloanii)

This analysis modelled observed length distributions of the New Zealand arrow squid (Nototodarus sloanii) fishery in an attempt to separate length cohorts in space and time, with a view to deriving catch-per-unit-effort (CPUE) indices that may track the successive depletion of these cohorts by the trawl fishery in SQU 1T (Stewart-Snares shelf) and SQU 6T (Auckland Islands).

To gain an understanding of length distributions over spatial and temporal scales, a range of plots were inspected for patterns in length (presented in a companion report, characterising the fishery). These analyses suggested coherent, but somewhat temporally separated, length dynamics at Auckland Islands and the Stewart-Snares shelf. The patterns further suggested the presence of two dominant cohorts in most years in each area; however, this pattern was not evident in all years, and, in some years, more than two length cohorts may be present.

Based on the descriptive analyses, we constructed a mixture model to predict whether a fishing event was fishing on an early-season (e.g., autumn) or late-season (e.g., spring) cohort. The model was then used to estimate cohort-specific CPUE, providing a proof-of-concept for jointly estimating cohort contributions to fishing events based on fishery length frequencies, and estimating within-season CPUE from these cohorts. The model was applied to a subset of years with considerable observer coverage, for which patterns in CPUE suggested consistent depletion of numbers in the late cohort, while also showing little consistency in trends for the early cohort in both areas (although the early cohort was only consistently fished at Auckland Islands for the years considered in the present model).

The development of an integrated model to capture fishing on separate cohorts, and the temporal evolution of CPUE within seasons, opens the possibility to apply within-season DeLury depletion type models for SQU 1T and SQU 6T. Although there are a number of improvements and extensions to the present model that would likely improve the accuracy of estimated trends by providing a closer match to data, the present model demonstrates the potential to develop such models, and to derive potentially valuable indices of cohort abundance.