Management implications of temporally and spatially varying catchability for the Gulf of Mexico menhaden fishery

Abstract

Catchability relates fishing effort to fishing mortality, and is an important component in fishery stock assessment models. Mis-specifying catchability can lead to inaccurate estimation of model parameters and bias in the determination of stock status. The Gulf of Mexico has one of the largest seasonal occurrences of hypoxia in the world and it overlaps in time and space with the Gulf menhaden Brevoortia patronus fishery, potentially leading to temporal and spatial patterns in stock distribution and thus catchability. These patterns are not currently modeled in the Gulf menhaden stock assessment. To better understand the implications of spatial and temporal patterns in catchability due to hypoxia, we constructed an operating model of Gulf menhaden fishery dynamics under various assumptions of spatial coverages and temporal patterns, and used the output from the operating model as input into estimation models with alternative approaches on modeling catchability. Under the most extreme assumptions about the spatial coverage and magnitude of variation in catchability, median absolute error in estimates of fishing mortality and spawning stock reference points (F30% and S30%) was 73% and 29%, respectively, and median absolute error in estimates of fishing mortality and spawning stock based stock status was 23% and 79%, supporting the notion that errors in catchability are important. Under more reasonable assumptions, median absolute error declined to 20% and 2.9% for F30% and S30%, respectively, and to 3.8% and 2.4% for fishing mortality and spawning stock-based stock status, respectively. Modeling catchability as a random walk further reduced median absolute error to 5.0% for F30% and 1.4% for S30%, but slightly increased median absolute error for stock status indicators to 4.0% and 3.3%. Our results show generally that the spatial coverage, temporal pattern, and estimation approach of catchability affects the influence of mis-specifying catchability; and show specifically that the Gulf menhaden stock assessment is robust to the effects of hypoxia on catchability if assuming random-walk catchability.