Impacts of density-dependent growth and maturation on assessment advice to rebuild depleted U.S. silver hake (Merluccius bilinearis) stocks

Abstract

We examined how density-dependent growth and maturation rates would affect scientific advice to rebuild U.S. silver hake (Merluccius bilinearis) stocks to a minimum biomass threshold (SSB50) using an age-structured stochastic projection model. Uncertainty in recruitment and initial stock sizes at age was incorporated to more realistically capture the stochastic nature of the stock's dynamics through time. Performance measures including spawning stock biomass (SSBt), risk (prob(SSBt< SSB50)), and fishery yields were examined under model assumptions of static life history parameters in contrast with density-dependent parameters for various constant fishing mortality rate (F) harvest policies. Model results indicated that unless compensatory mechanisms are accounted for, scientific advice may be too optimistic and lead to unrealistic expectations of F targets to achieve stock rebuilding, requiring longer rebuilding times and entailing more risk and unrealized sustainable yield. For instance, projected median southern stock SSBt exceeded the SSB50 of 104 000 metric tons (t) with 40% risk to the stock by year 20 from harvesting at F = 0.50. However, under the density-dependent assumption, median SSBt did not rebuild as expected, and after 20 years reached only 75 000 t with 85% risk to the stock. Also under this assumption, median yields increased from 9000 to 27 000 t by year 20 but were 30-40% lower than what would have been expected under density independence.