Extending integrated stock assessment models to use non-depensatory three-parameter stock-recruitment relationships

Abstract

Stock assessments based on the integrated paradigm often include an underlying stock-recruitment relationship. This, along with estimates of fishery selectivity and biological parameters, allows the biomass and fishing mortality associated with Maximum Sustainable Yield (BMSY and FMSY respectively) to be calculated. However, the estimates of these quantities may differ from the proxies assumed in the harvest control rules that are used to provide management advice. Moreover, the estimated values for BMSY and FMSY are related functionally in population dynamics models based on 2-parameter stock-recruitment relationships such as the commonly used Beverton-Holt or Ricker relationships. Use of 2-parameter stock-recruitment relationships (SRRs) consequently restricts the ability to fully quantify the uncertainty associated with estimating BMSY and FMSY because 2-parameter SRRs restrict the potential range of values for BMSY/B0. In principle, BMSY/B0 and FMSY can be more independent if the stock-recruitment relationship is more general than these 2-parameter SRRs. This paper outlines eleven potential 3-parameter stock-recruitment relationships and evaluates them in terms of whether they are able to match a wide range of specifications for BMSY (expressed relative to unfished spawning stock biomass, B0) and FMSY (expressed relative to natural mortality, M). Of the eleven 3-parameter stock-recruitment relationships considered, the Ricker-Power stock-recruitment relationship is found to best satisfy the characteristics of (a) being able to mimic a wide range of BMSY/B0 and FMSY/M values, (b) not to lead to negative recruitment for biomasses between 0 and B0, and (c) not to lead to increasing recruitment while approaching the limit of zero population size. Bayesian assessments of three example groundfish species off the US west coast (aurora rockfish, petrale sole, and cabezon) are conducted using Simple Stock Synthesis based on the Beverton-Holt and Ricker-Power stock-recruitment relationships to illustrate some of the impacts of allowing for a 3-parameter stock-recruitment relationship.