Composite per-recruits: Alternative metrics for deriving biological reference points of fishery resources

Abstract

Most exploited aquatic populations lack the fishery selectivity and life-history information, by age/size, needed to develop harvest control rules (HCRs). This study relies on stage-structured life-history and fishery characteristics inherent in delay-difference models to set out a typology of composite (age-aggregated) yield per-recruit (CYPR) models along with composite spawning stock per-recruit (CSSR) models and composite spawning per-recruits (CSPRs) and propose the related, conventional-like biological reference points, which may prove useful in devising HCRs, especially for data-poor stocks. CYPR, CSSR, and CSPR are equilibrium and interrelated metrics controlled by fishing mortality. Inputs to their development include growth and natural mortality parameters and, eventually, stage-specific selectivity, natural mortality, and maturity. In spite of numerous formulations of CYPRs denoted CYPR1 to CYPR15, CYPRs fall into three types of equations following from the Leslie–DeLury depletion model family for open populations (prototype: CYPR3), the Deriso–Schnute delay-difference model family (prototype: CYPR9), and some differential forms of the previous two model families (prototype: CYPR14). CYPR3, CYPR9, and CYPR14 exhibit, respectively, patterns increasing monotonically toward asymptotes and dome-shaped patterns which, beyond their maxima, trend toward the mean weight-at-recruitment and zero. Comparisons of fishing mortality-based biological reference points (FBRPs) from CYPRs and CSPRs with the fishing mortality producing the maximum sustainable yield (FMSY) or FMSY proxies from 53 data-rich stock assessments on the US East Coast indicate that some FBRPs are accurate estimators of FMSY or FMSY proxies. CYPR14 is the recommended CYPR for determining the plausible sustainability status of data-poor stocks because it accommodates more growth parameters, maximizes at a fishing mortality rate that qualifies for FMSY and has the greatest accuracy about FMSY for the majority of data-rich stocks. Composite per-recruit models should be used in stage-structured model assessments in the same way that conventional per-recruit models are used in age- and length-structured model assessments.