Catch curve stock-reduction analysis: An alternative solution to the catch equations

Legislative changes in the United States and elsewhere now require scientific advice on catch limits for data-poor fisheries. The family of stock reduction analysis (SRA) models is widely used to calculate sustainable harvest levels given a time series of harvest data. SRA works by solving the catch equation given an assumed value for spawning biomass relative to unfished levels in the final (or recent) year, and resulting estimates of recent fishing mortality are biased when this assumed value is mis-specified. We therefore propose to replace this assumption when estimating stock status by using compositional data in recent years to estimate a catch curve and hence estimating fishing mortality in those years. We compare this new “catch-curve stock reduction analysis” (CC-SRA) with an SRA or catch curve using simulated data for slow or fast life histories and various magnitudes of recruitment variability. Results confirm that the SRA yields biased estimates of current fishing mortality given mis-specified information about recent spawning biomass, and that the catch curve is biased due to changes in fishing mortality over time. CC-SRA, by contrast, is approximately unbiased for low or moderate recruitment variability, and less biased than other methods given high recruitment variability. We therefore recommend CC-SRA as a data-poor assessment method that incorporates compositional data collection in recent years, and suggest future management strategy evaluation given a data-poor control rule.

[1]  James T. Thorson,et al.  Standardizing compositional data for stock assessment , 2014 .

[2]  André E. Punt,et al.  Evaluating methods for setting catch limits in data-limited fisheries , 2014 .

[3]  E. E. Holmes,et al.  Estimating risks in declining populations with poor data , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[4]  J. Thorson,et al.  Random effect estimation of time-varying factors in Stock Synthesis , 2014 .

[5]  André E. Punt,et al.  Model performance analysis for Bayesian biomass dynamics models using bias, precision and reliability metrics , 2012 .

[6]  Rainer Froese,et al.  Using global catch data for inferences on the world's marine fisheries , 2013 .

[7]  S. E. Wayte,et al.  An effective harvest strategy using improved catch-curves , 2010 .

[8]  K. Cochrane,et al.  Overview of World Status of Data-Limited Fisheries: Inferences from Landings Statistics , 2005 .

[9]  Peter-John F. Hulson,et al.  Effects of process and observation errors on effective sample size of fishery and survey age and length composition using variance ratio and likelihood methods , 2011 .

[10]  Ray Hilborn,et al.  Compensatory density dependence in fish populations: importance, controversy, understanding and prognosis , 2001 .

[11]  André E. Punt,et al.  Model performance for the determination of appropriate harvest levels in the case of data-poor stocks , 2011 .

[12]  Daniel H. Ito,et al.  Generalized Stock Reduction Analysis , 1984 .

[13]  J. Rice,et al.  Apocalypse in world fisheries? The reports of their death are greatly exaggerated , 2011 .

[14]  Rainer Froese,et al.  A Bayesian approach for estimating length‐weight relationships in fishes , 2014 .

[15]  FrancisR.I.C. Chris,et al.  Data weighting in statistical fisheries stock assessment models , 2011 .

[16]  Ian G. Taylor,et al.  A comparison of parametric, semi-parametric, and non-parametric approaches to selectivity in age-structured assessment models , 2014 .

[17]  D. Pauly,et al.  What catch data can tell us about the status of global fisheries , 2012 .

[18]  R. Hilborn,et al.  Status and Solutions for the World’s Unassessed Fisheries , 2012, Science.

[19]  E. Charnov,et al.  Evolutionary assembly rules for fish life histories , 2013 .

[20]  John Sibert,et al.  AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models , 2012, Optim. Methods Softw..

[21]  Daniel Pauly,et al.  Fisheries: Does catch reflect abundance? , 2013, Nature.

[22]  R. Myers,et al.  Influence of fecundity on recruitment variability of marine fish , 1996 .

[23]  James T. Thorson,et al.  Using model-based inference to evaluate global fisheries status from landings, location, and life history data , 2012 .

[24]  Jameal F. Samhouri,et al.  Giants' shoulders 15 years later: lessons, challenges and guidelines in fisheries meta‐analysis , 2015 .

[25]  J. Thorson,et al.  Better Catch Curves: Incorporating Age-Specific Natural Mortality and Logistic Selectivity , 2011 .

[26]  Jon T. Schnute,et al.  The importance of noise in fish population models , 1991 .

[27]  Elise F. Zipkin,et al.  How variable is recruitment for exploited marine fishes? A hierarchical model for testing life history theory , 2014 .

[28]  K. Winemiller.  Life history strategies, population regulation, and implications for fisheries management , 2005 .

[29]  Adrian R. Hordyk,et al.  Some explorations of the life history ratios to describe length composition, spawning-per-recruit, and the spawning potential ratio , 2015 .

[30]  U. Rashid Sumaila,et al.  Food security implications of global marine catch losses due to overfishing , 2010 .

[31]  M. Wilberg,et al.  An Evaluation of Harvest Control Rules for Data-Poor Fisheries , 2013 .

[32]  Steven J. D. Martell,et al.  A stochastic approach to stock reduction analysis , 2006 .

[33]  Mark N. Maunder,et al.  Review and evaluation of likelihood functions for composition data in stock-assessment models: Estimating the effective sample size , 2011 .

[34]  J. Hoenig,et al.  Estimating Mortality from Mean Length Data in Nonequilibrium Situations, with Application to the Assessment of Goosefish , 2006 .

[35]  J. V. Tagart,et al.  Stock Reduction Analysis, Another Solution to the Catch Equations , 1982 .

[36]  Ransom A. Myers,et al.  Maximum reproductive rate of fish at low population sizes , 1999 .

[37]  Implications of life-history invariants for biological reference points used in fishery management , 2003 .

[38]  M. E. Conners,et al.  Managing non‐target, data‐poor species using catch limits: lessons from the Alaskan groundfish fishery , 2010 .

[39]  Rowan Haigh,et al.  Compositional analysis of catch curve data, with an application to Sebastes maliger , 2007 .

[40]  J. Thorson,et al.  A new role for effort dynamics in the theory of harvested populations and data-poor stock assessment , 2013 .

[41]  David B. Sampson,et al.  An exploration of the shapes and stability of population–selection curves , 2012 .

[42]  Richard D. Methot,et al.  Stock synthesis: A biological and statistical framework for fish stock assessment and fishery management , 2013 .

[43]  D. Robson.  THE ANALYSIS OF A CATCH CURVE , 1960 .

[44]  André E. Punt,et al.  Extending production models to include process error in the population dynamics , 2003 .

[45]  J. Thorson,et al.  The determination of data-poor catch limits in the United States: is there a better way? , 2015 .

[46]  P. Spencer,et al.  Using productivity and susceptibility indices to assess the vulnerability of United States fish stocks to overfishing , 2010 .

[47]  M. Mangel,et al.  Reproductive ecology and scientific inference of steepness: a fundamental metric of population dynamics and strategic fisheries management , 2010 .

[48]  S. Martell,et al.  A simple method for estimating MSY from catch and resilience , 2013 .

[49]  Jason M. Cope.  Implementing a statistical catch-at-age model (Stock Synthesis) as a tool for deriving overfishing limits in data-limited situations , 2013 .

[50]  Richard D. Methot,et al.  Adjusting for bias due to variability of estimated recruitments in fishery assessment models , 2011 .

[51]  Alan Hastings,et al.  FITTING POPULATION MODELS INCORPORATING PROCESS NOISE AND OBSERVATION ERROR , 2002 .

[52]  Alec D. MacCall,et al.  Depletion-Based Stock Reduction Analysis: A catch-based method for determining sustainable yields for data-poor fish stocks , 2011 .