Stochastic Stock Reduction Analysis (SRA) User Guide
Contents
1. mortality estimates Exploitation is calculated as catch vulnerable biomass Optional Input Files There are two optional input files for SRA length data csv and age data csv Optional data files can be provided that include single or multiple years of size and or age composition data sampled from the fishery When included data from these files are assumed to have been collected from representative multinomial sampling of the catch size age composition Age composition data files may contain any number of years of data from samples taken annually The order that these files are read into SRA does not matter Note The age and length sample tables do not need to involve contiguous years but must have the same number of age or size classes sampled every year Constructing length csv file The file contains the count of the number of fish per length bin for a specific number of years and length bins The first line contains three numbers the first number is the number of years sampled the second is the number of length bins included in the sample 1 and the third number is the number of lengths increments in the bins The numbers of increments between length bins are categorized as follows 0 lengths 0 to binwidth 1 lengths binwidth to 2 binwidth 2 lengths binwidth to 3 binwidth 3 lengths binwidth to 4 binwidth The user creates the binwidths The number of years in the length csv can be fewer years than the entire catch2. Current stock and harvest rate P overfishing 0 01 P overfished 0 00 B scaler U Umsy 0 Compensation ratio Ubar 2003 2005 EGG EGGo B Bo 12 Figure 4 Stochastic SRA model interface once MCMC iterations are manually or automatically stopped To save the interface enlarge the SRA interface CTRL Print Screen and Paste into Microsoft Powerpoint Word Ecel Remember to also save the output files in a separate folder a new compile of SRA will overwrite these output files pA Stochastic SRA parfile tilefish_23 1_all uncern par datafile Tilefish_23 1_all uncern csv Files i Parameters Run Priors Bhat 2003 6000000 Uhat 2008 01 growth von B K n growth linfinity cm r Show Posterior SD Bhat SD Uhat Prop of ISIR Samole ae ee CV length age p fisher N trials to run 7900 SD rec 05 ae the sample vear o nae o Recruitment autocorrelation rho oo IESE 100 max Future TAC kg 16000 eer Run MCMC sampling iLL Do MUMU eu A Age at maturity for SSB samol Sample individual survival for Na lt 1000 oor 2 Sample distribution of Umsy and MSY values P J 1 Bycatch params 500 Number of trials foao 000000 MSY min 10000 Umsy min 0 05 Smin 0 84 bycatch before MSY max 500000 Umsy max 9 5 S max 0 88 compensation Trials 654221 282764 ize di ae 0 future Prop of Mean NPY 4162 3 pee ed neor 00000001 o bueaich U RED Prop crashed a 09 ge distn weight 00000001 0 03 Szero sampl
3. averaged over simulation trials It only has meaning when you are comparing alternative future TAC or U policies RecK Good year s Recruitment Compensation Ratio recK is calculated from estimates of Umsy and MSY values and SRA s sampler will only except positive integers for recK Any combinations of Umsy and MSY that yield a negative recK are ignored Refer to the Compensation ratio plot see Figure 1D at the bottom of the interface for the distribution of calculated recK values Run Error SRA will occasionally stop and a Run Error window will appear Possibly causes for this error 1 Incorrect set up of csv file no blank lines are allowed check end of file 2 MCMC sampling is experiencing trouble sampling along a narrow ridge of parameter combinations re evaluate population parameters variation in index standard deviation of recruitment etc Suggest opening Par csv from the crashed model run to view parameter values normally in this kind of error there is no change in MSY Umsy S E year Eo U year Umsy and RecKs are mostly negative Survival rate Survival rate S is S exp M A general observation from Pauly s meta analysis of natural mortality M is that M should be between 1 1 von B K and 1 6 von B K where K is the von Bertalanffy metabolic parameter But another estimator of M would be the Hewitt Hoenig estimate from maximum age M 4 3 max age Considering setting the S range depending on the uncert
4. file line and after the relative abundance data on each of the lines in the data block You must edit out those spurious commas before using SRA A simpler option is to save the file as a txt in Excel and then open the txt file in a Text Editor e g TextPad and resave the file with a csv extension For example tilefishSRA csv red grouperSRA csv red snapper history csv 5 10 Yearl catchyrl agelyrlvul age2yrlvul age3yrlvul age4yrlvul aged5yrlvul Year2 catchyr2 agelyr2vul age2yr2vul age3yr2vul age4yr2vul age5yr2vul Yearl0 catchyrl10 agelyrl0vul age2yrl0vul age3yrl0vul age4yr1l0vul age5yr10vul Yearl index relative recruitment anomaly standard deviation Year2 index relative recruitment anomaly standard deviation Year6 index relative recruitment anomaly standard deviation Constructing life history parameters par file This file contains all population and recruitment parameters There are a total of 20 parameters A convenient way to generate a par file is to simply open the SRA executable file using an existing life history parameters file par for a species roughly similar to the one being modeled edit the parameters in the interface then save the modified life history parameter file par file under the new name Users should NEVER edit with the par file directly Rather use the SRA interface to build or modify the par file For example tilefishSRA par red grouper SRA par red snapper SRA par Table 1 List o
5. fit E Current stock and harvest rate P overfishing 0 36 P overfished 0 55 EGG EGGo B Bo 23 Appendix 3 Summary of SRA output parameters par cvs Purpose provides parameter summaries from output of Stochastic Stock Reduction Analysis SRA Data file Par csv ouput file from SRA Data output unique read table Par csv sep header T only unique rows used for analysis attach output output2 subset output output RecK gt 0 removes negative recK values from dataframe output3 subset output2 output2 RecK lt 101 removes larger than 101 recK values from dataframe biomassbenchmark output2 SSB2009 output2 SSBmsy Ucurrent output2 Umsy output2 U2009 Umsy Output print Summary Yellowedge Grouper WEST GOM CMLL Index print Estimates of Maximum sustainable yield print mean output2 MSY print sd output2 MSY print summary output2 MSY print Estimates of Exploitation at MSY print mean output2 Umsy print sd output2 Umsy print summary output2 Umsy print Estimates of Current Exploitation print mean Ucurrent print sd Ucurrent print Summary Ucurrent print Summary recK print recK all positive values print mean output2 Reck print sd output2 Reck print summary output2 Reck print recK all values between 1 and 100 print mean output3 Reck print sd output3 Reck print summary output3 ReckK print Summary Total Biomass last year pr
6. 0 MSY 19000 1 Age max 3 00 Umsy Min age fit E Current stock and harvest rate P overfishing Figure 1D P overfished 0 Compensation ratio U Umsy EGG EGGo B Bo Figure tH Executing SRA Platform specifications Microsoft Windows 2003 XP Download and save the executable SRA file to a folder labeled SRA Copy and paste the input files in this same folder It does not matter where in your directory this folder is located it only matters that the executable and the input files are located in the same folder Open the SRA executable file Install input files Files gt Read parameters gt select par file Files gt Read time series data gt select csv file Files gt Read length data gt select csv file optional Files gt Read age data gt select csv file optional Run Priors The user can indicate the number of trials Figure 1B as well as the number of years to simulate before either the MCMC or SIR sampling is conducted MCMC minimum 1 000 is the preferred sampling procedure since MCMC does not require as many priors as SIR procedure minimum 1 000 000 After the trails are compiled the user should visually inspect the distribution of data shown in the plots on the interface If the plot of the vulnerable biomass trajectories is not displayed correctly than either increase or decrease the biomass scaler default 0 5 Figure 1C If the sample distribution of Umsy and MSY values is
7. 1 Pop csv A grid of MCMC sample frequencies for biomass over time biomass grid points in columns relative frequencies of occurrence in rows Par csv The MCMC sampled estimates of maximum sustainable yield MSY exploitation at MSY Umsy survival rate S egg production for the final year of data egg production in the virgin year E year Eo exploitation for the final year of data exploitation at MSY U year Umsy Goodyear s recruitment compensation ratio RecK biomass total in final year of data Btot 2009 spawning stock biomass for the final year of data SSB 2009 and spawning stock biomass at maximum sustainable yield SSBmsy The output does not contain the first 200 MCMC burn in iterations This data is not automatically plotted R code is provided for basic plots of MSY Umsy S Ucurrent RecK and stock status see Appendix 2 The Par csv file contains multiple duplicate rows and rows of unique values The total number of trials equals the total number of rows The number of unique rows equals the number of accepted trials PopandU csv The best population pop estimates and exploitation u estimates for each year estimated as the mean values of the sampled biomass and exploitation combinations during the MCMC these modes do not necessarily correspond to any single trajectory sampled during the MCMC trials that trajectory is in bestfit csv This data is not automatically plotted Note The population estimates show
8. SB2009 outputalldata2 SSBmsy Provides the number of ratios nbiobenchmark length biomassbenchmark Proportion Overfished provides the number of biomass benchmarks are less than one noverfished length subset biomassbenchmark biomassbenchmark lt 1 0 percentoverfished noverfished nbiobenchmark 100 print Proportion Overfished print percentoverfished Provides the number of ratios nexploitbenchmark length outputalldata2 U2009 Umsy Proportion Overfishing provides the number of exploitation benchmarks are greater than one noverfishing length subset outputalldata2 U2009 Umsy outputalldata2 U2009 Umsy gt 1 0 percentoverfishing noverfishing nexploitobenchmark 100 print Proportion Overfishing print percentoverfishing Graphs Graph x and y limits may need to be adjusted given your data x11 width 80 height 50 pointsize 8 par mfrow c 2 1 utils str hist outputalldata2 MSY xlim c 30000 100000 ylim c 0 150000 breaks 30 col green3 labels TRUE xlab Maximum Sustainable Yield utils str hist outputalldata2 Umsy xlim c 0 05 0 20 ylim c 0 150000 breaks 25 col darkorange labels TRUE xlab Exploitation at MSY Graph x and y limits may need to be adjusted given your data x11 width 20 height 5 pointsize 8 utils str hist outputalldata3 RecK xlim c 0 100 ylim c 0 300000 breaks 25 col blue2 labels TRUE xlab Goodyear s Compen
9. Stochastic Stock Reduction Analysis SRA User Guide 1 3 2 3 Linda Lombardi and Carl Walters NOAA Fisheries Service gt 3500 Delwood Beach Road Panama City FL 32408 Linda Lombardi noaa gov GAN 2 S University of British Columbia Fisheries Centre British Columbia Vancouver c walters fisheries ubc ca ae UNIVERSITY of UF FLORIDA University of Florida Institute of Food and Agriculture Sciences School of Forest Resources and Conservation Fisheries and Aquatic Sciences Gainesville FL 32653 Panama City Laboratory Contribution 2011 03 Preface This manual provides procedures for the use of Stochastic Stock Reduction Analysis for the executable produced in January 2011 These procedures are subject to change given future model changes Opinions expressed herein are of the authors and do not imply endorsement by NOAA Fisheries Service National Marine Fisheries Service This report was subject to review by the NOAA Section 515 Information Quality Guidelines abiding by the Information Quality Act and Pre Dissemination Review Guidelines Citation Lombardi L and C Walters 2011 Stochastic Stock Reduction Analysis SRA User Guide NOAA Fisheries Service Southeast Fisheries Science Center Panama City Laboratory 3500 Delwood Beach Road Panama City Florida 32408 Panama City Laboratory Contribution 11 03 p 26 Introduction Stochastic stock reduction analysis SRA is a stochastic age structu
10. acific Coast Fishery Management Plan NOAA Technical Memorandum NOAA TM NMFS SWFSC 460 22 Figure A2 1 Stochastic SRA model interface for aurora rockfish Stochastic SRA parfile aura life history par datafile ARRA landings csv Files Run Priors Stop Parameters Bhat 2003 500 Uhat 2008 0 03 Show Posterior SD Bhat SD Uhat ISIR Samole Se oS N trials to run 10000 SD rec 19 5 een o Recruitment autocorrelation rho g 100 max Future TAC kg fo or Ufuture jor bas hueniemaa ds Age at maturity for SSB 5 7 Sample individual survival for Na lt 1000 Par Step Anom ster 1 Number of tnals 1000000 MSY min o Umsy min 00 Smin 0 92 bycatch before MSY max 100 Umsymax p72 Smax foe compensation Trials 1602587 ge future Mean NPV 1 7 PEA a sev 00000001 jo bycatch U Prop crashed ge distn weight 00000001 0 03 Szero Discount rate jog growth von B K growth linfinity cm C length age length maturity cr wt kg at 100 cm growth tzero Legal length Lorenzen survival Representation of parameter uncertainty Bycatch params Use historical anomaly estimates War of abundance index 04 6 747 5 Yul B B Catch Rec Aron Ubar 2003 2005 Se 1916 Assume flat U for yrs g to fo Prop of fisher sample Ocm Fish length cm Figure A2 1A Sample distribution of Umsy and MSY values 100 0 Compensation ratio 1 Age max Min age
11. ainty in the natural morality estimate for your species modeled Variance in Index of Abundance Labeled var of abundance index on the SRA interface is defaulted to 0 04 Figure LE This is the assumed observation variance of the log relative to the index of abundance e g log CPUE corresponding to catchability biomass mean value for each year The default value represents a standard deviation CV on arithmetic scale of around 0 2 a typical for relative abundance time series Using higher variance values Increasing the variance does not only assume the CPUE is noisy but has another effect namely to spread out the likelihood function so that the MCMC has higher acceptance rates allowing it to move over the parameter space more widely and thus find the ridge of high probability combinations for U 2009 Umsy and E year Eo Weight at 100cm Although your species may not reach this size this weight provides any easy way to parameterize the length weight relationship 18 Literature Cited Forrest R Martell S Melnychuk and C Walters 2008 Age structured model with leading management parameters incorporating age specific selectivity and maturity Can J Fish Aquat Sci 65 286 296 Schnute J T and A R Kronlund 1996 A management oriented approach to stock recruitment analysis Can J Fish Aquat Sci 53 1281 1293 Southeast Data Assessment and Review SEDAR 2005 Stock Assessment Report of SEDARO7 Gul
12. al future exploitation growth von B K 0 12 growth Linfinity 37 cm oat cant ck Values except for wt kg at 100 cm and CV length em at age reported in Dick and MacCall 2010 Age at maturity 5 wt kg at 100 cm 11 26 growth tzero 0 Range of MSY was manipulated until distribution of MSY Mor Tange 0 100 eect distributed Figure A2 1A The initial values of Umsy were set at Fmsy 0 05 Umsy range 0 01 0 12 Range of Umsy was manipulated until distribution of Umsy was normally distributed Figure A2 1A S range 0 92 0 96 M 0 06 maximum age 75 yr Dick and MacCall 2010 21 Constructing csv file Catch mt by year 1916 2009 Age vulnerabilities knife edge vulnerabilities beginning at age 5 No Index and No recruitment anomalies Table A2 1 Comparison of Overfishing Limits OFLs among three assessment models Stochastic Stock Reduction SRA Depletion Based Stock Reduction Analysis DB SRA Dick and MacCall 2010 and Simple Stock Synthesis SSS J Cope pers comm NWEFSC Seattle WA Overfishing limits in SRA were calculated by multiplying the predicted vulnerable biomass in the last year of data by Umsy Model OFLs in 2010 SRA Uhat 0 03 0 02 bot SRA Uhat 0 03 0 50 43 DB SRA 47 median SSS with symmetric depletion prior 56 median SSS with informed beta depletion prior 66 median Literature Cited Dick E J and A D MacCall 2010 Estimates of sustainable yield for 50 data poor stocks in the P
13. e Discount rate 0 97 Use historical anomaly estimates Var of abundance index 04 Ocm Fish length cm Lorenzen survival Representation of parameter uncertainty 11 002 316 1 Age max Vul B Jl Min age fit ni Current stock and harvest rate B P overfishing 0 01 P overfished 0 00 Catch An Rec Anoms CIN 1965 Assume Tie dl o tjo Ubar 2003 2005 EGG EGGo B Bo 0 Compensation ratio 13 Figure 5 Stochastic SRA interface with optional age data To use the optional age and length data within the model computations the user must change the Size or Age Distn weight value from the default 0 00000001 to a value within the range 0 1 1 0 1 0 age or length composition highly reliable F Stochastic SRA parfile red snapper par datafile Red Snapper history csy agedatafile red snapper age data csv Stop Pocdekh growth von B K 0 18 Bhat 2008 g000000 Uhat 2008 p 5 growth linfinity em 98 show Posterior SD Bhat SD Uhat Prop of ISIR Sample ee ate CV length age 0 08 isher length maturity om N trials to run 49000 SD rec 0 5 a kg at mt all i r sample Taars lo Smila Eo Recruitment autocorrelation rho g TERNE w 100 max Future TAC kg 1000 AOTEA QOcm Fishlength cm or Ufuture 0 2 DookeEsamnio Age at maturity for SSB fi pig F Sample individual survival for N ample individual survival for Na lt 1000 e Loreren suwal eee l 2 Re
14. e This file contains the total catch per year age and year specific vulnerabilities and an index of abundance The first row of the file has two numbers specifying the maximum age of fish to use in the simulations and number of years of historical catch data in the file Age vulnerabilities must be provided for each age 1 maximum age The following file rows one for each year specifies the total catch for that year in biomass units and age specific vulnerabilities for all ages these typically change over time so a separate schedule is allowed for each year Following the annual catch records is the relative abundance time series data CPUE or other index of abundance is entered Each row of the relative abundance data block has four numbers sample year abundance index value an independently estimated log normally distributed relative recruitment anomaly for that year value of 0 0 corresponds to average recruitment predicted by stock recruit relationship and the standard deviation of the relative abundance CPUE value of 1 0 moderate uncertainty in index The number of years in the index can be fewer years than the entire catch series Do not leave any blank lines at the end of the csv file This will cause a Run Error and SRA will stop compiling Note If you create a new csv comma delimited text data file and save it using Excel then Excel will insert a set of commas after the number of years and ages on the first
15. e file as a txt in Excel and then open the txt file in a Text Editor e g TextPad Tinn R and resave the file with a csv extension Figure 1 Stochastic SRA model interface Bi Stochastic SRA Parameters Bhat 2004 s0000 SD Bhat 10000 SD rec 0 6 Recruitment autocorrelation rho g Future TAC kg 10000 or Ufuture 0 2 growth von B K 0 0231 growth linfinity em 1412 8 C length age 0 09 length maturity cm 165 wt kg at 100 cm 97938 growth tzero Legal length g Age at maturity for SSB i Uhat 2004 g 2 SD Uhat Figure 1B 2 N trials to run fi 000 Years to simulate 50 100 maxi 50 Run MCMC sampling Do MLML samole Sample individual survival for Na lt f1000 Rarsteni 2 IS MICE eoesentaton of parameter uncertainty Smin 0 9 Anom Step 4 MSY min 19000 Umsy min MSY mas 25000 Umsy max S max fo 0 93 Number of trials 1000000 Size distn weight ooo00001 Figure 1E Age distn weight 00000001 7 Lorenzen survival Bycatch params bycatch before compensation future bycatch U 0 02 Szero Trials done NPV Figure 1G Prop Crashed Discount rate fo 97 20 554 666 Vul B Figure IC B scaler fos Use historical anomaly estimates Var of abundance index 104 C N Ubar 2003 2005 1880 Assume flat U for yrs fo to fo Prop of fisher sample Ocm Fish length em Figure 1A Sample distribution of Umsy and MSY values 2500
16. f of Mexico Red Snapper Report 1 SEDAR One Southpark Circle 306 Charleston SC 29414 SEDAR 2006a Stock Assessment Report of SEDAR10 Gulf of Mexico Gag Grouper Report 2 SEDAR One Southpark Circle 306 Charleston SC 29414 SEDAR 2006b Stock Assessment Report of SEDAR12 Gulf of Mexico Red Grouper Report 1 SEDAR One Southpark Circle 306 Charleston SC 29414 SEDAR 2008 SEDAR 15A Stock Assessment Report 3 SAR 3 of South Atlantic and Gulf of Mexico Mutton Snapper One Southpark Circle 306 Charleston SC 29414 SEDAR 2011a Stock Assessment Report of SEDAR 22 Gulf of Mexico Yellowedge Grouper Report 1 SEDAR One Southpark Circle 306 Charleston SC 29414 SEDAR 2011b Stock Assessment Report of SEDAR 22 Gulf of Mexico Golden Tilefish Report 1 SEDAR One Southpark Circle 306 Charleston SC 29414 Walters C J S J D Martell and J Korman 2006 A stochastic approach to stock reduction analysis Can J Fish Aquat Sci 63 212 223 19 Appendix 1 Editing par csv file for use in R The header of the par csv file needs a few edits before used in the following R files Original header MCMC MSY Umsy S E 2009 Eo U 2009 Umsy Reck Btot 2009 SSB 2009 SSBmsy Need to remove the following MCMC Space between E 2009 Space between U 2009 Space between Btot 2009 Space between SSB 2009 Edited header MSY Umsy S E2009 Eo U2009 Umsy RecK Btot2009 SSB2009 SSBmsy 20 Appendix 2 Model Example In Marc
17. f parameters for par input file Parameter Definition Bhat year Biomass in the last year will reflect last year of data SD Bhat Standard Deviation of Number of fish last year Uhat year Exploitation for the last year SD Uhat Standard Deviation of Uhat SD rec Standard Deviation of RecK Rec rho Recruitment Residuals Future Catch Amount of future landings catch Ufuture Future exploitation growth von B K growth Linfinity cm CV length age length maturity cm Age at maturity wt kg at 100 cm growth tzero MSY min MSY max Umsy min Umsy max S min S max von Bertalanffy growth coefficient von Bertalanffy asymptotic length Variation of length at age Length at maturity Age at maturity first age for spawning stock biomass Size weight of fish at 100 cm Size length cm at time zero Minimum of Maximum Sustainable Yield Maximum of Maximum Sustainable Yield Minimum of Exploitation at MSY Maximum of Exploitation at MSY Minimum Survivalship S 0 02 Maximum Survivalship S 0 02 The minimum and maximum values for Maximum Sustainable Yield MSY and Exploitation U at MSY are best visually estimated as priors are compiled Visually inspect the relationship between the sample distribution of MSY and Umsy when priors are run see Figure 1A Exploitation Uhat is best estimated from fishery independent tagging study If no such are data available then examine the difference between total and natural
18. h 2011 SRA was presented at the Assessment Tools Workshop Oregon State University Portland Oregon This workshop s focus was simple stock assessment models for data poor species Several models were discussed and SRA was applied to one of the 50 data poor stocks managed in the Pacific Coast Groundfish Fishery the aurora rockfish Sebastes aurora SRA results were compared to model runs from Depletion Based Stock Reduction Analysis DB SRA Dick and MacCall 2010 and Simple Stock Synthesis SSS J Cope pers comm NWFSC Seattle WA DB SRA and SSS are based on 4 main data inputs 1 natural mortality M 2 ratio of Fmsy M 3 ratio of Bmsy K K carrying capacity and 4 relative stock status SSS also requires weight length relationships as well as dimensioning of the length and age bins The comparisons of these three models provide an example of using limited data input through a variety of model compilations Resulting Overfishing Levels OFLs were similar among models Table A2 1 SRA model inputs Constructing par file Parameter Value Comment Initial value calculated using average historical catch 29 Bhat year 500 int divided by exploitation 0 05 SD Bhat 3000 Assumed large uncertainty in biomass Uhat year 0 03 The initial value for Uhat was 0 03 with SD Uhat 0 02 SD Uhat 0 05 SD Uhat was increased to 0 05 for final model runs SD rec 0 5 Default value Rec rho 0 Default value Future Catch 0 Ufuture 0 1 Based on minim
19. int mean output2 Btot2009 print sd output2 Btot2009 print summary output2 Btot2009 print Summary Spawning Stock Biomass last year print mean output2 SSB2009 print sd output2 SSB2009 print summary output2 SSB2009 print Summary Spawning Stock Biomass at MSY print mean output2 SSBmsy print sd output2 SSBmsy print summary output2 SSBmsy print Summary SSBcurrent SSBmsy print mean biomassbenchmark print sd biomassbenchmark print summary biomassbenchmark print Summary Ucurrent Umsy print mean output2 U2009 Umsy print sd output2 U2009 Umsy print summary output2 U2009 Umsy 24 Appendix 4 Plotting parameters of SRA output and Stock Status Figure Purpose plot simulated estimates of MSY Umsy recK Ucurrent and stock status from output of SRA Data file Par csv ouput file from SRA Data outputalldata unique read table Par csv sep header T only unique rows used for analysis attach outputalldata Restricts the dataset to only sample combinations resulting in a postive recK outputalldata2 subset outputalldata outputalldata Reck gt 0 Restricts the dataset to only sample combinations recK 1 100 outputalldata3 subset outputalldata2 outputalldata2 RecK lt 101 Calculating esimates of current exploitation Ucurrentalldata outputalldata2 Umsy outputalldata2 U2009 Umsy Calculate the ratios of SSBcurrentyr SSBmsy biomassbenchmark outputalldata2 S
20. io 1 Age max Min age fit i Current stock and harvest rate P overfishing P overfished Aske EGG EGGo B Bo 11 Figure 3 Stochastic SRA model interface as MCMC sampling is executing Stochastic SRA parfile tilefish_23 1_all uncern par datafile Tilefish_23 1_all uncern csv Files Run Priors Stoy Parameters _ Fun Pros Z Bhat 2009 6000000 Uhat 2009 g 4 paces fase Show Posterior SD Bhat 10000000 SD Uhat 0 02 ke Prop of ISIR Samole cy length age 0 08 fisher N trials to run 1000 SD rec 0 5 ath 100 e 0 A wt kg at 100 cm 11 Vane to anila fo Recruitment autocorrelation rho g EEG 100 max Future TAC kg 116000 Ocm Fish length cm or Ufuture Legal length g Age at maturity for SSB 2 Run MCMC sampling pag Sample individual survival for Na lt 1000 Par Step Anom Step 4 Number of trials Bycatch params MSY min Umsy min S min 1000000 10000 y T 0 84 r bycatch before MSY max 500000 Umsy max S max 0 88 compensation Trials 116166 51274 ize di 7 future i Prop of nev Figure 3A ra pri asi 00000001 lo bycatch U Seas Prop Crashed ge distn weight 00000001 0 03 Szero sample Discount rate 097 I Use historical anomaly estimates Var of abundance index 04 i 11 002 316 gt Lorenzen survival Representation of parameter uncertainty Sample distribution of Umsy and MSY values Sa 1 Age max Yul B Te ee a l Min age fit i
21. l prior distributions with or without autocorrelation The resulting trials of possible historical trajectories are used as a starting point for Markov Chain Monte Carlo simulation MCMC but if the SIR sampling is implemented more starting trials are necessary During SIR sampling regime SRA stores the priors and associated likelihoods SIR only resamples within these priors to find credible trials and only a few probable best fit values are outputted bestfit csv Summing frequencies of occurrence of different values of leading population parameter values over these sample amounts to solving the full state space estimation problem for the leading parameters i e find marginal probability distribution for the leading population parameters integrated over the probability distribution of historical state trajectories implied by recruitment process errors and by the likelihood of observed population trend indices The stochastic SRA is parameterized by taking Umsy annual exploitation rate producing MSY at equilibrium and MSY as leading parameters then calculating the Beverton Holt stock recruit parameters from these parameters and from per recruit fished and unfished eggs and vulnerable biomasses Forrest et al 2008 Under this parameterization we effectively assume a uniform Bayes prior for Umsy and MSY rather than a uniform prior for the stock recruitment parameters This is an age structured version of the stock recruitment parameterizatio
22. n in terms of policy parameters suggested by Schnute and Kronlund 1996 Natural mortality rate M is not treated as age independent and is determined from survival rate S e It is best to have fishery independent estimates of natural mortality if possible given the size selectivity practices of most fisheries Vulnerabilities at age can be calculated through a variety of methods such as VPA dome shaped or logistic selectivities Age specific vulnerabilities can vary by year to track changes in historical fishing practices targeting specific age class or specific size groups Most fisheries have a high variance in abundances of older ages thus vulnerabilities can be fixed at an age when the vulnerabilities become stable which may or may not be the maximum age Fecundity is assumed to be proportional to the differences between age specific body weight and weight at maturity calculated from user supplied parameters SRA provides probability distributions of leading parameters Umsy MSY and other population parameters vulnerable biomass catch exploitation as well as the probability of the population being overfished or undergoing overfishing based on the Pacific Fisheries Management Council 40 10 rule The probability of overfishing shown in the SRA interface Figure 1 is calculated from the PFMC 40 10 rule whereby F is targeted to be decremented below fishing mortality at maximum sustainable yield Fmsy when the stock is les
23. n in this file need to be scaled to the biomass scaler value as indicated on the interface The true values of the population estimates need to be multiplied by the biomass scaler bestfit csv The estimates of vulnerable biomass observed catch and exploitation U by year for the most likely parameter combination found during SIR procedure This file is only created when SIR sampling is compiled The user must indicate the number of priors to be compiled by the SIR posterior sampling It is advised that the number of priors is a minimum of 1 000 000 These output files will be created as the MCMC sampling is begun and will write over any previous model compilation output files If you wish to save a model s output than copy and paste these files in another folder before SRA is executed 16 Problem Solving and Further Guidelines in alphabetic order Age Vulnerabilities Considering the high variance in abundances of older ages fix the vulnerabilities at age not at the maximum age but at an age the vulnerabilities level off For example for red grouper maximum age 30 vulnerabilities were fixed at age 17 Exploitation Current U current Umsy U year Umsy Umsy and Uyear Umsy refer to the column headings in the Par csv output file NPV Mean NPV see Figure 1G is an index of economic performance for forward simulations from the end of the historical data It is the discounted sum of future catches over the simulation period
24. not fully distributed throughout the designated area than either decrease or increase the range of these two parameters Figure 2A Run Priors again If the display is satisfactory than save parameters Files gt Save parameters Executing SRA continued Close the SRA interface Re Open the SRA interface Install input files Files gt Read parameters gt select par file Files gt Read time series data gt select csv file Files gt Read length data gt select csv file optional Files gt Read age data gt select csv file optional Run Priors The user can indicate the number of trials Figure 1B as well as the number of years to simulate before either the MCMC or SIR sampling is conducted MCMC minimum 1 000 is the preferred sampling procedure since MCMC does not require as many priors as SIR procedure minimum 1 000 000 Do MCMC Sampling Figure 3 1 000 000 iterations is a suggested minimum number of iterations The number to the right of the number of iterations is the number of accepted iterations Simply divide the number of accepted iterations by the total number of iterations to calculate the acceptance rate of the MCMC integration An acceptance rate at least 30 is ideal It is advisable to let SRA run as long as it is possible however remember that each MCMC iterations will be saved A file containing 2 million MCMC iterations is 400 000 kilobytes in size Limitations on the number of iterations may be ca
25. presentation of parameter uncertainty Sample distribution of Umsy and MSY values P 1 Bycatch params TEREG aiaa m MSY min f1 Umsy min 0 1 Smin 0 85 r bycatch before i wees oS a MSY max 20 Umsy max 9 5 S max 0 9 compensation my Mean NPY 4447 Se dan woh OTT P ean eevee ee e Prop crashed 0 00 eG i 0 03 Szero Sei se sample Sem Discount rate 0 97 Use historical anomaly estimates Yar of abundance index 04 Oe aa ame i AN 1 Age ma Min age fit i Current stock and harvest rate P overfishing 0 18 P overfished 0 81 B scaler 0 Compensation ratio EGG EGGo B Bo an eme Seana 1872 Assume flat U for yrs g to fo Ubar 2003 2005 Markov Chain Monte Carlo simulation MCMC SRA uses MCMC with a Metropolis Hastings random walk algorithm to resample possible historical stock trajectories by summing frequencies of occurrence of different values of leading population parameter values over these sample amounts to solve the full state space estimation problem for the leading parameters i e find marginal probability distribution for the leading population parameters integrated over the probability distribution of historical state trajectories implied by recruitment process errors and by the likelihood of observed population trend indices MCMC convergence is usually most rapid when the acceptance rate is around 20 this is not a mathematical requirement but a practical one since very low acceptance rate
26. red population model with Beverton Holt stock recruitment function that estimates forward in time Walters et al 2006 SRA uses Umsy and MSY as leading parameters and given these parameters the model simulates changes in biomass by subtracting estimates of mortality and adding recruits A single trajectory of biomass over time is produced as well as estimates of MSY Umsy U2009 Goodyear s Compensation Ratio recK and stock status SRA is a less data intensive method which can help to estimate how large the stock needed to be to have produced the time series of observed landings SRA should not be a replacement for more computationally complex assessment models but used more as a tool to make possible conclusions of stock status based on historical catches and recent abundances SRA has been applied to several Gulf of Mexico species including red snapper Lutjanus campechanus SEDAR 2005 gag Mycteroperca microlepis SEDAR 2006a red grouper Epinephelus morio SEDAR 2006b mutton snapper Lutjanus analis SEDAR 2008 yellowedge grouper Hyporthodus flavolimbatus SEDAR 2011a and golden tilefish Lopholatilus chamaeleonticeps SEDAR 2011b In Stochastic SRA recruitment is assumed to have had lognormally distributed annual anomalies with variance estimated from VPA estimates of recent recruitment variability and to account for the effects of these a very large number of simulation runs is made with anomaly sequences chosen from norma
27. s lt 5 typically mean very slow sampling of the parameter space i e requirement for many millions of trials to adequately sample the space Very high acceptance rates likewise usually mean that the sampler is moving too slowly over the space accepting too many tiny moves There are two parameters Par step and Anom Step Figure 1F in SRA to bound the maximum sizes of random parameter changes tested by the MCMC sampling procedure These have to be adjusted manually in cases where the acceptance rate is too high or low Setting lower steps typically causes higher acceptance rates but slower movement over the parameter space watch the sample trial Umsy MSY combinations sampled over trials as the MCMC proceeds Currently SRA does not include more sophisticated MCMC routines such as multiple sample chains or tests for convergence as sample size increases Absent of such methods allow the model to run very very long runs e g 8hr 5 000 000 000 trials to obtain convergence of any Bayes posterior sampling methods and compare how the long against shorter runs 1 000 000 trials The speed of a run is dependent upon the processor of your computer the computer s bus speed and the speed of disk operations The number of trials completed as well as the number of trials accepted are shown on the interface Figure 3A number of trials right number of acceptable trials left 15 Output Files SRA provides four output files
28. s than 40 of virgin biomass and F is targeted at zero when the stock is less than or equal to 10 of virgin biomass This rule is shown as the diagonal line on Figure 1H SRA can also provide the proportion of overfished and overfishing as defined by the given maximum sustainable yield as a benchmark The probability of overfished occurs when the spawning stock biomass in the last year of data spawning stock biomass at maximum sustainable yield SSByear SSBmsy is less than one The probability of overfishing occurs when exploitation in the last year of data exploitation at maximum sustainable yield Uyear Umsy is greater than one SRA outputs a vector of exploitation in the last year of data Uyear exploitation at maximum sustainable yield Umsy as well as a vector of spawning stock biomass in the last year of data SSByear and a vector of spawning stock biomass at maximum sustainable yield SSBmsy The user can calculate the proportion of SSByear SSBmsy iterations that are less than one Each of these parameters is reported with a level of uncertainty determined through MCMC SRA has three main assumptions 1 the population is at virgin conditions the first year data is provided 2 there is stochastic variation in recruitment for all years and 3 survival rate is constant for all years Input Files There are two required input files for SRA catch data csv and life history parameters par Constructing catch data csv fil
29. sation ratio Graph x and y limits may need to be adjusted given your data x11 width 80 height 50 pointsize 8 utils str hist Ucurrentalldata xlim c 0 001 0 20 ylim c 0 250000 breaks 25 col lightblue3 labels TRUE xlab Current Exploitation x11 width 80 height 50 pointsize 8 25 Smooth Scatter color symbolizes density of points red highest density smoothScatter biomassbenchmark outputalldata2 U2009 Umsy colramp colorRampPalette c white blue green yellow orange red nrpoints 0 xlim c 0 0 3 0 ylim c 0 0 3 0 xlab SSBcurrent SSBmsy ylab Ucurrent Umsy main Stock Status abline h 1 col red abline v 1 col red text 0 2 2 5 Overfished and font 2 text 0 2 2 4 Overfishing font 2 text 0 1 0 1 Overfished font 2 text 2 0 2 5 Overfishing font 2 26
30. series There must be a number for each length bin place zeros in length and years for which no fish were sampled 0 entries For example red snapper length csv File Set up 3 50 2 1994 1995 2007 bin1 bin1 bin1 bin2 bin2 bin2 bin3 bin3 bin3 bin48 bin48 bin48 bin49 bin49 bin49 bin50 bin50 bin50 Constructing age csv file The file contains the count of the number of fish per age for a specific number of years The first line contains two numbers the first number is the number of years sampled and the second number is the number of age bins The number of years in the length csv can be fewer years than the entire catch series There must be a number for each age bin place zeros in age and years for which no fish were sampled 0 entries For example red snapper age data csv File Set up 20 15 1984 1985 1986 2001 2002 2003 Agel agel agel agel agel agel Age2 age2 age2 oe ey age2 age2 age2 Age3 age3 age3 age3 age3 age3 Agel13 agel3 agel3 age13 age13 agel3 Age1l4 agel4 agel4 agel4 agel14 agel4 Agel5 agel5agel5 agel5 agel5 agel5 Remember to create csv files If you create a new csv comma delimited text data file and save it using Excel then Excel will insert a set of commas after the number of years and ages on the first file line and after the relative abundance data on each of the lines in the data block You must edit out those spurious commas before using SRA A simpler option is to save th
31. used by the software you use to analyze the output and the amount of diskspace available for storing the MCMC output file Figure 2 Stochastic SRA model interface after Priors are run Stochastic SRA parfile tilefish_23 1_all uncern par datafile Tilefish_23 1_all uncern csy Parameters Bhat 2009 6000000 Uhat 2009 01 growth von B 0 11 SD Bhat SD Uhat growth linfinity cm gg he ae C length age 0 08 length maturity em 34 wt kg at 100 cm 11 growth tzero fo Show Posterior ISIR Samole N trials to run 1000 SD rec 0 5 vaasa simiag o Recruitment autocorrelation rho fo 100 max Future TAC kg 16000 or Ufuture Legal length g nunMeRERamnig Age at maturity for SSB 2 Do MUMLU sample Par Step 2 Anom Step 4 Number of trals A A 7000000 MSY min 10000 Umsy min 19 05 Smin 0 84 MSY max 500000 Umsy max 9 5 S max 0 88 Trials done 1000 Tan future NPY Size distn weight 00000001 o bycatch U Prop Crashed Age distn weight 99000001 003 Szero Discount rate 0 97 Use historical anomaly estimates Var of abundance index 4 Sample individual survival for Na lt 1000 eden ental Representation of parameter uncertainty Bycatch params bycatch before compensation B scaler E 1965 Assume flat U for yrs g to fo Ubar 2003 2005 Prop of fisher sample Ocm Fish length cm Figure 2A Sample distribution of Umsy and MSY values t Compensation rat
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