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GYM User's Manual - Australian Antarctic Division

1. e e e i 8 J 15000000 7 SEE L d e e 1 OPE 8 4 1 e m F 10000000 iil pom 4 S e i ep oes lit 8 4 e peace s 605067 e 9 9 7 MARERE Erba PEN 5000000 ll uus il gant gi di da h th H h ua a PH B bett L zi TLE NEM fi 0 077777 tq C T4 G0 m 7c GMT ccc 2000 2005 2010 2015 2020 2025 2030 2035 2000 2005 2010 2015 2020 2025 2030 2035 Year Year 00000000 nec SS SS SS 10 tt o LL02 F 0 04 LL02 0 04 e eee 87 15000000 s 4 ae LER e 4 2
2. 20000000 xc E 10 TR 5 LL03 F 0 0 LL03 F 0 0 i 8 L A e e L 4 e e d 9 15000000 e g i T e 8 99 a 1 amp 1 ge R 8 un ele i E 21 3 x 6j g i L eee e 8 8 2 10000000 TP i iu J eb 5 1 e z 4 e e e om 4 e z o A e 2 71 4 t4 H t4 H 4 ee E e 1 e 9 9 4 8 i qo e 5000000 il PLI r d 9 i aatal sst 1 Lob bob bbe H 55828 e B 7 e eee ie ee don ui ur 0 T s 71 rp TT Ty 0
3. 20000000 MCI EE po 25 poo N e LL01 F 0 0 1101 F 0 0 000 e ar e e 94 2 0 P e Ce 8 15000000 2 ilii eget T 8 an 8 2 2 5 fe E 338 000560 A e i tl ji PI Walini amp 10000000 77 n uli q 1 0 4 eeeoeuoeuonuonnonanooononponnos E esos 5000000 did e Yo asse pto l n n d D C E M MM CUL CN CMM CQ MI EE CE LE 00 2000 2005 2010 2015 2020 2025 2030 2035 2000 2005 2010 2015 2020 2025 2030 2035 20000000 2 5 joo 01 F 0 075 I e e LL01 F 0 075
4. 2000 2005 2010 2015 2020 2025 2030 2035 2000 me 2010 2015 2020 2025 2030 2035 Year Year 20000000 oo U LL03 F 0 04 1 1103 F 0 04 J L 4 e e 0 00 84 e 9 i 15000000 EE 3 i 1 2 E E un e 6 E e 67 F 4 8 o i e e 24 10000000 0 08 e l e 8 8 3 en e 9 069000 8 i d 45 L ao BELL LG e 8 gt e i ii i e e 99 e 9 9 5000000 ti NP PI i J iui iii i hi li dy cce mtt m M 1 sasi mA 0 rcp MSS o 0 E 2000 2005 2010 2015 2020 2025 2030 2035 2000 2005 2010 2015 2020 2025 2030 2035 Year Year Figure GLL13 Box plots 1001 trials of Total Biomass left and Spawning Biomass Status right over 35 years for the estimate of initial biomass of 1500 tonnes with CV 0 3 1 03 Top panels for F 0 0 Bottom panels for F 0 04 Dashed lines correspond with notional level of recovery 3 5 of initial spawning biomass and thresholds for further decline 0 8 of initial spawning biomass PART 5 Working Examples 162 Specifications for the Generalised Yield Model GYM Note If using a gener
5. 6 0439546457 ry QU0UD00DO 020000000 0523003769801 Part 4 Specifications of the 131 Generalised Yield Model GYM User s Manual 4 11 6 Cohort Status The Cohort Status files are similar to the population files but for each age class General incl SSB status ROOTname CG As for Population General but note the addition of the Age class for each line The test of yield either yBo Catch F the example below is catch The number of the respective trial can be used to relate this information to other files in a database The first year of the split year can be used to relate this information to other files in a database Example Test 1 Year Age Cohort biomass Cohort Number Spawn Biomass Vulnerable bms Catch 2815000 0 l 1985 2 7663399136 0 0000000 94790 409 0 0000000 2819000 0 1 19905 9 29913421 np p QUODODODO 1040811 3 0 0000000 2815000 0 1 1955 G L9o791074 9 1096923 0 0 0000000 li24559 1 0 0000000 2815000 0 le 1995 T SOP 2077 1 2990342 0 0 0000000 5806824 9 0 0000000 201950000 i gt LISD By 249909 7 1148549 8 0 0000000 23090989 9 1220000000 Part 4 Specifications of the 132 Generalised Yield Model GYM User s Manual Specified Survey times ROOTname CS As for Population Survey monitoring but with age class added All results are for the survey increment in each year The te
6. See Uncertainty 8 10 See Uncertainty 11 Stock recruitment relationship S 94 28 Empty Line Ex 86 4 5 See Ex See 88 Empty Line Ex Proportional recruitment function 89 Observed 8 11 Observed SD mean 89 11 t in 11 Empty Line 97 Empty Line Ex estimat used A range of of M can be incorporate uncertainty 97 33 97 see See P See mhigh 33 33 Empty Line m See high in 32 97 Empty Line Ex m t 97 in 32 incorporate See Generalised Yield Model GYM User s Manual ed Max Coefficient of Variation 9 Number of replicates 1 Use Standard Error of mean False x SBO for recruitment depletion x DS ee Vector of Recruitments Function with YEAR ESTIMATE CV I4 2X G14 6 2X G14 6 T 0 0 DD Use Recruitment SEs in bootstrap FALSE Parameters for recruitment related to M B est proportion of stock as recruits 0 0 SD of recruitment proportion 0 0 1 He Recruitment V Recruitment Function 9 age class that recruits 1st enter data points used to estimate proportion 1 NATURAL MORTALITY Mean Annual M 0 Min Mean Annual M es to Max Mean Annual M 0 15 SD of M between years within runs 0 0 Alter Mean Annual M by Multiplier FALSE Probability of M being multiplied 0 0 Amount Mean
7. e 2 0 7 15000000 e e e 2 96 xi 6 e e E ii C i ee 10000000 E T E e 7 es silla T ini ull z eg fe Qu Pe 5000000 Feo N J Pe SI oaaao ponnu asao asso T ssssesseesspeseeo 3 0 a 0 0 2000 2005 2010 2015 2020 2025 2030 2035 2000 2005 2010 2015 2020 2025 2030 2088 Figure GLL11 Box plots 1001 trials of Total Biomass left and Spawning Biomass Status right over 35 years for the basic projections above LL01 Dashed lines correspond with the escapement 0 5 of median pre exploitation SSB and depletion 0 2 of median pre exploitation SSB rules of CCAMLR PART 5 Working Examples 161 Specifications for the Generalised Yield Model GYM 20000000 10 e gt 1102 F 0 0 1 1102 F 0 0 e 4 H 4 e e 4 8
8. F 10000000 idi m amp SU P ME e e a E 2 i Poe le E ee jl e 7 6 e 5000000 Es ji 2095 6066 F 2 e a h e 8 i s ua 1 22 9 9 M 35 5 P ACT T de e n 0 TT TT 0 T T7366 3903373 3 633 3 cx 0413 6 2000 2005 2010 2015 2020 2025 2030 2035 2000 2005 2010 2015 2020 2025 2030 2035 Year Year Figure GLL12 Box plots 1001 trials of Total Biomass left and Spawning Biomass Status right over 35 years for the fixed initial biomass of 1500 tonnes LLO2 Top panels for F 0 0 Bottom panels for F 0 04 Dashed lines correspond with notional level of recovery 3 5 of initial spawning biomass and thresholds for further decline 0 8 of initial spawning biomass jesse L
9. Specifications for the Generalised Yield Model GYM FISHERIES FISHERY Longline Include fishery in Projection True Tolerance for resolving catches propn 0 01 Account for uncertainty False Initial year Catch by proportion True Catch 100 Fishing Selectivity with age 0 1 Relative fishing effort in each inc of year day month coefficient 01 01 1 Check Use the extract of the file LLO1 CG above in the examination of age structure using total biomass and spawning biomass at age for 2002 in Trial 1 from Test O vi Estimate vulnerability by dividing Vulnerable biomass by Cohort biomass Note that this is only approximate as the cohort biomass is estimated at the survey time and the vulnerable biomass is estimated at the time for estimating vulnerable biomass A more accurate calculation is by using the file vii Plot Vulnerability vs Age viii Plotted in LLO1 vulnerability O Vulnerability e EN 0 10 20 30 Age Figure GLL10 Approximate maturity function by age according to the relationship of total biomass and spawning biomass for each cohort at the time of spawning Drawn from file LLO1 CG Compare the results to length at age in order to check the maturity at length relationship PART 5 Working Examples 160 Specifications for the Generalised Yield Model GYM INITIAL POPULATION STRUCTURE Age structure from random recs True Known age structu
10. 14 i t S can be found as the root of the function las f S p t I A 15 which is solved using Newton s method using ETE 1 a PIS 0 ss a S A starting guess for the iteration should be S 1 Part 4 Specifications of the GYM 90 Generalised Yield Model GYM User s Manual For the krill example developed by de la Mare 1994 simulation tests showed that the value of survivorship calculated using the average value p t from net haul surveys as the value for estimating survivorship was slightly too high because p t is a random variable A less biased average value for the simulated t is obtained when the value for S is calculated using De t V pp t in place of in equations 15 and 16 This adjustment is used in the current version of the GYM Note that this formulation does not provide for age specific variation in mortality Thus age specific variation in M should not be included in the input parameters at this stage 2 Correcting the variance in t for the effects of variability in the population size Although we can use the average value of p t for generating random values of recruitment we are not able to use directly the observed variance estimate of t from independent samples to generate the random values This is because the variance of p t includes a component of variation due to the cumulative effects of variability in recruitment
11. 2 5833 45 03819 91328 49 1 0 1 2 6667 45 03819 91326 75 1 0 1 2 75 45 03819 91324 79 1 0 1 2 8333 45 03819 91322 54 1 0 1 2 9167 45 03819 91319 97 1 0 1 3 45 03819 91357 21 1 0 1 3 0833 47 23369 105109 3 1 4 1 3 1667 49 12337 118321 2 1 4 1 3 25 50 74983 130225 4 1 4 1 3 3333 50 74983 130720 1 1 0 1 3 4167 50 74983 130720 9 1 0 1 3 5 50 74983 130721 8 1 0 1 3 5833 50 74983 130722 6 1 0 1 PART 5 Working Examples 148 Specifications for the Generalised Yield Model GYM 3 6667 50 74983 130723 4 3 75 50 74983 130724 4 3 8333 50 74983 130725 5 3 9167 50 74983 130726 8 4 50 74983 130708 5 2 2 2A ooo dedo edo imis eds This table is derived from the G04 CI file to show the method for determining the lookup table used in a trial and in a given year Steps to obtain this part of the table are i extract the rows for Trial 1 and Year 2003 ii Add a column of Time Age Inc iii Delete values for Inc 1 0 iv Sort by Time v Length at Age is present in Length vi Weight at Age is Cohort Biomass divided by Cohort Number vil M coefficient at age is the value for M in the table divided by M read from G04 PG for Trial 1 Year 2003 divided by Number of Increments Incs 12 in this example viii coefficient at age is present in VinxEffort note fishing season is set to be contained within one quarter of a year summer ix Maturity at age is present in Maturity x Only rows for Time age from 1 to 4 are copied int
12. Ex h a t in 46 Maturity function by age if only length based then all 1 F7 3 2X G14 6 0 0 La m Empty Line Ex See 104 SPAWNING SEASON Part 4 Specifications of the GYM 119 Generalised Yield Model GYM User s Manual Description File Lines Empty Line t in 49 First Day of Spawning Season dd mm 01 07 t in 49 Last Day of Spawning Season dd mm 01 07 Empty Line Ex ACkCkCk KCck KC ckCck kck kck Kok ck ckck kk kck Kok ck kk kk Kock Kok ck kk kok Kok Kok ck kok kock kock k k ck kk kk End of file line End of File 100 4 10 3 Recruitment survey data lt ROOT Filename gt REC File lines are separated by dotted lines references are given in parentheses and equation parameter references are given in square brackets Explanation lines equivalent to Empty lines are indicated as Ex in the description MA Ex Title HIMI Recruitments dates relative to 1 December Purpose described at 87 Empty Line First age class in Age for estimating recruitment 0 population age structure Empty Line The numbers of the surveys should consecutive with an empty line between each set of survey information Dbar prime in Equation Total Expected Density t0 6 Ex a N and sigma Age Density SE of N in Equation 6 Il3 2X G014 6 2X 01 4 0 ud 0 0 Cao Next survey would End of File start here not then End of file line Empt
13. GYM 1200000 1000000 800000 600000 Number 400000 200000 0 0 5 10 15 20 25 30 Age Figure GLLO5 Natural mortality for a cohort with initial recruitment marginally greater than the mean recruitment Drawn from file LLO1 CG LENGTH AT AGE Growth Curve Type VB time 0 0 0 Linf 100 0 0 06 Check I In Excel Open File LLO1 LUK the lookup table ii Plot Length vs Age iii Plotted in LLO1 length ES O O O O O gt CREER Length mm 4 20 0 10 20 30 Age Figure GLL06 Length mm at age for the long lived species Drawn from file LLO1 LUK PART 5 Working Examples 156 Specifications for the Generalised Yield Model GYM WEIGHT AT AGE Weight length parameter A 0 000025 Weight length parameter B 2 8 Check I In Excel Open File LLO1 LUK the lookup table li Plot Weight vs Age 111 Plotted LLO1 weight Weight kg 0 0 10 20 30 Figure GLL07 Weight kg at age for the long lived species Drawn from LLO1 LUK MATURITY Maturity Type L Length 50 are mature 50 0 Range over which maturity occurs 20 0 Check 1 Use the extract of the 11 01 above the examination of age structure using total biomass and spawning biomass at age for 2002 in Trial 1 from Test O ii Estimate maturity by dividing Spawning biomass by Cohort biomass Note that thi
14. 173503 the cohort is identified in 1999 6 1 373555 this example in bold but 1999 7 0 271859 that there is no identifier 2000 0 0 874111 in the output table The 2000 1 0 59639 records can be sorted into 2000 2 0 943785 cohorts by generating 2000 3 0 491751 new column Cohort in 2000 4 1 135944 the table and copying a 2000 5 0 688199 formula into each record 2000 6 1 173503 of the column where 2000 7 1 373555 2001 0 2 227403 Cohort Year Age 2001 4 0 874111 2001 2 0 59639 2001 3 0 943785 2001 4 0 491751 2001 5 1 135944 2001 6 0 688199 2001 7 1 173503 PART 6 References 142 Specifications for the Generalised Yield Model GYM GYM Specification Example G02 Description Effects of annual natural mortality rate during the year and between years Base File rootname G02 Base File Details G01 Variation Annual Natural Mortality rate M 0 8 Annual Fishing Mortality rate F 0 0 Results observed in file G02 PG indicates the mortality rate each year Results example output Total Year Number M 1999 1 284648 0 8 2000 1 450888 0 8 2001 2 877046 0 8 2002 2 635682 0 8 2003 2 10595 0 8 2004 1 056519 0 8 2005 2 467218 0 8 2006 1 793559 0 8 2007 1 153582 0 8 Note that this is only an extract from the file Results observed in file G02 CG indicates the progression from one year to next in which the mortality rate can be estimated and validated Results example output Cohort Estimated Year Age Number Cohort M 1999
15. 33E 02 4 17E 03 0 675897 3 33E 02 4 17E 03 0 653803 3 33E 02 4 17E 03 0 631709 3 33E 02 4 17E 03 0 609614 3 33E 02 4 17E 03 0 58752 3 33E 02 4 17E 03 0 565425 3 33E 02 4 17E 03 0 543331 3 33E 02 4 17E 03 0 521237 3 33E 02 4 17E 03 0 499142 3 33E 02 4 17E 03 0 479972 3 33E 02 4 17E 03 0 462108 3 33E 02 4 17E 03 0 44522 3 33E 02 4 17E 03 0 428784 3 33E 02 4 17E 03 0 41295 3 33E 02 4 17E 03 146 2000 2000 2000 2000 Specifications for the Generalised Yield Model GYM 0 875 0 9167 0 9583 1 O OOO 0 397739 0 383094 0 368993 0 355387 3 33E 02 3 33E 02 3 33E 02 3 33E 02 4 17E 03 4 17E 03 4 17E 03 4 17E 03 0 80 0 10 This table is only part of the G03 CI file The records for one year were sorted by age to extract this subset of the table that shows the progression through the year of the Age 0 cohort Note that the table shows a mortality rate for the increment 1 0000 This is not used as the beginning of that increment is the end of the year with that increment being the first of the following year except that increment 1 0000 This check is shown in bold adjacent to the last record GYM Specification Example G04 Description Base File rootname Illustration of lookup tables based on the krill assessment for Area 48 Base File Details Variation Increments in year Number of increments in which growth occurs Results observed in file Results example outpu
16. 6 1 13E 02 1993 0 80 2000 7 5 08E 03 1993 1999 5 2 15E 02 1994 0 80 2000 6 9 66E 03 1994 1999 4 2 81E 02 1995 0 80 2000 5 1 26E 02 1995 1999 3 0 10305 1996 0 80 2000 4 4 63E 02 1996 1999 2 9 93E 02 1997 0 80 2000 3 4 46E 02 1997 1999 1 0 42407 1998 0 80 2000 2 0 190547 1998 1999 0 0 59639 1999 0 80 2000 1 0 267975 1999 This is only a partial extract of the file for the first two years of the projection giving the first 3 columns of the table above Cohort was estimated as described for Example 01 Estimated M was estimated as In Nyear 1ageti Nyear Age to check that the annual natural PART 5 Working Examples 143 Specifications for the Generalised Yield Model GYM mortality rate was as expected The table is sorted by Cohort then by Year before M is estimated Age Class 7 from 1999 is ignored as it has disappeared in 2000 Results observed in file Results example output Year 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 G02 CI Inc 0 0 0417 0 0833 0 125 0 1667 0 2083 0 25 0 2917 0 3333 0 375 0 4167 0 4583 0 5417 0 5833 0 625 0 6667 0 7083 0 75 0 7917 0 8333 0 875 0 9167 0 9583 1 Age OO OOo ooooOoOOoOOOOOOOOOOOOOOOGOO indicates the numbers at age at the beginning of each increment time step in the year and the mortality rate applied to that age over the course of that incremen
17. 9 5 3 583333 3 666667 3 75 3 833333 3 916667 4 50 74983 50 74983 50 74983 50 74983 50 74983 50 74983 50 74983 50 74983 50 74983 50 74983 130708 5 130708 5 130708 5 130708 5 130708 5 130708 5 130708 5 130708 5 130708 5 130708 5 Ll gt gt lI A This table is only part of GO4 LUK file for Ages 1 0 to 4 0 The columns on Age Class and Increment have been added to illustrate how the values apply during the year and for each Age Class Note that the age specific functions for maturity M and F do not include the length based functions Results observed in file Results example output G04 CI using information from G04 PG Maturity Time Length Weight coeff F coeff coeff 1 22 03221 10694 84 1 0 0 1 0833 27 43225 207532 1 0 0 1 1667 32 08011 33084 96 1 0 924495 0 1 25 36 08057 45133 16 1 2 702473 0 551713 1 3333 36 08057 46970 76 1 0 0 551713 1 4167 36 08057 46970 82 1 0 0 551713 1 5 36 08057 46970 87 1 0 0 551713 1 5833 36 08057 46970 94 1 0 0 551713 1 6667 36 08057 46971 01 1 0 0 551713 1 75 36 08057 46971 07 1 0 0 551713 1 8333 36 08057 46971 15 1 0 0 551713 1 9167 36 08057 46971 24 1 0 0 551713 2 36 08057 46969 94 1 0 0 551713 2 0833 39 52379 615544 1 4 1 2 1667 42 48739 76594 83 1 4 1 2 25 45 03819 88490 18 1 4 1 2 3333 45 03819 91333 5 1 0 1 2 4167 45 03819 91331 9 1 0 1 2 5 45 03819 91330 17 1 0 1
18. Kk CK K KK KK KK KK KK KU KK KU IK KK KI KK KK KG KG KG KG FILES Biological Parameters for Input OlDESAF1 bio File survey details for recruits OlDESAF1l rec File fishery details 1 1 Root Name for Output files OLDESAF1 RESULTS OF TESTS Test EScapement Depletion 2315000 0 56046522 00000000 j 4 11 2 Diagnostics Log File Correct data input can be checked in the LOG file Also errors that cause the program to crash will be written into the LOG file if they were trapped Logtime Temp File The LOGTIME TMP file is a temporary file generated by the graphic user interface and used by it to track and display progress information Part 4 Specifications of the GYM 125 Generalised Yield Model GYM User s Manual Summary of outputs in each of the Population and Cohort file types Characteristic Population Cohort as in file General Survey Allincs Time General Survey Allincs Test Trial Year Inc Incs Total bms Total N Spawn bms Xxx nib O Spawn N Vuln bms Vuln N F Annual Catch gt t Recruitment t 0 TY 4I Annual ce c c cm M Annual Annual SSB status S SBO median SBO CV estimate Age Cohort bms Cohort N Spawn bms Vuln bms Catch Length F Vulnerability Maturity Vuln x E where X categorical variable t status at beginning of increment or rate through increment or catch taken th
19. M to be multiplied by 5 Natural Mortality coefficient with F7 3 2X G14 0 Natural Mortality with time of year date coefficient I2 1X 12 Gl14 9 118 lU 0 0 Part 4 Specifications of the Generalised Yield Model GYM User s Manual m 01 01 d Empty Line Choose von Bertalnffy Type of Growth Curve to Generate VB VB or Length at Age input LAA Ex See 96 If von Bertalanffy type VB Equation 30 time 0 0 0 Equation 30 Linf 100 0 Equation 30 0 06 Date in the year for Ref date for growth curve dd mm 01 01 the point of origin of Lhe Crowe Curve in 31 Equation 30 Date to Date start growth period dd mm 01 01 estimare S CO Q Equation 30 Date to Date end growth period dd mm 31 12 estimate g Ex CkCkCkCk kCck kck Kok ck kck ck k ock kock k ok ck k ck k Ex See 96 If length at age to be input type LAA UB 6 2 0 D Empty Line Ex See 95 WEIGHT AT AGE Empty Line a in 29 Weight length parameter A 0 000025 B in 29 Weight length parameter B PES Empty Line Ex See 104 MATURITY Empty Line Ex Uncertainty Maturity length based if only age based then make these 0 incorporated as per 105 M in equation 47 Min length 50 are mature 20 0 Max length 50 are mature 50 0 M in equation 47 Range over which maturity occurs 20 0 Empty Line
20. Stock BIOMASS so xain tude saciadacihnevlensidddventsededessnshdcvessieaddvecdenaverstatdeievuanieventoeaeverens 104 Reference level for estimating spawning stock 106 4 4 3 Managing Time during 106 Time 0 OF the DI Ol CCUON 106 Years In IA DUM ANG QUU s inest Eats uis ln to Md 107 Timing of different functions to the reference start date in the 107 Years prior O Ne mME 107 FEO a A EEE A EAEE AEE 107 Morem S I a YOAT m 108 4 44 108 4 5 Assessing harvest 108 4 5 4 Types of harvest limits yBo Catch 108 4 5 2 CCAMLR Decision Rules sseessseesseseeseeeee nennen nennen nnns nain 109 Deplelon Probabili mm 109 Median escapement of spawning biomass 110 4 5 3 Alternative 55 5 110 ii Generalised Yield Model GYM User s Manual and Specifications 4 6 TRIER ER m m m 111 4 7 Guide to Parameter Input Table ee tem eite eue ue eate
21. at Age from Surveys Most instances for known recruitments will arise from estimates of abundance of different age classes from one or a number of surveys In order to convert these to estimates of abundance for a recruitment age in a given year the estimates from the survey will need to be projected backwards or forwards in time to the required recruitment age This is done by using an estimate of natural mortality to adjust the numbers at age to the appropriate recruitment age For example the abundance of age 2 fish from a survey could be adjusted to numbers of recruits at age 4 by removing the numbers that would have died over two years of natural mortality Thus such projections will depend upon the estimate of natural mortality Given the potential for natural mortality to be varied in these simulations between trials years and periods within years then a better method than estimating recruitments from surveys prior to the running of the GYM is to provide the survey information as input data and for these calculations to be made following the determination of natural mortality for a given trial This will ensure that the time series of recruitments in a trial is consistent with the estimates of natural mortality being applied in that trial The input data and calculations are based on the results arising from a method mixture analysis for assessing the abundance of individual cohorts from a length density distribution derived from a survey
22. biomass is monitored as described in equation 49 The vulnerable biomass during a year is monitored as the average over a period specified in a manner similar to spawning biomass 4 5 Assessing harvest strategies 4 5 1 Types of harvest limits yBo Catch F The GYM was designed as a tool to evaluate three types of methods for setting harvest limits into the future If there is a desire to examine the condition of the stock during a known catch period then the output files will need to be used in the evaluation The Generalised Yield Model can be used to evaluate the consequences to the stock of three types of scenarios i a constant catch set as a specified proportion of an estimate of the pre exploitation stock Bo ii a constant specified catch or iii a constant fishing mortality for example Fo This method for setting a catch limit is based on the work of Beddington amp Cooke 1983 and later elaborated in the krill yield model of Butterworth et a 1992 1994 It does not require estimates of mean recruitment but does need an estimate of the pre exploitation biomass Bo see Butterworth et al 1992 for discussion Uncertainty in the estimate is incorporated into the simulation by using the coefficient of variation in the survey estimate of biomass The value of gamma results in the calculation of the constant yield where yield for the single projection trial is 2 Y yb exp eZ from N 0 0 50 w
23. box plot is shown below PART 5 Working Examples 154 20 Recruits millions o Specifications for the Generalised Yield Model GYM BA C2 jem sep NO T Recruits millions jeje a i 0 Figure GLL04 Box plot showing the log normal distribution of recruitments the trials for F 0 Mean 1 million fish CV 1 0 Left panel shows the entire distribution while the right panel shows the distribution up to 5 million fish NATURAL MORTALITY Mean Annual M 0 15 SD of M between years within runs 0 0 Alter Mean Annual M by Multiplier False Probability of M being multiplied 0 0 Amount Mean M to be multiplied by 1 0 Natural Mortality coefficient with age 0 1 Natural Mortality with time of year date coefficient 01 01 1 Check ii 111 iv v vi vii In Excel Open File LLO1 CG Extract Trial 1 from Test O add Cohort Year age sort by Cohort Age Extract Year 2000 cohort Plot age 2 to 29 noting that age 30 is a plus class Plotted in LLO1 mortality PART 5 Working Examples 155 Specifications for the Generalised Yield Model
24. cohorts are extant relative to the other cohorts in a simulation T ET AA JANE EN Consequently the vector of M is constructed for each age class a as a 1 M m c T dt QU EFE 0 M 40 0 where o is the oldest age class and the vector of M is drawn according to the variability functions above Similarly fishing mortality can be added to this calculation such that the total mortality 2 replaces in the equations above and a 1 _ gt M m c t dt 2 f c c dc a gt r 41 0 Nominated Age Structure The initial age structure can be provided in place of using either of the above options In this case the numbers at age are drawn from a log normal distribution given the respective mean and standard errors provided for each age Part 4 Specifications of the GYM 102 Generalised Yield Model GYM User s Manual Scaling the Age Structure to an Initial Total Biomass An option to initiate each trial from a specified total biomass is available including all fish from the age at recruitment to the plus class Uncertainty can be incorporated such that a total biomass is sampled from a log normal distribution with a specified mean and CV at the beginning of each trial This is then applied in the nominated year A number of features have been included to take account of I the initial total biomass estimate being obtained a
25. in every age class If we put T Y S 17 i t l then equation 14 can be written as Pp t 18 from which it follows that 20 19 where A is the average number of recruits to be produced by the model If p t is replaced by a random observation with the appropriate properties it follows that the random recruitment is given by 2 2o 20 i l p t Clearly even though t can only take values in the range 0 1 A can have a large positive value as p t 1 The variance needed in generating random p t values by means of equation 20 is that which would apply when there is no variation in the total population older than the recruiting age class This variance is determined using the delta method approximation for the variance of a function of random variables de la Mare 1994 which gives Part 4 Specifications of the GYM 91 Generalised Yield Model GYM User s Manual 21 3 Estimating the parameters of the Beta Distribution A beta random variable has a probability density between 0 and 1 The parameters of the beta distribution a and b are derived from the mean proportion t and its adjusted variance V p 1 For the beta distribution of proportional recruitment the parameters are estimated by Us k EEAO 22 4 Drawing a random recruitment and correcting for the bias in the mean number of recruits Bec
26. original age structure Thus the appropriately scaled age class V is 45 0 1 0 1 m a t dt F u f jpg f 0 771 Ne 0 0 1 where the symbols are as described above for the known age structure 4 4 2 Estimating Spawning Stock Status The tests in the GYM are based on the status of the spawning stock The status is governed by estimating the spawning stock in each year and relating that to a specified level either as a median pre exploitation biomass or as the spawning biomass at the beginning of the projections Spawning Stock Biomass The spawning stock is specified in terms of its biomass The biomass of each age class a at time t during the year is determined during the projection from equation 2 The proportion of each age class that is able to spawn at time t during the year is determined from three functions 1 g t the proportion of fish of length being mature at time of year t 2 h a t the proportion of fish of age a being mature and Part 4 Specifications of the GYM 104 Generalised Yield Model GYM User s Manual 3 p t the proportion of the mature stock spawning at t spawning seasonality Thus the proportion of an age class spawning is given by 1 g L t h a t pC 46 This formulation allows for considerable flexibility in taking account of age and size specific maturity g t 1 if maturity is purely age dependent
27. prior to the projections Estimate the median pre exploitation spawning biomass by dividing the spawning biomass by the SSB status Plot a frequency histogram or box plot of the results Plotted in LLO1 median pre SSB hist and LLO1 median pre SSB box PART 5 Working Examples 158 Specifications for the Generalised Yield Model GYM 0 4 5 4 6 4 7 4 8 Median pre exploit spawning biomass 000 tonnes 4 8 e exploit spawning biomass 000 tonnes c N a 4 S 9 245 Figure GLL09 Histogram and box plot showing the distribution of estimates of median pre exploitation spawning biomass thousand tonnes CHARACTERISTICS OF A TRIAL Init pop structure with random recs True Years to remove initial age structure 1 Estimate median SBO before each run True Estimate med SBO deterministic random R Observations to use in median SBO 1001 Year 0 of projection 2002 Reference Start Date in year 01 01 Increments in year 12 Years to project stock in simulation 30 Reasonable upper bound for Annual F 5 0 Tolerance for finding F in each year 0 00001 GENERAL MONITORING OF STOCK 2002 01 03 Monitor all Years in projection True Start date for monitoring dd mm 01 03 End date for monitoring dd mm 01 04 Number of replicates 1 ESTIMATING B0 IN GAMMA CALCULATIONS Estimate BO log normal False CV of BO estimate 0 0 Coverage of survey 1 0 PART 5 Working Examples 159
28. summer first 3 increments in each year Derived from the outputs from GYM Specification Example GO4 Plots restricted to Agest 1 4 for Year 2003 in Trial 1 Interpolation within increments during the integration During the integration the adaptive Runge Kutta may seek values between increment values in the lookup table As described above a choice has been made to allow linear interpolation between Part 4 Specifications of the GYM 85 Generalised Yield Model GYM User s Manual increment values in the lookup tables This means that the results from the GYM may be slightly different from other yield calculations that expect constant values within an increment and a knife edge change from one increment to another Such differences will be most evident if there is only one or a few increments in a year Extracting a specified catch in a year If Catch gt 0 then F is solved using Newtons method encapsulated in ZBRENT Press et al 1992 which resolves the function FINDF minimising the difference between the specified catch and the catch determined from a nominated F in the Runge Kutta above returning the mean annual fishing mortality that gives the designated catch Sometimes the stock may be sufficiently low that the catch may require a very large fishing mortality in order for the catch to be removed or in fact cannot be removed n such cases a maximum F is required to keep the simulation going This maximum combined with a tole
29. the first year of fishing Normally this would be set to the year prior to or at the beginning of the recruitment series or the catch series or in a suitable reference year such as when the biomass has been estimated Periods in a Trial The trial can be effectively divided into two main periods excluding the period prior to the projections The first period comprises the catch and recruitment series up to the present followed by the second period projecting into the future The former case comprises all the years that would encompass the combined catch and recruitment series The latter case comprises the number of years nominated in the Characteristics of a Trial Part 4 Specifications of the GYM 107 Generalised Yield Model GYM User s Manual Increments in a Year Each year comprises a number of increments This can be set to the number of days in the year 365 or lesser numbers of increments Accuracy during the year will be potentially reduced with lower numbers of increments Thus care will be needed in defining the number of increments relative to the characteristics of the functions incorporated into the trials 4 4 4 Monitoring Monitoring can be undertaken for individual cohorts or for the whole population Monitoring at specific survey times such as in the total biomass in Year 0 gives the status for the increment in which the survey time falls in a given year This is the average status in that increment The spawning
30. the appropriate level of precision The parameters to examine are Parameter Trials Increments in Year Years in future projection Upper Bound for F Tolerance for finding F oeed for random number generator Sensitivity Primarily effects the precision on median spawning stock status at any time and probabilities of depletion below a critical level Greater number of increments will give better approximation to length maturity mortality functions Lower numbers of increments can help speed up the program The number of years needs to be at least a full generation to be confident that the yield being tested has been fully applied to the population This is set to stop the program from attempting to take fish when the catch is greater than the available stock If set too low then the program may stop sooner than necessary resulting in potentially incorrect stock trajectories Keeping it low in early tests can help speed up the finding of the yield that satisfies decision rules Large tolerance will potentially result in poor resolution of the catches in the catch series and larger variation than desired in the estimates of catch in the future projections Large tolerances could be used early to help find the yield that satisfies the decision rules The random number generator can be seeded with a specified value to ensure consistency between tests This can be reset to the same value for each test in a scenario if des
31. the estimated probability of depletion is calculated from the proportion of runs where m S min lt Da So 51 The second option based on the Monte Carlo method uses in place of S in estimating the probability of depletion that is D nin lt Das So 52 These two options should give similar results when there is no Monte Carlo integration over uncertainty in demographic parameters For cases where Monte Carlo integration is included it would be expected that the second option would be less biased particularly if the range of uncertainty in the parameters is large It is recommended that only the Monte Carlo method be used Part 4 Specifications of the GYM 109 Generalised Yield Model GYM User s Manual Median escapement of spawning biomass The recommended formulation for estimating the median escapement of the spawning biomass is E median 55 53 0 where 5 is the spawning biomass at the end of the projection and 5 is the median exploitation spawning biomass derived using the Monte Carlo method prior to each trial The method used in the original krill yield model Butterworth et al 1994 based on the deterministic method needs to be corrected by dividing by the estimate for when there is no yield from the stock that is median 55 So E 2 54 median So Note that a departure from 1 0 in the median escapement can be observed when there is no yield
32. 1 151 Based on the table above of input parameters the following checks were undertaken Specifications for the Generalised Yield Model GYM Account for uncertainty Initial year Catch by proportion Catch Fishing Selectivity with age Relative fishing effort in each inc of year day month coefficient INITIAL POPULATION STRUCTURE Age structure from random recs Known age structure Biomass amp CV to scale AGE STRUCTURE First age class in stock 2 Last age class in stock 30 Oldest age in last class 60 Check i i ii iv In Excel Open File LLO1 CG Extract numbers at age for 2002 in Trial 1 from Test 0 Plotted in LLO1 age structure 2002 Check that age 30 appears like a plus class PART 5 Working Examples False True 100 0 1 01 01 1 False 0 0 152 Number Specifications for the Generalised Yield Model GYM 2000000 1500000 1000000 500000 0 5 10 15 20 25 30 Figure GLLO1 Age structure of the long lived species with mean recruitment at Age 2 of 1 million fish Note the plus class at Age 30 Drawn from file LL01 CG RECRUITMENT Recruitment Function L Use recruitment surveys to est recs False Use recruitments in time series False Mean recruitment 1000000 0 Min Coefficient of Variation 1 0 Max Coefficient of Variation 1 0 Use Standard Error of Mean False Number of replicates 1 x SBO for recruitment depletion x 0 2 Chec
33. 7856037 15082862 OOIlT9STOS y 401056533 28352390 825357445 2815000 0 1 1923600000 860391306 B 10443230 p OSO0QGll78 2934140 7 t 290993195 49455920 9 etc Part 4 Specifications of the GYM 130 Generalised Yield Model GYM User s Manual In each increment The data are derived as for survey times but for each increment in each year The test of yield either yBo Catch F the example below is catch The number of the respective trial can be used to relate this information to other files in a database The first year of the split year can be used to relate this information to other files in a database Inc Increment in year as a fraction of the whole year time refers to the start of the increment Total Biomass Total biomass Total biomass Natural mortality rate in that increment Example Note in this example the lines are wrapped around Test Irial lotal biomass Total Number Spawn biomass Spawn Number Vulntbl BMS Number b x effort Catch M 0 0000000 Ly 1999 00000 39016 9554 n 26458 664 0 31131061 00000000 V0T0000 0 0000000 0 0000000 0 93003 7808 02 0 0000000 l 2999 041677 39952 115 r 16106431 31444 972 0525712551755 0 0000000 p 02 0000000 p 0 0000000 0 0000000 04 53003 7995 01 0 0000000 P Ll 1999089333 44823 4172 pP 3246594919 y 34991 8700 0 39546457 y
34. EF SIM file under General Output Details Relevant Data Inputs GENERAL OUTPUT DETAILS Run Time Log Files Lookup tables generated in setup True Input Output from setup True Updated Parameters in each trial False Percentile tables at end of each tests False Output files Population Status General incl SSB status True Specified Survey times True For CPUE integration True Qutpu ut files Cohort Stacus General incl SSB status True Specified Survey times True All increments in each year True MONITORING OF STOCK 12 X 10 1995 0 Monitor all Years in projection True Notes The general output details are used to specify the types of results to be entered into the files particularly the Run Time Log These outputs are chosen using T true or F false Yes or No can be used in the place of these logicals but are converted to logicals in the input code The monitoring of the stock specifies the date in each year when the stock is to be monitored This first date must be greater than or equal to the first day of Year O identified above Part 4 Specifications of the GYM 124 Generalised Yield Model GYM User s Manual 4 11 1 Results of the tests The results of the tests in terms of CCAMLR decision rules are given in GYDEF SUM This file will need to be renamed if it is to be retained Example 2001 WGFSA HIMI TOP ACKCkC CK KC Ck ok KC KC Kk ok K KC Kk ok Kk KC Kk Kok Ko Kk Kk ok Ko Kk
35. Generalised Yield Model Specifications Parts 4 amp 5 Generalised Generalised Yield Model GYM User s Manual and Specifications DEVELOPMENT amp ACKNOWLEDGEMENTS The GYM has been developed following input and GYM a flexible tool fi or advice from members of the Scientific Committee of CCAMLR and its working groups as well as combining f uncttons of from staff of the Australian Antarctic Division recruitment natur al Many thanks to all who have provided assistance morta lity growth matu rity and fishing mortality to analyse and explore VERSION population scenarios based INFORMATION on historical and future harvest strategies General Citation Constable A J amp W K de la Mare 2003 Generalised Yield Model version 5 01b Australian Antarctic Division Kingston Australia Current Version Version 5 01b Date Stamped 7 Aug 03 A Constable Australian Antarctic Division Deakin University Marine amp Ecological Research User Interface Development Australian Antarctic Division Developed by Verdant Pty Ltd for the Australian Antarctic Division User s Manual and Specifications Australian Antarctic Division Last Modified 7 Aug 03 Written by Constable Angela T Williamson and W de C e li 00 Australian Antarctic Division User s Manual amp Andrew J Constable and W de la Mare 1998 Specifications Introduction to the G
36. Mortalities Do yield per recruit analysis SIMULATION Number of runs in simulation PART 5 Working Examples False 1 0 0 15 0 0 False 0 0 0 1 01 01 1 VB 0 0 100 0 0 06 0 000025 2 8 50 0 20 0 01 07 01 07 0 0 4 0 2 0 3 0 4 0 5 False 1001 150 Specifications for the Generalised Yield Model GYM CHARACTERISTICS CHARACTERISTICS OF A TRIAL GENERAL MONITORING OF STOCK ESTIMATING BO IN GAMMA CALCULATIONS FISHERIES FISHERY Depletion Level for Test Seed for random number generator Reset seed to this value for each test Init pop structure with random recs Years to remove initial age structure Estimate median SBO before each run Estimate med SBO deterministic random Observations to use in median SBO Year 0 of projection Reference Start Date in year Increments in year Years to project stock in simulation Reasonable upper bound for Annual F Tolerance for finding F in each year Monitor all Years in projection Start date for monitoring dd mm End date for monitoring dd mm Number of replicates Estimate BO log normal CV of BO estimate Coverage of survey Longline Include fishery in Projection Tolerance for resolving catches propn PART 5 Working Examples 0 2 24189 True True True 1001 2002 01 01 12 30 5 0 0 00001 2002 01 03 True 01 03 01 04 False 0 0 1 0 True 0 0
37. Similarly A a t 1 if maturity is purely size dependent The size specific maturity function used in this model is based on length as described in Butterworth et al 1994 where 0 lt 1 m m m lt l lt m 47 1 d m where 2 A T the mean length of fish at age T a t m are constants which specify the range over which selection changes from 0 to 1 in the GYM input parameters and are specified from their midpoint Mm and range The spawning stock at time during the year is given by S t O a t B t 48 The mean spawning biomass over a spawning period is calculated as sed Sg Ee 49 Em 49 where f and f are the respective start and end times of the spawning season within the year This is the estimate used in determining spawning stock status Note that the spawning dates are converted by the program to the first and last increments in the year when spawning occurs If either date falls mid way through an increment then spawning is considered to occur throughout the increment If the first date is on the borderline between two increments then it is considered to be the start of the second increment If the last date is on a borderline then it is considered to be at the end of the first increment in the pair The number of increments in a year may be sufficiently few that setting these two dates to different points of the year may be operationally the sa
38. Since the original formulation of equation 24 the krill model was modified and equation 24 was revised to be B V p t See i 28 t 25 1 5 0 In addition the use of the random recruitments the initial population structure means that there is no need to project the population for a number of years until the initial population size is estimated Accounting for uncertainty in the estimates of the proportional recruitment distribution Uncertainty in the estimates of the mean and variance of proportional recruitment is incorporated into the simulations by drawing these from appropriate statistical distributions at the beginning of each trial and then recalculating the parameters above The variance of proportional recruitment V t can be approximated by a y2 distribution with N 1 degrees of freedom where N is the number of observations used in estimating the proportional recruitment distribution parameters Thus prior to starting each trial a new V t is generated by Qc P 26 where I x y denotes a random deviate from a gamma distribution with mean x and variance y If this is chosen first the value for the average value of p t for that trial can be drawn from a normal distribution Be 0 Be 0 V Len 4 27 where of denotes a random deviate from a normal distribution with mean u and variance o Given that the distrib
39. Specified Survey times 5 nnne snas 130 In each increment 1 131 4 11 6 COMO SLaltus i ete peat e ie ie o Guetta sue Lon tuat 132 General incl SSB status ROOTname CG sessi eene nennen nnns 132 Specified Survey times 133 All increments in each year 1 134 412 PROGRAM STRUCTURE 5 eee meds t autetn ka vtae ege dte reed 135 PART 5 VALIDATING THE GYM 2 eb vus are npa unu E e Pun tne 142 5 1 tute ua oet set a 142 5 2 Long Lived Species Examples 149 5 3 Projections based on starting biomass compared to general projections 161 REFERENCES dd noniine qu ie NT MEI 164 ii Generalised Yield Model User s Manual and Specifications GLOSSARY OF TERMS It is important to make note of the specific terminology used within the User s Manual and Specifications To facilitate its use we have attempted to formulate consistent terminology for GYM based on the standard stock assessment and programming language Scenario Test Trial Year Increment Parameters Batch Pointer The
40. Time 0 Thus the starting date of the projections will be 01 12 1982 Each subsequent year in this example will therefore be Projection Year otart Date End Date 0 01 12 1982 30 11 1983 01 12 1983 30 11 1984 01 12 1984 30 11 1985 01 12 1985 30 11 1986 01 12 1986 Part 4 Specifications of the GYM 106 Generalised Yield Model GYM User s Manual Years in Input and Output Convention normally has a split year quoted by the second year For ease of programming the reference to a split year is the year corresponding to the start date rather than the end date see bold years in table above Thus years referred to in the catch history and in the recruitment series need to correspond to the start date of the split year rather than the printed convention of the year corresponding to the end date There is no need to make such an alteration to the input of survey data for estimating recruitment because the dates of the survey will be handled appropriately within the GYM Timing of different functions to the reference start date in the year A number of functions will require being started at the reference start date rather than at the beginning of the calendar year Care will be needed in characterising the functions in this way such as intra annual variation in natural mortality fishing mortality and maturity The first date of these functions will need to correspond to the reference date of the projection year Similarly recruitment occ
41. al projection estimating the median pre exploitation spawning biomass and switching to a specific projection and monitoring status relative to a starting biomass then need to check the following 1 The median pre exploitation spawning biomass is NOT to be estimated this is important so that the estimates of status are with respect to the starting biomass 11 the level at which recruitment is considered to be affected It will need to be set in reference to the starting biomass that comprises the spawning stock rather than expecting it to be set relative to the pre exploitation median iil the level considered to be depleted will need to be set relative to the estimate of the initial biomass that comprises the spawning stock Points to note 1 the biomass in the PG may not be the same as the starting biomass PART 5 Working Examples 163 Generalised Yield Model GYM User s Manual References Agnew D J Everson L Kirkwood P and Parkes B 1998 Towards the development of a management plan for the mackerel icefish Champsocephalus gunnari in Subarea 48 3 CCAMLR Science 5 63 77 Beddington J R and Cooke J 1983 The potential yield of fish stocks FAO FisheriesTechnical Paper 242 47 p Butterworth D S Gluckman G R Thomson R B Chalis S Hiramatsu K Agnew D J 1994 Further computations of the consequences of setting the annual krill catch limit to a fixed fraction of the estimate of kril
42. ality rates each year and the catch arising from fishing mortality Results example output Total Year Number F Catch M 1999 1 284648 0 0 0 8 2000 1 450888 0 1 9 57E 02 0 8 2001 2 815225 0 1 0 185627 0 8 2002 2 487881 0 1 0 164043 0 8 2003 1 933456 0 1 0 127486 0 8 2004 0 896963 0 1 5 91 02 0 8 2005 2 357493 0 1 0 155445 0 8 2006 1 64416 0 1 0 10841 0 8 2007 1 016649 0 1 6 0E 02 0 8 Tthere is no fishing mortality in the first year because this is the year prior to exploitation This is only an extract from the file Results observed in file G03 CG indicates the progression from one year to next which the mortality rate can be estimated and validated Results example output Cohort Estimated Year Age Number Cohort Z 1999 7 1 01E 03 1992 1999 6 1 13E 02 1993 0 80 2000 7 5 08 03 1993 1999 5 2 15 02 1994 0 80 2000 6 9 66E 03 1994 0 90 2001 7 3 93E 03 1994 1999 4 2 81E 02 1995 0 80 2000 5 1 26 02 1995 0 90 2001 6 5 12 03 1995 1999 3 0 10305 1996 0 80 2000 4 4 63E 02 1996 0 90 2001 5 1 88E 02 1996 1999 2 9 93E 02 1997 0 80 2000 3 4 46E 02 1997 0 90 2001 4 1 81E 02 1997 PART 5 Working Examples 145 Specifications for the Generalised Yield Model GYM 1999 2000 2001 1999 2000 2001 2000 2001 2001 0 42407 1998 0 800001 0 190547 1998 0 9 7 15E 02 1998 0 59639 1999 0 800001 0 267975 1999 0 9 0 10895 1999 0 874111 2000 0 9 0 355387 2000 2 227403 2001 This is only a partial extract of th
43. aluating yields and the requirements for inputting parameters into the model It also details how different parts of the model can be manipulated to explore alternative functions The structure of the specifications begins with the formulation for projecting the stock over one year The order of the remainder of the specifications is governed by the derivation of parameters used in the annual projection followed by details of how to control various kinds of scenarios Finally some examples are presented to show how the GYM can be validated by the user The input and output files for these examples are available Part 4 Specifications of the GYM 80 Generalised Yield Model GYM User s Manual 4 2 The Population Model The model is a cohort model with the annual advance of each cohort in numbers and biomass being calculated by numerical integration over a one year period The model is initialised by setting up the number of fish in each age class at the start of the simulation period The starting year is nominated in order to ensure that known information on recruitment catch histories and other parameters can be correctly aligned in the projections if required Each age class is projected through one year by numerical integration of the basic population differential equations Catch and spawning stock is calculated for each age class during the projection At the completion of a projection over a single year the numbers surviving to the e
44. anual Constable et al 2003 and available with the software 4 9 Running GYM without the interface 4 9 1 Operation amp DOS Command Line The command line to drive the GYM from a DOS prompt is o GYMxxx where GYMxxx is the GYM version being used e g GYM500 4 10 Input Files Four input files are required 1 GYDEF SIM Main input file with simulation details 2 ROOT Filename gt BlO Biological parameters with recruitment model 3 ROOT Filename REC Recruitment survey data if available 4 ROOT Filename gt FSH Fisheries data 5 ROOT Filename STR Initial population structure The main input file specifies the ROOT Filename for which the output files will be named The input files are named separately but commonly sharing the ROOT Filename is helpful The scenario provided here as an example is for the long lived species with an estimate of initial biomass and population structure as used in example LLO3 below Part 4 Specifications of the GYM 113 Generalised Yield Model GYM User s Manual 4 10 1 Simulation parameters GYDEF SIM File lines are separated by dotted lines references are given in parentheses and equation parameter references are given in square brackets Explanation lines equivalent to Empty lines are indicated as Ex in the description Description EX i Title Empty Line Empty Line Empty Line Ex Empty Line Input Biological parameters Input results from recru
45. ause the number of recruits given by equation 20 has a random variable in the denominator the mean of the distribution of recruitments will be biased The delta method and subsequent simulation tests were used by de la Mare 1994 to determine a bias correction factor B in equation 20 such that recruitment in a year is estimated as A 720 a 23 l p f where Pr t 24 and is drawn from the beta distribution Notes for use of the GYM If recruitment is estimated to be less than zero in this procedure then the random variate is redrawn The number of such events in a test are printed to the log file and the summary results file They should occur only rarely Part 4 Specifications of the GYM 92 Generalised Yield Model GYM User s Manual de la Mare 1994 noted that this still appears to be slightly biased and further tinkering could reduce the bias further However bias correction is not necessary if the population model is used in a way which involves scaling results to the mean unexploited population size and the model is run for n years without exploitation prior to calculating the mean unexploited population size By that time the slight bias in recruitment will have worked its way through all the age classes He also noted that simulation trials showed that this method satisfactorily converted the observed parameters on proportional recruitment into numerical recruitments with the required properties
46. because of stochastic variability if the number of replicate trials is insufficient to account for variability in some of the input parameters Thus a preliminary assessment with yield set to zero is recommended for investigating whether the population is stable and to determine how many trials may be needed to ensure an appropriate level of precision for estimates of median escapement 4 5 3 Alternative assessments Alternative assessments can be formulated based on depletion probabilities and escapement For example an assessment of the stock trajectory based on an initial starting point can be evaluated in a similar way but using the initial spawning biomass rather than the median pre exploitation spawning biomass Similarly the output files could be used to examine stock status at different times using total spawning or vulnerable biomass or numbers If a stock recruitment relationship is not important in these scenarios then the maturity function could be used to mimic the total biomass or the vulnerable biomass to undertake a similar assessment using those assessment parameters instead of spawning stock status Part 4 Specifications of the GYM 110 Generalised Yield Model GYM User s Manual 4 6 Run Time The efficiency of the Generalised Yield Model can be governed by a number of parameters The user is encouraged to run sensitivity trials on these parameters to determine the minimum required to obtain estimates of the yield with
47. ches are taken This procedure is undertaken within the GYM Mixed gear fisheries A new version is currently being developed that will provide for mixed gear fisheries The structure of this can be observed in the user interface form Uncertainties in fishing vulnerability Uncertainties in fishing vulnerability can only be included as a length based function The sizes at which 50 of fish are recruited to the fishery Im can be used to allow for such uncertainty by drawing these at random from uniform distributions each with a specified range This can occur for each year of the catch history as well as just prior to the forward projection as described above Forward Projection Harvest Strategy to be Evaluated The forward projection extends from the current time to the end of the projection period shown in Fig 1 In a single test the model can project the stock forward under three different options i a constant catch set as a specified proportion y of an estimate of the pre exploitation stock Bo 1 a constant specified catch iii a constant fishing mortality for example These are described in more detail under Types of Tests considered in the General characteristics of Tests Scenarios Part 4 Specifications of the GYM 99 Generalised Yield Model GYM User s Manual 4 4 Characteristics of a Trial 4 4 1 Initial Population Structure General Age Structure The age structure of the population can hav
48. cients for each of the differential equations below The primary outputs are the numbers at age at the end of the year advanced to the next age and the catch in numbers and biomass taken during the year 4 3 1 Projection using Differential Equations The model is based on the usual differential equations which describe the rates of change in numbers and biomass in each age class and the accumulation of catch over one year The number in each age class satisfies the differential equation dN ES m a t y M f a t 1 where Na y is the number of fish in age class a at time of year t in year y The terms m a t y M and f a t y F give the rates of natural mortality and fishing mortality respectively which apply to age class at time of year t in year y These are illustrated in GYM Specification Examples G02 natural mortality and natural and fishing mortalities plus illustration of how the coefficients might be used to generate intra annual and age specific mortality functions The biomass Ba in each age class in each year satisfies the equation dB dN w t N a dt dt dt 2 where is a growth function which gives the average weight of fish of total age r where tT a t for fish of age a at time of year t The growth function covers the entire lifespan of a cohort The yield from each age class satisfies the equation dY p f a t y B 3 Numerical integra
49. cruitment Functions for when recruitment is eren 88 Recruitment Time Series in Projections essei isses sessanta 94 bj oBoglc 95 4 3 3 ZS AJE 95 von Bertalanffy growth functions eese isses essen anrea 96 Al age VOCON 96 4 3 4 Naturak VA ONT AMG wx tm tr rc bch nr tient esac tb 97 4 3 5 Harvest Strategy neasienauiaxnctaudasscaeamonnsdandauedenmien s 98 FISAN MON MY m 98 AKDOWDn caten TIISIOFV E Rau ard M d BRA A ru UE 99 Mixed gear fisheries 99 Uncertainties in fishing vulnerability nnns 99 Forward Projection Harvest Strategy to be 99 4 4 Characteristics of a Trial seessssessseessesessseee nennen nennen nennen 100 4 4 1 initial Population SIUUCIUUEIG rope tal aree arret denter tes Fer E base 100 General Age HN 100 Jie mur 100 4 4 2 Estimating Spawning Stock 1 104 Spawning
50. described by de la Mare 1994 and included in the software CMIX see de la Mare et al 2002 The outputs of this analysis are I Estimates of numerical density of each age class in survey observation Doa ii Standard errors of the density estimates lil Estimate of total survey area SA iv Observed mean density of fish for the survey area D v Estimated mean density of fish for the survey area D The estimated mean density arises from the sum of the densities estimated for each age class from the estimation procedure while the observed mean density arises from the mean density of fish observed in the surveys The numerical abundance at age in a survey and its standard error o estimated by N a E c D a om d 6 D where C 5 D If different procedures are used to give numerical abundances then the estimates of density could be equivalent to total abundance of each age class while the survey area and observed and estimated mean densities would all equal 1 0 A time series of recruitments can be estimated from a number of surveys such that multiple observations of a cohort can be combined using an inverse variance weighting of each observation following projection to the recruitment age SC CAMLR 1995 Report of the Working Group on Fish Stock Assessment such that an estimate of recruitment strength in a given year Ry for a cohort of a given age is given b
51. e 130 Specified Survey times FALSE See 131 At all increments FALSE Empty Line EX Output files Cohort Status See 132 General incl SSB status FALSE See 133 Specified Survey times FALSE See 134 All increments in each year FALSE Empty Line EX EVALUATION OF YIELD Empty Line Choose evaluation of Type of evaluation gamma G catch C or fishing mortality F 108 Empty Line EX Vector of Gammas Catches or Fishing Mortalities Ex Add values below this line and leave single blank line at Vector or values to De evaluated separated by a space Empty Line Option to have the Do yield per recruit analysis special case of yield per recruit undertaken indicate True if required False if not 95 Empty Line Ex SIMULATION CHARACTERISTICS Empty Line The number of trials Number of trials in simulation in a test will affect precision of outcome 111 Depletion level is a Depletion Level for Test proportion of median initial spawning biomass 109 52 Part 4 Specifications of the 115 Description See 106 See 106 See 108 111 Empty Line see 107 111 Empty Line Ex Empty Line See 100 See 85 it is recommended to leave this set to True Empty Line Ex monitoring Of Stock at specified dates 130 Format statement for reading in the array of year and date within year for monitoring Year Date dd mm E
52. e of recruitment for the following year iv Saved file as LL01 F 0 SSB and recs xls v Plotted in LLO1 SSB status recruits and LLO1 Stock rec X 1 5 J a 4 at Ei 4 EN Uu 4 1 0 4 Qi n n decl Turf gp pt th tht ege Uu t eet gee NEN i t i Lr ow fy 57 ON ET Re 4t E h gh ai X BG Ad V xu tent eee A Et t 4 EM T KA ut RUM a 0 T T opawning Stock Biomass thousand tonnes Figure GLLO2 Relationship between spawning stock biomass and recruitment for 1001 trials of 30 years for 0 Drawn from LLO1 PG 20 T c 4 Q9 15 2 10 i 5 Q 4 5 0 1 2 3 4 5 opawning Stock Status Figure GLLO3 Relationship between spawning stock status relative to the median pre exploitation spawning biomass and recruitment for 1001 trials of 30 years for No reduction in recruitment will have occurred because the spawning stock status did not decline below 0 2 Thus the recruitment parameters can be estimated from all the observations in the test 0 The summary parameters were estimated from the file above to be Mean Recruitment 999499 Coefficient of Variation 0 988 The distribution as a
53. e a recruitment age greater than or equal to and a plus class if required Recruitment occurs in the first age class identified The Last Age Class is the last age or plus class to be used in the projections A plus class is initiated by having the oldest age greater than the last age Initial Age Structure The initial age structure for a trial can be determined in three ways I Deterministic age structure ii Age structure drawn from random recruitments iii Nominated age structure The age structure can then be scaled to an initial biomass if required Deterministic age structure A deterministic age structure maintains comparability with the original krill yield model outlined by Butterworth et al 1994 Each successive age class is the product of the median value of the specified recruitment function R in the case of Butterworth et al 1994 this was equal to 1 0 at age 0 and the survivorship e from recruitment age r to the current age a detailed further below such that the number at age is N Re 37 In order to remove the influence of the initial deterministic age structure on the estimation of stock status in the early years of a trial it is recommended that this age structure be projected for a number of years prior to the first nominated year of the trial The number of years is recommended to be equivalent to at least one generation i e the number of age classes in the stock with recruitment vary
54. e file for the first two years of the projection giving the first 3 columns of the table above The remaining columns were estimated as for Example G02 Estimated Z is the total mortality expected from Z M F Note that the total mortality in 1999 was equal to natural mortality because of the absence of fishing in that year as described above Age 7 in 1999 and Age 0 in 2001 do not have estimates of Z Results observed in file Results example output Year 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 Inc 0 0 0417 0 0833 0 125 0 1667 0 2083 0 25 0 2917 0 3333 0 375 0 4167 0 4583 0 5 0 5417 0 5833 0 625 0 6667 0 7083 0 75 0 7917 0 8333 PART 5 Working Examples G03 CI indicates the numbers at age at the beginning of each increment time step in the year and the mortality rate applied to that age over the course of that increment The application of mortality per increment and by age enables the mortality rates to vary during the year and with age through intra annual and age specific functions for natural and fishing mortalities These are specified by varying the coefficients of M and F discussed below Cohort Annual Annual Number M F M F 0 874111 3 33E 02 4 17E 03 0 841939 3 33E 02 4 17E 03 0 813149 3 33E 02 4 17E 03 0 78436 3 33E 02 4 17E 03 0 755571 3 33E 02 4 17E 03 0 726781 3 33E 02 4 17E 03 0 697992 3
55. e model is based on length as described in Butterworth et al 1994 where 0 Ala t lt l s a t 4 4 a 4 L L 1 lt 35 1 A a t 5 L where A z is a function growth curve which gives the mean length of fish at age 7 a t and are constants which specify the range over which selection changes from 0 to 1 However alternative functional forms can be readily incorporated in the program The program input parameters and are specified from their midpoint and range that is l 36 2 2 where m and are the midpoint and range of and respectively Notes for use of the GYM 1 the first date in the vector of relative fishing effort should correspond to the reference start birth date of the year 2 each level of effort should have a specified period with a first date and a last date except for the last period which only requires a first date followed by the end of data date given by 1 Part 4 Specifications of the 98 Generalised Yield Model GYM User s Manual 3 the program determines the level of fishing effort in each increment of the year according to the dates given above If the boundary dates fall in the middle of a program increment then the fishing effort given for that increment is the average effort across the increment 4 the values in the lookup tables generated during the setup phase of the program are solely related to the age based func
56. eded 2 2 Set test parameters 2 3 Undertake test 2 4 Results incl fixes to prop recruits Write Headrun Test Print Results 139 Generalised Yield Model GYM User s Manual PART 4 Specifications of GYM 140 Part 5 WORKED EXAMPLES OF THE GENERALISED YIELD MODEL Generalised Yield Model GYM User s Manual PART 5 Validating the GYM The following examples illustrate how to validate the operation of the GYM These files are provided with the software These workings of the Generalised Yield Model use Version GYMS500 The contents of the files may vary as a result of different random number sequences used by different computers Nevertheless the calculations show the means by which the different aspects of the program can be validated 5 1 Basic Operation Examples GYM Specification Example G01 Description Illustration of a cohort advancing from one age class to the next over years with new recruits added at age 0 each year Base File rootname G01 Base File Details Ages in population 0 7 no plus class Weight at age function all ages 1 Annual Natural Mortality rate 0 Recruitment function log normal with mode at 1 0 Increments time steps per year 12 Variation None Results observed in file G01 CG Results example output Cohort Year Age Number 1999 0 0 59639 1999 1 0 943785 1999 2 0 491751 1999 3 1 135944 This table is only part of 1999 4 0 688199 the G01 CG file Note that 1999 5 1
57. effort in each inc of year day month coefficient T2 1X 12 614 6 01 01 1 0 0 0 Empty Line Each year of the known Year of fishery 1 catch history would be Part 4 Specifications of the GYM 122 added here Empty Line End of fishery End of file line 4 10 5 Generalised Yield Model GYM User s Manual l FISHERY Pl Initial Population Characteristics lt ROOT Filename gt STR File lines are separated by dotted lines references are given in parentheses and equation parameter references are given in square brackets Explanation lines equivalent to Empty lines are indicated as Ex in the description Description Ex Details are found in 100 Empty Line Empty Line Empty Line See 100 See 102 Empty Line Ex See 103 Bbar CV in 43 Empty Line Ex See 103 Empty Line Ex Empty Line End of file line Long lived 02 Initial population structure for each trial Age structure from random recs TRUE Known age structure FALSE Biomass to scale with CV G14 6 2X G14 6 1500000 0 0 3 Age Structure each line age abundance stand err last line with age 1 I2 2X G14 6 2X G14 960 sou Ds 0 Date of age structure and or biomass End of File 100 Part 4 Specifications of the 123 Generalised Yield Model GYM User s Manual 4 11 Outputs Output Files are generated according to the selections in the GYD
58. en determined from the appropriate function R and then based on the status of the spawning stock in the previous year B see below is adjusted such that the adjusted recruitment is Part 4 Specifications of the GYM 94 Generalised Yield Model GYM User s Manual B Sif B lt R B 1 28 R Sif B gt where is the critical status of the spawning stock say 0 2 of the median pre exploitation spawning biomass 5 see below below which the recruitment is adjusted proportionally Example time series of recruitments Examples 1 Surveys with and without uncertainty 2 Bootstrap Vector with and without uncertainty 3 Log normal with and without uncertainty 4 Proportional recruitment with and without uncertainty 5 Effect of stock recruitment relationship Yield per Recruit Yield per recruit is a special case built into the GYM It requires that the mean recruitment is equal to 1 0 Projections are only for one year This could be set up by constraining the relevant parameters or the function selected and the parameters will be constrained automatically Examples I Yield per recruit function selected ii Yield per recruit undertaken by constraining relevant parameters 4 3 3 Size at Age Size at age is currently modelled using a length at age function combined with a length to weight conversion Two methods can be used to generate a length at age vector 1 von B
59. eneralised Yield Model Paper presented to WG FSA 1998 Adapted from Copies available from authors or from CCAMLR Secretariat Manual Citation Constable A J A T Williamson amp W K de la Mare 2003 Generalised Yield Model GYM User s manual amp specifications Version 5 016 Australian Antarctic Division Kingston Australian Antarctic Division Generalised Yield Model GYM User s Manual and Specifications CONTENTS DEVELOPMENT amp VERSION INFORMATION 1 eere enne nennen nnn nnnm nnn GLOSSARY OF TERMS RR RR Ra aun IV PART 4 SPECIFICATIONS FOR THE GENERALISED YIELD MODEL 80 4 1 MRO CUCU GIN PERCHE CHE 80 4 2 The Population 81 4 3 Stock projection over one 83 4 3 1 Projection using Differential 83 Numerical integration over one 83 Extracting a specified catch in a 86 4 3 2 Recruitment EEEEEEEEEEEEEEEEEEEEEEMM 86 Known Estimates of Recruitment 86 Re
60. ertalanffy growth curve 2 user defined array of age and length The conversion from length L to weight W follows the usual formulation of W 29 where a and b input parameters Curently there are no provisions for incorporating uncertainties in the growth and length parameters Sensitivity to incorrect estimates or variability in growth need to be done using different simulation tests Part 4 Specifications of the GYM 95 Generalised Yield Model GYM User s Manual von Bertalanffy growth functions The von Bertalanffy growth function is specified in a single formulation which provides for all annual growth occurring within a fraction of the year based on the method for Antarctic krill specified by Rosenberg et al 1986 such that the length L for fish age a at time t during the year is L 1 e Xo Lift ge 1 80 L a t L 1l e If g tg 30 A 1 Mera dft g where L is the asymptotic length K is the growth rate t is the appropriate time adjustment for having a length at age go is the fraction of the year prior to the growth period and g is the fraction of the year including the initial period without growing plus the growth period Note the application of this formula in the GYM is in the determination of the lookup tables In that respect t in the formula is determined as the increment number of increments in the year Examples I von Bertalanffy
61. folder that groups all of the input output forms The use of a catch gamma or F value to run a set of simulation trials example 1 001 The use of a single set of parameters following a setup routine that 15 then projected over the years of the trial which might include a pre exploitation period a period with a catch and or recruitment history and a projection period The projection of the stock over one split year The time step within one year it 1s possible to have as many as 365 time steps in one year the simulation and biological data needed to create the input files required by GYMxxx exe A batch is a set of scenarios Within a batch each scenario is independent of the others This is simply a convenience for running a number of scenarios without the need for user interaction The visual graphic for the mouse position on the screen Part 4 SPECIFICATIONS FOR THE GENERALISED YIELD MODEL Generalised Yield Model GYM User s Manual PART 4 SPECIFICATIONS FOR THE GENERALISED YIELD MODEL 4 1 Introduction The Generalised Yield Model GYM was first developed in 1995 Constable amp de la Mare 1996 as a generalised form of the Krill Yield Model Butterworth et al 992 1994 which was based on the method for evaluating yield by developed by Beddington amp Cooke 1983 The first version incorporated options for assessing long term annual yield according to catches set by a proportion of an estimate of pre e
62. growth curve with growth over the whole year ii the same von Bertalanffy growth curve but with growth only during a fraction of the year The length at age relationship needs to be standardised to the nominated first day of the year which may not be the first of January or the date referenced by t in a von Bertalanffy function The reference date for f can be input into the set of parameters and the value of t will be adjusted so that the fish length at time 0 will coincide correctly with the first day of the year such that A fo x 31 where fear is the fraction of the year from 1 January to the start date of a projection year and fyg is the fraction of the year from 1 January to the reference date for fo Length at age vector In the user defined array the age can be input with fractions of the year In this way the pattern of growth within a year can be described even though it may not be a smooth function The program does not need to have every value of length at age for each increment in a year It assumes linear growth occurs between two consecutive points and will automatically interpolate between these to determine the appropriate values for the increments in each year in the life of the fish If no growth over a period is to occur then two consecutive points of age at the boundaries of the period in which no growth occurs should have the same length Examples I user defined length at age vector with interpolat
63. here 0 is a normal distribution with mean 0 and variance o 1 The second option allows projection of the stock under a constant catch specified by total weight In this case estimates of parameters for mean recruitment must reflect actual levels of recruitment The third option allows the performance of the stock to be examined under a given fishing mortality A special case is to nominate fishing mortalities to be analysed as for a yield per recruit analysis The yield per recruit analysis requires that a fixed fishing mortality is used in the setting up the initial population structure Part 4 Specifications of the GYM 108 Generalised Yield Model GYM User s Manual 4 5 2 CCAMLR Decision Rules The application of the CCAMLR decision rules requires multiple stochastic realisations of stock trajectories trials in order to produce statistical distributions of stock abundance for a given test level and to allow for Monte Carlo integration of uncertainty in key demographic parameters Monte Carlo integration is carried out by drawing key demographic parameters for each stock trajectory at random from appropriate statistical distributions described above A single realisation consists of three parts 1 setting basic demographic parameters 2 setting up the initial population age structure and 3 projecting the stock over a period of known catches followed by the required projection period in which the test value is a
64. ific Vulnerability Vulnrbity x effort Vulnerability x fishing effort in the increment Catch in Inc Catch taken during that increment Example Note in this example the lines are wrapped around Test lrial Year Inc Age Cohort biomass Cohort Number Length Maturity E Vlnrblty Vln x effort Carch Ine 0 0000000 hs 9991 0 DU 105 0000000 k DeadoooUusy 0 0000000 0 0000000 Us9003799E 01 0 0000000 0 0000000 QOUDDODU 0 0000000 etc Part 4 Specifications of the GYM 134 Generalised Yield Model GYM User s Manual 4 12 PROGRAM STRUCTURE The structure of the Generalised Yield Model Version 5 00 is illustrated in Figures GS3 GS6 These figures are ordered to start at the central point of the program the projection of the population over one year and progress to the upper layers of the program This is done to mirror the progression through the specifications PART 4 Specifications of GYM 135 Generalised Yield Model GYM User s Manual Figure GS3 Schematic showing the steps involved in projecting a population over one year Program routines are shown in bold italics Numbers are given for reference in the text 1 0 Project each age class over one year OneYear 1 1 Set M for year C Fn Get M Inc gt Fn RLognorm 1 2 Set Fishing vulnerability for year Fish vulnerability 1 3 Project age classes to end of year 2 0 P
65. iles below Note that the main outputs required for assessing the effects of fishing on the stock according to the 2 main decision rules of CCAMLR are found in the output file designated at run time Part 4 Specifications of the GYM 127 Generalised Yield Model GYM User s Manual 4 11 5 Population Status The population status files are used to monitor the stock over each year in a run These files will always begin in Year which is the year prior to the first year in the recruitment catch history or in the absence of that history prior to the first year of the future projection period In the case where the number of years to project the stock prior to the history or future projection is then the values for Year will be recorded as 0 i e there were no observations at that time These would need to be deleted in order to produce appropriate graphics Status of the stock in Year 0 in each trial ROOTname TO The status of the stock in Year O prior to exploitation Test The test of yield either yBo Catch F the example below is catch Trial The number of the respective trial can be used to relate this information to other files in a database SBO median The estimate of the median pre exploitation spawning biomass for the trial SBO CV The coefficient of variation for the vector of pre exploitation spawning biomasses used to estimate the median This variability can indicate the degree to which uncertainty in the inp
66. ing from year to year as specified in the recruitment function Note that the stock should be projected for at least one year prior to the trial projection in order to estimate the biomass prior to any exploitation if the initial biomass is not set see below Age structure drawn from random recruitments An age structure drawn from random recruitments as specified by the recruitment functions above introduces recruitment variability into the formulation of the initial age structure eliminating the need to project the stock forward one generation In this formulation each age class is assigned a different number of recruits R at recruitment age The numbers at age are determined using equation 37 by replacing R with Note that the stock should be projected for at least one year prior to the trial projection in order to estimate the biomass prior to any exploitation Part 4 Specifications of the GYM 100 Generalised Yield Model GYM User s Manual Handling a Plus Class A plus class is a sum to infinity of numbers at each age greater than or equal to the last age class in the simulated stock In a deterministic case with no variation in the annual mortality rate the plus class would be determined as M a a Ns Re 38 M e where is the age at which the plus class accumulates and a is the age of recruitment However variation in recruitment and or the annual rate of natural mortality can lead to this f
67. ion showing the potential for including negative growth Part 4 Specifications of the GYM 96 Generalised Yield Model GYM User s Manual 4 3 4 Natural Mortality M is the average rate of natural mortality over the life of a cohort and m z is a function which gives the ratio between the natural mortality rate for fish of total age tto the average value over the lifetime of a cohort This requires that mdr m d 32 Partitioning the natural mortality into an overall average level which can be modified by relative patterns against age and time of year is a convenient method for incorporating Monte Carlo integration over the effects of uncertainty in natural mortality rates into the assessments This is because only the average value needs to be modified for each trial projection The ability to specify a relative pattern allows sensitivity analyses on age specific and seasonal effects on natural mortality to be readily investigated Coefficients are entered as age specific mortality and as a function for the time of the year In the latter case it is assumed that all ages have the same time specific variation in natural mortality through the year Uncertainty Uncertainty in the annual average rate of natural mortality can be incorporated by drawing a value at random from a uniform distribution over specified ranges at the beginning of each trial M will automatically vary each trial with use of the proportional recrui
68. ired Part 4 Specifications of the GYM 111 Generalised Yield Model GYM User s Manual 4 7 Guide to Parameter Input Table This is an example of a parameter table for an assessment of Patagonian toothfish Table Parameters input to the GY model for Dissostichus eleginoides in SubArea 58 5 2 Category Age composition Characteristics of Year Natural mortality Fishing selectivity Fishing Season Determination of F Length at Age Weight length W aL Maturity Spawning Season Recruitment Simulation Characteristics Decision rules Parameter Recruitment age in simulation Number of age classes Plus class present years in plus class in initial age structure Reference Start Date in year Resolution Number of increments per year Mean annual M Age selectivity function Age Selectivity Effort by season Reasonable upper bound for annual fishing mortality Tolerance error for determining fishing mortality in each year von Bertalanffy time 0 von Bertalanffy Lo von Bertalanffy K a b Maturity at age function Age Proportion Mature Date when spawning begins Date when spawning ends Mean of log Recruits Standard error of the mean of loge Recruits Standard deviation of loge Recruits Type of Tests Number of trials in simulation for each test catch Formulation of initial age structure Deterministic or Random Years to project stock to remove effec
69. itment surveys 87 Input characteristics of the fishery historical and future 98 Input initial population structure 100 Root name that will be given to all output files with the relevant extension then added Empty Line Empty Line Ex Type of information printed to log files Lookup table printed to LUK file 83 127 Specify whether the GYM is run only to generate lookup tables used mainly by the interface Mirror inputs and outputs in the LOG file 124 Print parameters updated in each trial to the LOG file Print percentile tables from each test mostly not used any more 127 Empty Line 129 File Lines simulation file GYDEF sim for scenario Long lived 03 ACkCkCk C KCck Kk CckCck Kk Ck Kk Ck Kok KK CK KK KK OK KI KK UK UU KU KO KG KK OK KK KR KR KK KR kk FILES Biological Parameters for Input LL02 bio survey details for recruits LL02 rec fishery details LOZ eh initial population structure LLO3 str Name for Output files GENERAL OUTPUT DETAILS Run Time Log Files Lookup tables generated in setup Run only for lookup tables Input Output from setup Updated Parameters in each trial Percentile tables at end of each tests FALSE Output files Population Status General incl SSB status TRUE Part 4 Specifications of the GYM 114 Generalised Yield Model GYM User s Manual Description File Lines Se
70. iven year if using the CVs is set to True This assumes log normally distributed residuals Log normal recruitment function In the lognormal case recruitment Ry is drawn each year at random from a log normal distribution based on a specified mean and coefficient of variation such that 2 o R R exp n 75 8 where 7 is drawn randomly from N 0 0 which is a normal distribution with zero mean and variance which is estimated from CV by o n CV 9 Part 4 Specifications of the GYM 88 Generalised Yield Model GYM User s Manual These parameters can be adjusted to give a mean recruitment of 1 0 and variation greater than or equal to zero Uncertainty Parameters of the log normal recruitment function can be varied between trials in two ways taking account of uncertainty in these estimates The first method is by specifying a range in the coefficient of variation for situations when recruitment variability is not well estimated A value for the coefficient of variation for a trial is then randomly drawn from a uniform distribution between the minimum and maximum values of the CV Alternatively when the mean recruitment and its CV are estimated uncertainty in the estimates of recruitment can be incorporated in the loge domain where the parameters for the log normal function are determined from both equation 9 and 2 O g aR 19 SE gt Values for in a trial are then dra
71. k ii In a text editor or in the GYM post processing analysis open File LLO1 PG and extract the test F 0 and save to file The recruitment function for a natural population can be observed by plotting all values of recruitment against the spawning biomass from the previous year Given the changes in parameters between trials the median spawning biomass may vary from one trial to another The stock recruitment relationship in the GYM is governed by the median spawning biomass prior to the projections if the median is not estimated then it will be the spawning biomass in the year just prior to projections Thus the stock recruitment relationship is best plotted against the SSB status which is the spawning biomass for a year relative to the median pre exploitation spawning biomass for the trial This plot can be compared to a raw plot of the recruitment vs spawning biomass To create the plot file add a column to place the recruitment from the following year into the year of the spawning biomass Note that in Excel a global copy of the formula would need to exclude the last year of a trial from copying the PART 5 Working Examples 153 Specifications for the Generalised Yield Model GYM recruitment for the first year of the next trial In this example the formula used was if Year 2032 NA Recruitment in next year i e if Year is the last year of the trial then write to the cell a value for a missing value otherwise right the valu
72. l biomass from a survey CCAMLR Science 1 81 106 Butterworth D S Punt A E Basson M 1992 A simple approach for calculating the potential yield from biomass survey results SC CAMLR SSP 6 207 215 Constable A J and de la Mare W K 1994 Revised estimates of yield for Electrona carlsbergi based on a generalised version of the CCAMLR Krill Yield Model Working Paper WG FSA 94 21 Working Group on Fish Stock Assessment SC CAMLR XIII Hobart Australia Constable A J de la Mare W K Agnew D J Everson L and Miller D 2000 Managing fisheries to conserve the Antarctic marine ecosystem practical implementation of the Convention on the Conservation of Antarctic Marine Living Resources CCAMLR ICES Journal of Marine Science 57 778 791 Constable A J de la Mare W K 1996 A generalised model for evaluating yield and the long term status of fish stocks under conditions of uncertainty CCAMLR Science 3 31 54 Cooke J G 1999 Improvement of fishery management advice through simulation testing of harvest algorithms ICES Journal of Marine Science 56 797 810 de la Mare W K 1994 Modelling krill recruitment CCAMLR Science 1 49 54 de la Mare W K 1986 Simulation studies on management procedures Report of the International Whaling Commission 36 429 49 de la Mare W K 1987 Some principles for fisheries regulation from an ecosystem perspective Pages 323 340 in CCAMLR ed SC CAMLR Selected Scie
73. me as having them on the same day Better resolution of the spawning season can be obtained by increasing the number of increments in a year Uncertainty in the Maturity Function Uncertainties in the maturity function are incorporated in the same way as for the fishing vulnerability The length at which 50 of fish are mature mMm are taken into account by drawing these at random from uniform distributions each with a specified range This occurs at the beginning of each trial Part 4 Specifications of the GYM 105 Generalised Yield Model GYM User s Manual Reference level for estimating spawning stock status The reference level for estimating the status of the spawning stock during the trials can be determined in two ways I the spawning stock biomass in Year of the projection So ii estimate of the median pre exploitation spawning biomass In the first case the stock is projected over Year to give the estimate of 5 during the spawning season in that year Estimating Median Pre exploitation Spawning Biomass Two methods are available for determining the median pre exploitation spawning biomass at Time 0 i based on the deterministic initial age structure and ii Monte Carlo sampling of random initial age structures The approximation for the median pre exploitation spawning biomass based on the deterministic initial age structure is derived from Butterworth et al 1994 This initial age structure is then projec
74. nd of the period in each age class are assigned to the next highest age class and the lowest age class is assigned from a recruitment function see GYM Specification Example G01 Figure GS1 The process is repeated until the required time span is modelled to produce a single realisation trial of a stock trajectory Figure 5 1 Part 4 Specifications of the GYM 81 Generalised Yield Model GYM User s Manual 1999 2005 Em 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 Age 4 2000 2006 r r 0 S 0 1 2 3 4 5 6 T 0 1 2 3 4 5 6 7 2002 2008 1 2 3 4 5 6 2010 8 5 27 24 23 23 2 1 oe m 0 0 1 2 3 4 5 6 T 0 1 2 3 4 5 6 Age Ag Age Figure GS1 Age structure of a population over 12 years from the initial year nominated as 1999 These are derived from the outputs from GYM Specification Example G02 M 0 8 Ages 0 7 with no plus class Part 4 Specifications of the GYM Generalised Yield Model GYM User s Manual 4 3 Stock projection over one year The core of the model surrounds the projection of the population over one year The primary inputs for a year are the numbers in each age class and the catch rate specified as a catch or as a fishing mortality rate The other inputs include the coeffi
75. nd of array line Flag to monitor every year in projection from Year O T or only years specified for monitoring above F Empty Line Ex specify period over which the average fishable biomass is estimated 126 Used e g for adjustments based on a time series such as CPUE As for spawning biomass but using rrshable biomass t un 49 As for spawning biomass but using fishable biomass t in 49 Empty Line Ex Empty Line See 108 See 108 Used to adjust the BO Generalised Yield Model GYM User s Manual File Lines 2002 01 01 Year of projection Reference Start Date in year Increments in year 12 Years to project stock in simulation 30 STOCK PARAMETERS Last age class in stock 30 Coefficient values ramp between incs GENERAL MONITORING OF STOCK 14 2X Ley 2002 01703 O Monitor all Years in projection MONITORING OF FISHABLE BIOMASS DURING YEAR Start of Monitoring Period dd mm End of Monitoring Period dd mm ESTIMATING IN GAMMA CALCULATIONS Estimate BO log normal FALSE CV of BO estimate Coverage of survey 1 0 Part 4 Specifications of the 116 Generalised Yield Model GYM User s Manual Description estimate if survey area was greater than or less than the area to which assessment applies See 108 Empty Line End of file line 4 10 2 File lines are separated equation pa
76. ng Selectivity with age 1 if by length ET 3 240146 O Empty Line Ex E t in 98 34 Relative fishing effort in each inc of year day month coefficient 12 614 46 01 04 45 0 Part 4 Specifications of the GYM 121 Generalised Yield Model GYM User s Manual Descr File Lines iption Empty Line Each year of the known Year of fishery fishing history is added in chronological order although not necessarily every year with this header line When no more years to add then include this line but with a 1 as the year Then insert the catch Catch kg Du in the biomass units of the weight length relationship Then nominate whether Selectivity to vary from last one to use the vulnerability parameters from the previous year in the time series this would be the forward projection year if this year is the first in the series Empty Line Year of fishery 2004 Catch kg 10 If vulnerability is Selectivity to vary from last one varied from the previous year T then enter all the vulnerability information as for the projection details Empty Line Fishing Selectivity by length 0 if by age Min length 50 recruited 40 0 Max length 50 recruited 40 0 Range over which recruitment occurs 1040 Empty Line Fishing Selectivity with age 1 if by length F7 3 2X G14 6 0 0 Le 2 0 Empty Line Relative fishing
77. nly approximately recognising that the average biomass is a result of both change in the individual weight of a fish and the change in numbers of fish Thus the approximation for an appropriately scaled age class N is Part 4 Specifications of the GYM 103 Generalised Yield Model GYM User s Manual NZS 5 a s a x where s 2 Y x Fence zu 2 2 44 i 1 amen 1 Ps a 10 1 10 1 IL m a t dt F fanar e where s is the factor to scale the age structure to the estimate of biomass where the average weight of fish in the increment is determined from the average of W at the beginning fo and end t of the increment in which the survey was taken 5 the factor to give the number of fish in cohort a at the beginning of the increment rather than at the average point S is the factor to project the cohort back to the beginning of the year Note that biases in these approximations can be reduced by increasing the number of increments in the year Unknown age structure In the case of an unknown age structure the initial age structure at the beginning of the year is determined is first established using the deterministic or random methods above followed by scaling to the estimate of biomass taken during the year The scaling requires projecting the age structure forward to the time of the survey determining the scaling factor and then applying that to the
78. ntific Papers CCAMLR Hobart Australia de la Mare W K 1996 Some recent developments in the management of marine living resources In Frontiers of Ecology pp 599 616 R B Floyd A W Sheppard and P J De Barro Ed CSIRO Publishing Melbourne de la Mare W K 1998 Tidier fisheries management requires a new MOP Management orientated paradigm Reviews in Fish Biology and Fisheries 8 349 356 Kirkwood G P and Constable A J 2000 Integration of CPUE data into assessments using the generalised yield model Pages 10 PART 6 References 164 Specifications for the Generalised Yield Model GYM Press W H Teukolsky S A Vetterling W T and Flannery B P 1992 Numerical recipes in Fortran the art of scientific computing Cambridge University Press Cambridge 963 pp Press W H Teukolsky S A Vetterling W T Flannery B P 1992 Numerical recipes in Fortran the art of scientific computing 2nd edition Cambridge University Press Cambridge U K Rosenberg A A Beddington J R and Basson M 1986 Growth and longevity of krill during the first decade of pelagic whaling Nature 324 152 154 VI PART 6 References
79. o the table above for illustration 5 2 Long Lived Species Examples The following examples step through the checking for the example long lived species GYM Specification Example LL 01 Description Long lived species Base File rootname LLO1 Base File Details Long lived species Base input parameters AGE STRUCTURE First age class in stock 2 Last age class in stock 30 Oldest age in last class 60 RECRUITMENT Recruitment Function L Use recruitment surveys to False est recs Use recruitments in time False series Mean recruitment 1000000 0 Min Coefficient of Variation 1 0 Max Coefficient of Variation 1 0 PART 5 Working Examples 149 Specifications for the Generalised Yield Model GYM Use Standard Error of Mean Number of replicates x SBO for recruitment depletion x NATURAL MORTALITY Mean Annual M SD of M between years within runs Alter Mean Annual M by Multiplier Probability of M being multiplied Amount Mean M to be multiplied by Natural Mortality coefficient with age Natural Mortality with time of year date coefficient LENGTH AT AGE Growth Curve Type time 0 Linf WEIGHT AT AGE Weight length parameter A Weight length parameter B MATURITY Maturity Type Length 50 are mature Range over which maturity OCCUIS SPAWNING SEASON First Day of Spawning Season dd mm Last Day of Spawning Season dd mm EVALUATION OF YIELD Type of evaluation Vector of Gammas Catches or Fishing
80. ormulation being biased which will be particularly important if the plus class is a non trivial proportion of the stock The bias can be reduced by including a large number of ages in which interannual variability in recruitment and mortality can be applied This is achieved by increasing the Oldest Age of fish ao in the Plus Class to which such variability applies until the bias is reduced satisfactorily such that the plus class is M a a 1 a Re N J Re m d cza 1 39 The bias can be checked by examining whether the median spawning stock escapement see below departs appreciably from 1 for a test in which there is no catch i e the stock should remain stable note that a departure from 1 0 can also be observed because of stochastic variability if the number of replicate trials is insufficient to account for variability in some of the input parameters see below Note that the consequence of adding more years in the plus class is to slow down the computation of median pre exploitation spawning biomass Part 4 Specifications of the GYM 101 Generalised Yield Model GYM User s Manual Handling variability in Natural Mortality in the initial age structure Interannual variability in natural mortality requires that mortality for a given year is applied consistently across all age classes that are extant in that year This can be visualised in the following table showing an example of years in which
81. parameters change over time during a trial and how uncertainty in the parameters is evaluated between trials The lookup tables can be printed to a file during the setup phase of the program see GYM Specification Example GO4 However these outputs only apply to the forward projection functions and will not include the length based components of fishing selectivity or maturity as these may be varied between trials The updates of these length based components at the beginning of each trial and during a trial can be logged during the course of the simulations The application of different functions during a trial such as during the known fishing period will need to be checked by examining the outputs on stock and cohort status for the relevant years GYM Specification Example G04 presents the workings for this process Figure GS2 illustrates the lookup tables used in a trial as calculated in GYM Specification Example G04 Part 4 Specifications of the GYM 84 Generalised Yield Model GYM User s Manual 150000 4 Q gt 0 2 0 0 Te TOR IA coefficient 0 0 8 0 4 Maturity coefficient 0 2 00 Figure GS2 Illustration of lookup tables based on krill assessment for the South Atlantic with 12 increments per year the growth and fishing seasons restricted to
82. pplied The two estimates required by CCAMLR for the evaluation of a test value long term annual yield specified as yBo or Catch or a long term annual F a long term annual yield are i the probability of depletion at any time during the projection period where the spawning biomass falls below a specified proportion page e g 0 2 of the pre exploitation median level and ii the overall escapement E of spawning biomass given by the ratio of the median spawning biomass at the end of the specified period to the median pre exploitation spawning biomass These estimates are obtained by undertaking a large number of projection trials e g 1001 For each trial the program records the spawning stock biomass during the projection The performance measures require the lowest spawning biomass during the projection period and the spawning biomass at the end of the projection period to be converted to ratios of these values to the median pre exploitation biomass determined before the trial is undertaken The median pre exploitation biomass is determined for each trial because the demographic parameters will alter between trials when uncertainty in these is present see above Depletion probability The probability of depletion can be estimated using two methods based on the two different formulations of the median pre exploitation spawning biomass described above The first is that arising from the use of the deterministic formulation so that
83. r 112 4 8 Running GYM with a user interface sseessssssssssssseseeeenneeene nnne 113 4 9 Running GYM without the eene 113 4 9 1 Operation amp DOS Command Line iias au ben t eect eae peche dem Meis 113 4 10 TGS uin eite tico o tat 113 4 10 1 Simulation parameters 5 114 4 10 2 Biological parameters lt ROOT gt 117 4 10 3 Recruitment survey data ROOT Filename gt REC 120 4 10 4 Fisheries data and parameters lt ROOT Filename FSH 121 4 10 5 Initial Population Characteristics lt ROOT Filename gt STR 123 M REO Uie ENTE D PL 124 4 11 1 PRESUMES Olle ctc 125 Z 112 JOISgDoSleSscuatasaeqisside be checa ena KO eee sta Rot tonio bodas ace oS 125 aono LC DOE 127 AtA 3Percenile TADICS cece 127 4115 Population ios uc ees 128 Status of the stock in Year 0 in each trial 128 General incl SSB status 129
84. rameter references are given in square brackets OO End of File 100 Biological parameters lt ROOT Filename gt BIO by dotted lines Page references are given in parentheses and Explanation lines equivalent to Empty lines are indicated as Ex in the description Description EX Title Empty Line Empty Line Empty Line Empty Line Age of recruitment 36 Last age class monitored projections class 100 to be in the plus Oldest age used in the formulation of the plus class 101 98 39 Empty Line Empty Line See 88 See 87 See 86 Empty Line Ex See 88 8 A CV range can be used to incorporate uncertainty See Part 4 Specifications of the GYM R biological file for scenario Long lived 03 ACkCkCk Kok kckck kck kck Kock ck ckck ck Kkckck Kok kc Kok ck kok kock Kok ko ok ck kok kock kock k ck ck kk kk AGE STRUCTURE First age class in stock 2 au Last age class in stock Oldest age in last class RECRUITMENT Recruitment Function L Use recruitment surveys to est recs FALSE Use recruitments in time series FALSE Parameters for recruitment Recruitment from log normal distribution Recruitment Function L Mean recruitment 1000000 0 Min Coefficient of Variation 117 Description 88 89 8 9 A CV range can be us to uncertainty 88 89 8 9
85. rance in the solution of F will influence the accuracy of the solution and the resulting catches observed in the output 4 3 2 Recruitment The age structure of the population is determined in the first instance through the addition of recruits at a given recruitment age For some populations observations of Age fish will not be possible in such cases the first fully observed age class may be some years older say at Age 4 This reference age is used as the age at which the recruitment functions apply For a trial simulation estimates of recruitment may or may not be available for a given year When available these estimates can be used in a trial When they are not available recruitment for that year will be drawn as required from a recruitment function nominated by the user Known Estimates of Recruitment Estimates of recruitment for given years can be entered in two ways Vector of recruitments he vector of recruitments is based on estimates R with their associated coefficients of variation for given years The values used in a trial R will be drawn from a log normal distribution where 2 R 2 R exp 7 4 where 77 is drawn randomly from which is normal distribution with zero mean and variance o which is estimated from the CV by Ind CV 5 Part 4 Specifications of the GYM 86 Generalised Yield Model GYM User s Manual Estimated Numbers
86. re False Biomass amp CV to scale 0 0 5 3 Projections based on starting biomass compared to general projections The following projections have been undertaken 1 random projections according to the above requirements LL01 i1 projections from a fixed estimate of total biomass 1500 tonnes but with unknown age structure 11 02 iil projections from an estimate of total biomass 1500 tonnes with a CV of 0 3 and an unknown age structure LL03 The first set of projections aims to determine the fishing mortality according to CCAMLR decision rules for a 35 year projection period will be filled out in the final version The second and third projections consider the period the fishing mortality required to facilitate recovery with a low probability of further depletion say 0 1 probability of being depleted below 0 8 of the spawning biomass at the time of the survey The below figures illustrate the text that will be developed over the next couple of days
87. roject 2 1 Set F for year If fixed catch then Find F Fn Zbrent 1 4 Advance N at age at end of year to next 8580008000 9000 0000 00008600 0000 00220022002800240000000000006002000060020022005200220247 Rungekutta DEfunc Fn Average_RK 2 2 Integrate over year 2 3 Monitor attributes of population catch PART 4 Specifications of GYM 136 Generalised Yield Model GYM User s Manual Figure GS4 Schematic showing the steps involved in undertaking a test of a harvest scenario Program routines are shown in bold italics Numbers are given for reference in the text 2 1 Monitor Run Details 1 1 f Recruit Vector Set Median Recruits d EZ uu for run 1 2 Iterate runs 2 2 Monitor SSB Status 3 2 Iterate Years To Time 0 Catch F G 0 To 4 0 At left side 1 3 Determine SSB status for decision rules SaveSB 3 3 Estimate BO for gamma Test if required Fn Estimate BO Sort 3 4 Iterate Years Known Catches and or Recruits 4 0 One Year To 4 0 At left side 4 1 Set Recruitment for Year 3 5 Iterate Years Projection period To 4 0 At left side 4 2 Project age Classes through year Save monitoring data Save monitoring data PART 4 Specifications of GYM 137 Generalised Yield Model GYM User s Man
88. rough increment s increment in which survey occurs Annual annual rate S derived from average spawning biomass over spawning season derived from average vulnerable fishable biomass over nominated period to monitor Part 4 Specifications of the GYM 126 Generalised Yield Model GYM User s Manual 4 11 3 Look up Tables LUK an output file for printing the lookup tables for the coefficients This is useful for checking the input parameters were correctly used to generate the coefficients It is also required for graphical presentations in the GYM Interface Example LOOKUP TABLES OF COEFFICIENTS Age classes o Increments in year 24 AGE LENGTH WEIGHT SPAWN AT AGE M AT AGE F AT AGE 6 G14 8 1X 0 0000000 r 12696 y02 365405625E 01 10000000 p Lo0000008 y d0D00OU0DOO 0 41666667E 01 172 49874 0 38488428E 01 1 0000000 1 0000000 0 0000000 175 2671 0 4050431 78 01 1 0000000 1 0000000 0 0000000 0212500000 py 5190292205 U 42599137E 01 1 0000000 y 430000000 0 0000000 0 16606007 180 79401 0 44743988E 01 1 0000000 A 20000000 p das U 20033939 p 1034559243 0U 469699585E 01 1 0000000 p L4U0O0DOD 0 0000000 etc 4 11 4 Percentile tables Percentile tables are now obsolete However if they are chosen to be printed then they will appear in the PCT file This file was useful for validating the model and for monitoring the stock It has been superseded by the Population Status f
89. s is only approximate as the cohort biomass is estimated at the survey time and the spawning biomass is estimated at the time for spawning A more accurate calculation is by using the file iii Plot Maturity vs Age iv Plotted in LLO1 maturity PART 5 Working Examples 157 Specifications for the Generalised Yield Model GYM Maturity 0 10 20 30 Age Figure GLLO8 Approximate maturity function by age according to the relationship of total biomass and spawning biomass for each cohort at the time of spawning Drawn from file LLO1 CG Compare the results to length at age in order to check the maturity at length relationship SPAWNING SEASON First Day of Spawning Season dd mm 01 07 Last Day of Spawning Season dd mm 01 07 EVALUATION OF YIELD Type of evaluation F Vector of Gammas Catches or Fishing Mortalities 0 0 05 0 075 0 1 0 125 0 15 0 2 0 3 Do yield per recruit analysis False SIMULATION CHARACTERISTICS Number of runs in simulation 1001 Depletion Level for Test 0 2 Seed for random number generator 24189 Reset seed to this value for each test True Check i ii iii iv v vi vii The effect of uncertainties in the recruitment function maturity and natural mortality can be observed in the variation in the estimates of the median pre exploitation spawning biomass In Excel Open File LL01 PG Extract all Trials from Test F 0 Sort by Year and extract only 2002 the year
90. spawning stock number during the spawning season in the Year Example Note in this example the lines are wrapped around Test lrial Year Total biomass Total Number Spawn Biomass Spawn Number Vulnrbl BMS Mulnrbl Number F Catch Recruitment Status 2041500050 1 1985 906145279 14064680 56814937 29909758059 p 49447575 1867565 0 0 0000000 0 0000000 4048020 U l19911762 gt 120622061 20 L50000 1 1986 85844286 e 19434531705 29JDA4OT54 p 00394095 15399ll T 0 0000000 0 0000000 4708025 4 Ua doo Ld rez p 1 0415113 201500030 P Ly 1987 89259960741 p s 342967094 2940730149 2904037062 y 246605057 0 0000000 0 0000000 z UZI6CC lt eo pO Foe gt ex OlL40G 1 etc Part 4 Specifications of the GYM 129 Generalised Yield Model GYM User s Manual Specified Survey times ROOTname PS The data are derived for the specified survey date in each year All results are for the survey increment in each year The test of yield either yBo Catch F the example below is catch Example Test lrial Year Inc Total biomass Total Number Spawn Biomass Spawn Number Vulnrbl BMS Number 20150000 Le L92995 0 0000 919577919 r 4961452007 r 901152629834 2269902 0 p 128459330994 r DJs 2815000 0 i 1996 0 0000 2i050055 1906985989 202042924 603445 2 294909 95 2 40 2815000 0 Ly 10967 0 0000 6
91. st of yield either yBo Catch F the example below is catch The number of the respective trial can be used to relate this information to other files in a database The first year of the split year can be used to relate this information to other files in a database Increment in year as a fraction of the whole year time refers to the start of the increment Example Test lrial Year Day Age Cohort biomass Cohort Number Length m eV larly Maturity 201500040 j Ll 1995200000 4 TUSSOS OI 10468020 7 y p 100000000 y 00000000 j 0 0000000 28150000 tp L9909 00000 Sp 27252990040 p 2071090949 y 12 05700 0 0000000 0222000000 0 0000000 2901500040 ly 1989700000 6 195222996217 r p 0 9000000 U 90000000 j 0 0000000 etc Part 4 Specifications of the GYM 133 Generalised Yield Model GYM User s Manual increments in each year ROOTname Cl The status of each age class in each increment in each year of every trial This file needs to be used with caution A single test with Ages 4 35 running for the known catch and recruitment history 1985 to 2003 with 11 trials took up 28 MB of space The data are derived as for survey times but for each increment in each year The test of yield either yBo Catch F the example below is catch Increment in year as a fraction of the whole year time refers to the start of the increment ishi Vulnrbity Age specific x Length spec
92. t Age Class 1 hh hh ho o o Increment UNa amp 1 1 083333 1 166667 1 25 1 333333 1 416667 1 5 1 583333 1 666667 1 75 1 833333 1 916667 2 2 083333 2 166667 2 25 2 333333 2 416667 2 9 2 583333 2 666667 2 75 2 833333 2 916667 3 3 083333 3 166667 OOES48 As for krill 12 3 1 e summer G04 LUK Length 22 03221 27 43225 32 08011 36 08057 36 08057 36 08057 36 08057 36 08057 36 08057 36 08057 36 08057 36 08057 36 08057 39 52379 42 48739 45 03819 45 03819 45 03819 45 03819 45 03819 45 03819 45 03819 45 03819 45 03819 45 03819 47 23369 49 12337 PART 5 Working Examples Weight 10694 84 20643 55 33014 73 46969 94 46969 94 46969 94 46969 94 46969 94 46969 94 46969 94 46969 94 46969 94 46969 94 61741 27 76697 33 91357 21 91357 21 91357 21 91357 21 91357 21 91357 21 91357 21 91357 21 91357 21 91357 21 105379 4 118539 8 Maturity at Age 1 A gt LI LI LI Ls LI Ll lI Ll LI I R amp ooooocoocooc inn sHoocoooocoocoocoTnZi opcco The annual rate of mortality is checked by summing M for all records 147 C5 Co C5 Co Co Co Co W Co Specifications for the Generalised Yield Model GYM SR SCPANDAAAYW 3 25 3 333333 3 416667
93. t Cohort Number 0 59639 0 576838 0 559127 0 541416 0 523705 0 505994 0 488283 0 475393 0 462503 0 449613 0 436724 0 423834 0 410944 0 398054 0 385164 0 372275 0 359385 0 346495 0 333605 0 320715 0 307826 0 296357 0 286896 0 277436 0 267975 M Per Inc 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 3 33E 02 Annual 0 80 This table is only part of the 02 file The records for one year were sorted by age to extract this subset of the table that shows the progression through the year of the Age 0 cohort Note that the table shows a mortality rate for the increment 1 0000 This is not used as the beginning of that increment is the end of the year with that increment being the first of the following year The annual rate of mortality is checked by summing M for all records except that increment 1 0000 This check is shown in bold adjacent to the last record PART 5 Working Examples 144 Specifications for the Generalised Yield Model GYM GYM Specification Example G03 Description Effects of adding fishing mortality Base File rootname G03 Base File Details G01 Variation Annual Natural Mortality rate M 0 8 Annual Fishing Mortality rate F 0 1 Results observed in file G03 PG indicates the mort
94. t a time during the year rather than on the reference start date of the year ii the total biomass estimate for a given date in the simulations is the average biomass over the increment in which it falls and iii the age structure may or may not be estimated during that survey These three points are accounted for in the following two formulations Known age structure In the case of a known age structure estimated at the same time as the biomass survey the initial age structure at the beginning of the year is determined by first ensuring that the known age structure scales appropriately to the estimate of biomass and then projecting the age structure back to the beginning of the year Thus at the time of the survey numbers at age are drawn from log normal distribution based on a specified mean V and coefficient of variation such that 2 N where OF In 1 CV where 77 is drawn randomly from 0 om and the total biomass B is also drawn from a log 42 normal distribution based on a specified mean B and coefficient of variation such that 2 oa O5 B exp rn 2 43 where c In 1 C V where 77 is drawn randomly from N 0 6 The numbers at age are then re scaled to the estimate of biomass B keeping the relative proportions in tact This rescaling takes account of the biomass being the average biomass in an increment However it is undertaken o
95. ted one year to numerically solve equation 49 with F 0 to determine the approximate median unexploited spawning biomass S This formulation can contribute to a bias in the median spawning biomass Constable amp de la Mare 1998 The Monte Carlo method for estimating the median pre exploitation spawning biomass S allows So to be estimated from multiple applications of the random method used to set up the initial age structure This option has the advantage over S of being unbiased but requires more computation and is subject to sampling variability Consequently it is important to nominate a large number of replicate observations for estimating the pre exploitation median spawning biomass in this case Note that the stock recruitment relationship is not applied when the median pre exploitation spawning biomass is being estimated 4 4 3 Managing Time during a Test Time O of the projection Time 0 of the projection does not have to coincide with the beginning of the calendar year It can begin on any date nominated For example the fishing year may be best described as beginning on 1 December of one year and ending on 30 November in the following year The projection year is best undertaken in alignment with the fishing year rather than the calendar year In this context the user needs to input the reference start date in the year day month e g 01 12 as well as the reference year say 1982 as the elements for describing
96. that the natural mortality rate is plausible ii take note of the number of fixes that arise which result from the random proportional recruitment is outside the range of 0 to 1 If this is a substantial number relative to the number of trials then the results may not be reliable Recruitment Time Series in Projections A time series of recruitments in a projection is built as a combination of the known time series either as the vector of recruitments or from surveys and in years when the recruitment is not known the recruitment functions log normal bootstrap from a vector proportional recruitment The recruitment functions are the sole means for projecting into the future Currently the known recruitment period is modelled as part of the known catch period irrespective of whether the recruitment series is longer or shorter than the catch period In order to achieve this successfully zero catches should either be placed in years when no catch was taken but recruitment is estimated directly or such years will be filled automatically During the forward projection recruitment is set at the beginning of the year and can be based on the status of the spawning stock in the previous year the stock recruitment relationship Stock Recruitment Relationship A simple stock recruitment function can be applied during the time series for both the log normal and proportional recruitment functions This is applied after the recruitment has be
97. tion for the future projection period The length based function has provision for variation from one trial to another and can be varied from one year to another in the catch series Consequently the lookup tables for the Runge Kutta are completed for fishing mortality after these parameters are established prior to each year of the catch series and prior to the future projection 5 The fishing selectivity and vulnerability for the forward projection are entered first followed by the details for the catch series Known catch history In each year of a catch history the weight of catch taken along with all of the parameters detailed above can be varied It is possible to retain the same parameters from one year to the next without inputting all the data Similarly years when the catch was zero do not need to be entered In the first year and subsequent consecutive years of the known fishery it is possible not to specify fishing vulnerability and use that specified for the forward projection as the default However it is advisable to include the selectivity and vulnerability details in the first year of a catch history in order to avoid inadvertent errors in the application of the forward projection parameters early in the catch history The length of the period Known catch history is determined by combining the years in which catches have been taken with the years of known recruitments This may result in a number of years in which no cat
98. tion over one year The yield from each class taken over one year is calculated by simultaneous numerical integration of equations 1 2 and 3 using an adaptive Runge Kutta procedure Press et al 1992 The total yield is the sum of the yields from all age classes Look up Tables In order to speed computation the time dependent functions for natural mortality m 7 weight at age w r fishing mortality f a t and maturity a t below are calculated as vectors of discrete numeric values prior to numerical integration This is done to avoid the estimation of the parameters at each time step or during the integration Part 4 Specifications of the GYM 83 Generalised Yield Model GYM User s Manual The discrete points are calculated at a series of fixed points with a constant interval The interval can be selected to be sufficiently small to adequately approximate the required functional forms The values of the functions at any instant are calculated by linear interpolation between the nearest points included in the vectors of discrete values Thus the functions are replaced by piecewise continuous linear approximations n the case of functions which have fixed transition points corners the corners may be cut by the linear interpolation These vectors are stored in Lookup Tables As discussed below the lookup tables will be updated for each trial and for each known fishing year as required depending on how the different
99. tment function It is not recommended that age specific variation in mortality rate be applied at this stage when the proportional recruitment function is being used This is in the process of being incorporated Random variation around the mean annual natural mortality rate M can be included for each year a trial according to a log normal distribution if the coefficient of variation CV is greater than 0 An additional feature since 1997 is to allow for stochastic high mortality events as described by Agnew et al 1998 This is achieved by nominating the proportion by which the mean annual natural mortality will be increased a multiplier Mpig and the probability of this occurring in a given year m Thus random variation between years can follow a log normal function such that my UOD lt from N 0 0 33 U 0 1 gt p n 0 0 33 2 2 Moxo n where 7 is drawn randomly from 0 which is a normal distribution with zero mean and variance which is estimated from as for equation 9 The application of interannual variation in M is an important consideration in the development of the initial age structure see below The inclusion of annual variation in M does not affect the age specific or season specific variation in M There is no provision for uncertainty in the seasonal and age specific trends in natural mortality Thus the lookup tables generated in the Se
100. ts of initial age structure Year 0 of projection Estimate of median pre exploitation spawning biomass prior to trial Vector of real catches to project over known catch period tonnes Number of years to project stock following known catch period Seed for random numbers Reset set in each trial Reference point for depletion Part 4 Specifications of the GYM evaluation of precautionary yield of D eleginoides 4 56 21 01 11 360 0 12 0 20 0 0 3 0 3 5 0 07 4 5 0 311 5 5 0 699 6 5 1 0 7 5 1 038 8 5 0 849 95 0 579 10 5 0 341 1L5 0 179 12 5 0 085 13 5 0 037 14 5 0 015 15 0 Uniform effort over whole year 5 E 05 0 170 8 cm 0 088 2 5 E 05 2 8 0 0 1 39 0 0002 2 32 0 0009 3 10 0 0027 4 13 0 0096 4 82 0 0213 5 76 0 0564 6 56 0 117 7 67 0 270 8 45 0 418 9 49 0 617 10 70 0 792 11 59 0 871 12 58 0 924 14 07 0 964 16 08 0 985 18 90 0 995 21 48 1 0 July July knife edge 14 585 0 159 0 422 Catch 1001 Random 1 1996 Random method 1001 Observations Run 1 12061 Run 2 20261 35 24189 TRUE 0 2 SBgmedian 112 Generalised Yield Model GYM User s Manual 4 8 Running GYM with a user interface A user interface has been developed for the GYM It provides an easy to use directory structure for managing scenarios and using diagnostic tools Its use is fully described in the m
101. tup routine are not altered during the simulation trials Part 4 Specifications of the GYM 9 Generalised Yield Model GYM User s Manual 4 3 5 Harvest Strategy Fishing Mortality F in equation 1 is the average fishing mortality over all age classes in year and is a function which gives the relative distribution of the fishing mortality of age class a and at the time of year t This is partitioned to facilitate the numerical solution for fishing mortality in each year so that only the single parameter F needs to be evaluated The age and season specific multipliers allow for a number of different effects to be combined including the effects of age and size specific selectivity and the effects of the seasonality in fishing Specifically f a t is derived from three functions a size selectivity function s a t the usual modification to F arising from gear selectivity which is re expressed as an age selection function which depends on t because of growth during the year an age selectivity function a a allows for a fishery that targets specific age classes due to for example geographic or depth stratification of the stock according to age and variation in fishing effort through the year amp t e g open and closed seasons or relative fishing effort at different times based on the number of vessels Thus f a t s a dala Eelt 34 The size selectivity function currently used in the computer program for th
102. ual Figure GS5 Schematic showing the steps involved in setting up a test Setup Run indicated in Figure GS4 Program routines are shown in bold italics Numbers are given for reference in the text 1 0 Cem Setup_Run Get M from Generate RecSeries Fn RNormDev Convert _ 1 1 Set average M amp Recruitment If using recruitment Surveys 1 2 Estimate Median M amp Rec For plus class RecSeries to log domain Fn Median Recruits Fn Mean Mortality 1 3 et Maturity Function Length Ogive Calc Diffs Coeffs Po On Year Project Get 580 Median 77 pre exploitation SSB 1 5 Set Initial Age Structure 1 6 Set critical SSB In S R relationship Fn Scale MeanRec n Estimate from log normal Scale to Biomass Estimate Write Ages Known age structure PART 4 Specifications of GYM 138 Generalised Yield Model GYM User s Manual Figure GS6 Schematic showing the steps involved in undertaking all specified tests Program routines are shown in bold italics Numbers are given for reference in the text Main Program GYield 1 1 Clear screen 1 2 Input params from file amp setup 1 3 Iterate through tests Save monitoring data PART 4 Specifications of GYM Init Screen Setup 2 1 Reset seed if ne
103. umber of animals in age class and rn is the age of the oldest age class present in non negligible numbers in the population This can also be written Part 4 Specifications of the GYM 89 Generalised Yield Model GYM User s Manual A t A i t 1 Pn t 12 where A is the number of recruits in the population For a given year random proportions of recruits need to be drawn from a distribution with mean proportion equal to the observed mean p t and the variance V p calculated according to equation 21 below Since the proportion of recruits is bounded 1 a beta distribution would be appropriate for generating these random values Estimating recruitments from the mean proportional recruitment and its variance The following steps are undertaken to generate a series of random recruitments for the observed mean proportion and its variance 1 Estimating natural mortality from mean proportional recruitment For a given mean proportional recruitment the natural mortality rate must be such that the population declines to negligible levels by the n age class see equation 12 In an unexploited population which is on average in equilibrium the proportion of recruits is a function of S the survival rate from one age class to the next which is given by 13 If M is assumed independent of age up to n and infinite thereafter then in an equilibrium population t is P t
104. urs at the beginning of the year Also the length at age relationship needs to be standardised to the nominated first day of the year which may not be the first of January or the date referenced by t in a von Bertalanffy function Some thought will need to be given as to the timing of growth in the function as it can affect the outcome when abundance in biomass is being determined This is particularly pertinent with respect to estimates of biomass from set dates in the year but with variation in survey times between years such as in the case of estimating gamma for the krill fishery based on an estimate of biomass at a given time see GYM Manual for further explanation Years prior to the projection An option is available to run the simulation prior to the catch series or a projection time series with fishing This could be necessary for two reasons I to remove the effects of the initial age structure and ii to provide for estimating the total biomass and or spawning biomass in the year prior to fishing For this reason it has been termed Years to remove initial age structure If there of these options is required then this will be equal to 1 or greater Year in the table above will correspond to the final year in this projection On the other hand if there is no need for such estimation i e the starting biomass is specified and fishing must start immediately then this would be set to zero In this case Year would be
105. ut parameters will influence the spawning stock SBO Average spawning stock biomass during the spawning season in Year O TBO The total biomass at the time of the survey in Year 0 TBO estimate An estimate of total biomass arising from the input CV for the survey Example Test lrial 5BU median CV LBO estimate 2815000 0 ls 594280420574 0 24398224 9509014937 e BIOTIC 929 Js 2815000 0 2 2960365344 21350878 67664187 s 908941 75 4 993UBSLJ7D 20 15000 0 2 4254065506 pUaz0902495 y 49313955 PASSAIC r 201950000 4 0 11174549EBT09 0 21120483 0 11476499EB T09 0 1998984865 09 0 19898456E409 2815000 0 50 IDUSAZSLOETUS U0 21 101 3 Bo Ub DA 0 4147796395T09 0 14779639ET09 201500050 6 74239252 0421415955 p IAi6l1295190 U 12327 3160BT09 0 123273160ET09 201500040 de 63681700 p 2459945 U415499242mT09 0 15499242E5E 0 9 etc Part 4 Specifications of the GYM 128 Generalised Yield Model GYM User s Manual General incl SSB status ROOTname PG General characteristics of the population The test of yield either yBo Catch F the example below is catch Average rate of annual fishing mortality for the given year and trial SSB Status Status of the spawning biomass relative to the pre exploitation status median or SBO for the trial Average spawning stock biomass during the spawning season in the Year Spawn Number Average
106. ution of p 7 is bounded 1 and reasonably bell shaped the sampling distribution of t should approach a normal distribution for a relatively small sample size It is unlikely that random values of t will fall outside the range 0 1 and it should not introduce much bias if these are rare and the normal distribution truncated at the feasible range Part 4 Specifications of the GYM 93 Generalised Yield Model GYM User s Manual The model for recruitment variability provided by de la Mare 1994 is expected to result in a family of recruitment distributions which is consistent with the data used in estimating the observed mean and variance in proportional recruitment This family of distributions will converge on the true recruitment function as the number of observations N o provided of course the assumption holds that p 1 has a beta distribution Input parameters and important steps in the application of this method The parameters required for input are i mean recruitment at age A ii Mean proportional recruitment lil Standard deviation of proportional recruitment iv Age class in which the recruits enter v Number of observations of proportional recruitment Important steps in the configuration of a trial I This method can only be applied correctly if the age structure has no plus class It is important to have enough age classes so that the last age class will have negligible fish in it and
107. wn randomly from N w SE which is a normal distribution with mean uand variance SE Proportional recruitment function For a number of populations the abundance of recruits may be difficult to determine However the proportion of the population comprising newly recruited individuals might be readily estimated de la Mare 1994 presents a method for modelling krill recruitment such that the proportion of recruits are independently and identically distributed according to a beta distribution This method assumes that recruitment is independent of stock size over the range of interest the recruitment is a random variable with constant mean and variance estimated above as R and that is the recruitments over a series of years are independent identically distributed random variables If we can only estimate the proportion of recruits over time rather than the actual number of recruits then we need a method to convert the parameters we can estimate the mean and variance in the proportion of recruits into random numbers of recruits which in simulations will reproduce the observed mean and variance in the proportion of recruits Summary extracts of the development of this approach are provided here but the full derivation should be consulted in de la Mare 1994 The proportion of recruits p t is the ratio of numbers in age class t to the numbers in that age class and above that is p t 7 11 where A is the n
108. xploitation biomass as in krill a specified catch in the units of biomass and relative to the recruitment parameters as in toothfish or according to a constant fishing mortality F It also included the capacity to evaluate yield per recruit The capability to incorporate other features has mostly evolved for use in assessments of long term annual yield of Patagonian toothfish GYM Version 5 01b differs from earlier versions in 2 ways I improved storage of output population characteristics and presentation ii new features to allow specifying the starting biomass and or age structure of the population obtained from surveys during a year In addition S plus scripts have been developed to help with diagnostics The GYM User s Manual opecifications and Examples are also vastly improved These features now provide the flexibility to undertake a wide range of assessments on stocks not just specific to CCAMLR In CCAMLR the latest version of GYM can be used on I Antarctic krill for which a survey of abundance is used to undertake a precautionary assessment ii Patagonian toothfish for which recruitment surveys are used as the foundation for long term assessments and lil Mackerel icefish for which surveys of biomass and age structure are used to undertake short term assessments These specifications for the Generalised Yield Model Version 5 01b detail the population model used in the projection program the algorithm for ev
109. y Part 4 Specifications of the GYM 87 Generalised Yield Model GYM User s Manual Se EP where o is given observation from a survey N 0 is the estimated abundance and o is its standard error a is the designated age of recruitment a is the age class of the observed cohort and t is the time of the survey as a fraction of the year from the reference starting day in the year Recruitment Functions for when recruitment is unknown There are currently three functions for determining recruitment in years when no estimates are available 1 numbers of recruits are drawn randomly with replacement from a vector of recruitment estimates 2 numbers of recruits are independently and identically distributed according to a lognormal distribution with a possibility of recruitment being dependent on the status of the spawning biomass below a specified level and 3 proportions of recruits are independently and identically distributed according to a beta distribution with a possibility of recruitment being dependent on the status of the spawning biomass below a specified level de la Mare 1994 Bootstrap from a vector of recruits In this case recruitment for each year is determined using a bootstrap procedure where the numbers of recruits are drawn randomly with replacement from a vector of recruitment estimates This routine can also use the CV of each estimate in finding the value to be used in a g
110. y Line Part 4 Specifications of the GYM 120 Generalised Yield Model GYM User s Manual 4 10 4 Fisheries data and parameters lt ROOT Filename gt FSH File lines are separated by dotted lines references are given in parentheses and equation parameter references are given in square brackets Explanation lines equivalent to Empty lines are indicated as Ex in the description Descr File Lines iption Ex General details 2001 WGFSA Fishery information Long lived 02 trawl fishery for fishery file from present provided in 98 Ex x first selectivity below is Year zero and gives the selectivity for forward pro ection Empty Line Ex GENERAL Run time 111 Reasonable upper bound for Annual F 50 Run time 111 Tolerance for finding F in each year 0 00001 Empty Line Empty Line First line for fishery FISHERY Longline details Fisheries should be numbered consecutively at present only models for one fishery Empty Line Year O0 forward projection details Account for uncertainty FALSE Empty Line Ex ih Fishing Selectivity by length 0 if by age 98 34 i Used estimate Min length 50 recrurted 40 0 range in 35 Uncertainty Max length 50 recruited incorporated by making this value differ 99 i used to estimate Range over which recruitment occurs 10 0 range in 35 Empty Line Ex 5 ala in 98 34 Fishi

GYM User's Manual - Australian Antarctic Division

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