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# Sustainable Fishery Management / Sustainable and Optimum

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How to find a sustainable and optimal fishery.
Surplus production model
per Recruit analysis
Yield per Recruit

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• Brilliant presentation! Really elegantly simplified and illustrated the concepts.

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### Sustainable Fishery Management / Sustainable and Optimum

1. 1. 1 Sustainable and Optimum Fishery Yield Takashi Matsuishi At SERD, AIT, Thailand 24Feb-14Mar, 2014
2. 2. Surplus Production Model 2
3. 3. 3 Surplus Production Model  Calculate SustainableYield from Russell’s Equation Ye: Sustainable Yield V: Natural Growth  V depends on Biomass  V= 0 if B= 0  B have the upper limit K. V=0 at K  Ye =V will have a maximum point between B=0 and B= K  Maximum Sustainable Yield / MSY MGAVYe 
4. 4. MSY and MSYL 4 K0 V B MSY MSYL
5. 5. 5 Assumption of the Model 1. Equilibrium condition: Factors affecting the Population dynamics is stable 2. Single Population: Population is single and closed 3. Fishable population constant：The variance of age composition can be Ignored 4. Constant catchability 5. No time lag:
6. 6. 6 The formulation of the Model  Without Fishing   rta e K tB    1        K B rB dt dB 1 B(t) t
7. 7. 7 With Fishing  Basic Equation  r: intrinsic growth rate B:Biomass K：Carrying Capacity q：Catchability Coefficient E:Fishing Effort  At SustainableYield  qEB K B rB dt dB        1         K B rBqEBSY dt dB 1 0 quP PqXYu e /  V B SY        K B rB 1
8. 8. 8 CPUE and E at equilibrium                        r qE KB r qE K B K B r qE K B rqE K B rBqEBY 1 1 1 1 1 E r Kq qK E Y E r Kq qKEY r qE qEKqEBY 2 2 2 1          E r Kq qKCPUE 2 
9. 9. 9 Effort and SY        K B rBqEBSY 1 Biomass SustainableYield SurplusProduction Fishing Effort 2 2 E r Kq qKESY 
10. 10. 10 MSY 2 2 E r Kq qKESY  E vsSY SY E B vs SY        K B rBSY 1 B SY K 2K 4rK qr 2 4rK
11. 11. 11 Estimation of MSY from CPUE E r Kq qKCPUE E r Kq qKESY 2 2 2   bEaCPUE  brKq aqK   2       b a Kq r qK q r E b a rKq qKrK MSY MSY 22 1 2 444 2 2 2 2         baE baMSY MSY 2 42   E CPUE CPUE=a-bE
12. 12. 12 Example King 1995
13. 13. Per Recruit Analysis 13
14. 14. 14 Overfishing  Overfishing  A form of overexploitation in which fish stocks are depleted to unacceptable levels  Growth overfishing  Biomass is depleted because fish are caught in small size.  Mainly the age at first capture is too small.  Recruit Overfishing  Biomass is depleted because the spawning stock size is too small to make a sufficient next generation  Mainly the fishing mortality (fishing effort) is too large
15. 15. 15 Yield per Recruit Analysis  Yield per Recruit analysis is mainly for evaluate the stock is in the state of Growth overfishing or not  It can be calculated from  Growth curve parameters  natural mortality  age at first capture  fishing mortality  smallYPR means growth overfishing  It does not consider the spawning biomass.  use with SPR analysis
16. 16. 16 Instantaneous Catch  Yw:Yield  F: Fishing mortality  Nt: Population in number  wt: weight per fish tt w wNF dt dY 
17. 17. 17 Nt Population dynamics  Nt: Population  F:Fishing mortality  M:Natural mortality t t NMF dt dN )( 
18. 18. 18 wt weight growth  w∞: Asymptotic average maximum body size  K: growth rate coefficient  t0: hypothetical age which the species has zero length 3)( )1( 0ttK t eww   
19. 19. 19 Yw Lifetime Yield  t t w w c dt dt dY Y         1,3,3,1 3,2,1,0 nA n )( 0ttM w c eFRWY           3 0 ))(( )( 1 0 n ttnKMF ttnK n c c e nKMF eA 
20. 20. 20 YPR  Parameters )( rc ttMw eFW R Y YPR           3 0 ))(( )( 1 0 n ttnKMF ttnK n c c e nKMF eA  W∞, K, t0: Growth Curve Parameter M : Natural Mortality tr: age at recruit tλ: max age
21. 21. Calculation in Excel 21
22. 22. 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 tc F 2-2.2 1.8-2 1.6-1.8 1.4-1.6 1.2-1.4 1-1.2 0.8-1 0.6-0.8 0.4-0.6 0.2-0.4 0-0.2 22 YPR Contour H L Winf 14.8 K 0.19 t0 -0.73 M 0.25 tr 2 tl 10
23. 23. 23 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 tc YPR F 2-2.2 1.8-2 1.6-1.8 1.4-1.6 1.2-1.4 1-1.2 0.8-1 0.6-0.8 0.4-0.6 0.2-0.4 0-0.2
24. 24. 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 tc F 2-2.2 1.8-2 1.6-1.8 1.4-1.6 1.2-1.4 1-1.2 0.8-1 0.6-0.8 0.4-0.6 0.2-0.4 0-0.2 24 YPR Contour H L tc=2.5
25. 25. 25 0 0.5 1 1.5 2 0 0.5 1 1.5 YPR F tc=2.5 θ Fmax MSY/R
26. 26. 26 0 0.5 1 1.5 2 0 0.5 1 1.5 YPR F tc=2.5 θ FmaxF0.1 θ/10
27. 27. 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 tc F 2-2.2 1.8-2 1.6-1.8 1.4-1.6 1.2-1.4 1-1.2 0.8-1 0.6-0.8 0.4-0.6 0.2-0.4 0-0.2 27 YPR Contour H LF=0.5
28. 28. 28 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2 4 6 8 10 YPR tc F=0.5MSY/R tcmax
29. 29. 29 YPR/F  F∝E  Y/X=CPUE∝N  YPR/F ∝CPUE∝N in equilibrium
30. 30. 2 3 4 5 6 7 8 9.5 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 tc F 9-10 8-9 7-8 6-7 5-6 4-5 3-4 2-3 1-2 0-1 YPR/F 30 H L Winf 14.8 K 0.19 t0 -0.73 M 0.25 tr 2 tl 10
31. 31. 31 7.3ct Right fig. :YPR contour Left fig. : Section at tc=3.7 MSY at F=0.22 if recruit is constant growth over fishing at F>0.22
32. 32. 32 Increase biomass and catch together • Simplified graph • Curves at P(tc=3.7, F=0.73) Area Yw/R Yw/RF A + + B - + C - - D + -
33. 33. 33 SPR(Index for recruit overfishing) Spawning stock Per Recruitment  SSB×RPS=Recruit (SSB=Spawning Stock Biomass)  Recuirt×SPR=SSB  If SPR×RPS=1 then stable.  %SPR= SPRF=Fcurrent / SPRF=0  30%SPR or more is recommended
34. 34. 34 %SPR Contour 0 1 2 3 4 5 6 7 8 9 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 tc F 90%-100% 80%-90% 70%-80% 60%-70% 50%-60% 40%-50% 30%-40% 20%-30% 10%-20% 0%-10% H L
35. 35. 35 0 3.5 7 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 0.2 0.4 0.6 0.8 1 1.2 1.4 tc F 90%-100% 80%-90% 70%-80% 60%-70% 50%-60% 40%-50% 30%-40% 20%-30% 10%-20% 0%-10%
36. 36. Value per recruit analysis Pavarot, Matsuishi et al. (2011 FS) 36
37. 37. 37 VPR (Pavarot, Matsuishi et al. 2011)  Value per Recruit  Value =Yield x Unit price  Consider the price by size  max1 t t ttt c dtNFp R VPR       max c exp1 1 t ta aaa NMF MF F p R VPR
38. 38. 38 Price Curve of Kichiji
39. 39. 39 VPR and YPR
40. 40. 40 VPR Merit and Perspective  Bioeconomic Analysis  Including the size dependency of the price  Does not include the yield dependency  Equilibrium analysis