Sustainalbe Fishery Management / Fish Population Dynamics

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Recruitment : increase of the fish in to the stock at the age a fish can be caught …

Recruitment : increase of the fish in to the stock at the age a fish can be caught
Fish experience Mass Mortality at the early life stage. The magnitude will be less than 1/1000.
The S-R relationship is not clear and sometimes looks like no relationship between them.
S-R models are used for describing ideal relationship
Beverton and Holt Model
Ricker Model
MSY will be calculated from S-R curve.
VBGC is often used for describing the fish growth


Weight is converted by the allometric equation.
Instantaneous rate of mortality is used
Total mortality Z is observed from age composition.
Usually Natural Mortality Mis estimated from Empirical Equations
Fishing mortality F is estimated as Z minus M

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  • 1. Fish Population Dynamics Takashi Matsuishi At SERD, AIT, Thailand 24Feb-14Mar, 2014 1
  • 2. Russell’s Equation 2
  • 3. Basic Idea of Population Dynamics of Exploited Stock 3  Closed stock : without Immigration / Emigration  Stock size will be increase only by  Recruitment  Growth  Stock size will decrease only by  Natural Mortality  Fishing Mortality  If increasing factor and decreasing factor balance, then the stock size will be stable
  • 4. Russell’s Equation (Russell 1931)  Russel, E. S. 1931. Some theoretical considerations on the ‘overfishing’ problem. Journal du Conseil International pour l’Exploration de la Mer, 6: 3- 20.
  • 5. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  • 6. Stock Growth 6
  • 7. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  • 8. Stock Growth 8  Stock Growth is the increasing factors of the stock.  It is divided Recruitment and Individual Growth.  Recruitment is a factor of stock growth, which adding number of individuals in the stock.  Individual Growth (or simply Growth) is a factor of growth, which adding weight of each individual in the stock.
  • 9. Recruitment 9
  • 10. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  • 11. Definition of Recruitment 11  Recruitment is defined as the increase of the number of individual into the stock at the age a fish CAN be caught.  Cf.Age at First Capture  Recruitment will be affected both with life history and fishery.  Migration from Nursery ground to Fishing ground  Body length reaches to the minimum size for fishing
  • 12. Schematic Display of Population Dynamics 12 MassMortality Recruitment FirstCapture Maturation Longevity #Fish
  • 13. Mass Mortality 13  In the life history of fish from the hatching to the recruit, most fish species experience mass mortality.  The magnitude of the survival rate will be less than 0.001 level.  The factor of the mass mortality will be  Feeding  Unsuccessful transportation  Competition on feeding  Mismatch of the prey species  Predation  Physical Environment  Sea water temperature  Etc
  • 14. 14 Rough calculation of the early mass mortality of Walleye Pollock P-stock  Spawing stock 4×108 ind . (stock assessment)  Fecundity 1×106eggs (observation)  Hatching Rate 10% (observation)   #hatched juvenile 4×1013 ind.  # Recruitment at age 1 1×109 (Stock assessement)  Survival Rate from Hatched juvenile to Age 1 fish 0.000025  The survival rate will fluctuate widely.
  • 15. Two approach for dealing recruitment for fishery management 15  Estimate the relationship of recruitment and various factors  Spawning biomass  Physical environmental factors  Biological environmental factors (#prey, #predator)  Assume recruitment can not estimate or independent to the spawning stock, and only consider the ratio to recruitment  Per recruit analysis
  • 16. Examples of stock-recruitment relationship 16
  • 17. 17 Sardine Pacific Stock http://abchan.job.affrc.go.jp/digests19/details/1901.pdf Spawning Stock (1000t) Recruitment(million) R=19.85S
  • 18. 18 Chub mackerel, Pacific Stock http://abchan.job.affrc.go.jp/digests19/details/1905.pdf Recruitment(100million) SSB(1000t) Recruitment(100million) SSB(1000t) Curves are best fitted Ricker Curve
  • 19. 19 Walleye Pollock P-stock http://abchan.job.affrc.go.jp/digests19/details/1913.pdf SSB (1000t) Recruitment(millionatage0) DominantYC Acceptable Level
  • 20. 20 Japanese Flying Squid – J stock http://abchan.job.affrc.go.jp/digests19/details/1919.pdf Number of Spawners (100million) NumberofNextGeneration100million)
  • 21. Stock and Recruitment Relationship 21
  • 22. 22 Stock Recruitment Relationship  Quantitative relationship between the number of parents (t) generation and children (t+1) generation  It would be simple if the number is measured at same age in different generation.  For example; pink salmon  Come back to the original river exactly  Come back at 2 years old  Easy to count in the river.
  • 23. 23 Stock-Recruitment Curve  Theoretical Curve to describe the Parents Generation and Children Generation  On the replacement line (45- degree line), the number of t generation and t+1 generation is same  Cross point of the S-R curve and replacement line is the equilibrium point, here population does not increase and decrease in long term average. t+1generation t generation
  • 24. Example of S-R Curve 24
  • 25. 25 Beverton-Holt Recruitment Model Sb aS R   0 5000 10000 15000 20000 0 5000 10000 15000 20000 t+1generation t generation a, b: constant S: Spawning stock (t) R: Recruitment (t+1) Contest Competitiona=5, b=0.000267
  • 26. 26 Example S-R Relationship of Sea Bream (Okada 1974) Spawning Stock Recruitment
  • 27. 27 Ricker Model bS aSeR   Scramble Competition 0 5000 10000 15000 20000 0 5000 10000 15000 20000 t+1generation t generation a, b: constant S: Spawning stock (t) R: Recruitment (t+1) a= 4.482, b=0.0001
  • 28. 28 Sockeye Salmon in Kurlak River Alaska (Tanaka 1960) Spawning Stock Recruitment(100,000)
  • 29. 29 Sustainable Yield inferred from S-R Curve 1  Without Exploitation S1 is the equilibrium point. Recruit will be R1=S1 S1S2 R1
  • 30. C2 30 Sustainable Yield inferred from S-R Curve 2  If S2 ,recruit will be R2 which is S2+C2.  If C2 is caught, the rest of the stock is S2 and in the next generation R2 will come back.  You can catch C2 for ever.  It is Sustainable Yield. S1S2 R2 R1
  • 31. C3 31 Sustainable Yield inferred from S-R Curve 3  At S3, vertical distance between S-R curve and replacement curve is max.  C3 is also sustainable yield, and you can catch C3 for ever.  It is Maximum Sustainable Yield (MSY). S3
  • 32. Growth 32
  • 33. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  • 34. Growth of individuals 34  Growth is another component of stock production.  Growth is usually described by using theoretical growth curve.  Usually growth curve describe the relationship between age and length.  Weight growth curve can be used, but sometimes the weight is converted from length by using the allometric equation.
  • 35. Von Bertalanffy growth curve 35  Von Bertalanffy growth curve (VBGC) is most popular.  Lt : length at age t L∞: asymptotic average maximum body size K : growth rate coefficient t0: hypothetical age which the species has zero length    0 1 ttK t eLL   
  • 36. Von Bertalanffy Growth Curve 36 0 10 20 30 40 50 0 1 2 3 4 5 6 7 8 9 10 Length Age L∞=50, K=0.2, t0=-0.5
  • 37. Length – Weight relationship 37  Usually the relationship between weight and length follow the allometric equation  wt: weight at age t Lt: length at age t a: scaling constant b: allometric growth parameter (close to 3) b tt aLw 
  • 38. Example 38 0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 35 40 Weight(kg) Length(cm)a=0.00015, b=3
  • 39. Von Bertalanffy growth equation for body weight 39  Combined withVBGC and allometric equation VBGC for body weight ;  wt: weight at age t w∞: asymptotic average maximum body weight K : growth rate coefficient t0: hypothetical age which the species has zero length b: allometric growth parameter (often set to 3)    bttK t eww 0 1   
  • 40. Example of VBGC for body weight 40 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 7 8 9 10 Weight(kg) Agew∞=18.75, K=0.2, t0=-0.5, b=3
  • 41. VBGC for Length vs. Weight 41 0 10 20 30 40 50 0 1 2 3 4 5 6 7 8 910 Length Age 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 7 8 910 Weight(kg) Age
  • 42. Mortality 42
  • 43. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  • 44. Total Mortality 44  Total Mortality is the factor reducing the stock.  Total Mortality is divided to Natural Mortality and Fishery Mortality (=Yield, Harvest)  Usually, only total mortality can be observed from age composition.  Natural Mortality can be estimated from various method, and also estimated from various empirical equations.  Fishing Mortality is estimated from total mortality and natural mortality.  The estimated fishing mortality contains errors in estimating total mortality, and natural mortality.
  • 45. Index of Mortality 45  Usually mortality is measured by the instantaneous rate.  “Instantaneous rate of mortality” is simply called as “mortality”.  If you use the percentage of the died individuals to the population at the beginning of the year, it is called “mortality rate”, and is different to “instantaneous rate of mortality” .
  • 46. Equations of Mortality 46 MFZ TotalMortality FishingMortality NaturalMortality
  • 47.   Z Zt ZZt Zt tZ t t e eN eeN eN eN N N S         0 0 0 1 01 Mortality and Survival Rate 47 Zt t eNN   0 Survival Rate Mortality Rate SD 1
  • 48. Mortality and Population Dynamics 48 0 200 400 600 800 1,000 0 2 4 6 8 10 Population Age t Nt S 0 1,000 0.7 1 700 0.7 2 490 0.7 3 343 0.7 4 240 0.7 5 168 0.7 6 118 0.7 7 82 0.7 8 58 0.7 9 40 0.7 10 28 tt NNS 1Z=0.357
  • 49. Cf Constant Death 49 0 200 400 600 800 1,000 0 2 4 6 8 10 Population Age KtNNt  0 t Nt S 0 1,000 0.90 1 900 0.89 2 800 0.88 3 700 0.86 4 600 0.83 5 500 0.80 6 400 0.75 7 300 0.67 8 200 0.50 9 100 0.00 10 0 K=100
  • 50. Linear Scale Log Scale 50 0 200 400 600 800 1,000 0 2 4 6 8 10 Age 1 10 100 1,000 0 2 4 6 8 10 AgeZ=0.357 Population
  • 51. 0 1 2 3 4 5 6 0 2 4 6 8 10 Age Z=0.357 ln(Nt) 51 Population y = -0.357x + 6.908 t Nt ln(Nt) 0 1,000 6.91 1 700 6.55 2 490 6.19 3 343 5.84 4 240 5.48 5 168 5.12 6 118 4.77 7 82 4.41 8 58 4.05 9 40 3.70 10 28 3.34 X Y
  • 52. Estimation of Total Mortality 52 1. Get the N1, N2, N3, ..., NT or its index, from a same year class. 2. If impossible, and if you can assume the recruit and fishery is stable, use C1, C2, C3, ..., CT from a same year. 3. Calculate ln(Ci) (i=1,...,T) 4. Confirm that it declines monotonously. If not, omit it. It would be affected by gear selectivity. 5. Plot and make linear regression. 6. The coefficient for tangent is –Z.
  • 53. Realistic Example 53 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 ln(Ct) Age
  • 54. Schematic Display of Population Dynamics 54 MassMortality Recruitment FirstCapture Maturation Longevity #Fish M M+F ln(N)
  • 55. Natural Mortality 55
  • 56. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  • 57. Natural Mortality 1 57  Natural Mortality is a part of mortality caused by natural reason  Various Factors  Disease  Predation  Prey Shortage  Physical Environment  Competition  Unexpected Emigration  Unreported Fishery  Etc…
  • 58. Estimation of the Natural Mortality 58  Mark- Recapture Method  In Captivity  Total Mortality of Unexploited Stock  Estimated from the change of Fishing Effort  Empirical Method
  • 59. 59 Natural Mortality Estimation  Fishing mortality will be proportional to fishing effort f with coefficient q  Z and f has linear relation  Plot Z and f  M is estimated as the y- intercept of the regression line qfF  MqfMFZ  (Silliman 1943)Age ln(Ct) 1st period (1925-33) 2nd period (1937-42)
  • 60. Empirical Method 1 60  It is very difficult to conduct direct measurement of Natural mortality for each commercial species.  No enough data for analysis  The range of the fishing effort variation is small  Difficult to conduct mark-recapture experiment because of the lack of budget and man-power  Many empirical method are proposed  Collecting the results of the direct measurements  Find some relationship with available parameters
  • 61. Empirical Method 61  Mainly estimated from  Growth curve parameter,  Water Temperature,  Life history Parameter  Longevity,  age at Mature  etc  Results may have large variety.  Use  Common methods in consensus  Compare the results. Parameters used in Hewitt et al. (2007)  tm = age at maturity (years)  X = a constant taken from the given sources  K = von Bertalanffy growth coefficient (per year)  tmax = longevity(years)  CW∞ = asymptotic maximum carapace width (cm) from VBGC  T = grand annual mean of water temperature (degree Celcius)  W ∞ = asymptotic maximum weight (g) from VBGCw  W = wet weight (g)
  • 62. 62
  • 63. Methods and Results of Hewitt et al. (2007) 63
  • 64. Frequency distribution of the range of the results 64 Value currently used for stock assessment (Hewitt et al. 2007)
  • 65. Yield / Fishing Mortality 65
  • 66. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  • 67. Fishing Mortality 67  Fishing mortality is estimated from Z and M MFZ Total Mortality Fishing Mortality Natural Mortality MZF 
  • 68. Related Equations 68  Total Mortality  Survival Rate  Mortality Rate  Catch Equation MFZ  Z eS   SD 1 tt DN Z F C 
  • 69. Catch Equation 69  The relationship between Population, Mortality, and Catch tt DN Z F C CatchinNumber PopulationinNumber MortalityRate Portionofdiedfishbyfishery
  • 70. Catch Equation 70  The relationship between Population, Mortality, and Catch     t MF tt Ne MF F DN Z F C      1 C is a function of F, M, and N
  • 71. Feature of Fishing Mortality 71  Fishing Mortality will be calculated from Z and M  Fishing Mortality will be proportional to the fishing effort.  Fishing Mortality is not proportional to Catch. M N N MZF t t        1 ln qfF 
  • 72. Yield 72  Yield / Fishing Mortality is the only controllable component in the Russell's Equation  Given recruit, growth and natural mortality, if you would like to increase the stock more, the only way is to reduce yield.  To optimize the sustainable yield,  Monitor the stock biomass  Stock assessment  Optimize the fishing effort  MSY and other fishery models
  • 73. Key Points of This Section 73
  • 74. Key Points 1: Russell’s Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  • 75. Key Points 2 : Recruitment 75  Recruitment : increase of the fish in to the stock at the age a fish can be caught  Fish experience Mass Mortality at the early life stage. The magnitude will be less than 1/1000.  The S-R relationship is not clear and sometimes looks like no relationship between them.  S-R models are used for describing ideal relationship  Beverton and Holt Model  Ricker Model  MSY will be calculated from S-R curve.
  • 76. Key Points 3 : Growth Mortality 76  VBGC is often used for describing the fish growth  Weight is converted by the allometric equation.  Instantaneous rate of mortality is used  Total mortality Z is observed from age composition.  Usually Natural Mortality Mis estimated from Empirical Equations  Fishing mortality F is estimated as Z minus M    0 1 ttK t eLL   