Fish Population Dynamics
Takashi Matsuishi
At SERD, AIT, Thailand 24Feb-14Mar, 2014
1
Russell’s Equation
2
Basic Idea of Population Dynamics of
Exploited Stock
3
 Closed stock : without Immigration / Emigration
 Stock size will...
Russell’s Equation (Russell 1931)
 Russel, E. S. 1931. Some
theoretical considerations on the
‘overfishing’ problem.
Jour...
Russell's Equation
   YDGRBB tt 1
Biomassatt+1
Recruitment
Growth
NaturalMortality
Yield
Biomassatt
Stock Growth
6
Russell's Equation
   YDGRBB tt 1
Biomassatt+1
Recruitment
Growth
NaturalMortality
Yield
Biomassatt
Stock Growth
8
 Stock Growth is the increasing factors of the stock.
 It is divided Recruitment and Individual Growth.
...
Recruitment
9
Russell's Equation
   YDGRBB tt 1
Biomassatt+1
Recruitment
Growth
NaturalMortality
Yield
Biomassatt
Definition of Recruitment
11
 Recruitment is defined as the increase of the number of
individual into the stock at the ag...
Schematic Display of Population Dynamics
12
MassMortality
Recruitment
FirstCapture
Maturation
Longevity
#Fish
Mass Mortality
13
 In the life history of fish from the hatching to the recruit,
most fish species experience mass mortal...
14
Rough calculation of the early mass
mortality of Walleye Pollock P-stock
 Spawing stock 4×108 ind . (stock assessment)...
Two approach for dealing recruitment
for fishery management
15
 Estimate the relationship of recruitment and various
fact...
Examples of stock-recruitment relationship
16
17
Sardine Pacific Stock
http://abchan.job.affrc.go.jp/digests19/details/1901.pdf
Spawning Stock (1000t)
Recruitment(milli...
18
Chub mackerel, Pacific Stock
http://abchan.job.affrc.go.jp/digests19/details/1905.pdf
Recruitment(100million)
SSB(1000t...
19
Walleye Pollock P-stock
http://abchan.job.affrc.go.jp/digests19/details/1913.pdf
SSB (1000t)
Recruitment(millionatage0)...
20
Japanese Flying Squid – J stock
http://abchan.job.affrc.go.jp/digests19/details/1919.pdf
Number of Spawners (100million...
Stock and Recruitment Relationship
21
22
Stock Recruitment Relationship
 Quantitative relationship between the number of parents
(t) generation and children (t...
23
Stock-Recruitment Curve
 Theoretical Curve to describe
the Parents Generation and
Children Generation
 On the replace...
Example of S-R Curve
24
25
Beverton-Holt Recruitment Model
Sb
aS
R


0
5000
10000
15000
20000
0 5000 10000 15000 20000
t+1generation
t generatio...
26
Example
S-R Relationship of Sea Bream (Okada 1974)
Spawning Stock
Recruitment
27
Ricker Model
bS
aSeR 

Scramble Competition
0
5000
10000
15000
20000
0 5000 10000 15000 20000
t+1generation
t generat...
28
Sockeye Salmon in Kurlak River Alaska
(Tanaka 1960)
Spawning Stock
Recruitment(100,000)
29
Sustainable Yield inferred from S-R Curve 1
 Without Exploitation S1 is
the equilibrium point.
Recruit will be R1=S1
S...
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 ...
C3
31
Sustainable Yield inferred from S-R Curve 3
 At S3, vertical distance
between S-R curve and
replacement curve is ma...
Growth
32
Russell's Equation
   YDGRBB tt 1
Biomassatt+1
Recruitment
Growth
NaturalMortality
Yield
Biomassatt
Growth of individuals
34
 Growth is another component of stock production.
 Growth is usually described by using theoret...
Von Bertalanffy growth curve
35
 Von Bertalanffy growth curve (VBGC) is most popular.
 Lt : length at age t
L∞: asymptot...
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
Length – Weight relationship
37
 Usually the relationship between weight and length follow
the allometric equation
 wt: ...
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
Von Bertalanffy growth equation
for body weight
39
 Combined withVBGC and allometric equation
VBGC for body weight ;
 wt...
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
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
W...
Mortality
42
Russell's Equation
   YDGRBB tt 1
Biomassatt+1
Recruitment
Growth
NaturalMortality
Yield
Biomassatt
Total Mortality
44
 Total Mortality is the factor reducing the stock.
 Total Mortality is divided to Natural Mortality a...
Index of Mortality
45
 Usually mortality is measured by the instantaneous rate.
 “Instantaneous rate of mortality” is si...
Equations of Mortality
46
MFZ TotalMortality
FishingMortality
NaturalMortality
 
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
S...
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 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...
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
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 ...
Estimation of Total Mortality
52
1. Get the N1, N2, N3, ..., NT or its index, from a same year
class.
2. If impossible, an...
Realistic Example
53
0
1
2
3
4
5
6
7
8
9
10
0 2 4 6 8 10
ln(Ct)
Age
Schematic Display of Population Dynamics
54
MassMortality
Recruitment
FirstCapture
Maturation
Longevity
#Fish
M M+F
ln(N)
Natural Mortality
55
Russell's Equation
   YDGRBB tt 1
Biomassatt+1
Recruitment
Growth
NaturalMortality
Yield
Biomassatt
Natural Mortality 1
57
 Natural Mortality is a part of mortality caused by natural
reason
 Various Factors
 Disease
 P...
Estimation of the Natural Mortality
58
 Mark- Recapture Method
 In Captivity
 Total Mortality of Unexploited Stock
 Es...
59
Natural Mortality Estimation
 Fishing mortality will be
proportional to fishing
effort f with coefficient q
 Z and f ...
Empirical Method 1
60
 It is very difficult to conduct direct measurement of
Natural mortality for each commercial specie...
Empirical Method
61
 Mainly estimated from
 Growth curve parameter,
 Water Temperature,
 Life history Parameter
 Long...
62
Methods and Results of Hewitt et al. (2007)
63
Frequency distribution of the range of the
results
64
Value currently used for
stock assessment
(Hewitt et al. 2007)
Yield / Fishing Mortality
65
Russell's Equation
   YDGRBB tt 1
Biomassatt+1
Recruitment
Growth
NaturalMortality
Yield
Biomassatt
Fishing Mortality
67
 Fishing mortality is estimated from Z and M
MFZ Total
Mortality
Fishing
Mortality
Natural
Mortali...
Related Equations
68
 Total Mortality
 Survival Rate
 Mortality Rate
 Catch Equation
MFZ 
Z
eS 

SD 1
tt DN
Z
F
...
Catch Equation
69
 The relationship between Population, Mortality, and Catch
tt DN
Z
F
C CatchinNumber
PopulationinNumbe...
Catch Equation
70
 The relationship between Population, Mortality, and Catch
 
  t
MF
tt
Ne
MF
F
DN
Z
F
C





...
Feature of Fishing Mortality
71
 Fishing Mortality will be calculated from Z and M
 Fishing Mortality will be proportion...
Yield
72
 Yield / Fishing Mortality is the only controllable
component in the Russell's Equation
 Given recruit, growth ...
Key Points of This Section
73
Key Points 1: Russell’s Equation
   YDGRBB tt 1
Biomassatt+1
Recruitment
Growth
NaturalMortality
Yield
Biomassatt
Key Points 2 : Recruitment
75
 Recruitment : increase of the fish in to the stock at the
age a fish can be caught
 Fish ...
Key Points 3 : Growth Mortality
76
 VBGC is often used for describing the fish growth
 Weight is converted by the allome...
Upcoming SlideShare
Loading in …5
×

Sustainalbe Fishery Management / Fish Population Dynamics

2,489 views

Published on

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

Published in: Education
  • Be the first to comment

Sustainalbe Fishery Management / Fish Population Dynamics

  1. 1. Fish Population Dynamics Takashi Matsuishi At SERD, AIT, Thailand 24Feb-14Mar, 2014 1
  2. 2. Russell’s Equation 2
  3. 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. 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. 5. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  6. 6. Stock Growth 6
  7. 7. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  8. 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. 9. Recruitment 9
  10. 10. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  11. 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. 12. Schematic Display of Population Dynamics 12 MassMortality Recruitment FirstCapture Maturation Longevity #Fish
  13. 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. 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. 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. 16. Examples of stock-recruitment relationship 16
  17. 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. 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. 19 Walleye Pollock P-stock http://abchan.job.affrc.go.jp/digests19/details/1913.pdf SSB (1000t) Recruitment(millionatage0) DominantYC Acceptable Level
  20. 20. 20 Japanese Flying Squid – J stock http://abchan.job.affrc.go.jp/digests19/details/1919.pdf Number of Spawners (100million) NumberofNextGeneration100million)
  21. 21. Stock and Recruitment Relationship 21
  22. 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. 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. 24. Example of S-R Curve 24
  25. 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. 26 Example S-R Relationship of Sea Bream (Okada 1974) Spawning Stock Recruitment
  27. 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. 28 Sockeye Salmon in Kurlak River Alaska (Tanaka 1960) Spawning Stock Recruitment(100,000)
  29. 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. 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. 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. 32. Growth 32
  33. 33. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  34. 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. 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. 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. 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. 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. 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. 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. 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. 42. Mortality 42
  43. 43. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  44. 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. 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. 46. Equations of Mortality 46 MFZ TotalMortality FishingMortality NaturalMortality
  47. 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. 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. 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. 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. 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. 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. 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. 54. Schematic Display of Population Dynamics 54 MassMortality Recruitment FirstCapture Maturation Longevity #Fish M M+F ln(N)
  55. 55. Natural Mortality 55
  56. 56. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  57. 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. 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. 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. 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. 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. 62
  63. 63. Methods and Results of Hewitt et al. (2007) 63
  64. 64. Frequency distribution of the range of the results 64 Value currently used for stock assessment (Hewitt et al. 2007)
  65. 65. Yield / Fishing Mortality 65
  66. 66. Russell's Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  67. 67. Fishing Mortality 67  Fishing mortality is estimated from Z and M MFZ Total Mortality Fishing Mortality Natural Mortality MZF 
  68. 68. Related Equations 68  Total Mortality  Survival Rate  Mortality Rate  Catch Equation MFZ  Z eS   SD 1 tt DN Z F C 
  69. 69. Catch Equation 69  The relationship between Population, Mortality, and Catch tt DN Z F C CatchinNumber PopulationinNumber MortalityRate Portionofdiedfishbyfishery
  70. 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. 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. 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. 73. Key Points of This Section 73
  74. 74. Key Points 1: Russell’s Equation    YDGRBB tt 1 Biomassatt+1 Recruitment Growth NaturalMortality Yield Biomassatt
  75. 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. 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   

×