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Information about Sustainalbe Fishery Management / Fish Population Dynamics

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

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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Russell’s Equation 2

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

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.

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 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.

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 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

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 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 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.

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

Examples of stock-recruitment relationship 16

17 Sardine Pacific Stock http://abchan.job.affrc.go.jp/digests19/details/1901.pdf Spawning Stock (1000t) Recruitment(million) R=19.85S

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 Walleye Pollock P-stock http://abchan.job.affrc.go.jp/digests19/details/1913.pdf SSB (1000t) Recruitment(millionatage0) DominantYC Acceptable Level

20 Japanese Flying Squid – J stock http://abchan.job.affrc.go.jp/digests19/details/1919.pdf Number of Spawners (100million) NumberofNextGeneration100million)

Stock and Recruitment Relationship 21

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 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

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 generation a, b: constant S: Spawning stock (t) R: Recruitment (t+1) Contest Competitiona=5, b=0.000267

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 generation a, b: constant S: Spawning stock (t) R: Recruitment (t+1) a= 4.482, b=0.0001

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 S1S2 R1

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

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

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 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.

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

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: weight at age t Lt: length at age t a: scaling constant b: allometric growth parameter (close to 3) b tt aLw

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: 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

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 Weight(kg) Age

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 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.

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” .

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 Survival Rate Mortality Rate SD 1

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 1Z=0.357

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

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 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

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.

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 Predation Prey Shortage Physical Environment Competition Unexpected Emigration Unreported Fishery Etc…

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 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)

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

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

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 Mortality MZF

Related Equations 68 Total Mortality Survival Rate Mortality Rate Catch Equation MFZ Z eS SD 1 tt DN Z F C

Catch Equation 69 The relationship between Population, Mortality, and Catch tt DN Z F C CatchinNumber PopulationinNumber MortalityRate Portionofdiedfishbyfishery

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

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

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

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 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.

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

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