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Presented by: Jaffer YousufAEM-MA2-03

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Two types of overfishing.

1) Growth overfishing occurs when the effort is so high

that total yield decreases with increasing effort. The fishare caught before they can grow to a sufficiently large size

2) Recruitment overfishing occurs when the parent

stock (spawning stock biomass) comes to very low levelaffecting the recruitment to the fishery

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The first prediction models was developed in the thirties byThompson and Bell (1934)

Later on a simpler model, based on rigorous assumptions, but

requiring less calculations was developed by Beverton and Holt(1957) ~ "Yield per Recruit" model

Beverton and Holt's yield per recruit model ~ a specialapplication of the Thompson and Bell model which means that

any general conclusion derived from it also holds for theThompson and Bell model

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Inputs: woo (Asymptotic weight) t0 (Age at birth)

tc (Age at first capture) tr (Age at recruitment) M (Natural mortality) K (Growth co-efficient) Yield per recruit is obtained at various level of

Fishing mortality

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It is in principle a "steady state model ~ fishing

pattern has been the same for such a long time that all

fish alive have been exposed to it since they recruited

a) Recruitment is constant

b) All fish of a cohort hatched on the same date

c) Recruitment and selection are knife edge

d) F and M are constant from the entry to the

exploited phase

e) There is complete mixing with in the stock

f) The length-weight relationship is isometric

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The life history of a cohort as assumed in the Beverton

and Holt model

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The weight based model is

Y/R = F*exp(-M*(tc-tr))*W*[1/Z 3S/(Z+K)+

3S2/(Z+2K) S3/(Z+3K)]

It is assumed that growth parameters L,K and tzero are known

S = exp[-K*(Tc-t0)]

The model allows to calculate Y/R with varying inputs of theparameters, F and Tc

Predicts effect of various input values on the yield per recruitof the species under investigation

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Result of a yield assessment with the yield per recruit model

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Yield per recruit curves with different ages of first capture (Tc)

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The biomass per recruit model isB/R = exp(-M*(tc-tr))*W*[1/Z 3S/(Z+K)+

3S2/(Z+2K) S3/(Z+3K)]

The Y/R model from length data is

Y/R= F*A* W*[1/Z 3U/(Z+K) + 3U2/(Z+2K) U3/(Z+3K)]

Where,U = 1 Lc/LA= [(L - Lc)/(L - Lr)] M/K

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Thompson and Bell yield model is the exact opposite ofVPA or Cohort analysis(retrospective models)

VPA and cohort analysis are used to determine the numberof fish caught that must have been present in the sea, to

account for known catch and fishing mortality

Thompson and Bell model is a predictive model that wouldforecast the yield with the change in the fishing effort(fishing mortality) & mesh size

It works forward, given an array of fishing mortality indifferent age (or length) groups, recruitment (initialnumbers) natural mortality and weight at age array

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Inputs:

Recruitment (initial numbers) Natural mortality F- array ( fishing mortality for each age or length

group) Weight array for each age (length) group Value (price per Kg) in money terms of each age or

length group (for economic analysis)

Outputs:

Catch in numbers Yield in weight Biomass in weight Value in money

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For age frequency dataGiven: the recruitment (initial numbers in the sea for the first age

group)

natural mortality(M)

F-array

weight array and value array(v)

The recruitment and F values for each age(length) group is obtained from cohort analysis

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For each age group

Compute:

FNew= X*F (F is the original F values for each length or

age groups obtained from cohort analysis)

ZNew= M+X*FNew

N(t+t) = N(t) exp( -z* t)

(t is the time interval for each age group. For agefrequency data with interval of one year(or month) t =1)

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C= [Nt - N(t+t)] *(FNew/ZNew)W= weight at mid value of the age group (e.g. for the agegroup 1-2 , it is the weight at 1.5 yrs)

Y= C*W (Yiled)

B = Y/(FNew* t)

V= v*Y

Find the total yield, total biomass and total value bysumming the respective values of yield, biomass andvalue over all the age or length groups

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For a range of X values ( say from 0 to 3 with chosen step size) we will

obtain array of yield, biomass and value and plot these values against X.

F- factor

X

Total

yield

Total

biomass

Total

Value

X1 Y1 B1 V1

X2 Y2 B2 V2

- - - -

--- - - -

Xn Yn Bn Vn

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.4 0.8 1 1.2 1.5 2 3

X

Y

B

V

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REFERENCES

Sparre, P. and Venema, S.C., 1998. Introduction totropical fish stock assessment.FAO manual. 239-277

Beverton, R.J.H. and Holt, S.J., 1957. On the dynamicsof exploited fish populations.Fish. Invest. Minist. Agric.Fish. Food G.B.(2 Sea Fish.), 19:533 p

Thompson, W.F. and Bell, F.H., 1934. 1 Biologicalstatistics of the Pacific halibut fishery. 2. Effect ofchanges in intensity upon total yield and yield per unit ofgear.Rep. Int. Fish. (Pacific halibut) Comm., (8):49p

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