# Leyfileg hjálpargögn: hefti um stærðfræðilega fiskifræði

Fish Population Dynamics (Fiskifræði II)

5. May, 1998
Time: 9-13
Accessories allowed: Any inanimate objects
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1. The following figure shows the yield per recruit (Y/R) based on different assumptions on natural mortality (M=0, 0.1, 0.2, 0.3). Total mortality has been estimated using catch curve analysis as Z=0.5. What is the yield per recruit corresponding to present fishing mortlity for each assumption of M?

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2. Backcalculate yearclass strength using cohort analysis based on the assumption that F=1 in the last year and M=0.2 with the catch as given in the following table:

 age 1 2 3 4 catch in numbers at age 3 8 4 2

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3. The following figure depicts the development of catch and spawning stock of cod in Icelandic waters from 1928 to 1991. Justify which of the following harvest control rules are likely to correspond to sustainable use of the resources, based on the figure:
(a) Catch=60% of spawning stock biomass (Y=0.6*S).
(b) Catch=450 thousand tonnes per year (Y=450).
(c) Catch =50% of spawning stock biomass in excess of 200 thousand tonnes (Y=0.5*(S-200)).

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4. The following table contains fishing pattern, mean weight at age, natural morality and the proportion mature at age. Compute the yield per recruit and spawning stock biomass per recruit assuming the fishing mortality rate to be F=0.4 on 3-6 year old fish.

 Age Fishing Prop. Mean wt Natural pattern mature at age mortality 1 0.1 0.00 100 0.1 2 0.5 0.50 150 0.1 3 1.0 1.00 200 0.1 4 1.0 1.00 225 0.1 5 1.0 1.00 250 0.1 6 1.0 1.00 275 0.1

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5. The following table gives the population abundance in numbers by age in the beginning of the year 1995. It is belived that fishing mortality on 3-6 year old fish was 0.4 and a recruitment prediction estimates recruitment in 1996 at 600 million individuals. Use data on mean weight at age, natural mortality and selection from the table in question 4.
(a) Predict stock size in numbers by are in the beginning of 1996.
(b) Predict the catches in tonnes in 1996 corresponding to the same fishing mortality rate.

 Age Abundance (millions) 2 300 3 700 4 400 5 200 6 100 7 50

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6. Data on the spawning stock biomass (thousand tonnes) and recruitment (millions) are given in the following table as well as in graphical form. The recruitment is the result from the corresponding spawning. Also shown is a figure depicting the spawning stock biomass (in grammes) per recruit for various values of F.
(a) What is Fmed?

 Year Spawning Stock Biomass (S) Recruitment (R) S/R 85 30 80 0.4 86 25 60 0.4 87 10 30 0.3 88 20 100 0.2 89 20 90 0.2 90 20 50 0.4 91 10 50 0.2 92 5 30 0.2 93 15 25 0.6

(b) Justify whether fishery management according to Fmed is in accordance with the Precautionary Approach to the utilization of fish stocks.

(c) Spawning stock biomass and recruitment for the junk stock is given in the figure on the right. Justify whether fishery management according to Fmed is in accordance with the Precautionary Approach for this stock.
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7. The Shepherd stock and recruitment relationship between spawning stock biomass (S) and recruitment (R), is given by R=[alpha]S/(1+(S/K)[beta]) where the coefficients [alpha], [beta] and K are knwon positive numbers. This relationship has been used for a famous fish stock. Also known are the selection pattern, mean weight at age and proportion mature at age and hence it is posible to compute yield per recruit (Y/R) and spawning stock biomass per recruit (S/R) for a given fishing mortality rate, F.
Write down the equation(s) to describe the long-term yield (Y) from the stock, based on the quantities which are given above.