# 8.25 ESTIMATION OF Z

(7.7)

GROUP I

A swept area cruise allowed the scientists of the Marine Research Institute in Bergen, Norway, to estimate the abundance of the different age classes of the stock of cod fish, Gadus morhua, in January of 1995 (following table).

 Age (years) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 N95 (109) 1984 440 160 103 82 65 54 43 33 27 26 21 17 13 10

1. Represent on a graph, the logarithms of the numbers of survivors against the age.

2. Select the age interval from which the total mortality coefficient, Z, can be taken as constant.

3. Estimate the total mortality coefficient, Z, of the stock in January 1995.

GROUP II

The following table presents the mean catches by age, in number, of plaice, Pleuronectes platessa, per 100 trawl hours in two periods, 1929-1938 and 1950-1958.

 Age (years) 2 3 4 5 6 7 8 9 10 C/f 1929-38 125 1355 2352 1761 786 339 159 70 28 C/f 1950-58 98 959 1919 1670 951 548 316 180 105

1. Estimate the total mortality coefficient, Z, of the stock in each of the periods.

2. Consider that the mean fishing effort on the North Sea plaice during the two periods was 5 million hours of trawl in 1929-1938 and 3.1 million hours of trawl in 1950-1958. Estimate for each period:

a) the natural mortality coefficient, M;
b) the catchability coefficient, q;
c) and the fishing mortality coefficient, F.

GROUP III

The following table presents the annual composition of the catches by age from 1988 to 1994, in millions of individuals, for a certain resource:

CATCHES (million individuals)

 Age 1988 1989 1990 1991 1992 1993 1994 0 599 239 424 664 685 478 330 1 678 860 431 1004 418 607 288 2 1097 390 1071 532 335 464 323 3 275 298 159 269 203 211 243 4 40 54 75 32 69 86 80 5 6 9 13 18 8 25 31 6 1 8 3 5 5 3 8 7 6 0 1 0 1 1 1

1. Calculate the mean annual composition during 1988-1994.

2. Estimate Z, based on that mean composition.

3. Estimate Z, based on the mean age of the mean composition of the catch.

4. Estimate Z for each year of the given period.

5. Compare the annual Zs with the values of Z obtained in questions 2 and 3.

GROUP IV

The following table shows the length composition, in equilibrium, of a certain resource, with L = 100 cm and K = 0.2 year-1.

 Length class (cm) 35- 40- 45- 50- 55- 60- 65- 70- 75- 80- 85- 90- 95- Catch (Ci) in million 7 10 20 51 46 44 41 36 33 28 23 17 8

1. Calculate the relative ages corresponding to the lower limit of each length class.

2. Determine the age interval corresponding to each length class.

3. From which class can one consider Z constant?

4. Determine Z using:

a) The catches in each class.
b) The cumulative catches.
c) The mean length in the catch.

5. Compare the values of Z obtained by the different methods of question 4.

GROUP V

The length compositions of the catches for three different periods of time are known for a certain fishing resource.

 Period Length classes (cm) 45- 50- 55- 60- 65- 70- 75- 80- 85- 90- ≥95 1960-69 Catch (Ci) in million 256 237 211 187 161 138 113 87 62 36 12 1970-79 268 226 180 141 105 76 50 30 15 6 1 1980-89 212 161 116 79 52 31 17 8 3 1 0

Consider the 45 cm length class as the first class completely recruited.

Adopt K = 0.3 year-1 and L = 100 cm as the von Bertalanffy growth parameters for this resource.

1. Estimate the values of the total mortality coefficient, Z, for each period and comment on the results.