(7.9.1)
GROUP I
1. Consider a stock and an interval of time i, (ti, ti+1). Knowing that for this interval of time:
Mi = 0.4 year-1
Ti = 2.3 year
Ci = 230 million individualsa) Adopt the value 0.5 year-1 for the fishing mortality coefficient for the interval and calculate the numbers of survivors at the beginning and end of the interval.
2. Consider the interval of time i, (ti, ti+1). Knowing that in this interval of time:
Mi = 0.6 year-1
Ti = 0.9 year
Ci = 98 million individuals
Calculate the value of the fishing mortality coefficient, Fi, for the interval, taking the number of survivors, Ni, at the beginning of the interval, i, to be 172 million individuals.
3. Consider the interval of time (ti, t I+1). Knowing that in that interval of time:
Mi = 0.5 year-1
Ti = 1 year
Ci = 42 million individualsa) Calculate the value of the fishing mortality coefficient for the interval, knowing that the number of survivors at the end of the year was Ni+1 = 85 million individuals. Calculate the value of Fi using the Pope formula.
GROUP II
The data in the following table represent the catches in millions, of a cohort of hake, Merluccius merluccius, in the Iberic Peninsula waters.
|
Age (years) |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Ci (million) |
712 |
3941 |
8191 |
10311 |
5515 |
4149 |
3081 |
1185 |
549 |
Adopt a value of 0.2 year-1 for the natural mortality coefficient, constant for all the ages.
1. Suppose that the value of the fishing mortality coefficient at the last age (8 years) was 1.0 year-1. Calculate, by an iterative method and by the Pope method, for each age of the cohort:
a) The value of the fishing mortality coefficient.
b) The number of survivors at the beginning of the age.
c) Compare the results obtained by the two methods.
d) Represent, on a graph the values of Fi estimated against the age, and say what the recruitment of this cohort is at the exploited phase.
GROUP III
1. Aiming to analyse the influence of the chosen Fterminal, repeat the calculations of question 1 of Group II, using one of the previous methods, with 0.3 and 1.5 year-1 for the value of Fterminal.
a) Draw a graph with the estimated values of Fi and Ni against the age.
b) Comment on the differences between the graphs for the different values of Fterminal.
2. Aiming to analyse the influence of the choice of M, repeat the calculations of question 1 of Group II, using one of the previous methods, for values of M of 0.1 and 0.4 year-1.
a) Represent, on a graph, the estimated values of Fi and Ni against the age.
b) Comment on the differences between the graphs for the different values of M.
GROUP IV
The annual catches by age class, of a certain resource, for the years of 1985 to 1994, are presented in the following table.
|
Catches by age class (Million individuals) |
||||||||||
|
Years |
||||||||||
|
Age (years) |
1985 |
1986 |
1987 |
1988 |
1989 |
1990 |
1991 |
1992 |
1993 |
1994 |
|
0 |
67 |
88 |
104 |
290 |
132 |
90 |
63 |
38 |
52 |
90 |
|
1 |
532 |
1908 |
1841 |
1671 |
4172 |
1915 |
1284 |
906 |
541 |
704 |
|
2 |
2070 |
1756 |
4424 |
3178 |
2534 |
6320 |
2826 |
1911 |
1322 |
741 |
|
3 |
728 |
4016 |
2256 |
4042 |
2499 |
1972 |
4742 |
2115 |
1382 |
890 |
|
4 |
353 |
945 |
3309 |
1273 |
1926 |
1170 |
883 |
2102 |
896 |
540 |
|
5 |
97 |
439 |
733 |
1730 |
558 |
827 |
479 |
356 |
807 |
316 |
|
6 |
16 |
107 |
300 |
333 |
656 |
207 |
291 |
166 |
117 |
243 |
|
7 |
25 |
8 |
73 |
136 |
126 |
243 |
73 |
101 |
54 |
35 |
|
8 |
5 |
7 |
5 |
33 |
52 |
47 |
85 |
25 |
33 |
16 |
The modus operandi of the fishing fleet was constant during the period, but the number of vessels increased significantly. It is considered that, at present, the resource is intensively exploited.
Besides the information on the fishery, the estimates of the growth parameters of this resource and of the natural mortality coefficient are also available:
|
|
L∞ = 38.5 cm |
a = 0.021 of the relation W(g)-L(cm) |
|
|
K = 0.25 year-1 |
b = 2.784 of the relation W(g)-L(cm) |
|
|
to = - 0.51 year |
M = 0.3 year-1 |
1. Estimate the fishing mortality coefficient and the number of survivors at the beginning of the year for each age class and each year. Use the Pope Cohort Analyses method.
a) Start by selecting Fterminal = 0.5 year-1 for the last age of every year and for all the ages of the last year.
b) After analysing matrix F obtained in a), select new values for Fterminal and repeat the application of Pope’s method.
2. Besides the information given in the previous question, it is also known that the spawning takes place in a restricted period, around the beginning of the year. Research cruises using acoustic methods took place during the spawning period, in order to estimate the spawning biomass (kg/hour of trawl). The results obtained are shown in the following table:
|
Years |
1985 |
1986 |
1987 |
1988 |
1989 |
1990 |
1991 |
1992 |
1993 |
1994 |
|
Spawning biomass Index |
1270 |
1613 |
1629 |
1424 |
1300 |
1209 |
1000 |
718 |
476 |
326 |
The biological information collected during those cruises was also used to estimate the maturity ogive of the stock at the spawning period:
|
Age (years) |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
% Matures |
0 |
1 |
20 |
50 |
80 |
100 |
100 |
100 |
100 |
a) Calculate the spawning biomass in the spawning period of each year from 1985 to 1994 using the results of the Cohort Analyses obtained in question 1.b.
b) Use the information of the acoustic cruises to tune the Cohort Analyses.
c) Comment on the tuning results.
