(3.3)
GROUP I
According to the Assessment Working Group of ICES (ICES, 1996a) the relative instantaneous rates of total and natural mortality for the age of 3 years, of the stock of blue whiting, Micromesistius poutassou, in 1995, were estimated as being, respectively, Z_{3} = 0.4 year^{-1} and M_{3} = 0.2 year^{-1}. In that year, the number of survivors at the beginning of age 3 year was 2600 million individuals.
1. Calculate, for the cohort of 1992 and for the age of 3 years:
a) The total annual rates of survival and of mortality.
b) The relative instantaneous rate of fishing mortality.
c) The exploitation rate.
d) The number of deaths during the age.
e) The mean number of survivors during the age.
f) The total catch in number of 3 years old individuals.
g) The number of survivors at the end of the age.
GROUP II
The 4 year-old age group of the stock (Div. ICES VIIe-h) of whiting, Merlangius merlangus merlangus, is simultaneously exploited by the crustaceans trawl fleet and demersal fish trawl fleet.
The Working Group of ICES that evaluates this stock estimated (ICES, 1996a) that, in 1995, the total instantaneous mortality rate of that age (4 years) was Z = 1.3 year^{-1}. Suppose, for this exercise, that the instantaneous rate of fishing mortality caused by the crustaceans trawl fleet was Fc = 0.5 year^{-1}, while the corresponding value for the demersal fish trawl fleet was F_{f} = 0.6 year^{-1}. The Group also considered the natural instantaneous mortality rate, M = 0.2 year^{-1}.
1. In 1995 17.66 million individuals recruited at 4 years of age.
a) Calculate the total number of deaths during that age.
b) Calculate the mean number of survivors during the age.
c) Calculate the exploitation rate of each fleet.
d) Calculate the total exploitation rate.
e) Calculate the catch in number by each fleet and the total catch in number.
f) Calculate the number of survivors at the end of the age. (The solutions to the questions can be done in any order).
GROUP III
For this exercise, suppose that in 1990, the mean number of survivors of the cohort of a stock of anchovy, Engraulis encrasicholus, during the period of 2 years of age was calculated as about 50 million individuals. During 1992, 70 million individuals were caught, from which, 40 percent were caught by the national fleet, and it is estimated that 80 million died of natural causes.
1. For this age and this cohort:
a) Calculate the total exploitation rate and the exploitation rate of the national and foreign fleets.
b) Calculate the total, natural and fishing mortality coefficients.
c) Calculate the fishing instantaneous mortality rates caused by the national fleet and by the foreign fleet.
d) Calculate the number of survivors at the beginning and at the end of the age. (The solutions to the questions can be done in any order).
GROUP IV
According to the Assessment Working Group of ICES (ICES, 1997a) the fishing mortality coefficients applied to the 1976 cohort of the stock of common sole, Solea vulgaris, of the Celtic Sea were estimated in each age from 2 to 8 years (following table). The natural mortality coefficient for this stock is considered constant and equal to 0.1 year^{-1}. It was estimated that, at the beginning of age 6 years there were 1112 million survivors of this cohort.
Age |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
F_{i} |
0.07 |
0.22 |
0.33 |
0.41 |
0.45 |
0.41 |
0.74 |
1. Calculate the numbers of survivors of this cohort at the beginning of each of the above mentioned ages.
2. Calculate the number of deaths in each age referred in the table.
3. Calculate the exploitation rates of this cohort in each age.
4. Calculate the mean numbers of survivors during each of the above ages.
5. Calculate the catches, in numbers, extracted from this cohort during each of the ages mentioned above, using two different methods.