(7.6)
GROUP I
1. Estimate the 5 percent Tanaka survival curve for natural mortality coefficients between 0.0 and 5.0 year^{1} and longevities between 0 and 30 years.
2. Calculate the values of M corresponding to the longevity 1, 2, 3, 10, 15 and 30 years.
GROUP II
The parameters of von Bertalanffy equation for the Iberic stock (Div. VIIIc and IXa of ICES) of horsemackerel, Trachurus trachurus, are the following:
L_{∞} = 34.46 cm, TL (carapace length)
K = 0.225 year^{1}
1. Estimate the value of M for this stock, knowing that from 198595 in the distribution area of this stock in the Iberic Peninsula, the mean temperature of the sea water at the surface, was:
GROUP III
Consider a certain fishing stock for which the first maturity mean age was estimated as 2.3 year.
1. Obtain an approximate estimate of M for this stock.
GROUP IV
The reproductive biology of the stock of Atlantic mackerel, Scomber scombrus was studied and it was estimated that the mean gonadsomatic index (gonad weight/total weight) of the mature females in the spawning period was 0.13.
1. Estimate an approximate value for the natural mortality coefficient M for this stock, assuming that it is constant for all the ages and years.
GROUP V
The scientists responsible for the evaluation of the stock of a certain fishing resource, implemented an acoustic cruise every year in January, to estimate the abundance of the stock by age classes. Fishery statistics are also needed to estimate the catch by age during the year.
The following table presents the estimations of the abundance of the stock, by age classes, obtained on the cruises in 1993 and 1994, as well as the structure of the catches during 1993.
Age 
Number of survivals, N, in million 
Total catch in 1993 

January 1993 
January 1994 

2 
243 
353 
11 
3 
99 
189 
15 
4 
86 
67 
20 
5 
37 
52 
9 
6 
13 
22 
3 
7 
6 
8 
1 
Although this information is available, the scientists responsible for this stock have difficulties applying the assessment models to the resource because they do not have an estimation of M.
1. So, estimate the natural mortality coefficient for this resource in 1993, and help the group of scientists responsible for the resource.
GROUP VI
The following table presents the data on fishing effort, in million trawl hours, and the total mortality coefficent, Z, for a certain fishery for the period 1987 to 1995.
Years 
Effort 
Z (year^{1}) 
1987 
2.08 
1.97 
1988 
2.80 
2.05 
1989 
3.5 
1.82 
1990 
3.6 
2.32 
1991 
3.8 
2.58 
1992 
 
 
1993 
 
 
1994 
9.94 
3.74 
1995 
6.06 
3.74 
1. Determine M (natural mortality coefficient), assumed to be constant for the period 19871995.
2. Determine the catchability coefficient q.