# 8.5 COHORT - EVOLUTION IN NUMBER

(3.2)

GROUP I

From the stock of megrim, Lepidorhombus whiffiagonis, from Divisions VIIIc and IXa of the ICES, the Assessment Working Group of ICES (ICES, 1997a) estimated that the fish recruit to the exploitable phase, at the beginning of age 1 year, and that in 1996 the instantaneous rate of total mortality during the exploitable phase was 0.7 year-1.

Consider 1000 individuals of a cohort of megrim, recruited to the exploited phase, which starts at the beginning of age 1 and finishes at the end of age 7 years.

1.

a) What is the value of the rir of the variation of Nt in this interval?
b) What is the value of the rir of the mortality of Nt in this interval?
c) Calculate the annual rate of survival during the interval.
d) Calculate the annual rate of mortality during the interval.

2.

a) Calculate the number of survivors at the beginning of each age of that interval.

b) Calculate the number of survivors at the end of 7 years of age.

c) Draw the graph of the number of survivors in each age of that interval.

d) Calculate the number of deaths in each age of the interval.

e) Calculate the number of deaths during all the exploitable phase.

f) Determine the percentage of the initial number of 3 year-olds that survive until the beginning of their 6th year.

g) Determine the percentage of the initial number of 3 year-olds that die before the beginning of their 6th year.

h) Calculate the mean number of survivors during each age of the given interval.

i) Calculate the cumulative number of survivors during ages 3 to 5.

j) Calculate the mean number of survivors between the beginnings of ages 3 and 6.

GROUP II

The Working Group of ICES which evaluated the stock of iberic sardine, Sardina pilchardus, estimated the mortality rates in each age of 1995 (ICES, 1997b), presented in the following table:

 Age Group 0 1 2 3 4 5 6 Annual Rate of Mortality 0.36 0.43 0.54 0.63 0.66 0.68 0.72

Suppose that these rates correspond to a cohort.

1. As previously seen, there may be several types of rates (ex: amr, rmr, air and rir and the relative rates were referred to several values of the characteristics). What type of rate is the annual rate of mortality?

2. Calculate the survival rate in each age class.

3. Calculate the total mortality coefficient for each age class.

4. Calculate the survival rate between the beginning of age 1 and the end of age 4.

5. Calculate the annual mean rate of survival in the same interval of ages.

GROUP III

Consider a cohort of a certain species for which the number of survivors at the beginning of age 2 years is 4325, while the number of survivors at the end of age 2 years is 2040.

1. Calculate the mean number of 2 year-old individuals and the number of individuals at the age of 2.5 years. Compare the results.

2. If the annual rate of mortality of this cohort during the ages 3 and 4 is 70 and 60 percent respectively, calculate the percentage of the initial number of individuals at age 3 that will survive until the end of age 4.

Give the relation between the survival rate during the period that covers the ages 3 and 4 years and the annual survival rates of ages 3 and 4 years.