The mortality rate of Antarctic tin whale stocks 259 



shown by Baranov (1918) and others, the right limb of the curves representing the 

 age frequencies of the catches enables us to calculate the total mortality rates, pro- 

 vided that the following conditions are satisfied : 



1. For the age groups in question, the mortality rate, or its complement, 

 the survival rate, is uniform. 



2. In these age groups, the samples used for age analyses are representative 

 of the stocks. 



3. The recruitment is uniform over a period of years; that is, each age group 

 in question was initially of the same numerical strength as each of the others 

 under study. 



The first condition is satisfied as a rule in all stocks subject to high rates of fish- 

 ing. As mentioned above, the second condition is satisfied fairly well for the last six 

 seasons in our series. For the third condition, we can safely rule out the possibility 

 that the recruitment to the stocks is increasing from year to year. The best we can 

 hope for is a constant recruitment, or a recruitment fluctuating from year to year 

 around a constant average sufficiently high to balance the losses from natural causes 

 and from whaling operations. On the other hand, if the recruitment is decreasing, 

 as it well may be, then the mortality rates calculated from the age distributions will 

 be too low. 



From the age distributions in Fig. 1, it can be seen that only groups TV and V of 

 males and possibly groups III, IV and V of the females can be used in a direct calcula- 

 tion of survival or mortality rates. Thus, the ratios of Vs to IVs calculated for the 

 period 1947/48 through 1952/53 give annual mortality rates which vary considerably 

 from season to season, from a minimum of 0T7 (females. 1951/52) to a maximum 

 of 0-65 (males, 1948/49). The means for the period are 0-42 and 0-40 for males and 

 females respectively. Great seasonal variations might be expected if there were great 

 fluctuations in the numerical strength of the year classes. This seems unlikely in a 

 mammal such as a whale. 



Systematic errors in our interpretation of the baleen records may, however, result 

 in over-emphasis of age group V, because some older animals may be placed in that 

 group. Such mistakes might vary in number from season to season. If this is the 

 case, the calculated mortality rates will be lower than the actual ones. 



Consequently, it is desirable to develop a formula which enables us to consider 

 the total material contained in the right limb of the age-distribution curve. This is 

 possible if we assume that the older animals telescoped into our age groups VI -f, 

 VII+, and VIII- should in reality be spread in a regular way over a number of older 



age groups. 



/A-\- B . . 

 Thus such a formula for the annual mortality rate is: a = 1 —^ - — . where A 



is the sum of two age groups supposed to be fully represented in the catches, and B 

 the sum of all higher age groups: hence, A ^ B \s the sum of all age groups 



considered. 



We have formed the sum A from age groups III and IV of the females, and IV and 

 V of the males, and used it in calculating the mortality rate for the individual seasons. 

 These results show much less seasonal variation; namely a minimum of 019 and a 

 maximum of 0-34 for females, and a minimum of 0-29 and a maximum of 0-49 for 



