3S 8 DISCOVERY REPORTS 



rate of reduction is not a local phenomenon; it is not confined to the catch of the Pesca 

 company, neither is it increased when the activities of the other stations are taken into 

 consideration. It is the rate at which the stock has been reduced, at South Georgia or 

 elsewhere, by hunting, by natural death, disease or any other cause of elimination. 



The validity of the rate of reduction, granting the acceptance of the method of age 

 determination, depends upon two postulates, (i) the annual recurrence of the same 

 stock to these waters, and (ii) the representativeness of the sample considered. Both of 

 these difficult questions are discussed later on. It will be noticed that up to the present 

 they have been taken as facts. As to the sample, i.e. the catch, one source of error has 

 been pointed out and eliminated by the omission of the figures for the partial seasons 

 1924-5 and 1927-8. A further possible difficulty has been brought to light by the 

 analysis into one-year groups. Throughout these figures a serious shortage of lactating 

 and resting whales is evident. As regards the former an artificial check on the numbers 

 captured lies in the protection by law of female whales running with calves, though I 

 think that the whaling community would agree that unless a calf is present it is not 

 possible to distinguish a lactating whale at sea and certainly a number are brought in to 

 the stations. With females in the resting condition there is no such explanation and the 

 fact can only mean that a certain proportion of whales in the post-pregnant condition 

 do not accompany the main migratory schools, or, at all events, they do not appear on 

 the South Georgia grounds during the fishing season. Is this, however, a serious draw- 

 back to the calculation of a rate of reduction? Fewer lactating whales may mean that the 

 fishery falls more heavily upon the pregnant whales but it would appear from the figures 

 that the proportion of absent females of each age is approximately constant. In the 

 first five age groups the percentage pregnant is 65, 63, 61, 68, and 57. Pregnant 

 whales can be considered as a two-year series, apart from lactating and resting whales, 

 and these latter if fully represented should make another series. The numbers in the 

 former series are not large, and as has been said, those in the latter are reduced by the 

 operation of the regulations of whaling to still smaller numbers. Probably owing to the 

 paucity of data, neither series exhibits a constant rate of reduction. Since, however, the 

 total number in each of the first five age groups of Table II is made up of pregnant 

 whales on the one hand and lactating and resting whales on the other in approximately 

 constant proportions, it seems legitimate to treat the data in the age groups of that 

 table as representative, notwithstanding the fact that the condition of the whales in each 

 group is not homogeneous. Fig. 2 illustrates the reduction of stock as unanalysed and 

 in the light of the conditions found within the various groups. 



We now come to consideration of the series of numbers, 130, 95, 72, 53, 37, 28, 10, 

 4, 1, 1 which represents the number of females taken during five seasons which could 

 be allocated into successive two-year age groups. 



Edser's conclusions and comments may be summarized as follows: The series of 

 numbers suggests the terms of a geometric progression of the form 



or, ar(i - r), ar (1 - r) 2 ,. . . 

 where a represents the initial stock of mature females and r the rate of reduction. 



