AGE AND GROWTH OF THE CISCO 
255 
The study of the relationship between the density of population in marine fishes 
and their rate of growth received considerable stimulation from the observation of the 
conditions that resulted from the almost complete suspension of fishing operations in 
the North Sea during the World War. During the war there occurred an accumula- 
tion of the stock of plaice. Large fish became more plentiful but the average rate of 
growth decreased. With the resumption of fishing on a large scale the accumulated 
population was largely fished out. Large fish became relatively scarce and the aver- 
age rate of growth increased. Further investigations disclosed the fact that in general 
in regions with a dense population of plaice the rate of growth tended to be low and 
vice versa . 18 
Buckmann (1932) expressed the relationship between growth in weight and the 
density of population as being inversely proportional and referred to it as a “Verein- 
fachtes Wachstumgesetz” which he defined: “Die Gewichtzunahme verhalt sich 
umgekehrt proportional zur Bestandsdichte.” Buckmann expressed this law by the 
equation, 
i n 
w — w— v 
n 1 
where w is the weight increase per individual in a population of n individuals and w 1 
is the increase in weight that would occur if the number of individuals were changed 
from n to n 1 . Buckmann recognized the law to be inexact and mentioned certain 
disturbing influences. He pointed out that it is incorrect to assume that all the food 
consumed is applied toward increase in size. A certain definite amount is utilized to 
maintain individual metabolism. The percentage of the food that is so used varies 
according to the total amount of food available to each individual. Further, the 
efficiency with which a fish makes use of its food varies according to the abundance 
of food at hand . 19 Yet another complicating factor is the competitive action of other 
species. Biickmann developed a growth formula that contained correcting factors 
for these sources of error. 
Russell (1932) made a somewhat similar analysis of the relationship between 
growth and population density in fishes. 
In some species fluctuations in the density of the population appear to have no 
effect on the rate of growth. Concerning the haddock Bowman (1932) stated: 
It cannot be inferred from the results of the extensive and continuous investigations that, in 
comparable areas, the average growth rates of successive broods in their first year of life vary with 
differences in brood densities. 
Hjort (1932) pointed out that growth in the Norwegian cod and herring stocks 
is remarkably uniform from year to year and quite independent of the density of the 
stock. He contended that growth was determined by specific conditions in the sea 
rather than by the numbers of fish in the population. 
Marine populations, particularly round fishes, can wander freely over extensive 
areas. It is possible for them to seek out those regions with the most suitable food 
conditions, and in some instances it is probable that the role of food as a limiting 
factor for growth is insignificant as compared to other environmental influences. 
Within the restricted limits of a small inland lake a closer dependence of the growth 
18 The following papers listed in the bibliography touch upon the question of the relationship between density of population in 
marine fishes (largely the plaice) and their rates of growth: Strodtmann and Langhammer (1925), Heincke and Buckmann (1926), 
Garstang (1926), Jensen (1928) and (1932), Buckmann (1932), Bowman (1932), Hjort (1932), and Russel! (1932). These papers are 
only representative of the rather voluminous literature of the subject. 
” Buckmann referred to Dawes’ (1930, 1931) feeding experiments with plaice. 
