J. L. BROOKS 97 



The diagonal lines in Figs. 3 and 4 trace the history of the new- 

 born of each sample. 



With this brief description of the population in mind, we can 

 proceed with a consideration of the correlation between the 

 characteristics of the phenotypic variants and the environmental 

 conditions under which these variants developed. Measurements 

 of the relative size of head and carapace of the individuals of 

 the population provide insight into the relative developmental 

 rate of the helmet as compared with that of the rest of the body, 

 of which carapace length is taken as a characteristic dimension. 

 Furthermore, the ratio of head length to carapace length in the 

 newborn provides an index to the rate of relative growth prior 

 to birth. Field and laboratory studies indicated that the relative 

 length of the head at birth is controlled by the temperature 

 during development. However, the rate of relative growth of 

 the helmet after birth when the animal is free-swimming is not 

 directly correlated with the temperature. It appears that both 

 high temperature (above 18-20° C. for many species) and turbu- 

 lence of the water are necessary conditions for the development 

 of helmets of the maximum size of which a population is capable 

 (Brooks, 1946, 1947). The details of the interrelation of these 

 major determinants of the relative growth rate of the helmet have 

 not been worked out, but a promising hypothesis is that both 

 factors ( temperature and turbulence ) have their effect by raising 

 the metabolic rate. 



Although laboratory experiments to determine the importance 

 of turbulence in species other than Daphnia galeata have not as 

 yet been done, there is a considerable body of observational evi- 

 dence indicating that large helmets develop in those lake-dwelling 

 species that live in the upper waters of a lake. In the majority of 

 lakes in the temperate zone this will mean that these populations 

 during the winter months will live in water that is less than 4° C, 

 often near 0° C. However, in midsummer these water strata are 

 commonly above 18-20° C. except in very large lakes, in which, 

 incidentally, large helmets usually are not found. These animals 

 thus have to swim, feed, grow, and reproduce in a very wide 

 temperature range. The exuberant form which develops at high 



