J. L. BROOKS 99 



several kinds of information should possibly be considered here 

 that are not consistent with the hypothesis of advantage con- 

 ferred by the helmet. The first such evidence is presented in Fig. 

 5, which indicates the range of Daphnia retrocurva and some of 

 the forms of the helmet. The animal at the top is a reminder that 

 most of the individuals in any population have a small helmet, 

 smaller than the one depicted. In Bantam Lake, for example, the 

 population size when the helmets were large was less than one- 

 tenth that when the helmets were unspectacular (cf. Figs. 3 and 

 4). The other three specimens of retrocurva indicate the geo- 

 graphical variation in the extreme form of the helmet. One of 

 the elaborate hypotheses (Woltereck, 1930) for the functional 

 significance of the helmet maintains that a retrocurved helmet, of 

 which the specimen from Lake Mendota is probably the most 

 extreme in the genus, has a different effect from one which is 

 elongated in the body axis. Many specimens of D. retrocurva 

 have tall helmets that are not retrocurved. The specimen drawn 

 as characteristic of the Canadian and West Coast areas has a 

 more retrocurved helmet than many in these areas. The special 

 pleading necessary to account for this cline and for the fact that 

 most of the helmeted forms are intermediate in shape between 

 the two extremes, with ( supposedly ) quite different effects, tends 

 to cast doubt on the various hypotheses of this type so far pro- 

 posed. 



However, rather different and more telling evidence is avail- 

 able which makes it improbable that the ability to produce a 

 helmet is maintained in the genotype because of selective ad- 

 vantage conferred by the helmet itself. This comes from the 

 consideration of species such as Daphnia longiremis, which usu- 

 ally has no more than the slight crest indicated on the topmost 

 of the three specimens drawn in Fig. 6. Throughout the indicated 

 range in North America, and in northern Eurasia as well, longi- 

 remis occurs in populations of such round-headed individuals. 

 On rare occasions, however, populations occur in which helmeted 

 individuals are common. The places where such populations have 

 been found in North America are indicated on the map. Two 

 types of helmets occur, and the differences are probably geneti- 



