MAYER: STAUROCEPHALUS GREGARICQS. 9 



unless the water has been quiet for some days." " When the con- 

 ditions are favorable, they come forth soon after dark and swim rapidly 

 about at the surface, sometimes in almost incredible numbers." 



It would probably be advantageous to any species of worm already 

 possessed of some such egg-laying habits as those of Nereis to have the 

 duration of the egg-laying period restricted to as short a time as pos- 

 sible, and also to have it occur in that part of the year most favorable 

 for the safety and development of the larvae. With equal numbers of 

 mature individuals of two species (a) and (6), if (a) possess a long 

 egg-laying period and (h) a short one, there will be more individuals 

 of (b) discharging sperm or ova at any given moment than there will 

 be of (a), whose breeding season is longer. Consequently the eggs of 

 (h) will be more certain of fertilization, other things being equal, than 

 those of (a). For example, if N represent the total number of individuals 

 of species (a), and also of species (b) ; and if 7" represent the duration 

 of the egg-laying period of species (a) and t that of species (6) : then 



N 

 in any definite unit of time there will be — individuals of species (a) 



iV . 

 discharging sperm and ova, while at the same time — individuals of 



species (6) will be engaged in the same act. Consequently, if the areas 



of the breeding-grounds of the two species are equal, there will be 



J^ y T 



f- ^ or — times as many individuals of species (b) discharging sperm 



or ova at any moment, in a unit of area, than there are of species (a) 



engaged in the same act. Then in an area containing m individuals of 



VI T 

 species (a) there are individuals of species (6). Therefore the 



/— - 1 

 average distance apart of the individuals of species C*^) is t 



Vwi — 1 

 times as far as in the case of species (b). Hence the spermatozoa^ of 



species (a) will be obliged to travel '^ t times as far as those of 



•s/m — 1 

 species (6). We see, then, that a shortening of the egg-laying season 

 causes a greater concentration of breeding individuals, and therefore 

 shortens the average distance that the spermatozoa must travel in order 

 to fertilize the ova ; and as spermatozoa cannot survive for any great 

 length of time, this is an advantage to the species. In this connection 



