The Annual Distribution of the Crustacea . P03 
ing a point of greatest depression about the last of August. 
During this period of decline, most of the periodic species are 
introduced, but their numbers do not usually compensate for the 
falling off in the number of the permanent species. In 1896, how¬ 
ever, Chydorus increased so rapidly during this time as to more 
than counterbalance the decline in other species. 
In September a rise in the number of Crustacea begins, caused 
chiefly by increase in Daphnia of all species and in Cyclops. 
This increase culminates in the last of September or in October. 
This is the fail maximum, which, in general, is decidedly greater 
than the early summer maximum, the Crustacea at this time 
reaching a number perhaps two-thirds as great as that of the 
spring maximum. During the later part of the fall and the 
early winter, the number declines very rapidly at first, and then 
more or less slowly, until the winter conditions are established 
with the freezing of the lake in December or early January. 
The rapidity of the decline varies in different seasons, depend¬ 
ing upon the abundance of the periodic forms and upon the num¬ 
ber of young Cyclops and Daphnia hyalina , which are produced 
in late autumn. The climatic conditions also affect the rapidity 
of decline; the rate of fall of temperature, the storms, etc., hav¬ 
ing a decided influence in hastening or retarding the approach 
of the winter conditions. Near the last of December, however, 
these conditions are fairly established, and the Crustacea pass 
through the winter with but little change in number and aver¬ 
aging from 100,000 to 200,000 per sq. m. of surface. 
A glance at Fig. 6 will show that this complex rhythm 
recurred with an exactness quite surprising. While the abso¬ 
lute number of Crustacea present varies considerably, the shape 
of the curves indicating the movement of the limnetic popula¬ 
tion is strikingly similar. The resemblance is the more surpris¬ 
ing when we consider that these maxima and minima are due to 
the increase and decrease of eight species of Crustacea, whose 
numbers are independent of each other, and which appear in 
very different numbers at different seasons and at the same sea¬ 
son in different years. The lines of diagram 6 represent, there¬ 
fore, the sums of a number of independent variables, never fewer 
