Vol,. 8, 1922 
BIOLOGY: PEARL AND PARKER 
215 
imagoes produced in 16 days. These absolute figures vary of course with 
the accidental circumstances affecting the mated population. (g) The 
observed rate of reproduction, given as number of offspring imagoes per 
mated female per day. (h) The theoretical rate of reproduction (number 
of imagoes per mated female per day) as calculated from equation (i) below. 
TABLE 1 
Experimental Data 
PAIRS PER 
BOTTLE AT 
START 
MEAN POP. 
AVERAGE 
16 DAYS 
MEAN FLIES 
PER CM 3 OF 
SPACE 
MEAN PLIES 
PER CM2 of 
FOOD AREA 
TOTAL 
9 
DAYS 
TOTAL 
IMAGOES 
IN 16 DAY 
IMAGOES 
PER 
MATED? 
PER DAY 
y 
FROM 
EQUATION 
1 
2.00 
.015 
.084 
63 
1348 
21.4 
21.1 
2 
3.40 
.026 
.143 
89 
1124 
12.6 
14.5 
3 
5.50 
.042 
.231 
173.5 
1877 
10.8 
10.2 
4 
7.32 
.056 
.308 
232 
2100 
9.1 
8.1 
5 
9.29 
.071 
.391 
267 
1585 
5.9 
6.7 
6 
10.29 
.079 
.433 
298.5 
2034 
6.8 
6.2 
7 
11.51 
.089 
.484 
377.5 
1951 
5.2 
5.6 
8 
14.48 
.111 
.609 
436.5 
1996 
4.6 
4.6 
9 
16.62 
.128 
.700 
519 
2117 
4.1 
4.0 
10 
18.74 
.144 
.789 
275 
855 
3.1 
3.6 
12 
21.70 
.167 
.913 
504 
1746 
3.5 
3.1 
15 
26.02 
.200 
1.095 
609.5 
1389 
2.3 
2.5 
20 
34.02 
.262 
1.432 
754 
1666 
2.2 
1.8 
25 
47.75 
.367 
2.010 
384 
388 
1.0 
1.1 
30 
47.73 
.367 
2.009 
1069.5 
1272 
1.2 
1.1 
50 
90.66 
.697 
3.816 
1446.5 
474 
.33 
.34 
It is at once apparent from this table that there is a profound and regular 
change in the rate of reproduction of Drosophila, under the conditions of 
these experiments, with increasing density of population. The rate of 
reproduction per mated female per day declines as density of population 
increases, at first extremely rapidly and then more and more slowly at 
higher densities. The total number of progeny flies (23,922) is great 
enough to give confidence in the results. 
A better appreciation may be obtained of the nature and regularity of 
this change if we put the results in graphic form. This is done in Fig. 1. 
The smooth curve passing through the circles is the graph of equation 
(i) fitted to the observations by the method of least squares. In this 
equation y denotes imagoes per mated female per day, and x denotes mean 
density of the mated population (measured as flies per bottle) over the 
whole 16 day period. 
y = 34.53 ^--^i"* X-''' (i) 
Or, in logarithmic form, 
log y = 1.54:- .008 x - .658 log x (ii) 
