216 
BIOLOGY: PEARL AND PARKER Proc. N. A. S. 
It is at once apparent that this 
equation describes the observed 
facts with extraordinary precision. 
Rarely, even in a physical or chemi- 
cal experiment, does one get such 
close agreement as is here shown 
between observation and theory. 
Plainly the curve is the expression 
of the law relating these two phe- 
nomena, rate of reproduction and 
density of population. 
It is of interest to note that this 
equation is essentially identical in 
form with Farr's Law relating death- 
rate to population. Farr's original 
equation was the following, put in 
logarithmic form: 
log D = log a -\- k log d 
where D denotes death-rate and d 
density of population and a and k 
are constants . B rownlee has slightly 
modified the constants but the essen- 
tial form remains the same. Now 
in our equation (ii) the term in % 
is obviously of no practical impor- 
tance, and could be left out entirely 
without visibly affecting the fit. It 
was only put in in a spirit of meticu- 
lous curve-fitting accuracy. With 
this term out our equation becomes 
in form identical with Farr's except 
that we have shifted the origin. The 
only essential difference is that in his case death-rate is shown to vary directly 
with density of population, while in the present case rate of reproduction 
varies inversely with density, but according to the same law. Death and re- 
production are both fundamental and antithetical biological phenomena. 
What we know about the matter suggests that density of population has 
a profound effect upon many if not all general and fundamental biological 
processes. Brownlee points out that the same law holds in racing for the 
relationship between the record time for any definite length of course 
and the length itself, and for other biological and biochemical phenomena. 
20 30 40 50 60 
MEAN rUES PER BOTTLE 
FIG. 1 
Showing changes in rate of reproduction 
of Drosophila with increasing density of 
the mated population. The circles give 
the observations and the smooth curve is 
thegraph of the logarithmic equation dis- 
cussed in the text. 
