ON THE ANALYSIS
OF SIGMOID CURVES
L. G. M. IBAAS 'BECKING Ph. D., D. Sc.
(With 9 text-figures and x plate)"
(Received 19. VIII. x945)
TO MAJOR-GENERAL F. DAUBANTON M.D.~ D.P.H., F. S. S.
The sigmoid, or S-shaped ci~rve represents, in a large number of cases
the changes in number of a population, as well as changes in length or in
volume or in weight of a cell, an organ or an organism; all as a function
of time. It is most remarkable that such a heterogeneous group of processes
should be characterized by graphical expressions so closely akin. The lite-
rature ̀ on this subject is almost unlimited but, while speculation has been
abundant, no definite results have been obtained tending to show the appli-
cability of a single basic equation, expressing growth. WlsrSOR (1932) in
a remarkable paper on "A comparison o.f certain symmetrical Growth
Curves" states the pro~blem very clearly (p. 73).
"We may have, or think we have, a priori knowledge of the mechanics
of the p~henomenon, from .w~hich we may deduce that ~he data should follow'
a certain law. More often, in biological work, the underlying causes and
their mode of action are so ~bscu~e that we are in no position to make sound
deductions about laws; we have to in'fer our law from the observations".
In the latter case, we simply meet with curve-fitting but, where the
number of mathematical expressions fitting the sigmoid curve are almost
unlimited, it often remains a matter of (often not unbiased) choice which
of those expressions should fit. And from this 5it the underlying curve
The writer stressed this same point in a former paper in this journal
(1937) where a number of statistical distributions were considered and
their mode of origin discussed. We do not want a master-key or a jimmy,
as these tools cannot teach us much about the make-up of the lock--we
AlgALYSIS OF SIGMOID CURVES
want to find the key that belongs to the particular lock. And inasmuch as
"growth" is one of the most