PREDICTIONS – 10 Years Later - Santa Fe Institute

1. SCIENCE AND FORETELLING
out. Finally we reach zero growth and the end of the life cycle; the
growth process in question comes to an end. The bell curve depicting
the rate of natural growth goes back to zero, while the S-curve of cumulative
growth reaches its ceiling.
What is hidden under the graceful shape of the S-curve is the fact
that natural growth obeys a strict law which is seeded with knowledge
of the final ceiling, the amount of growth remaining to be accomplished.
Therefore, accurate measurements of the growth process, even
during its early phases, can be used to determine the law quantitatively,
thus revealing the final size (the value of the ceiling) ahead of time. This
is why the S-curve approach possesses predictive power.
Controls on Rabbit Populations
There is an inherent element of competition in logistic growth—
competition for space, food, or any resource that may be the limiting
factor. This competition is responsible for the final slowing down of
growth. A species population grows through natural multiplication. Besides
feeding, rabbits do little else but multiply. The food on their range
is limited, however, with a capacity for feeding only a certain number of
rabbits. As the population approaches this number, the growth rate has
to slow down. How does this happen? Perhaps by means of increased
kit mortality, diseases, lethal fights between overcrowded rabbits, or
even other more subtle forms of behavior that rabbits may act out unsuspectingly.
Nature imposes population controls as needed, and in a
competitive environment, only the fittest survive.
Since the growth of a rabbit population follows an S-curve from the
beginning, one may conclude that these natural controls are so sophisticated
that they take effect from the very first rabbit couple on the range.
The same mathematical function describes the process from beginning
to end. The function can be determined, in principle, after only a few
early measurements on the rabbit population. Theoretically, therefore, as
soon as this function is defined, the fate of the growth of the rabbit
population is sealed.
I became suspicious the first time I was confronted with this notion. I
could not explain how the first rabbit couple would have to behave “in
accordance” with a final limitation it had not yet felt. My doubts were
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