  We conducted an investigation of the effect that extreme variability of the
individual's environment has in the individual's adaptability and, in general,
in the co-evolution of a population. First we assume that the individuals are a
kind of perceptrons with a given memory size that adapt to their environment;
second we consider co-evolution not only of the individual actions but also of
the memory size, depending on the individual's fitness; and third we assume
strong variability of the environment. We show that changes in the intensity of
the environmental fluctuations introduce a phase transition in the frequency of
cooperators and the diversity of the population. We also find out that extreme
variability of the environment induces changes in the critical exponents and
that this variability can promote more diversity in the population.
