This paper addresses the question of optimal phenotypic plasticity as a
response to environmental fluctuations while optimizing the cost/benefit ratio,
where the cost is energetic expense of plasticity, and benefit is fitness. The
dispersion matrix \Sigma of the genes' response (H = ln|\Sigma|) is used: (i)
in a numerical model as a metric of the phenotypic variance reduction in the
course of fitness optimization, then (ii) in an analytical model, in order to
optimize parameters under the constraint of limited energy availability.
Results lead to speculate that such optimized organisms should maximize their
exergy and thus the direct/indirect work they exert on the habitat. It is shown
that the optimal cost/benefit ratio belongs to an interval in which differences
between individuals should not substantially modify their fitness.
Consequently, even in the case of an ideal population, close to the optimal
plasticity, a certain level of genetic diversity should be long conserved, and
a part, still to be determined, of intra-populations genetic diversity probably
stem from environment fluctuations. Species confronted to monotonous factors
should be less plastic than vicariant species experiencing heterogeneous
environments. Analogies with the MaxEnt algorithm of E.T. Jaynes (1957) are
discussed, leading to the conjecture that this method may be applied even in
case of multivariate but non multinormal distributions of the responses
