  The "Law of the Minimum" states that growth is controlled by the scarcest
resource (limiting factor). This concept was originally applied to plant or
crop growth (Justus von Liebig, 1840) and quantitatively supported by many
experiments. Some generalizations based on more complicated "dose-response"
curves were proposed. Violations of this law in natural and experimental
ecosystems were also reported. We study models of adaptation in ensembles of
similar organisms under load of environmental factors and prove that violation
of Liebig's law follows from adaptation effects. If the fitness of an organism
in a fixed environment satisfies the Law of the Minimum then adaptation
equalizes the pressure of essential factors and therefore acts against the
Liebig's law. This is the the Law of the Minimum paradox: if for a randomly
chosen pair "organism-environment" the Law of the Minimum typically holds,
then, in a well-adapted system, we have to expect violations of this law.
  For the opposite interaction of factors (a synergistic system of factors
which amplify each other) adaptation leads from factor equivalence to
limitations by a smaller number of factors.
  For analysis of adaptation we develop a system of models based on Selye's
idea of the universal adaptation resource (adaptation energy). These models
predict that under the load of an environmental factor a population separates
into two groups (phases): a less correlated, well adapted group and a highly
correlated group with a larger variance of attributes, which experiences
problems with adaptation. Some empirical data are presented and evidences of
interdisciplinary applications to econometrics are discussed.
