  The concept of biological adaptation was closely connected to some
mathematical, engineering and physical ideas from the very beginning. Cannon in
his "The wisdom of the body" (1932) used the engineering vision of regulation.
In 1938, Selye enriched this approach by the notion of adaptation energy. This
term causes much debate when one takes it literally, i.e. as a sort of energy.
Selye did not use the language of mathematics, but the formalization of his
phenomenological theory in the spirit of thermodynamics was simple and led to
verifiable predictions. In 1980s, the dynamics of correlation and variance in
systems under adaptation to a load of environmental factors were studied and
the universal effect in ensembles of systems under a load of similar factors
was discovered: in a crisis, as a rule, even before the onset of obvious
symptoms of stress, the correlation increases together with variance (and
volatility). During 30 years, this effect has been supported by many
observations of groups of humans, mice, trees, grassy plants, and on financial
time series. In the last ten years, these results were supplemented by many new
experiments, from gene networks in cardiology and oncology to dynamics of
depression and clinical psychotherapy. Several systems of models were
developed: the thermodynamic-like theory of adaptation of ensembles and several
families of models of individual adaptation. Historically, the first group of
models was based on Selye's concept of adaptation energy and used fitness
estimates. Two other groups of models are based on the idea of hidden attractor
bifurcation and on the advection--diffusion model for distribution of
population in the space of physiological attributes. We explore this world of
models and experiments, starting with classic works, with particular attention
to the results of the last ten years and open questions.
