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 Selyes 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.
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