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) systematically 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, as a physical quantity, i.e. a sort of energy. Selye did not use the language of mathematics systematically, 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.

生物适应的概念从一开始就与一些数学、工程和物理思想密切相关。坎农在他的《身体的智慧》（1932）中系统地使用了调控的工程视野。1938 年，Selye 通过适应能量的概念丰富了这种方法。当人们从字面上理解这个术语时，它会引起很多争论，作为一个物理量，即一种能量。Selye 没有系统地使用数学语言，但他的现象学理论在热力学精神下的形式化很简单，并导致了可验证的预测。在 1980 年代，研究了适应大量环境因素的系统中的相关性和方差动力学，并发现了在类似因素负载下的系统集合中的普遍效应：在危机中，通常，即使在明显的压力症状出现之前，相关性也会随着方差（和波动性）的增加而增加。30 年来，这种效应得到了对人类、老鼠、树木、草本植物和金融时间序列的许多观察结果的支持。在过去十年中，这些结果得到了许多新实验的补充，从心脏病学和肿瘤学中的基因网络到抑郁症和临床心理治疗的动力学。开发了几个模型系统：类似热力学的整体适应理论和几个个体适应模型系列。从历史上看，第一组模型是基于 Selye 的适应能量概念并使用适应度估计。另外两组模型基于隐藏吸引子分岔的思想和生理属性空间中人口分布的对流-扩散模型。我们探索这个模型和实验的世界，从经典作品开始，特别关注过去十年的结果和开放性问题。