Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organism’s environment, and evolution in changing environments is still poorly understood. We study a particular model of antibiotic resistance evolution in bacteria where the antibiotic concentration is an environmental parameter and the fitness landscapes incorporate trade-offs between adaptation to low and high antibiotic concentration. With evolutionary dynamics that follow fitness gradients, the evolution of the system under slowly changing antibiotic concentration resembles the athermal dynamics of disordered physical systems under external drives. Exploiting this resemblance, we show that our model can be described as a system with interacting hysteretic elements. As in the case of the driven disordered systems, adaptive evolution under antibiotic concentration cycling is found to exhibit hysteresis loops and memory formation. We derive a number of analytical results for quasistatic concentration changes. We also perform numerical simulations to study how these effects are modified under driving protocols in which the concentration is changed in discrete steps. Our approach provides a general framework for studying motifs of evolutionary dynamics in biological systems in a changing environment.

中文翻译：

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在不断变化的环境中进行生物进化的驱动无序系统方法

种群的生物进化由适应度景观控制，这是从基因型到适应度的地图。然而，适应性景观取决于生物体的环境，并且对不断变化的环境中的进化仍然知之甚少。我们研究了细菌中抗生素耐药性进化的特定模型，其中抗生素浓度是一个环境参数，而适应度环境则结合了对低和高抗生素浓度的适应之间的权衡。随着适应度梯度的进化动力学，缓慢变化的抗生素浓度下系统的进化类似于外部驱动下无序物理系统的无热动力学。利用这种相似性，我们表明我们的模型可以描述为具有交互滞后元素的系统。与驱动无序系统的情况一样，发现抗生素浓度循环下的适应性进化表现出滞后回线和记忆形成。我们得出了一些准静态浓度变化的分析结果。我们还进行数值模拟，以研究在浓度以离散步骤改变的驱动协议下如何修改这些影响。我们的方法为在不断变化的环境中研究生物系统中进化动力学的基序提供了一个通用框架。我们还进行数值模拟，以研究在浓度以离散步骤改变的驱动协议下如何修改这些影响。我们的方法为在不断变化的环境中研究生物系统中进化动力学的基序提供了一个通用框架。我们还进行数值模拟，以研究在浓度以离散步骤改变的驱动协议下如何修改这些影响。我们的方法为在不断变化的环境中研究生物系统中进化动力学的基序提供了一个通用框架。