AI 中文总结
研究表型可塑性和遗传同化机制，通过连接连续时间价格方程与时间尺度分离概念形式化相关过程，证明遗传同化是解决自身压力的动态松弛过程，实现勒夏特列原理，给出相关预测及通用响应规律。
AI 中文摘要
表型可塑性和遗传同化在适应性进化中起关键作用，但其潜在机制缺乏统一的物理描述。主要理论困难在于时间尺度的根本差异，表型可塑性在一代内迅速发生，而遗传变化在多代间缓慢积累。我们通过将进化动力学的基础方程——连续时间价格方程与时间尺度分离的物理概念相联系，对这些过程进行形式化。突然的环境变化会导致表型相对于缓慢的基因型变量发生快速的塑性位移。通过基因型 - 表型耦合，这种位移产生内部遗传压力。我们证明遗传同化是一种动态松弛过程，其中基因型进化以解决这种自身产生的压力。这些进化动力学在数学上实现了勒夏特列原理，即缓慢的遗传反应自然地在同一方向上放大初始的塑性变化。该理论预测，较弱的恢复力（可表现为更大的克隆表型波动）需要更长的进化时间尺度来进行同化。在无成本、完美适应性可塑性的理想极限下，松弛时间发散，因此同化有效地停滞。这种表述为遗传同化提供了一种宏观物理机制，为快速表型反应先于缓慢遗传变化的进化系统提供了一种通用的响应规律。
英文摘要
Phenotypic plasticity and genetic assimilation play key roles in adaptive evolution, yet their underlying mechanism has lacked a unified physical description. A major theoretical difficulty lies in the fundamental difference in timescales, as phenotypic plasticity occurs rapidly within a generation whereas genetic changes accumulate slowly across generations. Here, we formalize these processes by bridging the continuous-time Price equation, a foundational equation of evolutionary dynamics, with the physical concept of timescale separation. A sudden environmental change induces a fast plastic displacement of the phenotype relative to the slow genotypic variable. Through genotype--phenotype coupling, this displacement generates an internal genetic stress. We demonstrate that genetic assimilation is a dynamical relaxation process in which the genotype evolves to resolve this self-generated stress. These evolutionary dynamics mathematically realize Le Chatelier's principle, where the slow genetic response naturally amplifies the initial plastic shift in the same direction. The theory predicts that a weaker restoring force, which can manifest as larger clonal phenotypic fluctuations, requires a longer evolutionary timescale for assimilation. In the ideal limit of cost-free, perfectly adaptive plasticity, the relaxation time diverges, so assimilation effectively stalls. This formulation provides a macroscopic physical mechanism for genetic assimilation, offering a universal response law for evolutionary systems in which rapid phenotypic responses precede slower genetic change.
Comments14 pages, 2 figures
