Frank Steven A
Department of Ecology and Evolutionary Biology University of California Irvine CA USA.
Ecol Evol. 2017 Apr 4;7(10):3381-3396. doi: 10.1002/ece3.2922. eCollection 2017 May.
The Price equation shows the unity between the fundamental expressions of change in biology, in information and entropy descriptions of populations, and in aspects of thermodynamics. The Price equation partitions the change in the average value of a metric between two populations. A population may be composed of organisms or particles or any members of a set to which we can assign probabilities. A metric may be biological fitness or physical energy or the output of an arbitrarily complicated function that assigns quantitative values to members of the population. The first part of the Price equation describes how directly applied forces change the probabilities assigned to members of the population when holding constant the metrical values of the members-a fixed metrical frame of reference. The second part describes how the metrical values change, altering the metrical frame of reference. In canonical examples, the direct forces balance the changing metrical frame of reference, leaving the average or total metrical values unchanged. In biology, relative reproductive success (fitness) remains invariant as a simple consequence of the conservation of total probability. In physics, systems often conserve total energy. Nonconservative metrics can be described by starting with conserved metrics, and then studying how coordinate transformations between conserved and nonconserved metrics alter the geometry of the dynamics and the aggregate values of populations. From this abstract perspective, key results from different subjects appear more simply as universal geometric principles for the dynamics of populations subject to the constraints of particular conserved quantities.
普赖斯方程表明了生物学中变化的基本表达式、种群的信息和熵描述以及热力学方面之间的统一性。普赖斯方程将两个种群之间一个度量的平均值变化进行了划分。一个种群可能由生物体、粒子或我们可以赋予概率的集合中的任何成员组成。一个度量可能是生物适应性、物理能量或一个任意复杂的函数的输出，该函数为种群成员赋予定量值。普赖斯方程的第一部分描述了在保持成员的度量值不变（一个固定的度量参考框架）时，直接施加的力如何改变赋予种群成员的概率。第二部分描述了度量值如何变化，从而改变度量参考框架。在典型例子中，直接力平衡了变化的度量参考框架，使平均或总度量值保持不变。在生物学中，相对繁殖成功率（适应性）作为总概率守恒的一个简单结果而保持不变。在物理学中，系统通常守恒总能量。非守恒度量可以通过从守恒度量开始描述，然后研究守恒和非守恒度量之间的坐标变换如何改变动力学的几何结构和种群的总量值来进行描述。从这个抽象的角度来看，不同学科的关键结果更简单地表现为受特定守恒量约束的种群动力学的通用几何原理。
