Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92697-2525, USA.
Philos Trans R Soc Lond B Biol Sci. 2020 Apr 27;375(1797):20190351. doi: 10.1098/rstb.2019.0351. Epub 2020 Mar 9.
The Price equation describes the change in populations. Change concerns some value, such as biological fitness, information or physical work. The Price equation reveals universal aspects for the nature of change, independently of the meaning ascribed to values. By understanding those universal aspects, we can see more clearly why fundamental mathematical results in different disciplines often share a common form. We can also interpret more clearly the meaning of key results within each discipline. For example, the mathematics of natural selection in biology has a form closely related to information theory and physical entropy. Does that mean that natural selection is about information or entropy? Or do natural selection, information and entropy arise as interpretations of a common underlying abstraction? The Price equation suggests the latter. The Price equation achieves its abstract generality by partitioning change into two terms. The first term naturally associates with the direct forces that cause change. The second term naturally associates with the changing frame of reference. In the Price equation's canonical form, total change remains zero because the conservation of total probability requires that all probabilities invariantly sum to one. Much of the shared common form for the mathematics of different disciplines may arise from that seemingly trivial invariance of total probability, which leads to the partitioning of total change into equal and opposite components of the direct forces and the changing frame of reference. This article is part of the theme issue 'Fifty years of the Price equation'.
价格方程描述了种群的变化。变化涉及一些值，如生物适应性、信息或物理工作量。价格方程揭示了变化的普遍方面，而与所赋予的值的含义无关。通过理解这些普遍方面，我们可以更清楚地看到为什么不同学科的基本数学结果往往具有共同的形式。我们也可以更清楚地解释每个学科内的关键结果的含义。例如，生物学中的自然选择的数学形式与信息论和物理熵密切相关。这是否意味着自然选择与信息或熵有关？还是自然选择、信息和熵是作为一个共同的基本抽象的解释而出现的？价格方程表明了后者。价格方程通过将变化分为两个术语来实现其抽象的普遍性。第一个术语自然与导致变化的直接力相关联。第二个术语自然与变化的参照系相关联。在价格方程的规范形式中，总变化保持为零，因为总概率的守恒要求所有概率不变地加起来等于一。不同学科的数学中许多共同的常见形式可能源于总概率的这种看似微不足道的不变性，这导致总变化被分为直接力和变化参照系的相等且相反的分量。本文是主题为“价格方程五十年”的一部分。
