论文标题
进化的数学:价格方程,自然选择和环境变化
The Mathematics of Evolution: The Price Equation, Natural Selection, and Environmental Change
论文作者
论文摘要
乔治·普莱斯(George Price)引入了他著名的方程式,以研究离散人群中的选择性和环境影响。我们将价格的框架扩展到可测量和量子案例,将所有进化过程分解为选择性和环境组成部分。我们还扩展了Fisher的基本定理,表明相对适应性的选择性变化等于相对适应性的方差。 我们介绍了新颖的选择性和环境熵功能。选择性熵是非阳性的,代表生物原质,环境熵是非负的,代表物理熵。环境熵进一步分解为分散和混合熵。 我们证明了四个新颖的自然选择定律,这表明选择始终如一地行动以增加选择,但环境变化可能会破坏。我们将凸分析应用于方差和熵功能及其选择性变化,并出现平衡过程以优化这些不等式。这些定律的灵感来自于经典的热力学定律。 我们的零定律是对费舍尔定理的改进,表明相对适应性的差异在下面取决于育儿人的数量。我们的第一定律表明,根据差异,相对健身的选择性加速也有限。这是热力学第一法的非保守,选择性版本。我们的第二定律表明,选择性熵的选择性更改及其选择性加速度类似地由非阳性常数界定。这是热力学第二定律的正式严格版本。我们的第三定律表明,对于一类平衡过程,环境熵的选择性更改消失,否则可能会在零附近的开放窗口中有所不同。这是热力学第三定律的选择性版本。
George Price introduced his famous equation to study selective and environmental effects in discrete populations. We extend Price's framework to the measurable and quantum cases, decomposing all evolutionary processes into selective and environmental components. We also extend Fisher's fundamental theorem, showing that selective change of relative fitness equals variance of relative fitness. We introduce novel selective and environmental entropy functionals. Selective entropy is non-positive, representing biological negentropy, and environmental entropy is non-negative, representing physical entropy. Environmental entropy further decomposes into dispersion and mixing entropies. We prove four novel Laws of Natural Selection, showing that selection consistently acts to increase selection, but can be disrupted by environmental change. We apply convex analysis to variance and entropy functionals and their selective changes, and equilibrium processes arise to optimize these inequalities. These laws are inspired by but distinct from the classical Thermodynamic Laws. Our Zeroth Law is a refinement of Fisher's theorem, showing that variance of relative fitness is bounded below by a quantity depending on the child-bearing population. Our First Law shows that selective acceleration of relative fitness is also bounded below, depending on the variance. This is a non-conservative, selective version of the Thermodynamic First Law. Our Second Law shows that the selective change of selective entropy and its selective acceleration are similarly bounded by non-positive constants. This is a formal, rigorous version of the Thermodynamic Second Law. Our Third Law shows that for a class of equilibrium processes, selective change of environmental entropy vanishes, and otherwise may vary in an open window around zero. This is a selective version of the Third Law of Thermodynamics.