A Tale of Two Equations Ludi Vitae or Motus Vital

• 作者: Chuang Liu
• 来源期刊: 复旦人文社会科学论丛:英文版
• 学科: 数学
• 关键词: Philosophy of biology Evolutionary game EQUIVALENCE REDUCTION
• 年，卷（期）: 2020,（3）
• 页码范围: 337-355
• 页数: 19页
• 分类号: O17

摘要

In this paper,we investigate the meaning and significance of a remarkable fact:the equivalence of the core equations in two apparently disconnected areas in biology.The core equation in evolutionary game theory expresses the dynamic law known as the replicator equation,and the core equation of population dynamics expresses the dynamic law known as the Lotka-Volterra equation.They are proven equivalent by a simple transformation of variables.What does it mean?Does it mean that evolution via natural selection is better modeled as a process of game playing--ludi vitae--or that of mechanical motion--motus vita?We analyze the complexity of this question in this paper.