Nowak Martin A, McAvoy Alex, Allen Benjamin, Wilson Edward O
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138.
Department of Mathematics, Harvard University, Cambridge, MA 02138.
Proc Natl Acad Sci U S A. 2017 May 30;114(22):5665-5670. doi: 10.1073/pnas.1701805114. Epub 2017 May 16.
Hamilton's rule asserts that a trait is favored by natural selection if the benefit to others, [Formula: see text], multiplied by relatedness, [Formula: see text], exceeds the cost to self, [Formula: see text] Specifically, Hamilton's rule states that the change in average trait value in a population is proportional to [Formula: see text] This rule is commonly believed to be a natural law making important predictions in biology, and its influence has spread from evolutionary biology to other fields including the social sciences. Whereas many feel that Hamilton's rule provides valuable intuition, there is disagreement even among experts as to how the quantities [Formula: see text], [Formula: see text], and [Formula: see text] should be defined for a given system. Here, we investigate a widely endorsed formulation of Hamilton's rule, which is said to be as general as natural selection itself. We show that, in this formulation, Hamilton's rule does not make predictions and cannot be tested empirically. It turns out that the parameters [Formula: see text] and [Formula: see text] depend on the change in average trait value and therefore cannot predict that change. In this formulation, which has been called "exact and general" by its proponents, Hamilton's rule can "predict" only the data that have already been given.
汉密尔顿法则断言，如果对他人的益处（用[公式：见正文]表示）乘以亲缘系数（用[公式：见正文]表示）超过了对自身的代价（用[公式：见正文]表示），那么自然选择就会青睐某一性状。具体而言，汉密尔顿法则指出，种群中平均性状值的变化与[公式：见正文]成正比。人们普遍认为这条法则是一条自然规律，能在生物学中做出重要预测，其影响已从进化生物学传播到包括社会科学在内的其他领域。尽管许多人觉得汉密尔顿法则提供了有价值的直觉，但即便在专家中，对于给定系统中[公式：见正文]、[公式：见正文]和[公式：见正文]这些量应如何定义也存在分歧。在此，我们研究一种得到广泛认可的汉密尔顿法则的表述形式，据说它与自然选择本身一样具有普遍性。我们表明，在这种表述形式下，汉密尔顿法则无法做出预测，也无法通过实证进行检验。结果发现，参数[公式：见正文]和[公式：见正文]取决于平均性状值的变化，因此无法预测该变化。在其支持者称之为“精确且通用”的这种表述形式中，汉密尔顿法则只能“预测”已给出的数据。
