A New Foundation for the Propensity Interpretation of Fitness

Abstract

The propensity interpretation of fitness (PIF) is commonly taken to be subject to a set of simple counterexamples. We argue that three of the most important of these are not counterexamples to the PIF itself, but only to the traditional mathematical model of this propensity: fitness as expected number of offspring. They fail to demonstrate that a new mathematical model of the PIF could not succeed where this older model fails. We then propose a new formalization of the PIF that avoids these (and other) counterexamples. By producing a counterexample-free model of the PIF, we call into question one of the primary motivations for adopting the statisticalist interpretation of fitness. In addition, this new model has the benefit of being more closely allied with contemporary mathematical biology than the traditional model of the PIF. 1 Introduction 1.1 The ‘Generality Problem’ 1.2 Counterexamples to the PIF 1.2.1 The moments problem 1.2.2 The delayed selection problem 1.2.3 Timing of reproduction 1.3 The need for a new model2 A New Formalization 2.1 The new model and biological theory3 Possible Objections to 3.1 Objection 1: Natural selection is short term 3.2 Objection 2: Descendants are only minimally related to ancestors 3.3 Objection 3: Evolutionary time scale is pragmatically determined 3.4 Objection 4: Long-term fitness is lineage fitness 3.5 Objection 5: The theory of evolution by natural selection fundamentally concerns trait fitness, not individual fitness4 Response to Counterexamples 4.1 Timing of reproduction 4.2 Delayed selection 4.3 The moments problem5 Conclusion