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The Arithmetic Mean of What? A Cautionary Tale About the Use of the Geometric Mean as a Measure of Fitness

Takacs, Peter and Bourrat, Pierrick (2022) The Arithmetic Mean of What? A Cautionary Tale About the Use of the Geometric Mean as a Measure of Fitness. [Preprint]

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Abstract

Showing that the arithmetic mean number of offspring for a trait type often fails to be a predictive measure of fitness was a welcome correction to the philosophical literature on fitness. While the higher mathematical moments (variance, skew, kurtosis, etc.) of a probability-weighted offspring distribution can influence fitness measurement in distinct ways, the geometric mean number of offspring is commonly singled out as the most appropriate measure. For it is well-suited to a compounding (multiplicative) process and is sensitive to variance in offspring number. The geometric mean thus proves to be a predictively efficacious measure of fitness in examples featuring discrete generations and within- or between-generation variance in offspring output. Unfortunately, this advance has subsequently led some to conclude that the arithmetic mean is never (or at best infrequently) a good measure of fitness and that the geometric mean should accordingly be the default measure of fitness. We show not only that the arithmetic mean is a perfectly reasonable measure of fitness so long as one is clear about what it refers to (in particular, when it refers to growth rate), but also that it functions as a more general measure when properly interpreted. It must suffice as a measure of fitness in any case where the geometric mean has been effectively deployed as a measure. We conclude with a discussion about why the mathematical equivalence we highlight cannot be dismissed as merely of mathematical interest.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Takacs, Peterpeter.takacs@sydney.edu.au0000-0003-1557-9601
Bourrat, Pierrickp.bourrat@gmail.com0000-0002-4465-6015
Additional Information: Forthcoming (Biology & Philosophy)
Keywords: fitness; natural selection; evolutionary theory; propensity; measurement; geometric mean; arithmetic mean; population growth rate; population dynamics; prediction; explanation
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Biology > Ecology/Conservation
Specific Sciences > Biology > Evolutionary Theory
General Issues > Evidence
General Issues > Explanation
General Issues > Models and Idealization
Depositing User: Dr. Peter Takacs
Date Deposited: 03 Mar 2022 17:50
Last Modified: 03 Mar 2022 17:50
Item ID: 20295
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Biology > Ecology/Conservation
Specific Sciences > Biology > Evolutionary Theory
General Issues > Evidence
General Issues > Explanation
General Issues > Models and Idealization
Date: 24 February 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/20295

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