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]
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 probabilityweighted 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 wellsuited 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 betweengeneration 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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The Arithmetic Mean of What? A Cautionary Tale About the Use of the Geometric Mean as a Measure of Fitness. (deposited 28 Feb 2022 03:45)
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