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]
This is the latest version of this item.
![[img]](https://philsci-archive.pitt.edu/style/images/fileicons/text.png) |
Text
Takacs_and Bourrat_BP_24Feb2022_preprint_1.docx Download (77kB) |
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.
| Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
| Social Networking: |
Available Versions of this Item
-
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)
- The Arithmetic Mean of What? A Cautionary Tale About the Use of the Geometric Mean as a Measure of Fitness. (deposited 03 Mar 2022 17:50) [Currently Displayed]
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
 |
View Item |
![[feed]](http://philsci-archive.pitt.edu/style/images/feed-icon-32x32.png){kind=icon}