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Revisiting the “fallacy of averages” in ecology: Expected gain per unit time equals expected gain divided by expected time

Broom, M. ORCID: 0000-0002-1698-5495, Cressman, R. and Křivan, V. (2019). Revisiting the “fallacy of averages” in ecology: Expected gain per unit time equals expected gain divided by expected time. Journal of Theoretical Biology, 483, 109993.. doi: 10.1016/j.jtbi.2019.109993

Abstract

Fitness is often defined as the average payoff an animal obtains when it is engaged in several activities, each taking some time. We point out that the average can be calculated with respect to either the time distribution, or to the event distribution of these activities. We show that these two averages lead to the same fitness function. We illustrate this result through two examples from foraging theory, Holling II functional response and the diet choice model, and one game-theoretic example of Hamilton’s rule applied to the time-constrained Prisoner’s dilemma (PD). In particular, we show that in these models, fitness defined as expected gain per unit time equals fitness defined as expected gain divided by expected time. We also show how these fitnesses predict the optimal outcome for diet choice and the prevalence of cooperation in the repeated PD game.

Publication Type: Article
Additional Information: © 2019 Elsevier Ltd. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Diet choice model, Fallacy of averages, Functional response Hamilton’s rule, Prisoner’s dilemma game
Subjects: G Geography. Anthropology. Recreation > GF Human ecology. Anthropogeography
Q Science > QA Mathematics
Q Science > QH Natural history > QH301 Biology
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: https://openaccess.city.ac.uk/id/eprint/23534
[img] Text - Accepted Version
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