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Evolution of vertical and oblique transmission under fluctuating selection

Yoav Ram, Uri Liberman and Marcus W. Feldman
PNAS January 23, 2018. 201719171; published ahead of print January 23, 2018. https://doi.org/10.1073/pnas.1719171115
Yoav Ram
aDepartment of Biology, Stanford University, Stanford, CA 94305-5020;
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Uri Liberman
bSchool of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
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Marcus W. Feldman
aDepartment of Biology, Stanford University, Stanford, CA 94305-5020;
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  • For correspondence: mfeldman@stanford.edu
  1. Contributed by Marcus W. Feldman, December 22, 2017 (sent for review November 2, 2017; reviewed by Hamish G. Spencer and Mark M. Tanaka)

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Significance

Evolutionary dynamics of phenotypes in populations depend on how the traits are transmitted across generations and how the environments that cause selection on the traits fluctuate over time. We show that, under periodically fluctuating selection, a gene that increases the rate of vertical transmission is disfavored when the periods are short but approaches an intermediate stable rate for longer periods. This stable rate differs markedly from the rate that maximizes the geometric mean fitness. The evolution of learning rules thus differs qualitatively from the evolution of genetically modified rules of genetic transmission.

Abstract

The evolution and maintenance of social learning, in competition with individual learning, under fluctuating selection have been well-studied in the theory of cultural evolution. Here, we study competition between vertical and oblique cultural transmission of a dichotomous phenotype under constant, periodically cycling, and randomly fluctuating selection. Conditions are derived for the existence of a stable polymorphism in a periodically cycling selection regime. Under such a selection regime, the fate of a genetic modifier of the rate of vertical transmission depends on the length of the cycle and the strength of selection. In general, the evolutionarily stable rate of vertical transmission differs markedly from the rate that maximizes the geometric mean fitness of the population. The evolution of rules of transmission has dramatically different dynamics from the more frequently studied modifiers of recombination, mutation, or migration.

  • periodic selection
  • phenotypic polymorphism
  • modifier theory
  • fitness optimum
  • evolutionary stability

Footnotes

  • ↵1To whom correspondence should be addressed. Email: mfeldman{at}stanford.edu.
  • Author contributions: Y.R., U.L., and M.W.F. designed research, performed research, analyzed data, and wrote the paper.

  • Reviewers: H.G.S., University of Otago; and M.M.T., University of New South Wales.

  • The authors declare no conflict of interest.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1719171115/-/DCSupplemental.

  • Copyright © 2018 the Author(s). Published by PNAS.

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

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Evolution of transmission in varying environments
Yoav Ram, Uri Liberman, Marcus W. Feldman
Proceedings of the National Academy of Sciences Jan 2018, 201719171; DOI: 10.1073/pnas.1719171115

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Evolution of transmission in varying environments
Yoav Ram, Uri Liberman, Marcus W. Feldman
Proceedings of the National Academy of Sciences Jan 2018, 201719171; DOI: 10.1073/pnas.1719171115
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