A dynamical model for the origin of anisogamy

Joseph D. Johnson; Nathan L. White; Alain Kangabire; Daniel M. Abrams

doi:10.1016/j.jtbi.2021.110669

A dynamical model for the origin of anisogamy

Joseph D. Johnson^*, Nathan L. White, Alain Kangabire, Daniel M. Abrams

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via “mean-field coupling,” whereby the likelihood that a gamete survives is an increasing function of its size relative to the population's mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

Original language	English (US)
Article number	110669
Journal	Journal of Theoretical Biology
Volume	521
DOIs	https://doi.org/10.1016/j.jtbi.2021.110669
State	Published - Jul 21 2021

Funding

The authors gratefully acknowledge support of the National Science Foundation through the program on Research Training Groups in the Mathematical Sciences, grant 1547394. We also thank Northwestern University's Office of Undergraduate Research for support through URP 758SUMMER1915627 and URP 758SUMMER1915476. We also thank Christina Goss for help with translation of reference (Kalmus, 1932). The authors gratefully acknowledge support of the National Science Foundation through the program on Research Training Groups in the Mathematical Sciences, grant 1547394. We also thank Northwestern University’s Office of Undergraduate Research for support through URP 758SUMMER1915627 and URP 758SUMMER1915476. We also thank Christina Goss for help with translation of reference ( Kalmus, 1932 ).

Keywords

Anisogamy
Evolution
Evolutionary game theory
Isogamy
Natural selection

ASJC Scopus subject areas

General Agricultural and Biological Sciences
Applied Mathematics
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
Statistics and Probability
Modeling and Simulation

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10.1016/j.jtbi.2021.110669

Cite this

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title = "A dynamical model for the origin of anisogamy",

abstract = "The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via “mean-field coupling,” whereby the likelihood that a gamete survives is an increasing function of its size relative to the population's mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.",

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AU - White, Nathan L.

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AU - Abrams, Daniel M.

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N2 - The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via “mean-field coupling,” whereby the likelihood that a gamete survives is an increasing function of its size relative to the population's mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

AB - The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via “mean-field coupling,” whereby the likelihood that a gamete survives is an increasing function of its size relative to the population's mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

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A dynamical model for the origin of anisogamy

Abstract

Funding

Keywords

ASJC Scopus subject areas

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