---
_id: '1863'
abstract:
- lang: eng
  text: The Levene model is the simplest mathematical model to describe the evolution
    of gene frequencies in spatially subdivided populations. It provides insight into
    how locally varying selection promotes a population’s genetic diversity. Despite
    its simplicity, interesting problems have remained unsolved even in the diallelic
    case. In this paper we answer an open problem by establishing that for two alleles
    at one locus and J demes, up to 2J−1 polymorphic equilibria may coexist. We first
    present a proof for the case of stable monomorphisms and then show that the result
    also holds for protected alleles. These findings allow us to prove that any odd
    number (up to 2J−1) of equilibria is possible, before we extend the proof to even
    numbers. We conclude with some numerical results and show that for J>2, the
    proportion of parameter space affording this maximum is extremely small.
acknowledgement: FWF 21305
author:
- first_name: Sebastian
  full_name: Sebastian Novak
  id: 461468AE-F248-11E8-B48F-1D18A9856A87
  last_name: Novak
citation:
  ama: Novak S. The number of equilibria in the diallelic Levene model with multiple
    demes. <i>Theoretical Population Biology</i>. 2011;79(3):97-101. doi:<a href="https://doi.org/10.1016/j.tpb.2010.12.002">10.1016/j.tpb.2010.12.002</a>
  apa: Novak, S. (2011). The number of equilibria in the diallelic Levene model with
    multiple demes. <i>Theoretical Population Biology</i>. Academic Press. <a href="https://doi.org/10.1016/j.tpb.2010.12.002">https://doi.org/10.1016/j.tpb.2010.12.002</a>
  chicago: Novak, Sebastian. “The Number of Equilibria in the Diallelic Levene Model
    with Multiple Demes.” <i>Theoretical Population Biology</i>. Academic Press, 2011.
    <a href="https://doi.org/10.1016/j.tpb.2010.12.002">https://doi.org/10.1016/j.tpb.2010.12.002</a>.
  ieee: S. Novak, “The number of equilibria in the diallelic Levene model with multiple
    demes,” <i>Theoretical Population Biology</i>, vol. 79, no. 3. Academic Press,
    pp. 97–101, 2011.
  ista: Novak S. 2011. The number of equilibria in the diallelic Levene model with
    multiple demes. Theoretical Population Biology. 79(3), 97–101.
  mla: Novak, Sebastian. “The Number of Equilibria in the Diallelic Levene Model with
    Multiple Demes.” <i>Theoretical Population Biology</i>, vol. 79, no. 3, Academic
    Press, 2011, pp. 97–101, doi:<a href="https://doi.org/10.1016/j.tpb.2010.12.002">10.1016/j.tpb.2010.12.002</a>.
  short: S. Novak, Theoretical Population Biology 79 (2011) 97–101.
date_created: 2018-12-11T11:54:25Z
date_published: 2011-05-01T00:00:00Z
date_updated: 2021-01-12T06:53:42Z
day: '01'
doi: 10.1016/j.tpb.2010.12.002
extern: 1
fulldoi: https://doi.org/10.1016/j.tpb.2010.12.002
intvolume: '        79'
issue: '3'
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '05'
page: 97 - 101
publication: Theoretical Population Biology
publication_status: published
publisher: Academic Press
publist_id: '5236'
quality_controlled: 0
status: public
title: The number of equilibria in the diallelic Levene model with multiple demes
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
volume: 79
year: '2011'
...