---
_id: '4324'
abstract:
- lang: eng
  text: The maintenance of polygenic variation through a balance between mutation
    and stabilizing selection can be approximated in two ways. In the ‘Gaussian’ approximation,
    a normal distribution of allelic effects is assumed at each locus. In the ‘House
    of Cards’ approximation, the effect of new mutations is assumed to be large compared
    with the spread of the existing distribution. These approximations were developed
    to describe models where alleles may have a continuous range of effects. However,
    previous analyses of models with only two alleles have predicted an equilibrium
    variance equal to that given by the ‘House of Cards’ approximation. These analyses
    of biallelic models have assumed that, at equilibrium, the population mean is
    at the optimum. Here, it is shown that many stable equilibria may coexist, each
    giving a slight deviation from the optimum. Though the variance is given by the
    ‘House of Cards’ approximation when the mean is at the optimum, it increases towards
    a value of the same order as that given by the ‘Gaussian’ approximation when the
    mean deviates from the optimum. Thus, the equilibrium variance cannot be predicted
    by any simple model, but depends on the previous history of the population.
acknowledgement: Thanks are due to J. Felsenstein, J. Gillespie, S. Rouhani, M. Slatkin,
  and M. Turelli for stimulating discussions, and for their comments on the manuscript.
  This work was sup- ported by a travel grant from the Royal Society, and by a research
  grant from the SERC
article_processing_charge: No
article_type: original
author:
- first_name: Nicholas H
  full_name: Barton, Nicholas H
  id: 4880FE40-F248-11E8-B48F-1D18A9856A87
  last_name: Barton
  orcid: 0000-0002-8548-5240
citation:
  ama: Barton NH. The maintenance of polygenic variation through a balance between
    mutation and stabilising selection. <i>Genetical Research</i>. 1986;47(3):209-216.
    doi:<a href="https://doi.org/10.1017/S0016672300023156">10.1017/S0016672300023156</a>
  apa: Barton, N. H. (1986). The maintenance of polygenic variation through a balance
    between mutation and stabilising selection. <i>Genetical Research</i>. Cambridge
    University Press. <a href="https://doi.org/10.1017/S0016672300023156">https://doi.org/10.1017/S0016672300023156</a>
  chicago: Barton, Nicholas H. “The Maintenance of Polygenic Variation through a Balance
    between Mutation and Stabilising Selection.” <i>Genetical Research</i>. Cambridge
    University Press, 1986. <a href="https://doi.org/10.1017/S0016672300023156">https://doi.org/10.1017/S0016672300023156</a>.
  ieee: N. H. Barton, “The maintenance of polygenic variation through a balance between
    mutation and stabilising selection,” <i>Genetical Research</i>, vol. 47, no. 3.
    Cambridge University Press, pp. 209–216, 1986.
  ista: Barton NH. 1986. The maintenance of polygenic variation through a balance
    between mutation and stabilising selection. Genetical Research. 47(3), 209–216.
  mla: Barton, Nicholas H. “The Maintenance of Polygenic Variation through a Balance
    between Mutation and Stabilising Selection.” <i>Genetical Research</i>, vol. 47,
    no. 3, Cambridge University Press, 1986, pp. 209–16, doi:<a href="https://doi.org/10.1017/S0016672300023156">10.1017/S0016672300023156</a>.
  short: N.H. Barton, Genetical Research 47 (1986) 209–216.
date_created: 2018-12-11T12:08:15Z
date_published: 1986-06-01T00:00:00Z
date_updated: 2022-01-31T14:31:48Z
day: '01'
doi: 10.1017/S0016672300023156
extern: '1'
external_id:
  pmid:
  - '3744046'
intvolume: '        47'
issue: '3'
language:
- iso: eng
month: '06'
oa_version: None
page: 209 - 216
pmid: 1
publication: Genetical Research
publication_identifier:
  eissn:
  - 1469-5073
  issn:
  - 0016-6723
publication_status: published
publisher: Cambridge University Press
publist_id: '1718'
quality_controlled: '1'
status: public
title: The maintenance of polygenic variation through a balance between mutation and
  stabilising selection
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 47
year: '1986'
...