---
_id: '3660'
abstract:
- lang: eng
  text: "The maintenance of polygenic variability by a balance between mutation and
    stabilizing selection has been analysed using two approximations: the ‘Gaussian’
    and the ‘house of cards’. These lead to qualitatively different relationships
    between the equilibrium genetic variance and the parameters describing selection
    and mutation. Here we generalize these approximations to describe the dynamics
    of genetic means and variances under arbitrary patterns of selection and mutation.
    We incorporate genetic drift into the same mathematical framework.\r\nThe effects
    of frequency-independent selection and genetic drift can be determined from the
    gradient of log mean fitness and a covariance matrix that depends on genotype
    frequencies. These equations describe an ‘adaptive landscape’, with a natural
    metric of genetic distance set by the covariance matrix. From this representation
    we can change coordinates to derive equations describing the dynamics of an additive
    polygenic character in terms of the moments (means, variances, …) of allelic effects
    at individual loci. Only under certain simplifying conditions, such as those derived
    from the Gaussian and house-of-cards approximations, do these general recursions
    lead to tractable equations for the first few phenotypic moments. The alternative
    approximations differ in the constraints they impose on the distributions of allelic
    effects at individual loci. The Gaussian-based prediction that evolution of the
    phenotypic mean does not change the genetic variance is shown to be a consequence
    of the assumption that the allelic distributions are never skewed. We present
    both analytical and numerical results delimiting the parameter values consistent
    with our approximations."
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
- first_name: Michael
  full_name: Turelli, Michael
  last_name: Turelli
citation:
  ama: Barton NH, Turelli M. Adaptive landscapes, genetic distance, and the evolution
    of quantitative characters. <i>Genetical Research</i>. 1987;49(2):157-174. doi:<a
    href="https://doi.org/10.1017/S0016672300026951">10.1017/S0016672300026951</a>
  apa: Barton, N. H., &#38; Turelli, M. (1987). Adaptive landscapes, genetic distance,
    and the evolution of quantitative characters. <i>Genetical Research</i>. Cambridge
    University Press. <a href="https://doi.org/10.1017/S0016672300026951">https://doi.org/10.1017/S0016672300026951</a>
  chicago: Barton, Nicholas H, and Michael Turelli. “Adaptive Landscapes, Genetic
    Distance, and the Evolution of Quantitative Characters.” <i>Genetical Research</i>.
    Cambridge University Press, 1987. <a href="https://doi.org/10.1017/S0016672300026951">https://doi.org/10.1017/S0016672300026951</a>.
  ieee: N. H. Barton and M. Turelli, “Adaptive landscapes, genetic distance, and the
    evolution of quantitative characters,” <i>Genetical Research</i>, vol. 49, no.
    2. Cambridge University Press, pp. 157–174, 1987.
  ista: Barton NH, Turelli M. 1987. Adaptive landscapes, genetic distance, and the
    evolution of quantitative characters. Genetical Research. 49(2), 157–174.
  mla: Barton, Nicholas H., and Michael Turelli. “Adaptive Landscapes, Genetic Distance,
    and the Evolution of Quantitative Characters.” <i>Genetical Research</i>, vol.
    49, no. 2, Cambridge University Press, 1987, pp. 157–74, doi:<a href="https://doi.org/10.1017/S0016672300026951">10.1017/S0016672300026951</a>.
  short: N.H. Barton, M. Turelli, Genetical Research 49 (1987) 157–174.
date_created: 2018-12-11T12:04:29Z
date_published: 1987-04-01T00:00:00Z
date_updated: 2022-02-04T10:54:31Z
day: '01'
doi: 10.1017/S0016672300026951
extern: '1'
intvolume: '        49'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://www.cambridge.org/core/journals/genetics-research/article/adaptive-landscapes-genetic-distance-and-the-evolution-of-quantitative-characters/25C2D277AC7554F805D67F6C32579549
month: '04'
oa_version: None
page: 157 - 174
publication: Genetical Research
publication_identifier:
  eissn:
  - 1469-5073
  issn:
  - 0016-6723
publication_status: published
publisher: Cambridge University Press
publist_id: '2723'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Adaptive landscapes, genetic distance, and the evolution of quantitative characters
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 49
year: '1987'
...