---
_id: '15358'
abstract:
- lang: eng
  text: 'We consider how a population of N haploid individuals responds to directional
    selection on standing variation, with no new variation from recombination or mutation.
    Individuals have trait values z1,…,zN, which are drawn from a distribution ψ;
    the fitness of individual i is proportional to [Formula: see text] . For illustration,
    we consider the Laplace and Gaussian distributions, which are parametrised only
    by the variance V0, and show that for large N, there is a scaling limit which
    depends on a single parameter NV0. When selection is weak relative to drift (NV0≪1),
    the variance decreases exponentially at rate 1/N, and the expected ultimate gain
    in log fitness (scaled by V0), is just NV0, which is the same as Robertson''s
    (1960) prediction for a sexual population. In contrast, when selection is strong
    relative to drift (NV0≫1), the ultimate gain can be found by approximating the
    establishment of alleles by a branching process in which each allele competes
    independently with the population mean and the fittest allele to establish is
    certain to fix. Then, if the probability of survival to time t∼1/V0 of an allele
    with value z is P(z), with mean P¯, the winning allele is the fittest of NP¯ survivors
    drawn from a distribution ψP/P¯. The expected ultimate change is ∼2log(1.15NV0)
    for a Gaussian distribution, and ∼-12log0.36NV0-log-log0.36NV0 for a Laplace distribution.
    This approach also predicts the variability of the process, and its dynamics;
    we show that in the strong selection regime, the expected genetic variance decreases
    as ∼t-3 at large times. We discuss how these results may be related to selection
    on standing variation that is spread along a linear chromosome.'
acknowledgement: We thank Emmanuel Schertzer and two reviewers for comments on this
  manuscript. NB thanks the European Research Council for support via the grant “HaplotypeStructure”
  101055327. We would also like to give our sincere thanks to Alison Etheridge for
  her insight, inspiration and support over the years.
article_processing_charge: Yes (via OA deal)
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: Himani
  full_name: Sachdeva, Himani
  id: 42377A0A-F248-11E8-B48F-1D18A9856A87
  last_name: Sachdeva
citation:
  ama: Barton NH, Sachdeva H. Limits to selection on standing variation in an asexual
    population. <i>Theoretical Population Biology</i>. 2024;157:129-137. doi:<a href="https://doi.org/10.1016/j.tpb.2024.04.001">10.1016/j.tpb.2024.04.001</a>
  apa: Barton, N. H., &#38; Sachdeva, H. (2024). Limits to selection on standing variation
    in an asexual population. <i>Theoretical Population Biology</i>. Elsevier. <a
    href="https://doi.org/10.1016/j.tpb.2024.04.001">https://doi.org/10.1016/j.tpb.2024.04.001</a>
  chicago: Barton, Nicholas H, and Himani Sachdeva. “Limits to Selection on Standing
    Variation in an Asexual Population.” <i>Theoretical Population Biology</i>. Elsevier,
    2024. <a href="https://doi.org/10.1016/j.tpb.2024.04.001">https://doi.org/10.1016/j.tpb.2024.04.001</a>.
  ieee: N. H. Barton and H. Sachdeva, “Limits to selection on standing variation in
    an asexual population,” <i>Theoretical Population Biology</i>, vol. 157. Elsevier,
    pp. 129–137, 2024.
  ista: Barton NH, Sachdeva H. 2024. Limits to selection on standing variation in
    an asexual population. Theoretical Population Biology. 157, 129–137.
  mla: Barton, Nicholas H., and Himani Sachdeva. “Limits to Selection on Standing
    Variation in an Asexual Population.” <i>Theoretical Population Biology</i>, vol.
    157, Elsevier, 2024, pp. 129–37, doi:<a href="https://doi.org/10.1016/j.tpb.2024.04.001">10.1016/j.tpb.2024.04.001</a>.
  short: N.H. Barton, H. Sachdeva, Theoretical Population Biology 157 (2024) 129–137.
corr_author: '1'
date_created: 2024-05-05T22:01:03Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2025-09-04T13:56:11Z
day: '01'
ddc:
- '570'
department:
- _id: NiBa
doi: 10.1016/j.tpb.2024.04.001
external_id:
  isi:
  - '001237016800001'
  pmid:
  - '38643838'
file:
- access_level: open_access
  checksum: 78f36488d24f868d5913624e9c8d88bf
  content_type: application/pdf
  creator: dernst
  date_created: 2024-05-13T08:22:21Z
  date_updated: 2024-05-13T08:22:21Z
  file_id: '15383'
  file_name: 2024_TheorPopulationBiology_Barton.pdf
  file_size: 1098292
  relation: main_file
  success: 1
file_date_updated: 2024-05-13T08:22:21Z
has_accepted_license: '1'
intvolume: '       157'
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language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: 129-137
pmid: 1
project:
- _id: bd6958e0-d553-11ed-ba76-86eba6a76c00
  grant_number: '101055327'
  name: Understanding the evolution of continuous genomes
publication: Theoretical Population Biology
publication_identifier:
  eissn:
  - 1096-0325
  issn:
  - 0040-5809
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Limits to selection on standing variation in an asexual population
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 157
year: '2024'
...
---
OA_type: closed access
_id: '3610'
abstract:
- lang: eng
  text: For a model of diallelic loci with arbitrary epistasis, Barton and Turelli
    [2004. Effects of genetic drift on variance components under a general model of
    epistasis. Evolution 58, 2111–2132] gave results for variances among and within
    replicate lines obtained by inbreeding without selection. Here, we discuss the
    relation between their population genetic methods and classical quantitative genetic
    arguments. In particular, we consider the case of no dominance using classical
    identity by descent arguments, which generalizes their results from two alleles
    to multiple alleles. To clarify the connections between the alternative methods,
    we obtain the same results using an intermediate method, which explicitly identifies
    the statistical effects of sets of loci. We also discuss the effects of population
    bottlenecks on covariances among relatives.
article_processing_charge: No
article_type: original
author:
- first_name: William
  full_name: Hill, William
  last_name: Hill
- 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: Hill W, Barton NH, Turelli M. Prediction of effects of genetic drift on variance
    components under a general model of epistasis. <i>Theoretical Population Biology</i>.
    2006;70(1):56-62. doi:<a href="https://doi.org/10.1016/j.tpb.2005.10.001">10.1016/j.tpb.2005.10.001</a>
  apa: Hill, W., Barton, N. H., &#38; Turelli, M. (2006). Prediction of effects of
    genetic drift on variance components under a general model of epistasis. <i>Theoretical
    Population Biology</i>. Academic Press. <a href="https://doi.org/10.1016/j.tpb.2005.10.001">https://doi.org/10.1016/j.tpb.2005.10.001</a>
  chicago: Hill, William, Nicholas H Barton, and Michael Turelli. “Prediction of Effects
    of Genetic Drift on Variance Components under a General Model of Epistasis.” <i>Theoretical
    Population Biology</i>. Academic Press, 2006. <a href="https://doi.org/10.1016/j.tpb.2005.10.001">https://doi.org/10.1016/j.tpb.2005.10.001</a>.
  ieee: W. Hill, N. H. Barton, and M. Turelli, “Prediction of effects of genetic drift
    on variance components under a general model of epistasis,” <i>Theoretical Population
    Biology</i>, vol. 70, no. 1. Academic Press, pp. 56–62, 2006.
  ista: Hill W, Barton NH, Turelli M. 2006. Prediction of effects of genetic drift
    on variance components under a general model of epistasis. Theoretical Population
    Biology. 70(1), 56–62.
  mla: Hill, William, et al. “Prediction of Effects of Genetic Drift on Variance Components
    under a General Model of Epistasis.” <i>Theoretical Population Biology</i>, vol.
    70, no. 1, Academic Press, 2006, pp. 56–62, doi:<a href="https://doi.org/10.1016/j.tpb.2005.10.001">10.1016/j.tpb.2005.10.001</a>.
  short: W. Hill, N.H. Barton, M. Turelli, Theoretical Population Biology 70 (2006)
    56–62.
date_created: 2018-12-11T12:04:14Z
date_published: 2006-08-01T00:00:00Z
date_updated: 2026-08-27T14:03:43Z
day: '01'
doi: 10.1016/j.tpb.2005.10.001
extern: '1'
external_id:
  pmid:
  - '16360188'
intvolume: '        70'
issue: '1'
language:
- iso: eng
month: '08'
oa_version: None
page: 56 - 62
pmid: 1
publication: Theoretical Population Biology
publication_identifier:
  eissn:
  - 1096-0325
  issn:
  - 0040-5809
publication_status: published
publisher: Academic Press
publist_id: '2773'
status: public
title: Prediction of effects of genetic drift on variance components under a general
  model of epistasis
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 70
year: '2006'
...
---
_id: '3657'
abstract:
- lang: eng
  text: Shifts between adaptive peaks, caused by sampling drift, are involved in both
    speciation and adaptation via Wright's “shiftingbalance.” We use techniques from
    statistical mechanics to calculate the rate of such transitions for apopulation
    in a single panmictic deme and for apopulation which is continuously distributed
    over one- and two-dimensional regions. This calculation applies in the limit where
    transitions are rare. Our results indicate that stochastic divergence is feasible
    despite free gene flow, provided that neighbourhood size is low enough. In two
    dimensions, the rate of transition depends primarily on neighbourhood size N and
    only weakly on selection pressure (≈sk exp(− cN)), where k is a number determined
    by the local population structure, in contrast with the exponential dependence
    on selection pressure in one dimension (≈exp(− cN √s)) or in a single deme (≈exp(−
    cNs)). Our calculations agree with simulations of a single deme and a one-dimensional
    population.
acknowledgement: "We thank M. Shaw, J. Felsenstein, M. Kirkpatrick, S. Via, J. S.
  Jones, M. Slatkin, J. Mallet, and B. Charlesworth for their helpful comments. This
  work was supported by grants from the SERC (GR/C/91529), the University of London
  Central Research Fund, and the Nufield Foundation. \r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Shahin
  full_name: Rouhani, Shahin
  last_name: Rouhani
- 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: Rouhani S, Barton NH. Speciation and the &#38;quot;shifting balance&#38;quot;
    in a continuous population. <i>Theoretical Population Biology</i>. 1987;31(3):465-492.
    doi:<a href="https://doi.org/10.1016/0040-5809(87)90016-5">10.1016/0040-5809(87)90016-5</a>
  apa: Rouhani, S., &#38; Barton, N. H. (1987). Speciation and the &#38;quot;shifting
    balance&#38;quot; in a continuous population. <i>Theoretical Population Biology</i>.
    Elsevier. <a href="https://doi.org/10.1016/0040-5809(87)90016-5">https://doi.org/10.1016/0040-5809(87)90016-5</a>
  chicago: Rouhani, Shahin, and Nicholas H Barton. “Speciation and the &#38;quot;Shifting
    Balance&#38;quot; in a Continuous Population.” <i>Theoretical Population Biology</i>.
    Elsevier, 1987. <a href="https://doi.org/10.1016/0040-5809(87)90016-5">https://doi.org/10.1016/0040-5809(87)90016-5</a>.
  ieee: S. Rouhani and N. H. Barton, “Speciation and the &#38;quot;shifting balance&#38;quot;
    in a continuous population,” <i>Theoretical Population Biology</i>, vol. 31, no.
    3. Elsevier, pp. 465–492, 1987.
  ista: Rouhani S, Barton NH. 1987. Speciation and the &#38;quot;shifting balance&#38;quot;
    in a continuous population. Theoretical Population Biology. 31(3), 465–492.
  mla: Rouhani, Shahin, and Nicholas H. Barton. “Speciation and the &#38;quot;Shifting
    Balance&#38;quot; in a Continuous Population.” <i>Theoretical Population Biology</i>,
    vol. 31, no. 3, Elsevier, 1987, pp. 465–92, doi:<a href="https://doi.org/10.1016/0040-5809(87)90016-5">10.1016/0040-5809(87)90016-5</a>.
  short: S. Rouhani, N.H. Barton, Theoretical Population Biology 31 (1987) 465–492.
date_created: 2018-12-11T12:04:28Z
date_published: 1987-06-01T00:00:00Z
date_updated: 2022-02-04T12:30:10Z
day: '01'
doi: 10.1016/0040-5809(87)90016-5
extern: '1'
intvolume: '        31'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://www.sciencedirect.com/science/article/pii/0040580987900165?via%3Dihub
month: '06'
oa_version: None
page: 465 - 492
publication: Theoretical Population Biology
publication_identifier:
  eissn:
  - 1096-0325
  issn:
  - 0040-5809
publication_status: published
publisher: Elsevier
publist_id: '2726'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Speciation and the &quot;shifting balance&quot; in a continuous population
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 31
year: '1987'
...
---
_id: '3662'
abstract:
- lang: eng
  text: The evolution of the probabilities of genetic identity within and between
    tandemly repeated loci of a multigene family is investigated analytically and
    numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random
    genetic drift, and mutation to new alleles are incorporated. Generations are discrete
    and nonoverlapping; the diploid, monoecious population mates at random. Under
    the restriction that there is at most one crossover in the multigene family per
    individual per generation, the dependence on location of the probabilities of
    identity is treated exactly. In the “homogeneous” approximation to this “exact”
    model, end effects are disregarded; in the “exchangeable” approximation, to which
    all previous work was confined, all position dependence is neglected. Numerical
    results indicate that (i) the exchangeable and homogeneous models are both qualitatively
    correct, (ii) the exchangeable model is sometimes too inaccurate for quantitative
    conclusions, and (iii) the homogeneous model is always more accurate than the
    exchangeable one and is always sufficiently accurate for quantitative conclusions.
acknowledgement: Supported by National Science Foundation Grant DEB81-03530
article_processing_charge: No
article_type: original
author:
- first_name: Thomas
  full_name: Nagylaki, Thomas
  last_name: Nagylaki
- 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: Nagylaki T, Barton NH. Intrachromosomal gene conversion, linkage, and the evolution
    of multigene families. <i>Theoretical Population Biology</i>. 1986;29(3):407-437.
    doi:<a href="https://doi.org/10.1016/0040-5809(86)90017-1">10.1016/0040-5809(86)90017-1</a>
  apa: Nagylaki, T., &#38; Barton, N. H. (1986). Intrachromosomal gene conversion,
    linkage, and the evolution of multigene families. <i>Theoretical Population Biology</i>.
    Academic Press. <a href="https://doi.org/10.1016/0040-5809(86)90017-1">https://doi.org/10.1016/0040-5809(86)90017-1</a>
  chicago: Nagylaki, Thomas, and Nicholas H Barton. “Intrachromosomal Gene Conversion,
    Linkage, and the Evolution of Multigene Families.” <i>Theoretical Population Biology</i>.
    Academic Press, 1986. <a href="https://doi.org/10.1016/0040-5809(86)90017-1">https://doi.org/10.1016/0040-5809(86)90017-1</a>.
  ieee: T. Nagylaki and N. H. Barton, “Intrachromosomal gene conversion, linkage,
    and the evolution of multigene families,” <i>Theoretical Population Biology</i>,
    vol. 29, no. 3. Academic Press, pp. 407–437, 1986.
  ista: Nagylaki T, Barton NH. 1986. Intrachromosomal gene conversion, linkage, and
    the evolution of multigene families. Theoretical Population Biology. 29(3), 407–437.
  mla: Nagylaki, Thomas, and Nicholas H. Barton. “Intrachromosomal Gene Conversion,
    Linkage, and the Evolution of Multigene Families.” <i>Theoretical Population Biology</i>,
    vol. 29, no. 3, Academic Press, 1986, pp. 407–37, doi:<a href="https://doi.org/10.1016/0040-5809(86)90017-1">10.1016/0040-5809(86)90017-1</a>.
  short: T. Nagylaki, N.H. Barton, Theoretical Population Biology 29 (1986) 407–437.
date_created: 2018-12-11T12:04:30Z
date_published: 1986-06-01T00:00:00Z
date_updated: 2022-02-01T15:50:10Z
day: '01'
doi: 10.1016/0040-5809(86)90017-1
extern: '1'
intvolume: '        29'
issue: '3'
language:
- iso: eng
month: '06'
oa_version: None
page: 407 - 437
publication: Theoretical Population Biology
publication_identifier:
  eissn:
  - 1096-0325
  issn:
  - 0040-5809
publication_status: published
publisher: Academic Press
publist_id: '2721'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Intrachromosomal gene conversion, linkage, and the evolution of multigene families
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 29
year: '1986'
...