---
_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. Theoretical Population Biology. 2024;157:129-137. doi:10.1016/j.tpb.2024.04.001
apa: Barton, N. H., & Sachdeva, H. (2024). Limits to selection on standing variation
in an asexual population. Theoretical Population Biology. Elsevier. https://doi.org/10.1016/j.tpb.2024.04.001
chicago: Barton, Nicholas H, and Himani Sachdeva. “Limits to Selection on Standing
Variation in an Asexual Population.” Theoretical Population Biology. Elsevier,
2024. https://doi.org/10.1016/j.tpb.2024.04.001.
ieee: N. H. Barton and H. Sachdeva, “Limits to selection on standing variation in
an asexual population,” Theoretical Population Biology, 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.” Theoretical Population Biology, vol.
157, Elsevier, 2024, pp. 129–37, doi:10.1016/j.tpb.2024.04.001.
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
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file_date_updated: 2024-05-13T08:22:21Z
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intvolume: ' 157'
isi: 1
language:
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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'
...
---
_id: '952'
abstract:
- lang: eng
text: A novel strategy for controlling the spread of arboviral diseases such as
dengue, Zika and chikungunya is to transform mosquito populations with virus-suppressing
Wolbachia. In general, Wolbachia transinfected into mosquitoes induce fitness
costs through lower viability or fecundity. These maternally inherited bacteria
also produce a frequency-dependent advantage for infected females by inducing
cytoplasmic incompatibility (CI), which kills the embryos produced by uninfected
females mated to infected males. These competing effects, a frequency-dependent
advantage and frequency-independent costs, produce bistable Wolbachia frequency
dynamics. Above a threshold frequency, denoted pˆ, CI drives fitness-decreasing
Wolbachia transinfections through local populations; but below pˆ, infection frequencies
tend to decline to zero. If pˆ is not too high, CI also drives spatial spread
once infections become established over sufficiently large areas. We illustrate
how simple models provide testable predictions concerning the spatial and temporal
dynamics of Wolbachia introductions, focusing on rate of spatial spread, the shape
of spreading waves, and the conditions for initiating spread from local introductions.
First, we consider the robustness of diffusion-based predictions to incorporating
two important features of wMel-Aedes aegypti biology that may be inconsistent
with the diffusion approximations, namely fast local dynamics induced by complete
CI (i.e., all embryos produced from incompatible crosses die) and long-tailed,
non-Gaussian dispersal. With complete CI, our numerical analyses show that long-tailed
dispersal changes wave-width predictions only slightly; but it can significantly
reduce wave speed relative to the diffusion prediction; it also allows smaller
local introductions to initiate spatial spread. Second, we use approximations
for pˆ and dispersal distances to predict the outcome of 2013 releases of wMel-infected
Aedes aegypti in Cairns, Australia, Third, we describe new data from Ae. aegypti
populations near Cairns, Australia that demonstrate long-distance dispersal and
provide an approximate lower bound on pˆ for wMel in northeastern Australia. Finally,
we apply our analyses to produce operational guidelines for efficient transformation
of vector populations over large areas. We demonstrate that even very slow spatial
spread, on the order of 10-20 m/month (as predicted), can produce area-wide population
transformation within a few years following initial releases covering about 20-30%
of the target area.
article_processing_charge: No
author:
- first_name: Michael
full_name: Turelli, Michael
last_name: Turelli
- 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: 'Turelli M, Barton NH. Deploying dengue-suppressing Wolbachia: Robust models
predict slow but effective spatial spread in Aedes aegypti. Theoretical Population
Biology. 2017;115:45-60. doi:10.1016/j.tpb.2017.03.003'
apa: 'Turelli, M., & Barton, N. H. (2017). Deploying dengue-suppressing Wolbachia:
Robust models predict slow but effective spatial spread in Aedes aegypti. Theoretical
Population Biology. Elsevier. https://doi.org/10.1016/j.tpb.2017.03.003'
chicago: 'Turelli, Michael, and Nicholas H Barton. “Deploying Dengue-Suppressing
Wolbachia: Robust Models Predict Slow but Effective Spatial Spread in Aedes Aegypti.”
Theoretical Population Biology. Elsevier, 2017. https://doi.org/10.1016/j.tpb.2017.03.003.'
ieee: 'M. Turelli and N. H. Barton, “Deploying dengue-suppressing Wolbachia: Robust
models predict slow but effective spatial spread in Aedes aegypti,” Theoretical
Population Biology, vol. 115. Elsevier, pp. 45–60, 2017.'
ista: 'Turelli M, Barton NH. 2017. Deploying dengue-suppressing Wolbachia: Robust
models predict slow but effective spatial spread in Aedes aegypti. Theoretical
Population Biology. 115, 45–60.'
mla: 'Turelli, Michael, and Nicholas H. Barton. “Deploying Dengue-Suppressing Wolbachia:
Robust Models Predict Slow but Effective Spatial Spread in Aedes Aegypti.” Theoretical
Population Biology, vol. 115, Elsevier, 2017, pp. 45–60, doi:10.1016/j.tpb.2017.03.003.'
short: M. Turelli, N.H. Barton, Theoretical Population Biology 115 (2017) 45–60.
date_created: 2018-12-11T11:49:22Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2025-07-10T12:01:49Z
day: '01'
ddc:
- '576'
department:
- _id: NiBa
doi: 10.1016/j.tpb.2017.03.003
external_id:
pmid:
- '28411063'
file:
- access_level: open_access
checksum: 9aeff86fa7de69f7a15cf4fc60d57d01
content_type: application/pdf
creator: dernst
date_created: 2019-04-17T06:39:45Z
date_updated: 2020-07-14T12:48:16Z
file_id: '6327'
file_name: 2017_TheoreticalPopulationBio_Turelli.pdf
file_size: 2073856
relation: main_file
file_date_updated: 2020-07-14T12:48:16Z
has_accepted_license: '1'
intvolume: ' 115'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '06'
oa: 1
oa_version: Submitted Version
page: 45 - 60
pmid: 1
publication: Theoretical Population Biology
publication_identifier:
issn:
- 0040-5809
publication_status: published
publisher: Elsevier
publist_id: '6463'
pubrep_id: '972'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Deploying dengue-suppressing Wolbachia: Robust models predict slow but effective
spatial spread in Aedes aegypti'
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
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 115
year: '2017'
...
---
_id: '626'
abstract:
- lang: eng
text: 'Our focus here is on the infinitesimal model. In this model, one or several
quantitative traits are described as the sum of a genetic and a non-genetic component,
the first being distributed within families as a normal random variable centred
at the average of the parental genetic components, and with a variance independent
of the parental traits. Thus, the variance that segregates within families is
not perturbed by selection, and can be predicted from the variance components.
This does not necessarily imply that the trait distribution across the whole population
should be Gaussian, and indeed selection or population structure may have a substantial
effect on the overall trait distribution. One of our main aims is to identify
some general conditions on the allelic effects for the infinitesimal model to
be accurate. We first review the long history of the infinitesimal model in quantitative
genetics. Then we formulate the model at the phenotypic level in terms of individual
trait values and relationships between individuals, but including different evolutionary
processes: genetic drift, recombination, selection, mutation, population structure,
…. We give a range of examples of its application to evolutionary questions related
to stabilising selection, assortative mating, effective population size and response
to selection, habitat preference and speciation. We provide a mathematical justification
of the model as the limit as the number M of underlying loci tends to infinity
of a model with Mendelian inheritance, mutation and environmental noise, when
the genetic component of the trait is purely additive. We also show how the model
generalises to include epistatic effects. We prove in particular that, within
each family, the genetic components of the individual trait values in the current
generation are indeed normally distributed with a variance independent of ancestral
traits, up to an error of order 1∕M. Simulations suggest that in some cases the
convergence may be as fast as 1∕M.'
article_processing_charge: No
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: Alison
full_name: Etheridge, Alison
last_name: Etheridge
- first_name: Amandine
full_name: Véber, Amandine
last_name: Véber
citation:
ama: 'Barton NH, Etheridge A, Véber A. The infinitesimal model: Definition derivation
and implications. Theoretical Population Biology. 2017;118:50-73. doi:10.1016/j.tpb.2017.06.001'
apa: 'Barton, N. H., Etheridge, A., & Véber, A. (2017). The infinitesimal model:
Definition derivation and implications. Theoretical Population Biology.
Academic Press. https://doi.org/10.1016/j.tpb.2017.06.001'
chicago: 'Barton, Nicholas H, Alison Etheridge, and Amandine Véber. “The Infinitesimal
Model: Definition Derivation and Implications.” Theoretical Population Biology.
Academic Press, 2017. https://doi.org/10.1016/j.tpb.2017.06.001.'
ieee: 'N. H. Barton, A. Etheridge, and A. Véber, “The infinitesimal model: Definition
derivation and implications,” Theoretical Population Biology, vol. 118.
Academic Press, pp. 50–73, 2017.'
ista: 'Barton NH, Etheridge A, Véber A. 2017. The infinitesimal model: Definition
derivation and implications. Theoretical Population Biology. 118, 50–73.'
mla: 'Barton, Nicholas H., et al. “The Infinitesimal Model: Definition Derivation
and Implications.” Theoretical Population Biology, vol. 118, Academic Press,
2017, pp. 50–73, doi:10.1016/j.tpb.2017.06.001.'
short: N.H. Barton, A. Etheridge, A. Véber, Theoretical Population Biology 118 (2017)
50–73.
corr_author: '1'
date_created: 2018-12-11T11:47:34Z
date_published: 2017-12-01T00:00:00Z
date_updated: 2025-09-11T07:29:31Z
day: '01'
ddc:
- '576'
department:
- _id: NiBa
doi: 10.1016/j.tpb.2017.06.001
ec_funded: 1
external_id:
isi:
- '000417668700005'
file:
- access_level: open_access
checksum: 7dd02bfcfe8f244f4a6c19091aedf2c8
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:45Z
date_updated: 2020-07-14T12:47:25Z
file_id: '4964'
file_name: IST-2017-908-v1+1_1-s2.0-S0040580917300886-main_1_.pdf
file_size: 1133924
relation: main_file
file_date_updated: 2020-07-14T12:47:25Z
has_accepted_license: '1'
intvolume: ' 118'
isi: 1
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 50 - 73
project:
- _id: 25B07788-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '250152'
name: Limits to selection in biology and in evolutionary computation
publication: Theoretical Population Biology
publication_identifier:
issn:
- 0040-5809
publication_status: published
publisher: Academic Press
publist_id: '7169'
pubrep_id: '908'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The infinitesimal model: Definition derivation and implications'
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: 118
year: '2017'
...
---
_id: '4263'
abstract:
- lang: eng
text: 'We introduce a general recursion for the probability of identity in state
of two individuals sampled from a population subject to mutation, migration, and
random drift in a two-dimensional continuum. The recursion allows for the interactions
induced by density-dependent regulation of the population, which are inevitable
in a continuous population. We give explicit series expansions for large neighbourhood
size and for low mutation rates respectively and investigate the accuracy of the
classical Malécot formula for these general models. When neighbourhood size is
small, this formula does not give the identity even over large scales. However,
for large neighbourhood size, it is an accurate approximation which summarises
the local population structure in terms of three quantities: the effective dispersal
rate, σe; the effective population density, ρe; and a local scale, κ, at which
local interactions become significant. The results are illustrated by simulations.'
acknowledgement: This work was supported by grants from the EPSRC (GR/L10048 and an
advanced fellowship for A.M.E.) and NERC (GR3/11635) and by the Darwin Trust of
Edinburgh. We thank Anja Sturm for her assistance with the project and anonymous
reviewers for helpful comments. This paper is dedicated to Charlotte, A.M.E.’s daughter
born during the gestation of the manuscript.
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: Frantz
full_name: Depaulis, Frantz
last_name: Depaulis
- first_name: Alison
full_name: Etheridge, Alison
last_name: Etheridge
citation:
ama: Barton NH, Depaulis F, Etheridge A. Neutral evolution in spatially continuous
populations. Theoretical Population Biology. 2002;61(1):31-48. doi:10.1006/tpbi.2001.1557
apa: Barton, N. H., Depaulis, F., & Etheridge, A. (2002). Neutral evolution
in spatially continuous populations. Theoretical Population Biology. Academic
Press. https://doi.org/10.1006/tpbi.2001.1557
chicago: Barton, Nicholas H, Frantz Depaulis, and Alison Etheridge. “Neutral Evolution
in Spatially Continuous Populations.” Theoretical Population Biology. Academic
Press, 2002. https://doi.org/10.1006/tpbi.2001.1557.
ieee: N. H. Barton, F. Depaulis, and A. Etheridge, “Neutral evolution in spatially
continuous populations,” Theoretical Population Biology, vol. 61, no. 1.
Academic Press, pp. 31–48, 2002.
ista: Barton NH, Depaulis F, Etheridge A. 2002. Neutral evolution in spatially continuous
populations. Theoretical Population Biology. 61(1), 31–48.
mla: Barton, Nicholas H., et al. “Neutral Evolution in Spatially Continuous Populations.”
Theoretical Population Biology, vol. 61, no. 1, Academic Press, 2002, pp.
31–48, doi:10.1006/tpbi.2001.1557.
short: N.H. Barton, F. Depaulis, A. Etheridge, Theoretical Population Biology 61
(2002) 31–48.
date_created: 2018-12-11T12:07:55Z
date_published: 2002-02-01T00:00:00Z
date_updated: 2023-06-06T09:57:49Z
day: '01'
doi: 10.1006/tpbi.2001.1557
extern: '1'
external_id:
pmid:
- '11895381'
intvolume: ' 61'
issue: '1'
language:
- iso: eng
month: '02'
oa_version: None
page: 31 - 48
pmid: 1
publication: Theoretical Population Biology
publication_identifier:
issn:
- 0040-5809
publication_status: published
publisher: Academic Press
publist_id: '1830'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Neutral evolution in spatially continuous populations
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 61
year: '2002'
...
---
_id: '4272'
abstract:
- lang: eng
text: 'Analysis of multilocus evolution is usually intractable for more than n ~
10 genes, because the frequencies of very large numbers of genotypes must be followed.
An exact analysis of up to n ~ 100 loci is feasible for a symmetrical model, in
which a set of unlinked loci segregate for two alleles (labeled ''0'' and ''1'')
with interchangeable effects on fitness. All haploid genotypes with the same number
of 1 alleles can then remain equally frequent. However, such a symmetrical solution
may be unstable: for example, under stabilizing selection, populations tend to
fix any one genotype which approaches the optimum. Here, we show how the 2'' x
2'' stability matrix can be decomposed into a set of matrices, each no larger
than n x n. This allows the stability of symmetrical solutions to be determined.
We apply the method to stabilizing and disruptive selection in a single deme and
to selection against heterozygotes in a linear cline. (C) 2000 Academic Press.'
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: Max
full_name: Shpak, Max
last_name: Shpak
citation:
ama: Barton NH, Shpak M. The stability of symmetrical solutions to polygenic models.
Theoretical Population Biology. 2000;57(3):249-263. doi:10.1006/tpbi.2000.1455
apa: Barton, N. H., & Shpak, M. (2000). The stability of symmetrical solutions
to polygenic models. Theoretical Population Biology. Academic Press. https://doi.org/10.1006/tpbi.2000.1455
chicago: Barton, Nicholas H, and Max Shpak. “The Stability of Symmetrical Solutions
to Polygenic Models.” Theoretical Population Biology. Academic Press, 2000.
https://doi.org/10.1006/tpbi.2000.1455.
ieee: N. H. Barton and M. Shpak, “The stability of symmetrical solutions to polygenic
models,” Theoretical Population Biology, vol. 57, no. 3. Academic Press,
pp. 249–263, 2000.
ista: Barton NH, Shpak M. 2000. The stability of symmetrical solutions to polygenic
models. Theoretical Population Biology. 57(3), 249–263.
mla: Barton, Nicholas H., and Max Shpak. “The Stability of Symmetrical Solutions
to Polygenic Models.” Theoretical Population Biology, vol. 57, no. 3, Academic
Press, 2000, pp. 249–63, doi:10.1006/tpbi.2000.1455.
short: N.H. Barton, M. Shpak, Theoretical Population Biology 57 (2000) 249–263.
date_created: 2018-12-11T12:07:58Z
date_published: 2000-05-01T00:00:00Z
date_updated: 2023-04-19T12:36:39Z
day: '01'
doi: 10.1006/tpbi.2000.1455
extern: '1'
external_id:
pmid:
- '10828217'
intvolume: ' 57'
issue: '3'
language:
- iso: eng
month: '05'
oa_version: None
page: 249 - 263
pmid: 1
publication: Theoretical Population Biology
publication_identifier:
issn:
- 0040-5809
publication_status: published
publisher: Academic Press
publist_id: '1820'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The stability of symmetrical solutions to polygenic models
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 57
year: '2000'
...
---
_id: '3649'
abstract:
- lang: eng
text: Selection on polygenic characters is generally analyzed by statistical methods
that assume a Gaussian (normal) distribution of breeding values. We present an
alternative analysis based on multilocus population genetics. We use a general
representation of selection, recombination, and drift to analyze an idealized
polygenic system in which all genetic effects are additive (i.e., both dominance
and epistasis are absent), but no assumptions are made about the distribution
of breeding values or the numbers of loci or alleles. Our analysis produces three
results. First, our equations reproduce the standard recursions for the mean and
additive variance if breeding values are Gaussian; but they also reveal how non-Gaussian
distributions of breeding values will alter these dynamics. Second, an approximation
valid for weak selection shows that even if genetic variance is attributable to
an effectively infinite number of loci with only additive effects, selection will
generally drive the distribution of breeding values away from a Gaussian distribution
by creating multilocus linkage disequilibria. Long-term dynamics of means can
depart substantially from the predictions of the standard selection recursions,
but the discrepancy may often be negligible for short-term selection. Third, by
including mutation, we show that, for realistic parameter values, linkage disequilibrium
has little effect on the amount of additive variance maintained at an equilibrium
between stabilizing selection and mutation. Each of these analytical results is
supported by numerical calculations.
acknowledgement: 'We thank R. Burger, J. A. Coyne, W. G. Hill, A. A. Hoffmann, J.
H. Gillespie, M. Slatkin, T. Nagylaki and Z.-B. Zeng for helpful discussions and
comments on earlier drafts. Our research is supported by grants from the National
Science Foundation (BSR-8866548), the Science and Engineering Research Council,
and the Institute of Theoretical Dynamics at UCD. '
article_processing_charge: No
article_type: original
author:
- first_name: Michael
full_name: Turelli, Michael
last_name: Turelli
- 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: Turelli M, Barton NH. Dynamics of polygenic characters under selection. Theoretical
Population Biology. 1990;38(1):1-57. doi:10.1016/0040-5809(90)90002-D
apa: Turelli, M., & Barton, N. H. (1990). Dynamics of polygenic characters under
selection. Theoretical Population Biology. Academic Press. https://doi.org/10.1016/0040-5809(90)90002-D
chicago: Turelli, Michael, and Nicholas H Barton. “Dynamics of Polygenic Characters
under Selection.” Theoretical Population Biology. Academic Press, 1990.
https://doi.org/10.1016/0040-5809(90)90002-D.
ieee: M. Turelli and N. H. Barton, “Dynamics of polygenic characters under selection,”
Theoretical Population Biology, vol. 38, no. 1. Academic Press, pp. 1–57,
1990.
ista: Turelli M, Barton NH. 1990. Dynamics of polygenic characters under selection.
Theoretical Population Biology. 38(1), 1–57.
mla: Turelli, Michael, and Nicholas H. Barton. “Dynamics of Polygenic Characters
under Selection.” Theoretical Population Biology, vol. 38, no. 1, Academic
Press, 1990, pp. 1–57, doi:10.1016/0040-5809(90)90002-D.
short: M. Turelli, N.H. Barton, Theoretical Population Biology 38 (1990) 1–57.
date_created: 2018-12-11T12:04:26Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2026-03-16T13:25:00Z
day: '01'
doi: 10.1016/0040-5809(90)90002-D
extern: '1'
intvolume: ' 38'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 1 - 57
publication: Theoretical Population Biology
publication_identifier:
issn:
- 0040-5809
publication_status: published
publisher: Academic Press
publist_id: '2734'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dynamics of polygenic characters under selection
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '1990'
...
---
_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 "shifting balance"
in a continuous population. Theoretical Population Biology. 1987;31(3):465-492.
doi:10.1016/0040-5809(87)90016-5
apa: Rouhani, S., & Barton, N. H. (1987). Speciation and the "shifting
balance" in a continuous population. Theoretical Population Biology.
Elsevier. https://doi.org/10.1016/0040-5809(87)90016-5
chicago: Rouhani, Shahin, and Nicholas H Barton. “Speciation and the "Shifting
Balance" in a Continuous Population.” Theoretical Population Biology.
Elsevier, 1987. https://doi.org/10.1016/0040-5809(87)90016-5.
ieee: S. Rouhani and N. H. Barton, “Speciation and the "shifting balance"
in a continuous population,” Theoretical Population Biology, vol. 31, no.
3. Elsevier, pp. 465–492, 1987.
ista: Rouhani S, Barton NH. 1987. Speciation and the "shifting balance"
in a continuous population. Theoretical Population Biology. 31(3), 465–492.
mla: Rouhani, Shahin, and Nicholas H. Barton. “Speciation and the "Shifting
Balance" in a Continuous Population.” Theoretical Population Biology,
vol. 31, no. 3, Elsevier, 1987, pp. 465–92, doi:10.1016/0040-5809(87)90016-5.
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 "shifting balance" 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. Theoretical Population Biology. 1986;29(3):407-437.
doi:10.1016/0040-5809(86)90017-1
apa: Nagylaki, T., & Barton, N. H. (1986). Intrachromosomal gene conversion,
linkage, and the evolution of multigene families. Theoretical Population Biology.
Academic Press. https://doi.org/10.1016/0040-5809(86)90017-1
chicago: Nagylaki, Thomas, and Nicholas H Barton. “Intrachromosomal Gene Conversion,
Linkage, and the Evolution of Multigene Families.” Theoretical Population Biology.
Academic Press, 1986. https://doi.org/10.1016/0040-5809(86)90017-1.
ieee: T. Nagylaki and N. H. Barton, “Intrachromosomal gene conversion, linkage,
and the evolution of multigene families,” Theoretical Population Biology,
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.” Theoretical Population Biology,
vol. 29, no. 3, Academic Press, 1986, pp. 407–37, doi:10.1016/0040-5809(86)90017-1.
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'
...