---
_id: '4314'
abstract:
- lang: eng
text: 'Polygenic variation can be maintained by a balance between mutation and stabilizing
selection. When the alleles responsible for variation are rare, many classes of
equilibria may be stable. The rate at which drift causes shifts between equilibria
is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1.
This integral can be found exactly, by numerical integration, or can be approximated
by assuming that the full distribution of allele frequencies is approximately
Gaussian. These methods are checked against simulations. Over a wide range of
population sizes, drift will keep the population near an equilibrium which minimizes
the genetic variance and the deviation from the selective optimum. Shifts between
equilibria in this class occur at an appreciable rate if the product of population
size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian
approximation is accurate even when the underlying distribution is strongly skewed.
Reproductive isolation evolves as populations shift to new combinations of alleles:
however, this process is slow, approaching the neutral rate (approximately mu)
in small populations.'
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 divergence of a polygenic system under stabilising selection,
mutation and drift. Genetical Research. 1989;54(1):59-78. doi:10.1017/S0016672300028378
apa: Barton, N. H. (1989). The divergence of a polygenic system under stabilising
selection, mutation and drift. Genetical Research. Cambridge University
Press. https://doi.org/10.1017/S0016672300028378
chicago: Barton, Nicholas H. “The Divergence of a Polygenic System under Stabilising
Selection, Mutation and Drift.” Genetical Research. Cambridge University
Press, 1989. https://doi.org/10.1017/S0016672300028378.
ieee: N. H. Barton, “The divergence of a polygenic system under stabilising selection,
mutation and drift,” Genetical Research, vol. 54, no. 1. Cambridge University
Press, pp. 59–78, 1989.
ista: Barton NH. 1989. The divergence of a polygenic system under stabilising selection,
mutation and drift. Genetical Research. 54(1), 59–78.
mla: Barton, Nicholas H. “The Divergence of a Polygenic System under Stabilising
Selection, Mutation and Drift.” Genetical Research, vol. 54, no. 1, Cambridge
University Press, 1989, pp. 59–78, doi:10.1017/S0016672300028378.
short: N.H. Barton, Genetical Research 54 (1989) 59–78.
date_created: 2018-12-11T12:08:12Z
date_published: 1989-08-01T00:00:00Z
date_updated: 2022-02-09T14:18:28Z
day: '01'
doi: 10.1017/S0016672300028378
extern: '1'
external_id:
pmid:
- '2806907'
intvolume: ' 54'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://www.cambridge.org/core/journals/genetics-research/article/divergence-of-a-polygenic-system-subject-to-stabilizing-selection-mutation-and-drift/95DF5B589A5C32376F1AAEE99F3200D8
month: '08'
oa_version: None
page: 59 - 78
pmid: 1
publication: Genetical Research
publication_identifier:
eissn:
- 1469-5073
issn:
- 0016-6723
publication_status: published
publisher: Cambridge University Press
publist_id: '1741'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The divergence of a polygenic system under stabilising selection, mutation
and drift
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 54
year: '1989'
...
---
_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. Genetical Research. 1987;49(2):157-174. doi:10.1017/S0016672300026951
apa: Barton, N. H., & Turelli, M. (1987). Adaptive landscapes, genetic distance,
and the evolution of quantitative characters. Genetical Research. Cambridge
University Press. https://doi.org/10.1017/S0016672300026951
chicago: Barton, Nicholas H, and Michael Turelli. “Adaptive Landscapes, Genetic
Distance, and the Evolution of Quantitative Characters.” Genetical Research.
Cambridge University Press, 1987. https://doi.org/10.1017/S0016672300026951.
ieee: N. H. Barton and M. Turelli, “Adaptive landscapes, genetic distance, and the
evolution of quantitative characters,” Genetical Research, 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.” Genetical Research, vol.
49, no. 2, Cambridge University Press, 1987, pp. 157–74, doi:10.1017/S0016672300026951.
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'
...
---
_id: '4322'
abstract:
- lang: eng
text: A method is developed for calculating the probability of establishment of
an allele which is favoured in some places, but not others, in a large subdivided
population. This method is quite general, and could be used to calculate the chance
that any system which is linear near an absorbing boundary will move away from
that boundary. The results are applied to a population distributed along one dimension.
Only mutants which arise within a distance σ/ √2s of the region in which they
are favoured stand an appreciable chance of establishment. The net chance of establishment
of mutations distributed randomly across the habitat will be decreased by gene
flow if selection against them is sufficiently strong. However, if the mutations
are only weakly deleterious outside some limited region, gene flow may increase
the net chance of establishment.
acknowledgement: "This work was supported by a grant from the Science and Engineering
Research Council (GR/D/91529). Shahin\r\nRouhani supplied the proof that no positive
solution to (6) exists when all eigenvalues are negative (Appendix);\r\nM. Slatkin,
M. Turelli, T. Nagylaki and he also gave helpful comments on 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
citation:
ama: Barton NH. The probability of establishment of an advantageous mutation in
a subdivided population. Genetical Research. 1987;50(1):35-40. doi:10.1017/S0016672300023314
apa: Barton, N. H. (1987). The probability of establishment of an advantageous mutation
in a subdivided population. Genetical Research. Cambridge University Press.
https://doi.org/10.1017/S0016672300023314
chicago: Barton, Nicholas H. “The Probability of Establishment of an Advantageous
Mutation in a Subdivided Population.” Genetical Research. Cambridge University
Press, 1987. https://doi.org/10.1017/S0016672300023314.
ieee: N. H. Barton, “The probability of establishment of an advantageous mutation
in a subdivided population,” Genetical Research, vol. 50, no. 1. Cambridge
University Press, pp. 35–40, 1987.
ista: Barton NH. 1987. The probability of establishment of an advantageous mutation
in a subdivided population. Genetical Research. 50(1), 35–40.
mla: Barton, Nicholas H. “The Probability of Establishment of an Advantageous Mutation
in a Subdivided Population.” Genetical Research, vol. 50, no. 1, Cambridge
University Press, 1987, pp. 35–40, doi:10.1017/S0016672300023314.
short: N.H. Barton, Genetical Research 50 (1987) 35–40.
date_created: 2018-12-11T12:08:15Z
date_published: 1987-01-01T00:00:00Z
date_updated: 2022-02-03T10:16:16Z
day: '01'
doi: 10.1017/S0016672300023314
extern: '1'
external_id:
pmid:
- '3653687 '
intvolume: ' 50'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 35 - 40
pmid: 1
publication: Genetical Research
publication_identifier:
eissn:
- 1469-5073
issn:
- 0016-6723
publication_status: published
publisher: Cambridge University Press
publist_id: '1725'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The probability of establishment of an advantageous mutation in a subdivided
population
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 50
year: '1987'
...
---
_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. Genetical Research. 1986;47(3):209-216.
doi:10.1017/S0016672300023156
apa: Barton, N. H. (1986). The maintenance of polygenic variation through a balance
between mutation and stabilising selection. Genetical Research. Cambridge
University Press. https://doi.org/10.1017/S0016672300023156
chicago: Barton, Nicholas H. “The Maintenance of Polygenic Variation through a Balance
between Mutation and Stabilising Selection.” Genetical Research. Cambridge
University Press, 1986. https://doi.org/10.1017/S0016672300023156.
ieee: N. H. Barton, “The maintenance of polygenic variation through a balance between
mutation and stabilising selection,” Genetical Research, 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.” Genetical Research, vol. 47,
no. 3, Cambridge University Press, 1986, pp. 209–16, doi:10.1017/S0016672300023156.
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'
...