---
_id: '4231'
abstract:
- lang: eng
text: The evolution of quantitative characters depends on the frequencies of the
alleles involved, yet these frequencies cannot usually be measured. Previous groups
have proposed an approximation to the dynamics of quantitative traits, based on
an analogy with statistical mechanics. We present a modified version of that approach,
which makes the analogy more precise and applies quite generally to describe the
evolution of allele frequencies. We calculate explicitly how the macroscopic quantities
(i.e., quantities that depend on the quantitative trait) depend on evolutionary
forces, in a way that is independent of the microscopic details. We first show
that the stationary distribution of allele frequencies under drift, selection,
and mutation maximizes a certain measure of entropy, subject to constraints on
the expectation of observable quantities. We then approximate the dynamical changes
in these expectations, assuming that the distribution of allele frequencies always
maximizes entropy, conditional on the expected values. When applied to directional
selection on an additive trait, this gives a very good approximation to the evolution
of the trait mean and the genetic variance, when the number of mutations per generation
is sufficiently high (4Nμ > 1). We show how the method can be modified for
small mutation rates (4Nμ → 0). We outline how this method describes epistatic
interactions as, for example, with stabilizing selection.
acknowledgement: "N.B. was supported by the Engineering and Physical Sciences Research
Council (GR/T11753 and GR/T19537) and by the Royal Society.\r\nWe are grateful to
Ellen Baake for helping to initiate this project and for her comments on this manuscript.
We also thank Michael Turelli for his comments on the manuscript and I. Pen for
discussions and support in this project. This project was a result of a collaboration
supported by the European Science Foundation grant “Integrating population genetics
and conservation biology.” "
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: Harold
full_name: De Vladar, Harold
last_name: De Vladar
citation:
ama: Barton NH, De Vladar H. Statistical mechanics and the evolution of polygenic
quantitative traits. Genetics. 2009;181(3):997-1011. doi:10.1534/genetics.108.099309
apa: Barton, N. H., & De Vladar, H. (2009). Statistical mechanics and the evolution
of polygenic quantitative traits. Genetics. Genetics Society of America.
https://doi.org/10.1534/genetics.108.099309
chicago: Barton, Nicholas H, and Harold De Vladar. “Statistical Mechanics and the
Evolution of Polygenic Quantitative Traits.” Genetics. Genetics Society
of America, 2009. https://doi.org/10.1534/genetics.108.099309.
ieee: N. H. Barton and H. De Vladar, “Statistical mechanics and the evolution of
polygenic quantitative traits,” Genetics, vol. 181, no. 3. Genetics Society
of America, pp. 997–1011, 2009.
ista: Barton NH, De Vladar H. 2009. Statistical mechanics and the evolution of polygenic
quantitative traits. Genetics. 181(3), 997–1011.
mla: Barton, Nicholas H., and Harold De Vladar. “Statistical Mechanics and the Evolution
of Polygenic Quantitative Traits.” Genetics, vol. 181, no. 3, Genetics
Society of America, 2009, pp. 997–1011, doi:10.1534/genetics.108.099309.
short: N.H. Barton, H. De Vladar, Genetics 181 (2009) 997–1011.
corr_author: '1'
date_created: 2018-12-11T12:07:44Z
date_published: 2009-03-01T00:00:00Z
date_updated: 2025-09-30T09:52:35Z
day: '01'
department:
- _id: NiBa
doi: 10.1534/genetics.108.099309
external_id:
isi:
- '000270213500018'
intvolume: ' 181'
isi: 1
issue: '3'
language:
- iso: eng
month: '03'
oa_version: None
page: 997 - 1011
publication: Genetics
publication_status: published
publisher: Genetics Society of America
publist_id: '1882'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Statistical mechanics and the evolution of polygenic quantitative traits
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 181
year: '2009'
...
---
_id: '4242'
abstract:
- lang: eng
text: 'Felsenstein distinguished two ways by which selection can directly strengthen
isolation. First, a modifier that strengthens prezygotic isolation can be favored
everywhere. This fits with the traditional view of reinforcement as an adaptation
to reduce deleterious hybridization by strengthening assortative mating. Second,
selection can favor association between different incompatibilities, despite recombination.
We generalize this “two allele” model to follow associations among any number
of incompatibilities, which may include both assortment and hybrid inviability.
Our key argument is that this process, of coupling between incompatibilities,
may be quite different from the usual view of reinforcement: strong isolation
can evolve through the coupling of any kind of incompatibility, whether prezygotic
or postzygotic. Single locus incompatibilities become coupled because associations
between them increase the variance in compatibility, which in turn increases mean
fitness if there is positive epistasis. Multiple incompatibilities, each maintained
by epistasis, can become coupled in the same way. In contrast, a single-locus
incompatibility can become coupled with loci that reduce the viability of haploid
hybrids because this reduces harmful recombination. We obtain simple approximations
for the limits of tight linkage, and strong assortment, and show how assortment
alleles can invade through associations with other components of reproductive
isolation.'
acknowledgement: "This work was supported by a Royal Society/Wolfson Research Merit
award, and by a grant from the Natural Environment Research Council.\r\nWe are very
grateful for insightful comments from S. P. Otto, and for helpful suggestions from
the referees and the Associate Editor, Maria Servedio."
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: Maria
full_name: De Cara, Maria
last_name: De Cara
citation:
ama: Barton NH, De Cara M. The evolution of strong reproductive isolation. Evolution;
International Journal of Organic Evolution. 2009;63(5):1171-1190. doi:10.1111/j.1558-5646.2009.00622.x
apa: Barton, N. H., & De Cara, M. (2009). The evolution of strong reproductive
isolation. Evolution; International Journal of Organic Evolution. Wiley.
https://doi.org/10.1111/j.1558-5646.2009.00622.x
chicago: Barton, Nicholas H, and Maria De Cara. “The Evolution of Strong Reproductive
Isolation.” Evolution; International Journal of Organic Evolution. Wiley,
2009. https://doi.org/10.1111/j.1558-5646.2009.00622.x.
ieee: N. H. Barton and M. De Cara, “The evolution of strong reproductive isolation,”
Evolution; International Journal of Organic Evolution, vol. 63, no. 5.
Wiley, pp. 1171–1190, 2009.
ista: Barton NH, De Cara M. 2009. The evolution of strong reproductive isolation.
Evolution; International Journal of Organic Evolution. 63(5), 1171–1190.
mla: Barton, Nicholas H., and Maria De Cara. “The Evolution of Strong Reproductive
Isolation.” Evolution; International Journal of Organic Evolution, vol.
63, no. 5, Wiley, 2009, pp. 1171–90, doi:10.1111/j.1558-5646.2009.00622.x.
short: N.H. Barton, M. De Cara, Evolution; International Journal of Organic Evolution
63 (2009) 1171–1190.
corr_author: '1'
date_created: 2018-12-11T12:07:48Z
date_published: 2009-05-01T00:00:00Z
date_updated: 2025-09-30T09:52:11Z
day: '01'
ddc:
- '570'
department:
- _id: NiBa
doi: 10.1111/j.1558-5646.2009.00622.x
external_id:
isi:
- '000265145800006'
file:
- access_level: open_access
checksum: 1920d2e25ef335833764256c1a47bbfb
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:46Z
date_updated: 2020-07-14T12:46:25Z
file_id: '4903'
file_name: IST-2016-551-v1+1_BartonDeCaraRevNew.pdf
file_size: 720913
relation: main_file
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checksum: c1c51bbc10d4f328fc96fc5b0e5dc25d
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:47Z
date_updated: 2020-07-14T12:46:25Z
file_id: '4904'
file_name: IST-2016-551-v1+2_BartonDeCaraRevNewSI.pdf
file_size: 290160
relation: main_file
file_date_updated: 2020-07-14T12:46:25Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Submitted Version
page: 1171 - 1190
publication: Evolution; International Journal of Organic Evolution
publication_status: published
publisher: Wiley
publist_id: '1866'
pubrep_id: '551'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The evolution of strong reproductive isolation
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 63
year: '2009'
...
---
_id: '3870'
abstract:
- lang: eng
text: Games on graphs with omega-regular objectives provide a model for the control
and synthesis of reactive systems. Every omega-regular objective can be decomposed
into a safety part and a liveness part. The liveness part ensures that something
good happens “eventually.” Two main strengths of the classical, infinite-limit
formulation of liveness are robustness (independence from the granularity of transitions)
and simplicity (abstraction of complicated time bounds). However, the classical
liveness formulation suffers from the drawback that the time until something good
happens may be unbounded. A stronger formulation of liveness, so-called finitary
liveness, overcomes this drawback, while still retaining robustness and simplicity.
Finitary liveness requires that there exists an unknown, fixed bound b such that
something good happens within b transitions. While for one-shot liveness (reachability)
objectives, classical and finitary liveness coincide, for repeated liveness (Buchi)
objectives, the finitary formulation is strictly stronger. In this work we study
games with finitary parity and Streett objectives. We prove the determinacy of
these games, present algorithms for solving these games, and characterize the
memory requirements of winning strategies. We show that finitary parity games
can be solved in polynomial time, which is not known for infinitary parity games.
For finitary Streett games, we give an EXPTIME algorithm and show that the problem
is NP-hard. Our algorithms can be used, for example, for synthesizing controllers
that do not let the response time of a system increase without bound.
acknowledgement: "This research was supported in part by the AFOSR MURI grant F49620-00-1-0327,
the NSF grants CCR-0132780, CNS-0720884, and CCR- 225610, by the Swiss National
Science Foundation, by the COMBEST project of the European Union, and EU-TMR network
Games.\r\nWe thank anonymous reviewers for useful comments."
article_number: '1'
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Florian
full_name: Horn, Florian
id: 37327ACE-F248-11E8-B48F-1D18A9856A87
last_name: Horn
citation:
ama: Chatterjee K, Henzinger TA, Horn F. Finitary winning in omega-regular games.
ACM Transactions on Computational Logic. 2009;11(1). doi:10.1145/1614431.1614432
apa: Chatterjee, K., Henzinger, T. A., & Horn, F. (2009). Finitary winning in
omega-regular games. ACM Transactions on Computational Logic. ACM. https://doi.org/10.1145/1614431.1614432
chicago: Chatterjee, Krishnendu, Thomas A Henzinger, and Florian Horn. “Finitary
Winning in Omega-Regular Games.” ACM Transactions on Computational Logic.
ACM, 2009. https://doi.org/10.1145/1614431.1614432.
ieee: K. Chatterjee, T. A. Henzinger, and F. Horn, “Finitary winning in omega-regular
games,” ACM Transactions on Computational Logic, vol. 11, no. 1. ACM, 2009.
ista: Chatterjee K, Henzinger TA, Horn F. 2009. Finitary winning in omega-regular
games. ACM Transactions on Computational Logic. 11(1), 1.
mla: Chatterjee, Krishnendu, et al. “Finitary Winning in Omega-Regular Games.” ACM
Transactions on Computational Logic, vol. 11, no. 1, 1, ACM, 2009, doi:10.1145/1614431.1614432.
short: K. Chatterjee, T.A. Henzinger, F. Horn, ACM Transactions on Computational
Logic 11 (2009).
corr_author: '1'
das_tickbox: '1'
date_created: 2018-12-11T12:05:37Z
date_published: 2009-10-01T00:00:00Z
date_updated: 2026-07-07T14:02:53Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.1145/1614431.1614432
ec_funded: 1
external_id:
isi:
- '000272039900001'
file:
- access_level: open_access
checksum: 139c4586d24f11e5da31fb3a0cf96ef4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:08Z
date_updated: 2020-07-14T12:46:20Z
file_id: '5125'
file_name: IST-2012-53-v1+1_Finitary_winning_in_omega-regular_games.pdf
file_size: 180082
relation: main_file
file_date_updated: 2020-07-14T12:46:20Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
issue: '1'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Submitted Version
project:
- _id: 25EFB36C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '215543'
name: COMponent-Based Embedded Systems design Techniques
publication: ACM Transactions on Computational Logic
publication_status: published
publisher: ACM
publist_id: '2309'
pubrep_id: '53'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finitary winning in omega-regular games
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2009'
...
---
_id: '517'
article_processing_charge: No
article_type: comment
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. Identity and coalescence in structured populations: A commentary
on “Inbreeding coefficients and coalescence times” by Montgomery Slatkin. Genetics
Research. 2008;89(5-6):475-477. doi:10.1017/S0016672308009683'
apa: 'Barton, N. H. (2008). Identity and coalescence in structured populations:
A commentary on “Inbreeding coefficients and coalescence times” by Montgomery
Slatkin. Genetics Research. Cambridge University Press. https://doi.org/10.1017/S0016672308009683'
chicago: 'Barton, Nicholas H. “Identity and Coalescence in Structured Populations:
A Commentary on ‘Inbreeding Coefficients and Coalescence Times’ by Montgomery
Slatkin.” Genetics Research. Cambridge University Press, 2008. https://doi.org/10.1017/S0016672308009683.'
ieee: 'N. H. Barton, “Identity and coalescence in structured populations: A commentary
on ‘Inbreeding coefficients and coalescence times’ by Montgomery Slatkin,” Genetics
Research, vol. 89, no. 5–6. Cambridge University Press, pp. 475–477, 2008.'
ista: 'Barton NH. 2008. Identity and coalescence in structured populations: A commentary
on ‘Inbreeding coefficients and coalescence times’ by Montgomery Slatkin. Genetics
Research. 89(5–6), 475–477.'
mla: 'Barton, Nicholas H. “Identity and Coalescence in Structured Populations: A
Commentary on ‘Inbreeding Coefficients and Coalescence Times’ by Montgomery Slatkin.”
Genetics Research, vol. 89, no. 5–6, Cambridge University Press, 2008,
pp. 475–77, doi:10.1017/S0016672308009683.'
short: N.H. Barton, Genetics Research 89 (2008) 475–477.
date_created: 2018-12-11T11:46:55Z
date_published: 2008-10-29T00:00:00Z
date_updated: 2026-04-29T07:15:43Z
day: '29'
department:
- _id: NiBa
doi: 10.1017/S0016672308009683
external_id:
isi:
- '000207048900023'
intvolume: ' 89'
isi: 1
issue: 5-6
language:
- iso: eng
month: '10'
oa_version: None
page: 475 - 477
publication: Genetics Research
publication_status: published
publisher: Cambridge University Press
publist_id: '7302'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Identity and coalescence in structured populations: A commentary on ''Inbreeding
coefficients and coalescence times'' by Montgomery Slatkin'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 89
year: '2008'
...