---
_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: 2022-02-23T14:48:49Z
day: '01'
doi: 10.1016/0040-5809(90)90002-D
extern: '1'
intvolume: ' 38'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://www.sciencedirect.com/science/article/pii/004058099090002D?via%3Dihub
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: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 38
year: '1990'
...
---
_id: '3651'
abstract:
- lang: eng
text: 'It is widely held that each gene typically affects many characters, and that
each character is affected by many genes. Moreover, strong stabilizing selection
cannot act on an indefinitely large number of independent traits. This makes it
likely that heritable variation in any one trait is maintained as a side effect
of polymorphisms which have nothing to do with selection on that trait. This paper
examines the idea that variation is maintained as the pleiotropic side effect
of either deleterious mutation, or balancing selection. If mutation is responsible,
it must produce alleles which are only mildly deleterious (s & 10(-3)), but
nevertheless have significant effects on the trait. Balancing selection can readily
maintain high heritabilities; however, selection must be spread over many weakly
selected polymorphisms if large responses to artificial selection are to be possible.
In both classes of pleiotropic model, extreme phenotypes are less fit, giving
the appearance of stabilizing selection on the trait. However, it is shown that
this effect is weak (of the same order as the selection on each gene): the strong
stabilizing selection which is often observed is likely to be caused by correlations
with a limited number of directly selected traits. Possible experiments for distinguishing
the alternatives are discussed.'
acknowledgement: Thanks to JERRY COYNE, BILL HILL, LINDA PARTRIDGE, MICHAEL TURELLI,
and two anonymous reviewers for their critical comments. This work was supported
by grants from the National Science Foundation (BSR-8866548) the Science and Engineering
Research Council (GR/E/08507), and by the Institute of Theoretical Dynamics, University
of California, Davis.
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. Pleiotropic models of quantitative variation. Genetics. 1990;124(3):773-782.
doi:10.1093/genetics/124.3.773
apa: Barton, N. H. (1990). Pleiotropic models of quantitative variation. Genetics.
Genetics Society of America. https://doi.org/10.1093/genetics/124.3.773
chicago: Barton, Nicholas H. “Pleiotropic Models of Quantitative Variation.” Genetics.
Genetics Society of America, 1990. https://doi.org/10.1093/genetics/124.3.773 .
ieee: N. H. Barton, “Pleiotropic models of quantitative variation,” Genetics,
vol. 124, no. 3. Genetics Society of America, pp. 773–782, 1990.
ista: Barton NH. 1990. Pleiotropic models of quantitative variation. Genetics. 124(3),
773–782.
mla: Barton, Nicholas H. “Pleiotropic Models of Quantitative Variation.” Genetics,
vol. 124, no. 3, Genetics Society of America, 1990, pp. 773–82, doi:10.1093/genetics/124.3.773 .
short: N.H. Barton, Genetics 124 (1990) 773–782.
date_created: 2018-12-11T12:04:26Z
date_published: 1990-03-01T00:00:00Z
date_updated: 2022-02-23T10:41:43Z
day: '01'
doi: '10.1093/genetics/124.3.773 '
extern: '1'
external_id:
pmid:
- '2311921'
intvolume: ' 124'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://academic.oup.com/genetics/article/124/3/773/5999956?login=true
month: '03'
oa: 1
oa_version: Published Version
page: 773 - 782
pmid: 1
publication: Genetics
publication_identifier:
issn:
- 0016-6731
publication_status: published
publisher: Genetics Society of America
publist_id: '2732'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pleiotropic models of quantitative variation
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 124
year: '1990'
...
---
_id: '4067'
abstract:
- lang: eng
text: This paper proves an O(m 2/3 n 2/3+m+n) upper bound on the number of incidences
between m points and n hyperplanes in four dimensions, assuming all points lie
on one side of each hyperplane and the points and hyperplanes satisfy certain
natural general position conditions. This result has application to various three-dimensional
combinatorial distance problems. For example, it implies the same upper bound
for the number of bichromatic minimum distance pairs in a set of m blue and n
red points in three-dimensional space. This improves the best previous bound for
this problem.
acknowledgement: Research of the first author was supported by the National Science
Foundation under grant CCR-8714565. Work of the second author was supported by Office
of Naval Research Grants DCR-83-20085 and CCR-89-01484, and by grants from the U.S.-Israeli
Binational Science Foundation, the NCRD — the Israeli National Council for Research
and Development, and the Fund for Basic Research in Electronics, Computers and Communication
administered by the Israeli Academy of Sciences.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: 'Edelsbrunner H, Sharir M. A hyperplane Incidence problem with applications
to counting distances. In: Proceedings of the International Symposium on Algorithms.
Vol 450. Springer; 1990:419-428. doi:10.1007/3-540-52921-7_91'
apa: 'Edelsbrunner, H., & Sharir, M. (1990). A hyperplane Incidence problem
with applications to counting distances. In Proceedings of the International
Symposium on Algorithms (Vol. 450, pp. 419–428). Tokyo, Japan: Springer. https://doi.org/10.1007/3-540-52921-7_91'
chicago: Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem
with Applications to Counting Distances.” In Proceedings of the International
Symposium on Algorithms, 450:419–28. Springer, 1990. https://doi.org/10.1007/3-540-52921-7_91.
ieee: H. Edelsbrunner and M. Sharir, “A hyperplane Incidence problem with applications
to counting distances,” in Proceedings of the International Symposium on Algorithms,
Tokyo, Japan, 1990, vol. 450, pp. 419–428.
ista: Edelsbrunner H, Sharir M. 1990. A hyperplane Incidence problem with applications
to counting distances. Proceedings of the International Symposium on Algorithms.
SIGAL: Special Interest Group on Algorithms, International Symposium on Algorithms
, LNCS, vol. 450, 419–428.
mla: Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with
Applications to Counting Distances.” Proceedings of the International Symposium
on Algorithms, vol. 450, Springer, 1990, pp. 419–28, doi:10.1007/3-540-52921-7_91.
short: H. Edelsbrunner, M. Sharir, in:, Proceedings of the International Symposium
on Algorithms, Springer, 1990, pp. 419–428.
conference:
end_date: 1990-08-18
location: Tokyo, Japan
name: 'SIGAL: Special Interest Group on Algorithms, International Symposium on
Algorithms '
start_date: 1990-08-16
date_created: 2018-12-11T12:06:45Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-22T14:31:26Z
day: '01'
doi: 10.1007/3-540-52921-7_91
extern: '1'
intvolume: ' 450'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/chapter/10.1007/3-540-52921-7_91
month: '01'
oa_version: None
page: 419 - 428
publication: Proceedings of the International Symposium on Algorithms
publication_identifier:
isbn:
- 978-3-540-52921-7
publication_status: published
publisher: Springer
publist_id: '2056'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A hyperplane Incidence problem with applications to counting distances
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 450
year: '1990'
...
---
_id: '4066'
abstract:
- lang: eng
text: 'We consider several problems involving points and planes in three dimensions.
Our main results are: (i) The maximum number of faces boundingm distinct cells
in an arrangement ofn planes isO(m 2/3 n logn +n 2); we can calculatem such cells
specified by a point in each, in worst-case timeO(m 2/3 n log3 n+n 2 logn). (ii)
The maximum number of incidences betweenn planes andm vertices of their arrangement
isO(m 2/3 n logn+n 2), but this number is onlyO(m 3/5– n 4/5+2 +m+n logm), for
any>0, for any collection of points no three of which are collinear. (iii)
For an arbitrary collection ofm points, we can calculate the number of incidences
between them andn planes by a randomized algorithm whose expected time complexity
isO((m 3/4– n 3/4+3 +m) log2 n+n logn logm) for any>0. (iv) Givenm points andn
planes, we can find the plane lying immediately below each point in randomized
expected timeO([m 3/4– n 3/4+3 +m] log2 n+n logn logm) for any>0. (v) The maximum
number of facets (i.e., (d–1)-dimensional faces) boundingm distinct cells in an
arrangement ofn hyperplanes ind dimensions,d>3, isO(m 2/3 n d/3 logn+n d–1).
This is also an upper bound for the number of incidences betweenn hyperplanes
ind dimensions andm vertices of their arrangement. The combinatorial bounds in
(i) and (v) and the general bound in (ii) are almost tight.'
acknowledgement: "Supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by
NSF Grant CCR-8714565. Work on this paper by the first author has been supported
by Amoco Fnd. Fac. Dev. Comput. Sci. I-6-44862 and by NSF Grant CCR-87t4565. Work
by the third author has been supported by Office of Naval Research Grant N00014-87-K-0129,
by National Science Foundation Grant DCR-82-20085, by grants from the Digital Equipment
Corporation, and the IBM Corporation, and by a research grant from the NCRD--the
Israeli National Council for Research and Development. An abstract of this\r\npaper
has appeared in the Proceedings of the 13th International Mathematical Programming
Symposium, Tokyo, 1988, p. 147"
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: Edelsbrunner H, Guibas L, Sharir M. The complexity of many cells in arrangements
of planes and related problems. Discrete & Computational Geometry.
1990;5(1):197-216. doi:10.1007/BF02187785
apa: Edelsbrunner, H., Guibas, L., & Sharir, M. (1990). The complexity of many
cells in arrangements of planes and related problems. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/BF02187785
chicago: Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity
of Many Cells in Arrangements of Planes and Related Problems.” Discrete &
Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187785.
ieee: H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity of many cells in
arrangements of planes and related problems,” Discrete & Computational
Geometry, vol. 5, no. 1. Springer, pp. 197–216, 1990.
ista: Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity of many cells in
arrangements of planes and related problems. Discrete & Computational Geometry.
5(1), 197–216.
mla: Edelsbrunner, Herbert, et al. “The Complexity of Many Cells in Arrangements
of Planes and Related Problems.” Discrete & Computational Geometry,
vol. 5, no. 1, Springer, 1990, pp. 197–216, doi:10.1007/BF02187785.
short: H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry
5 (1990) 197–216.
date_created: 2018-12-11T12:06:44Z
date_published: 1990-03-01T00:00:00Z
date_updated: 2022-02-22T11:02:41Z
day: '01'
doi: 10.1007/BF02187785
extern: '1'
intvolume: ' 5'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02187785
month: '03'
oa_version: None
page: 197 - 216
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2054'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The complexity of many cells in arrangements of planes and related problems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '1990'
...
---
_id: '4072'
abstract:
- lang: eng
text: We show that the total number of edges ofm faces of an arrangement ofn lines
in the plane isO(m 2/3– n 2/3+2 +n) for any>0. The proof takes an algorithmic
approach, that is, we describe an algorithm for the calculation of thesem faces
and derive the upper bound from the analysis of the algorithm. The algorithm uses
randomization and its expected time complexity isO(m 2/3– n 2/3+2 logn+n logn
logm). If instead of lines we have an arrangement ofn line segments, then the
maximum number of edges ofm faces isO(m 2/3– n 2/3+2 +n (n) logm) for any>0,
where(n) is the functional inverse of Ackermann's function. We give a (randomized)
algorithm that produces these faces and takes expected timeO(m 2/3– n 2/3+2 log+n(n)
log2 n logm).
acknowledgement: The first author is pleased to acknowledge partial support by the
Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and the National Science Foundation
under Grant CCR-8714565. Work on this paper by the third author has been supported
by Office of Naval Research Grant N00014-82-K-0381, by National Science Foundation
Grant DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM
Corporation, and by a research grant from the NCRD-the Israeli National Council
for Research and Development. A preliminary version of this paper has appeared in
theProceedings of the 4th ACM Symposium on Computational Geometry, 1988, pp. 44–55.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: Edelsbrunner H, Guibas L, Sharir M. The complexity and construction of many
faces in arrangements of lines and of segments. Discrete & Computational
Geometry. 1990;5(1):161-196. doi:10.1007/BF02187784
apa: Edelsbrunner, H., Guibas, L., & Sharir, M. (1990). The complexity and construction
of many faces in arrangements of lines and of segments. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/BF02187784
chicago: Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity
and Construction of Many Faces in Arrangements of Lines and of Segments.” Discrete
& Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187784.
ieee: H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity and construction
of many faces in arrangements of lines and of segments,” Discrete & Computational
Geometry, vol. 5, no. 1. Springer, pp. 161–196, 1990.
ista: Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity and construction
of many faces in arrangements of lines and of segments. Discrete & Computational
Geometry. 5(1), 161–196.
mla: Edelsbrunner, Herbert, et al. “The Complexity and Construction of Many Faces
in Arrangements of Lines and of Segments.” Discrete & Computational Geometry,
vol. 5, no. 1, Springer, 1990, pp. 161–96, doi:10.1007/BF02187784.
short: H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry
5 (1990) 161–196.
date_created: 2018-12-11T12:06:46Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-22T09:27:30Z
day: '01'
doi: 10.1007/BF02187784
extern: '1'
intvolume: ' 5'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02187784
month: '01'
oa_version: None
page: 161 - 196
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2053'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The complexity and construction of many faces in arrangements of lines and
of segments
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '1990'
...