--- _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' ...