کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4502848 | 1320605 | 2010 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Proof of the Feldman-Karlin conjecture on the maximum number of equilibria in an evolutionary system
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کلمات کلیدی
موضوعات مرتبط
علوم زیستی و بیوفناوری
علوم کشاورزی و بیولوژیک
علوم کشاورزی و بیولوژیک (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Proof of the Feldman-Karlin conjecture on the maximum number of equilibria in an evolutionary system Proof of the Feldman-Karlin conjecture on the maximum number of equilibria in an evolutionary system](/preview/png/4502848.png)
چکیده انگلیسی
Feldman and Karlin conjectured that the number of isolated fixed points for deterministic models of viability selection and recombination among n possible haplotypes has an upper bound of 2nâ1. Here a proof is provided. The upper bound of 3nâ1 obtained by Lyubich et al. (2001) using Bézout's Theorem (1779) is reduced here to 2n through a change of representation that reduces the third-order polynomials to second order. A further reduction to 2nâ1 is obtained using the homogeneous representation of the system, which yields always one solution 'at infinity'. While the original conjecture was made for systems of selection and recombination, the results here generalize to viability selection with any arbitrary system of bi-parental transmission, which includes recombination and mutation as special cases. An example is constructed of a mutation-selection system that has 2nâ1 fixed points given any n, which shows that 2nâ1 is the sharpest possible upper bound that can be found for the general space of selection and transmission coefficients.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Theoretical Population Biology - Volume 77, Issue 4, June 2010, Pages 263-269
Journal: Theoretical Population Biology - Volume 77, Issue 4, June 2010, Pages 263-269
نویسندگان
Lee Altenberg,