Skip Navigation

Mathematical Medicine and Biology 2001 18(4):327-341; doi:10.1093/imammb/18.4.327
© 2001 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Vargas, J. A.
Right arrow Articles by del Castillo, R. F.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Vargas, J. A.
Right arrow Articles by del Castillo, R. F.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Genetic associations under mixed mating systems: the Bennett–Binet effect

J. A. Vargas1 and Rafael F. del Castillo2

1 Independent scholar, Constitución 204 Oaxaca, Oaxaca 68000, México 2 CIIDIR-IPN Oaxaca, Calle Hornos 1003, Xoxocotlán, Oaxaca 71230, México

Using elementary algebraic geometry and computational commutative algebra, supported by the program Macaulay2, we studied and developed operators that define the zygotic and gametic evolution under a mixed-mating system with parameters s selfing rate, r recombination rate, and g relative fitness of inbreeders, for any possible combination of initial zygotic or gametic frequencies with two alleles at each of two loci. We found that (i) the allelic frequencies are preserved in every generation; (ii) the gametic frequencies converge to values that depend exclusively on the allelic frequencies; (iii) every zygotic population converges to a population in equilibrium with double heterozygotes equally frequent; (iv) the rate of convergence decreases to arbitrary small values with sufficiently small values of r or with sufficiently large values of s and (v) as g decreases, the maximal ‘association between the two loci’ occurs with higher values of selfing. We also found generalizations for the case of several alleles at each locus.

Keywords: Bennett–Binet; two loci; mixed mating; recombination; projective space; rational map; zygotic algebra

Received 11 December 2000. Revised 19 December 2001.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.