Originally published as Genetics Published Articles Ahead of Print on June 18, 2006.

Genetics, Vol. 173, 2391-2398, August 2006, Copyright © 2006
doi:10.1534/genetics.106.057539

Population Models of Genomic Imprinting. II. Maternal and Fertility Selection

Hamish G. Spencer^*,1, Timothy Dorn^,2 and Thomas LoFaro

^* Allan Wilson Centre for Molecular Ecology and Evolution, Department of Zoology, University of Otago, Dunedin, 9054 New Zealand and Department of Mathematics and Computer Science, Gustavus Adolphus College, Saint Peter, Minnesota 56082-1498

¹ Corresponding author: Allan Wilson Centre for Molecular Ecology and Evolution, Department of Zoology, University of Otago, 340 Great King St., P.O. Box 56, Dunedin, 9054 New Zealand.
E-mail: h.spencer{at}otago.ac.nz

Under several hypotheses for the evolutionary origin of imprinting, genes with maternal and reproductive effects are more likely to be imprinted. We thus investigate the effect of genomic imprinting in single-locus diallelic models of maternal and fertility selection. First, the model proposed by Gavrilets for maternal selection is expanded to include the effects of genomic imprinting. This augmented model exhibits novel behavior for a single-locus model: long-period cycling between a pair of Hopf bifurcations, as well as two-cycling between conjoined pitchfork bifurcations. We also examine several special cases: complete inactivation of one allele and when the maternal and viability selection parameters are independent. Second, we extend the standard model of fertility selection to include the effects of imprinting. Imprinting destroys the "sex-symmetry" property of the standard model, dramatically increasing the number of degrees of freedom of the selection parameter set. Cycling in all these models is rare in parameter space.

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