TITLE:
Nucleocytoplasmic Gynodioecy
AUTHORS:
R. Doroteo, J. A. Vargas
KEYWORDS:
Population Genetics; Gynodioecy; Dynamical System; Nucleocytoplasmic Interaction; Matrix of Linear Forms
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.12,
December
3,
2013
ABSTRACT: We study the evolution of a gynodioecious species under
mixed-mating through a nucleocytoplasmic male sterility model. We consider two
cytoplasmic types and a nuclear locus with two alleles. Here, the interaction
between one cytoplasmic type and a recessive nuclear male-sterility factor gives
rise to only one female genotype, while the remaining types correspond to
hermaphroditic plants. We include two fitness paramaters: the advantageous
female fitness t of females
relative to that of hermaphrodites; and a silent and dominant cost of
restoration, that is, a diminished fitness for plants carrying a dominant
restorer gene relative to that of hermaphrodites. The parameter related to the
cost of restoration is assumed to be present on outcrossing male fertility only. We find
that every population converges to a stable population. We also determine the
nature of the attracting stable population, which could be a nucleocytoplasmic
polymorphism, a nuclear polymorphism or another population with some
genotypes absent. This depends on the position of t with respect to critical values expressed in terms of the other
parameters and also on the initial population.