Nucleocytoplasmic Gynodioecy

Affiliation(s)

Departamento de Ciencias Básicas, Instituto Tecnológico de Oaxaca, Oaxaca, México.

CIIDIR-Oaxaca, Instituto Politécnico Nacional, Xoxocotlán, México.

Departamento de Ciencias Básicas, Instituto Tecnológico de Oaxaca, Oaxaca, México.

CIIDIR-Oaxaca, Instituto Politécnico Nacional, Xoxocotlán, México.

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.

Cite this paper

Doroteo, R. and Vargas, J. (2013) Nucleocytoplasmic Gynodioecy.*Applied Mathematics*, **4**, 1658-1668. doi: 10.4236/am.2013.412226.

Doroteo, R. and Vargas, J. (2013) Nucleocytoplasmic Gynodioecy.

References

[1] E. Caspari, S. Watson and W. Smith, “The Influence of Cytoplasmic Pollen Sterility on Gene Exchange between Population,” Genetics, Vol. 53, 1966, pp. 741-746.

http://www.genetics.org/content/53/4/741.full.pdf

[2] D. Charlesworth and F.R. Ganders, “The Population Genetics of Gynodioecy with Cytoplasmic-Genic Male-Sterility,” Heredity, Vol. 43, 1979, pp. 213-218.

http://dx.doi.org/10.1038/hdy.1979.76

[3] G. S. Watson and E. Caspari, “The Behavior of Cytoplasmic Pollen Sterility in Populations,” Evolution, Vol. 14, No. 1, 1960, pp. 56-63.

http://dx.doi.org/10.2307/2405922

[4] M. F. Bailey, L. F. Delph and C. M. Lively, “Modelling Gynodioecy: Novel Scenarios for Maintaining Polymorphism,” The American Naturalist, Vol. 161, No. 5, 2003, pp. 762-776.

http://dx.doi.org/10.1086/374803

[5] M. Dufay, P. Touzet, S. Maurice and J. Cuguen, “Modelling the Maintenance of Male-Fertile Cytoplasm in a Gynodioecious Population,” Heredity, Vol. 99, 2007, pp. 349-356.

http://dx.doi.org/10.1038/sj.hdy.6801009

[6] P. H. Gouyon, F. Vichot and J. M. M. van Damme, “Nuclear-Cytoplasmic Male Sterility: Single-Point Equilibria versus Limit Cycles,” The American Naturalist, Vol. 134, No. 4, 1991, pp. 498-513.

http://www.jstor.org/discover/10.2307/2462377?uid=3738664uid=2129uid=2uid=70uid=4sid=21102745687371

[7] R. Hartshorne, “Algebraic Geometry,” In: Graduate Texts in Mathematics, Vol. 52, Springer, New York, 1977.

[8] D. R. Grayson and M. E. Stillman, “Macaulay2, a Software System for Research in Algebraic Geometry.”

http://www.math.uiuc.edu/Macaulay2

[9] X. Delannay, P. H. Gouyon and G. Valdeyron, “Mathematical Study of the Evolution of Gynodioecy with Cytoplasmic Inheritance under the Effect of a Nuclear Restorer Gene,” Genetics, Vol. 99, 1981, pp. 169-181.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1214488/

[10] M. D. Ross and B. S. Weir, “Maintenance of Male Sterility in Plant Populations III. Mixed Selfing and Random Mating,” Heredity, Vol. 35, 1975, pp. 21-29.

http://dx.doi.org/10.1038/hdy.1975.64

[11] K. E. Holsinger, M. W. Feldman and F. B. Christiansen, “The Evolution of Self-Fertilization in Plants,” The American Naturalist, Vol. 124, 1984, pp. 446-453.

http://www.jstor.org/discover/10.2307/2461472?uid=3738664uid=2129uid=2uid=70uid=4sid=21102745754551

[12] J. A. Vargas and R. F. del Castillo, “Nuclear Androdioecy and Gynodioecy,” Journal of Mathematical Biology, Vol. 47, No. 3, 2003, pp. 199-221.

http://dx.doi.org/10.1007/s00285-003-0200-3

[13] R. W. Cruden, “Pollen-Ovule Ratios: A Conservative Indicator of Breeding Systems in Flowering Plants,” Evolution, Vol. 31, 1977, pp. 32-46.

http://www.jstor.org/discover/10.2307/2407542?uid=3738664uid=2129uid=2uid=70uid=4sid=21102745773421

[14] C. Damgaard and R. J. Abbott, “Positive Correlations between Selfing Rate and Pollen-Ovule Ratio within Plant Populations,” Evolution, Vol. 49, 1995, pp. 214-217.

http://www.jstor.org/discover/10.2307/2410307?uid=3738664uid=2129uid=2uid=70uid=4sid=21102745773421

[15] P. Holgate, “Selfing in Genetic Algebras,” Journal of Mathematical Biology, Vol. 6, No. 2, 1978, pp. 197-206.

http://dx.doi.org/10.1007/BF02450789

[16] M. Hirsch and S. Smale, “Differential Equations, Dynamical Systems and Linear Algebra,” Academic Press, New York, 1974.

[1] E. Caspari, S. Watson and W. Smith, “The Influence of Cytoplasmic Pollen Sterility on Gene Exchange between Population,” Genetics, Vol. 53, 1966, pp. 741-746.

http://www.genetics.org/content/53/4/741.full.pdf

[2] D. Charlesworth and F.R. Ganders, “The Population Genetics of Gynodioecy with Cytoplasmic-Genic Male-Sterility,” Heredity, Vol. 43, 1979, pp. 213-218.

http://dx.doi.org/10.1038/hdy.1979.76

[3] G. S. Watson and E. Caspari, “The Behavior of Cytoplasmic Pollen Sterility in Populations,” Evolution, Vol. 14, No. 1, 1960, pp. 56-63.

http://dx.doi.org/10.2307/2405922

[4] M. F. Bailey, L. F. Delph and C. M. Lively, “Modelling Gynodioecy: Novel Scenarios for Maintaining Polymorphism,” The American Naturalist, Vol. 161, No. 5, 2003, pp. 762-776.

http://dx.doi.org/10.1086/374803

[5] M. Dufay, P. Touzet, S. Maurice and J. Cuguen, “Modelling the Maintenance of Male-Fertile Cytoplasm in a Gynodioecious Population,” Heredity, Vol. 99, 2007, pp. 349-356.

http://dx.doi.org/10.1038/sj.hdy.6801009

[6] P. H. Gouyon, F. Vichot and J. M. M. van Damme, “Nuclear-Cytoplasmic Male Sterility: Single-Point Equilibria versus Limit Cycles,” The American Naturalist, Vol. 134, No. 4, 1991, pp. 498-513.

http://www.jstor.org/discover/10.2307/2462377?uid=3738664uid=2129uid=2uid=70uid=4sid=21102745687371

[7] R. Hartshorne, “Algebraic Geometry,” In: Graduate Texts in Mathematics, Vol. 52, Springer, New York, 1977.

[8] D. R. Grayson and M. E. Stillman, “Macaulay2, a Software System for Research in Algebraic Geometry.”

http://www.math.uiuc.edu/Macaulay2

[9] X. Delannay, P. H. Gouyon and G. Valdeyron, “Mathematical Study of the Evolution of Gynodioecy with Cytoplasmic Inheritance under the Effect of a Nuclear Restorer Gene,” Genetics, Vol. 99, 1981, pp. 169-181.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1214488/

[10] M. D. Ross and B. S. Weir, “Maintenance of Male Sterility in Plant Populations III. Mixed Selfing and Random Mating,” Heredity, Vol. 35, 1975, pp. 21-29.

http://dx.doi.org/10.1038/hdy.1975.64

[11] K. E. Holsinger, M. W. Feldman and F. B. Christiansen, “The Evolution of Self-Fertilization in Plants,” The American Naturalist, Vol. 124, 1984, pp. 446-453.

http://www.jstor.org/discover/10.2307/2461472?uid=3738664uid=2129uid=2uid=70uid=4sid=21102745754551

[12] J. A. Vargas and R. F. del Castillo, “Nuclear Androdioecy and Gynodioecy,” Journal of Mathematical Biology, Vol. 47, No. 3, 2003, pp. 199-221.

http://dx.doi.org/10.1007/s00285-003-0200-3

[13] R. W. Cruden, “Pollen-Ovule Ratios: A Conservative Indicator of Breeding Systems in Flowering Plants,” Evolution, Vol. 31, 1977, pp. 32-46.

http://www.jstor.org/discover/10.2307/2407542?uid=3738664uid=2129uid=2uid=70uid=4sid=21102745773421

[14] C. Damgaard and R. J. Abbott, “Positive Correlations between Selfing Rate and Pollen-Ovule Ratio within Plant Populations,” Evolution, Vol. 49, 1995, pp. 214-217.

http://www.jstor.org/discover/10.2307/2410307?uid=3738664uid=2129uid=2uid=70uid=4sid=21102745773421

[15] P. Holgate, “Selfing in Genetic Algebras,” Journal of Mathematical Biology, Vol. 6, No. 2, 1978, pp. 197-206.

http://dx.doi.org/10.1007/BF02450789

[16] M. Hirsch and S. Smale, “Differential Equations, Dynamical Systems and Linear Algebra,” Academic Press, New York, 1974.