Epistasis in Predator-Prey Relationships
ABSTRACT
Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator-prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.
Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator-prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.
Cite this paper
Inozemtseva, I. and Braselton, J. (2014) Epistasis in Predator-Prey Relationships. Open Journal of Applied Sciences, 4, 473-491. doi: 10.4236/ojapps.2014.49046.
Inozemtseva, I. and Braselton, J. (2014) Epistasis in Predator-Prey Relationships. Open Journal of Applied Sciences, 4, 473-491. doi: 10.4236/ojapps.2014.49046.
References
[1] Karlin, S. (1972) Some Mathematical Models of Population Genetics. American Mathematical Monthly, 79, 699-739.
http://dx.doi.org/10.2307/2316262 [2] Dean, L. (2005) Blood Groups and Red Cell Antigens. National Center for Biotechnology Information. [3] Lotka, A.J. (1956) Elements of Mathematical Biology. Dover, New York [4] Abell, M. and Braselton, J. (2010) Introductory Differential Equations with Boundary Value Problems. 3rd Edition, Academic Press, Boston. [5] Beltrami, E. (2013) Mathematical Models for Society and Biology. 2nd Edition, Academic Press, Boston. [6] Murray, J. (2007) Mathematical Biology: I. An Introduction. 3rd Edition, Springer, New York. [7] Braselton, J., Abell, M. and Braselton, L. (2005) Selective Mating in a Continuous Model of Epistasis. Applied Mathematics and Computation, 171, 225-241.
http://dx.doi.org/10.1016/j.amc.2005.01.059 [8] Szathmáry, E. (1993) A Note on the Reduction of the Dynamics of Multilocus Diploid Genetic Systems with Multiplicative Fitness. Journal of Theoretical Biology, 164, 351-358.
http://dx.doi.org/10.1006/jtbi.1993.1159 [9] Wolfram Research, Inc. (2013) Dominance, Population Size, and Delayed Inheritance. Evolution, 67, 2011-2023.
[1] Karlin, S. (1972) Some Mathematical Models of Population Genetics. American Mathematical Monthly, 79, 699-739.
http://dx.doi.org/10.2307/2316262 [2] Dean, L. (2005) Blood Groups and Red Cell Antigens. National Center for Biotechnology Information. [3] Lotka, A.J. (1956) Elements of Mathematical Biology. Dover, New York [4] Abell, M. and Braselton, J. (2010) Introductory Differential Equations with Boundary Value Problems. 3rd Edition, Academic Press, Boston. [5] Beltrami, E. (2013) Mathematical Models for Society and Biology. 2nd Edition, Academic Press, Boston. [6] Murray, J. (2007) Mathematical Biology: I. An Introduction. 3rd Edition, Springer, New York. [7] Braselton, J., Abell, M. and Braselton, L. (2005) Selective Mating in a Continuous Model of Epistasis. Applied Mathematics and Computation, 171, 225-241.
http://dx.doi.org/10.1016/j.amc.2005.01.059 [8] Szathmáry, E. (1993) A Note on the Reduction of the Dynamics of Multilocus Diploid Genetic Systems with Multiplicative Fitness. Journal of Theoretical Biology, 164, 351-358.
http://dx.doi.org/10.1006/jtbi.1993.1159 [9] Wolfram Research, Inc. (2013) Dominance, Population Size, and Delayed Inheritance. Evolution, 67, 2011-2023.