# American Institute of Mathematical Sciences

December  2011, 4(6): 1577-1586. doi: 10.3934/dcdss.2011.4.1577

## Algebraic model of non-Mendelian inheritance

 1 Mathematics Department, College of William and Mary, Williamsburg, VA 23187, United States

Received  April 2009 Revised  October 2009 Published  December 2010

Evolution algebra theory is used to study non-Mendelian inheritance, particularly organelle heredity and population genetics of Phytophthora infectans. We not only can explain a puzzling feature of establishment of homoplasmy from heteroplasmic cell population and the coexistence of mitochondrial triplasmy, but also can predict all mechanisms to form the homoplasmy of cell populations, which are hypothetical mechanisms in current mitochondrial disease research. The algebras also provide a way to easily find different genetically dynamic patterns from the complexity of the progenies of Phytophthora infectans which cause the late blight of potatoes and tomatoes. Certain suggestions to pathologists are made as well.
Citation: Jianjun Paul Tian. Algebraic model of non-Mendelian inheritance. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1577-1586. doi: 10.3934/dcdss.2011.4.1577
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