Algebraic model of non-Mendelian inheritance

Jianjun Paul Tian

doi:10.3934/dcdss.2011.4.1577

Article Contents

2011, Volume 4, Issue 6: 1577-1586. Doi: 10.3934/dcdss.2011.4.1577

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Algebraic model of non-Mendelian inheritance

Jianjun Paul Tian^1,

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

Received: March 31, 2009

Revised: September 30, 2009

Published: November 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 17D99, 17D92; Secondary: 92D10.

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References

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