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.
Highlights
In this article, we apply evolution algebra theory to the study of non-Mendelian genetics
As Mendelian genetics, non-Mendelian inheritance is a huge family in genetics
We focus on two particular genetic phenomena to show how evolution algebras work for them
Summary
We apply evolution algebra theory to the study of non-Mendelian genetics. By non-Mendelian inheritance component (2), alleles of organelle genes may or may not segregate during meiosis following vegetative segregation, so that the frequency of each gene in the generation can vary. We have an evolution algebra, denoted by Ah, generated by G0, G1 and G2 and subject to the defining relations (1)-(4).
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