Predicting our Future: Genetics and Linear Algebra
The science of Genetics is a mixture of biology and chemistry. It is the science of the hereditary evolution of a species over a period of time based upon their chemically make-up; a.k.a. their DNA. A field of genetics that is undergoing extensive research today is Population genetics. The field focuses on the genetic structure of certain populations, such as humans, and then tries to scientifically explain the movement of genes from one generation to the next. Within this field are several forms of genetic inheritance, but this paper will focus only on two of these forms: Autosomal inheritance (also known as Mendelian inheritance) and X-linked inheritance. Both of these forms of inheritance are found in humans and plant species, but the methods of gene movement differ between the two. This paper will discuss the mathematics that take place in both forms of inheritance and provide a brief history of the formation of the math behind the science. This math is known as genetic algebra. Applications of genetic algebra and population genetics to the real world will also be discussed. The linear algebra techniques of formation of matrices, solving for eigenvalues and eigenvectors, and methods of diagonalization of a matrix are used in this paper. The science of Genetics and the math behind it provide useful tools that can predict our future based upon our genetic make-up.
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