ABSTRACT
This chapter discusses to applications of stochastic processes to biology and more par- ticularly to dynamic populations and evolutionary processes. It starts with a presentation of discrete generation birth and death type processes. The cells of most organisms contain a specific hereditary material called DNA (deoxyribonu- cleic acid). The DNA is a double helix formed with base pairs attached to a sugar-phosphate backbone. These base pair sequences encode information in terms of four chemical bases: A (adenine), C (cytosine), G (guanine), and T (thymine). Proteins are sophisticated and complex molecules in cells that serve different functionalities. For instance, messenger proteins transmit signals to coordinate biological processes between cells, tissues, or organs. The Kolmogorov-Petrovskii-Piskunov equation also known as the Fisher's equation was introduced in 1937 by A.N. Kolmogorov, I.G. Petrovskii, N.S. Piskunov in and by R. A. Fisher. This dynamic population model describes the spatial spread of an advantageous allele.
