Mathematical model for adaptive evolution of populations based on a complex domain

Abstract

A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function.

Microbial enhanced oil recovery: interfacial tension and biosurfactant-bacteria growth

“…An evolution in the bacteria itself is not observable in our data. A study to consider a mutation, natural assortment, or adaptive evolution may consider fractional differential equation (Ibrahim et al 2016). However, it is unlikely to happen for MEOR bacteria.…”

Periodicity computation of generalized mathematical biology problems involving delay differential equations

“…Using the idea of the fractional calculus (see Podlubny, 1999), Eq. (1) is developed (see Ibrahim et al, 2016a, Ibrahim et al, 2016b, Ibrahim et al, 2016c). Recently, Rakkiyappan et al (2016) presented the periodicity by applying fractional neural network model.…”