**ABSTRACT**

The mathematics and biology are the interdisciplinary approaches in the field of scientific research. Both, mathematics and biology deserve a wide range of applications. Mathematical biology or biomathematics is the study of mathematics for biology. One can derive the quantitative genetics through consideration of infinitesimal effects at a large number of gene loci, together with the assumption of linkage equilibrium or quasi-linkage equilibrium. Ronald Fisher made the intensive work on fundamental advances in statistics (Example: Analysis of Variance). This achievement by Ronald Fisher was through his work on quantitative genetics. The phylogenetics is one more important branch of population genetics that led to the extensive development of Biological sciences through Mathematics. The Phylogenetics is the branch dealing with the reconstruction and analysis of phylogenetic (evolutionary) trees and network based on inherited characteristics. Assumptions on the “Constant Population Size” belongs to many “Population Genetics” models. The population dynamics is treating the “Variable Population Size” as absence of genetic variation. History of such type of work goes back to the 19^{th} century. Even as far as 1798. In 1798, Thomas Malthus formulated the first principle of population dynamics. This principle later became popularize as the “Malthusian Growth Model”. Alfred J. Lotka, in 1910 proposed the model of autocatalytic chemical reactions. __Vito Volterra__ tried his best to extend this work and titled as “Lotka – Volterra Predator-Prey Equations”. Basically, Vito Volterra was Mathematician. The mathematical epidemiology is the study of infectious disease affecting populations. Upto some extent, the “Population dynamics” use to overlaps mathematical epidemiology. The mathematics and Biology, both are serving a lot to orchestrate the progression of the global research.

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