A formulation of the foundations of genetics and evolution

Area of Science:

• Genetics
• Evolutionary Biology
• Mathematical Biology

Background:

• Foundational theories of genetics and evolution require robust mathematical models.
• Simulating complex genetic phenomena like phenotype expression and natural selection is crucial for advancing biological understanding.

Purpose of the Study:

• To propose a mathematical formulation for simulating core genetic and evolutionary processes.
• To demonstrate the application of matrix expressions in modeling Mendelian inheritance and its variations.

Main Methods:

• Development of a theoretical framework based on mathematical expressions.
• Utilization of matrix algebra to represent genetic principles.
• Simulation of phenotype expression, reproduction, mutation, and natural selection.

Main Results:

• Mendelian inheritance can be accurately simulated using matrix expressions.
• The proposed method extends to modeling quantitative traits and polygenic inheritance.
• Mathematical simulation of modifications to basic Mendelian principles is achievable.

Conclusions:

• The developed mathematical formulation provides a powerful tool for simulating genetic and evolutionary dynamics.
• This approach offers a unified framework for understanding both basic and complex inheritance patterns.
• The study highlights the utility of mathematical modeling in advancing the foundations of genetics and evolution.