Population Genetics and Evolution: Foundations, Equilibria, and Applications

Population genetics is the foundational study of how genetic variation is distributed and transmitted across generations within populations. This article presents a comprehensive overview of the principles governing genetic change, emphasizing both theoretical frameworks and biological applications. A central concept is the Hardy-Weinberg equilibrium, which models allele and genotype frequencies in an idealized population. For a gene with two alleles (A and a) at frequencies p and q, respectively, the expected genotype distribution is given by:

This expression predicts the frequencies of homozygous dominant (AA), heterozygous (Aa), and homozygous recessive (aa) genotypes, assuming random mating and no evolutionary pressures.

We also examine the linkage disequilibrium decay equation,

which describes how the association between alleles at two loci diminishes across generations through recombination (r), especially when genes are unlinked or only loosely linked.

To quantify genetic composition in populations, allele frequencies are calculated from phenotypic or genotypic data using formulas such as:

where D, H, and R represent counts of homozygous dominant, heterozygous, and homozygous recessive individuals, respectively, in a sample of size N.

The article extends these principles to multiallelic and sex-linked traits, introduces molecular evolution and the role of neutral mutations, and explores natural selection through case studies like sickle-cell anemia and coat color in cats. By combining mathematical models with real-world examples, this work offers a cohesive framework for understanding how populations evolve at both genetic and phenotypic levels..