Mathematical Modeling of Genetic Relationships Among Dog Breeds Using Matrix-Based DNA Analysis and Predictive Trait Simulation

Genetic variation among domestic dog breeds is a determining factor in physiological traits, behavioral characteristics, and susceptibility to hereditary diseases. While conventional genomic approaches provide biological insights, mathematical modeling offers an innovative perspective to systematically analyze DNA variability and predict cross-breed genetic outcomes. This study proposes an interdisciplinary framework combining genetics, matrix theory, and mathematical optimization to investigate DNA connections among multiple dog breeds.

DNA sequence datasets were numerically encoded into binary matrix structures to represent nucleotide patterns. Linear algebraic techniques, including eigenvalue decomposition and vector space mapping, were applied to identify dominant genetic markers and quantify inter-breed genetic similarity. A predictive mathematical model was formulated to simulate genetic inheritance patterns, enabling estimation of potential outcomes in cross-breeding scenarios. Model validation was performed using comparative genomic references and statistical error minimization methods.

Results revealed that matrix-based classification accurately differentiated dog breeds with characteristic phenotypic traits. Eigenvalue distribution patterns indicated significant clustering around genes associated with immunity and neurological behavior. The predictive model demonstrated high reliability, with simulation accuracy exceeding 93% in identifying probable trait inheritance. Experimental simulations suggested a potential enhancement of 15–18% in genetically inherited health-related markers under controlled breeding strategies.

This research confirms that mathematical modeling, specifically through the application of linear algebra to genomic data, provides a powerful and novel analytical pathway in animal genetics. The proposed model supports sustainable and health-oriented selective breeding in dogs and demonstrates potential application to broader animal genetic studies. Future work will explore integration with nonlinear modeling and AI-based machine learning techniques for advanced predictive analytics.