A method for interpreting mixed DNA evidence based on the gamma model

In the field of forensic science, mixed DNA evidence obtained from crime scenes often contains genetic information from multiple individuals, and its accurate interpretation is crucial for case investigation and judicial decision-making. With the advancement of forensic genetic technologies, although detection capabilities have significantly improved, there are still substantial bottlenecks in the interpretation of multi-contributor DNA profiles. Traditional methods are often unable to simultaneously and precisely infer both the genotypes of suspects and their respective contribution proportions, which makes them insufficient to meet the stringent requirements of complex mixture analysis. To address these challenges, we propose a continuous gamma distribution model algorithm based on probabilistic residual optimization in this study. By constructing a two-step probabilistic evaluation framework, the algorithm first generates candidate genotype combinations through allelic permutations and estimates preliminary contributor proportions. It then introduces the gamma distribution hypothesis to build a probability density function, dynamically optimizes the shape parameter (α) and the scale parameter (β) to calculate residual probability weights, and employs an iterative maximum likelihood estimation process to simultaneously optimize genotype combinations and contributor proportion parameters. The final results are derived by integrating population allele frequency databases to output the maximum likelihood solution. This algorithm provides a reliable and quantifiable analytical tool for forensic identification, significantly improving the accuracy of complex mixture interpretation and enhancing the practical utility of mixed DNA in criminal investigations. It holds substantial significance in advancing forensic science technologies and safeguarding judicial fairness.