MATHEMATICAL MODELING OF CONSANGUINEOUS MARRIAGES: PROBABILITY THEORY AND MENDELIAN GENETICS ANALYSIS OF HOMOZYGOSITY RISK IN POPULATION HEALTH
Abstract
Marriages between close relatives, though culturally important in many communities, carry considerable genetic dangers owing to heightened homozygosity of harmful recessive alleles. We investigate the genetic consequences of such unions through a rigorous mathematical framework grounded in probability theory and Mendelian genetics. The research initiates with the delineation of core genetic tenets, such as allele segregation and independent assortment, and methodically progresses to examine interactions among multiple genes and dynamics at the population level. The Hardy-Weinberg equilibrium serves as a reference for analyzing genotype frequencies in populations with random mating, whereas the inclusion of selection pressures and inbreeding coefficients measures departures from panmixia. Specifically, the inbreeding coefficient is employed to measure the elevated risk of homozygosity for harmful recessive traits in consanguineous unions, demonstrating that the probability of recessive homozygosity scales with both allele frequency and the degree of relatedness. Numerical simulations and theoretical derivations indicate that first-cousin marriages, for example, show a noticeable rise in recessive disorder prevalence relative to non-consanguineous unions. The proposed methodology not only elucidates the mechanistic foundations of these risks but also presents a broadly applicable instrument for evaluating population health effects under different levels of consanguinity. Moreover, including recombination frequencies for linked genes improves the model’s relevance to actual genetic situations. This work establishes a quantitative basis for public health policies designed to reduce the negative consequences of consanguineous marriages by connecting theoretical genetics to practical risk assessment. The findings underscore the importance of genetic counseling and education in populations where such practices are prevalent, thereby contributing to broader efforts in preventive medicine and population genetics.
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