A MATHEMATICAL MODEL TO STUDY THE JOINT EFFECTS OF GENETICS AND DIET ON OBESITY
Victoria Kelley2, Fangyuan Hong1, Kevin Molina3, Demetrius Rhodes4, Karen Rios-Soto3.
1Mount Holyoke College, South Hadley, MA, 2James Madison University, Harrisonburg, VA, 3University of Puerto Rico, Mayaguez Campus, Mayaguez, PR, 4University of South Carolina-Beaufort, Bluffton, SC.
Obesity has become one of the most pervasive epidemics facing North America today. Obesity is correlated with health threats such as diabetes and cardiovascular diseases that increase an individual’s mortality risk. Previous studies show that a particular single nucleotide polymorphism (SNP), rs9939609, in the fat mass and obesity-associated FTO gene is associated with obesity. A poor choice of diet and nutrition may lead to obesity. In this study, we build a system of non-linear ordinary differential equations that considers both genetic and environmental effects on populations with 3 distinct genotypes (AA, Aa, and aa). The autosomal dominant allele is A; therefore, individuals who have the genotypes AA and Aa express the FTO gene. Equilibria analysis and simulation results show that over a long period of time, when the birth frequency of each genotype is dependent on current allele frequencies, the proportion of populations with the dominant allele goes to 0, or the dominant allele A is outbred by the recessive gene allele. Simulation results show that having the allele A has a stronger impact on obesity than the diet environment. The effects of environmental factors on the dynamics of obesity are negligible at best. Fitness and genetic selection trumps any environmental bias. This study provides a significantly new insight into the synergic impact that genetics and diet play on obesity, which is rarely studied by traditional biological tools, such as GWAS.