Generalized Stable Population and Agent-Based Models of Phenotypic Transmission in Human Populations, with an Application to Body Size.

introductionWe show that generalizations of stable population (GSPM) and agent-based models (ABMs) are useful tools to simulate trajectories of human phenotypes. Although mathematically very different, both classes of models can simultaneously account for multiple determinants of the population distribution of a phenotype across time and space. These include genetic transmission, assortative mating, differential fertility, vertical and horizontal cultural heredity, gene-environments interactions (GxE), and environmental feedback. We propose an application to obesity, a condition that has spread rapidly around the globe, increasing the risk of adult chronic illnesses and mortality.

methodsWe choose body mass index as the target phenotype, and formulate GSPM and ABMs that include genetic inheritance, GxE, assortative mating, and fertility differentials. We exclude, in this version, the role of vertical cultural heredity. The GSPM is built on time-varying stochastic matrices that trace the trajectory of the phenotype by groups. The ABM models the behavior of individual agents integrating a stochastic component modifying each agent's behavior.

resultsThere are four key results. First, differential fertility dominates the phenotype's time trajectory, followed by assortative mating and GxE. Second, contrary to research in other phenotypes, the impact of assortative mating cannot offset the influence of fertility differentials. Third, concerning the formal representation of the transmission process, we show that the use of simple Mendelian models to represent complex phenotypes can produce badly biased inferences. Fourth, despite their mathematical differences, the GSPM and ABM produce virtually identical results.

conclusionsModeling phenotypes with complex genetic transmission and heavily dependent on regimes of fertility differentials, assortative mating and GxE ought not to rely on excessive simplifications, as has traditional been done in past research. Both, the GSPM and ABM are useful, accessible, and effective tools to introduce more realism in the modeling of these phenotypes, and can be used as guides for policy interventions.