Abstract
Genetic studies of complex traits often show disparities in estimated heritability depending on the method used, whether by genomic associations or twin and family studies. We present a simulation of individual genomes with dynamic environmental conditions to consider how linear and nonlinear effects, gene-by-environment interactions, and gene-by-environment correlations may work together to govern the long-term development of complex traits and affect estimates of heritability from common methods. Our simulation studies demonstrate that the genetic effects estimated by genome wide association studies in unrelated individuals are inadequate to characterize gene-by-environment interaction, while including related individuals in genome-wide complex trait analysis (GCTA) allows gene-by-environment interactions to be recovered in the heritability. These theoretical findings provide an explanation for the "missing heritability" problem and bridge the conceptual gap between the most common findings of GCTA and twin studies. Future studies may use the simulation model to test hypotheses about phenotypic complexity either in an exploratory way or by replicating well-established observations of specific phenotypes.