On the Limits of Standard Quantitative Genetic Modeling of Inter‐Individual Variation

Abstract

This chapter has two distinct purposes. First, a review is given of work exploring the boundaries of the standard genetic factor model underlying much of applied quantitative genetic modeling. This review includes aspects of longitudinal genetic modeling, testing for interactions between genetic and environmental factors, and genetic decomposition of mean differences. It summarizes innovative work in which I have been involved before my perspective on standard quantitative genetic modeling changed substantially when I discovered the fundamental implications of a general mathematical theorem about stochastic processes – the so-called individual ergodic theorem of Birkhoff (1931). These implications invalidate the quantitative genetic analysis based on inter-individual variation of a large class of phenotypic processes, the so-called non-ergodic processes. Instead it is necessary to base quantitative genetic modeling of non-ergodic phenotypic processes on intra-individual variation (time series analysis). In the second part of this chapter the implications of the individual ergodic theorem will be explained at some length, including an excursion to relevant results of mathematical modeling of nonlinear epigenetic processes and possible solutions to arrive at valid quantitative genetic analyses of non-ergodic processes. The discussion of these solutions will touch upon an entirely innovative approach to carry out quantitative genetic modeling at the level of individual twin pairs.