Dynamic Models of Biological Pattern Formation Have Surprising Implications for Understanding the Epigenetics of Development

The impact of epigenetic processes is elaborated, in a general developmental context and with respect Q1 to quantitative genetics. Then a class of mathematical models of self-organizing biological growth is considered. These so-called models of biological pattern formation give rise to variation in morphogenetic structures that is caused by self-organizing forces of diffusive origin. In the next section it is proved that the heterogeneity caused by biological pattern formation invalidates standard statistical analysis techniques used in quantitative genetics. The statistical techniques concerned all are based on analysis of interindividual variation, requiring homogeneous populations of subjects. In the penultimate section it is argued that application of quantitative genetic techniques to heterogeneous populations requires their adaptation in subject-specific ways. This is illustrated by the recently developed technique to determine subject-specific heritabilities based on intra-individual variation.