The target article by Charney discusses what is called a paradigm shift in genomics and its significance for behavior genetics and gene association studies. In what follows I will focus on some of the implications for behavior genetics, in particular assumption HS1 (100% of the genes of MZ [monozygotic] twins are genetically identical, on average 50% of the genes of DZ [dizygotic] twins and non-twin siblings are genetically identical) and to a lesser degree on assumption HS2 (the percentages of genetic identity in HS1 never change).
The implications of the paradigm shift concerned are summarized in the target paper as follows: MZ twins, in addition to not possessing identical mitochondrial DNA, do not possess identical nuclear DNA. Their genomes differ in the polyploidy and heteroplasmy of their mitochondrial DNA, in the number and location of retrotransposition events and copy number variations, in replications and deletions of whole or partial chromosomes, and in their epigenomes. To the extent that heritability estimates depend upon HS1, they will be unable to provide reliable estimates. Moreover, the presumed percentages of genetic identity between MZ twins, DZ twins and non-twin siblings are likely a moving target, thus violating HS2.
The standard behavior genetic model for the analysis of p-variate phenotypes of MZ and DZ twins is the genetic factor model of Martin & Eaves (Reference Martin and Eaves1977), composed of additive genetic, common environmental, and specific environmental factors. The p-variate phenotypes of each member of a twin pair are stacked in a 2p-variate supervector, while the correlation of the additive genetic factors within twin pairs is fixed at 1.0 for MZ twins and 0.5 for DZ twins. The factor loadings of the additive genetic factors are assumed to be equal within and across all twin pairs. The extension of the standard genetic factor model to p-variate phenotypes obtained with MZ and DZ twins in a longitudinal design with T repeated measurement occasions is straightforward, again consisting of the stacking of the observations in a 2pT-dimensional supervector. At each measurement occasion the factor model described above obtains, while the relationships between measurement occasions are explained by regressing the additive genetic, common environmental, and specific environmental factors on their analogs at earlier measurement occasions (cf. Molenaar Reference Molenaar, Hood, Halpern, Greenberg and Lerner2010).
The consequence of violation of HS1 is that the correlation of the additive genetic factor within MZ twin pairs in the standard genetic factor model no longer can be fixed at 1.0. Given the dependence on environmental contingencies of several of the causes, which according to the target paper underlie this violation (e.g., DNA methylation, maternal effects), it also would seem that the degrees of violation of HS1 are subject-specific, that is, yielding different genomes for different twins. This would imply that the correlation of the additive genetic factors in the standard genetic factor model becomes subject-specific. Violation of HS1 also would seem to lead to a decrease in the average correlation of the additive genetic factors of DZ twin pairs. Furthermore, the dependence on environmental contingencies then also yields subject-specific violations of HS2 with the same consequences for the standard longitudinal genetic factor model.
We have emphasized that the consequences of nonlinear epigenetic processes for the standard (longitudinal) genetic factor model may even be more severe in that not only the genetic correlations, but also the genetic factor loadings, become subject-specific (cf. Kan et al. Reference Kan, Ploeger, Raijmakers, Dolan and van der Maas2010; Molenaar Reference Molenaar2007; Reference Molenaar, Hood, Halpern, Greenberg and Lerner2010; Molenaar et al. Reference Molenaar, Boomsma and Dolan1993). The standard (longitudinal) genetic factor model is fitted to the data by pooling across twin pairs (analysis of interindividual variation). It was shown in simulation studies (Molenaar et al. Reference Molenaar, Huizenga, Nesselroade, Staudinger and Lindenberger2003) and by analytic proof (Kelderman & Molenaar Reference Kelderman and Molenaar2007) that such subject-specific variation of factor loadings is invisible standard factor analyses of interindividual variation.
The only principled way to identify subject-specific variation in genetic correlations and factor loadings is to accommodate the standard genetic longitudinal factor model for applications to multivariate phenotypic time series (intraindividual variation) obtained with a single pair of genetically related subjects (e.g., a single MZ or DZ twin pair). Therefore the standard genetic longitudinal factor model was generalized as a genetic state space model for multivariate phenotypic time series (Molenaar Reference Molenaar, Hood, Halpern, Greenberg and Lerner2010). A special feature of this so-called iFACE model is that the correlation between the additive genetic factor series is estimated (not fixed a priori). Moreover, the model allows for subject-specific factor loadings for the additive genetic, common environmental, and specific environmental factors. It turns out that this iFACE model is almost always identifiable (i.e., the derivative of its likelihood function with respect to the free parameters has null space of dimension zero; cf. Bekker et al. Reference Bekker, Merckens and Wansbeek1994).
The iFACE was applied to the quantitative genetic analysis of multilead event-related potentials obtained with a single DZ twin pair (Molenaar et al. 2011). It was found that the correlation between the additive genetic factors is about 0.40. Moreover, importantly, it was found that the patterns of genetic factor loadings differ substantially between twin 1 and twin 2. Heritability is high for twin 1 at the central parietal lead, whereas it is high for twin 2 at the left and right lateral parietal leads.
In conclusion, the iFACE – a direct generalization of the standard longitudinal genetic factor model for the analysis of interindividual phenotypic variation to the subject-specific analysis of intraindividual variation – can accommodate the implications of violations of HS1 and HS2 for behavior genetic analyses.
The target article by Charney discusses what is called a paradigm shift in genomics and its significance for behavior genetics and gene association studies. In what follows I will focus on some of the implications for behavior genetics, in particular assumption HS1 (100% of the genes of MZ [monozygotic] twins are genetically identical, on average 50% of the genes of DZ [dizygotic] twins and non-twin siblings are genetically identical) and to a lesser degree on assumption HS2 (the percentages of genetic identity in HS1 never change).
The implications of the paradigm shift concerned are summarized in the target paper as follows: MZ twins, in addition to not possessing identical mitochondrial DNA, do not possess identical nuclear DNA. Their genomes differ in the polyploidy and heteroplasmy of their mitochondrial DNA, in the number and location of retrotransposition events and copy number variations, in replications and deletions of whole or partial chromosomes, and in their epigenomes. To the extent that heritability estimates depend upon HS1, they will be unable to provide reliable estimates. Moreover, the presumed percentages of genetic identity between MZ twins, DZ twins and non-twin siblings are likely a moving target, thus violating HS2.
The standard behavior genetic model for the analysis of p-variate phenotypes of MZ and DZ twins is the genetic factor model of Martin & Eaves (Reference Martin and Eaves1977), composed of additive genetic, common environmental, and specific environmental factors. The p-variate phenotypes of each member of a twin pair are stacked in a 2p-variate supervector, while the correlation of the additive genetic factors within twin pairs is fixed at 1.0 for MZ twins and 0.5 for DZ twins. The factor loadings of the additive genetic factors are assumed to be equal within and across all twin pairs. The extension of the standard genetic factor model to p-variate phenotypes obtained with MZ and DZ twins in a longitudinal design with T repeated measurement occasions is straightforward, again consisting of the stacking of the observations in a 2pT-dimensional supervector. At each measurement occasion the factor model described above obtains, while the relationships between measurement occasions are explained by regressing the additive genetic, common environmental, and specific environmental factors on their analogs at earlier measurement occasions (cf. Molenaar Reference Molenaar, Hood, Halpern, Greenberg and Lerner2010).
The consequence of violation of HS1 is that the correlation of the additive genetic factor within MZ twin pairs in the standard genetic factor model no longer can be fixed at 1.0. Given the dependence on environmental contingencies of several of the causes, which according to the target paper underlie this violation (e.g., DNA methylation, maternal effects), it also would seem that the degrees of violation of HS1 are subject-specific, that is, yielding different genomes for different twins. This would imply that the correlation of the additive genetic factors in the standard genetic factor model becomes subject-specific. Violation of HS1 also would seem to lead to a decrease in the average correlation of the additive genetic factors of DZ twin pairs. Furthermore, the dependence on environmental contingencies then also yields subject-specific violations of HS2 with the same consequences for the standard longitudinal genetic factor model.
We have emphasized that the consequences of nonlinear epigenetic processes for the standard (longitudinal) genetic factor model may even be more severe in that not only the genetic correlations, but also the genetic factor loadings, become subject-specific (cf. Kan et al. Reference Kan, Ploeger, Raijmakers, Dolan and van der Maas2010; Molenaar Reference Molenaar2007; Reference Molenaar, Hood, Halpern, Greenberg and Lerner2010; Molenaar et al. Reference Molenaar, Boomsma and Dolan1993). The standard (longitudinal) genetic factor model is fitted to the data by pooling across twin pairs (analysis of interindividual variation). It was shown in simulation studies (Molenaar et al. Reference Molenaar, Huizenga, Nesselroade, Staudinger and Lindenberger2003) and by analytic proof (Kelderman & Molenaar Reference Kelderman and Molenaar2007) that such subject-specific variation of factor loadings is invisible standard factor analyses of interindividual variation.
The only principled way to identify subject-specific variation in genetic correlations and factor loadings is to accommodate the standard genetic longitudinal factor model for applications to multivariate phenotypic time series (intraindividual variation) obtained with a single pair of genetically related subjects (e.g., a single MZ or DZ twin pair). Therefore the standard genetic longitudinal factor model was generalized as a genetic state space model for multivariate phenotypic time series (Molenaar Reference Molenaar, Hood, Halpern, Greenberg and Lerner2010). A special feature of this so-called iFACE model is that the correlation between the additive genetic factor series is estimated (not fixed a priori). Moreover, the model allows for subject-specific factor loadings for the additive genetic, common environmental, and specific environmental factors. It turns out that this iFACE model is almost always identifiable (i.e., the derivative of its likelihood function with respect to the free parameters has null space of dimension zero; cf. Bekker et al. Reference Bekker, Merckens and Wansbeek1994).
The iFACE was applied to the quantitative genetic analysis of multilead event-related potentials obtained with a single DZ twin pair (Molenaar et al. 2011). It was found that the correlation between the additive genetic factors is about 0.40. Moreover, importantly, it was found that the patterns of genetic factor loadings differ substantially between twin 1 and twin 2. Heritability is high for twin 1 at the central parietal lead, whereas it is high for twin 2 at the left and right lateral parietal leads.
In conclusion, the iFACE – a direct generalization of the standard longitudinal genetic factor model for the analysis of interindividual phenotypic variation to the subject-specific analysis of intraindividual variation – can accommodate the implications of violations of HS1 and HS2 for behavior genetic analyses.