1 Introduction

As described in Chapter 6, the basic univariate ACE model allows us to estimate genetic and environmental components of phenotypic variance from like-sex MZ and DZ twin data. When data are available from both male and female twin pairs, an investigator may be interested in asking whether the variance profile of a trait is similar across the sexes or whether the magnitude of genetic and environmental influences are sex-dependent. To address this issue, the ACE model may be fitted independently to data from male and female twins, and the parameter estimates compared by inspection. This approach, however, has three severe limitations: (1) it does not test whether the heterogeneity observed across the sexes is significant; (2) it does not attempt to explain the sex differences by fitting a particular sex-limitation model; and (3) it discards potentially useful information by excluding dizygotic opposite-sex twin pairs from the analysis. In the first part of this chapter (Section 9.2), we outline three models for exploring sex differences in genetic and environmental effects (i.e., models for sex-limitation) and provide an example of each by analyzing twin data on body mass index (BMI) (Section 9.2.4). Just as the magnitude of genetic and environmental influences may differ according to sex, they also may vary under disparate environmental conditions. If differences in genetic variance across environmental exposure groups result in differential heritability estimates for these groups, a genotype $\times$ environment interaction is said to exist. Historically, genotype $\times$ environment (G $\times$ E) interactions have been noted in plant and animal species (Mather and Jinks, 1982); however, there is increasing evidence that they play an important role in human variability as well (Heath and Martin, 1986; Heath et al., 1989b). A simple method for detecting G $\times$ E interactions is to estimate components of phenotypic variance conditional on environmental exposure (Eaves, 1982). In the second part of this chapter (Section 9.3), we illustrate how this method may be employed by suitably modifying models for sex-limitation. We then apply the models to depression scores of female twins and estimate components of variance conditional on a putative buffering environment, marital status (Section 9.3.2).