14.6 The genetic composition (genome) of a person is derived from that of the parents, but the way they are combined involves a random process. We will consider the process for a small group of' related individuals. Elaine and Juan have two children. Fred and Rosalia. Shanti and Nur have a child Gauri. Rosalia has a child with Gauri, named Billy. Later she has a child with Yun-fat, named Liz. F d and Ludmilla (a woman unrelated to any of the other individuaIs listed) have a child named Mariko.
Draw a diagram representing the conditional relationships among the genomes of the different people in this family, in the style of Figure 14.1(b). (Hi?& the variable at each node represents the genome of one person, either the complete genome or a specific characteristic.)
What individuals' genomes would you condition on to make the genomes for Liz and Bilt conditionally independent? What about Liz and Mariko? (For which can you give more than one answer?)
Compare this diagram to a standard family tree. How are they different or similar in terms of thc information conveyed? (This is not a technical question, just a question of interpretation.)
Comment on the extent to which the models associated with this diagram fit the informal chwdcterization of hierarchical models in Section 14.2.2.
An individual's observable characteristics (without DNA sequencing}
reflect some combination of cffccts of the genome and of various kinds of environmental influences. Supposing that the environmental influences are independent for each individual, augment your diagrdm to show where variables for the observable characteristics of Mariko, Rosalia, and Bill would appear.
How plausible is this assumption of independence, for example, for Fred and Rosalia? Explain your view, and suggest the possible consequences of assuming indepcndcnce of environmental effects if they are not in fact independent.
Note: mdcls of this general form are common in a number of fields concerned with inherited Characteristics. In animal husbandry, the variable might be a single characteristic such as the animal's weight (corrected for sex differences), and a variance component model similar to (14.5) might be appropriate. In studies of inheritance of genetically linked diseases, the variable might represent the expression of a specific gene and the conditional distributions are based on the laws of heredity.