Structural model analysis of multiple quantitative traits

Abstract

We introduce a method for the analysis of multilocus, multitrait genetic data that provides an intuitive and precise characterization of genetic architecture. We show that it is possible to infer the magnitude and direction of causal relationships among multiple correlated phenotypes and illustrate the technique using body composition and bone density data from mouse intercross populations. Using these techniques we are able to distinguish genetic loci that affect adiposity from those that affect overall body size and thus reveal a shortcoming of standardized measures such as body mass index that are widely used in obesity research. The identification of causal networks sheds light on the nature of genetic heterogeneity and pleiotropy in complex genetic systems.

Figure 1. Causal Relationships among a QTL and Two Phenotypes

Single-headed arrows indicate causal effects and doubled-headed arrows indicate unresolved associations between the two phenotypes. Phenotypes are indicated by A and B; QTL by Q.

Figure 2. Relationship of Mesenteric Fat Pad Weight to Lean Body Weight for Female and Male Animals

Both phenotypes are square root transformed. The dotted line indicates the ratio standard of constant adiposity index. The solid line is the regression of mesenteric fat pad weight on lean body weight.

Figure 3. Genome-Wide Scans for Mesenteric Fat Pad Weight at 2 cM Resolution

Genome scans shown are (A) mesenteric fat pad weight with sex as an additive covariate; (B) mesenteric fat pad weight with sex and lean body weight as additive covariates; (C) difference in LOD scores between scans in (A) and (B); and (D) lean body weight with sex as an additive covariate. LBWT, lean body weight; MES, mesenteric fat pad weight.

Figure 4. Graphical Representation of the SEM for Mesenteric Fat Pad Weight

Genetic loci are indicated by Q followed by the chromosome number, and @ followed by the cM position of the LOD peak. Single-headed arrows indicate causal paths, and the thickness of each arrow is proportion to the effect size (path coefficient). A negative sign from a QTL to a trait indicates that the NZB allele is associated with high trait values. E1 and E2 denote unobserved residual error.

Figure 5. Genome-Wide Scans for Multiple Fat Pad Traits at 2 cM Resolution

Genome scans shown are (A) the four fat pad traits (inguinal, gonadal, peritoneal, and mesenteric fat pad weight) with sex as an additive covariate; (B) the four fat pad traits with sex and lean body weight as additive covariates; and (C) the difference in LOD scores between scans in (A) and (B). FP, the four fat pad traits; LBWT, lean body weight.

Figure 6. Structural Equation Model for Adiposity and Lean Body weight

The four fat pad traits are gonadal (GON); inguinal (ING); mesenteric (MES); and peritoneal (PERI). Single-headed arrows indicate causal paths, and the thickness of each arrow is proportional to the effect sizes. Doubled-headed arrows denote unresolved covariance. The boxes indicate measured traits or QTL and the oval denotes a latent variable. E1, E2, E3, E4, and E5 denote unobserved residual error. The negative sign from a QTL to a trait indicates that the NZB allele is associated with high trait values.

Figure 7. Structural Equation Model for Bone Geometry

Genetic effects have been grouped. Sign and magnitude of path coefficients can be found in Table 5. Group Q1 includes loci with effects that are specific to PCIR (Q4@66, Q5@84, Q6@32, Q7@50, and Q11@68). Group Q2 includes loci have pleiotropic effects on PCIR and BWT (Q19@50, Q1@20, and Q8@0). Group Q3 includes loci with pleiotropic effects on PCIR and FLEN (Q10@64, Q5@52, Q15@10, and Q12@56). Group Q4 loci are pleiotropic loci that affect all three traits (Q12@2, Q2@66, and Q3@30). E1, E2, and E3 denote N(0,1) residual error.

Figure 8. Model Comparison for the Bone Geometry Data

Model comparisons for the bone geometry data were derived from the model in Figure 7 by varying the relationships among body weight, femur length, and periostial circumference.