Genetic influences on growth and body composition in mice: multilocus interactions

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The genetic architecture of body weight and body composition is complex because these traits are normally influenced by multiple genes and their interactions, even after controlling for the environment. Bayesian methodology provides an efficient way of estimating these interactions.

Subjects and measurements:

We used Bayesian model selection techniques to simultaneously estimate the main effects, epistasis and gene–sex interactions on age-related body weight (at 3, 6 and 10 weeks, denoted as WT3wk, WT6wk and WT10wk) and body composition (organ weights and fat-related traits) in an F2 sample obtained from a cross between high-growth (M16i) mice and low-growth (L6) mice.


We observed epistatic and main-effect quantitative trait loci (QTL) that controlled both body weight and body composition. Epistatic effects were generally more significant for WT6wk than WT10wk. Chromosomes 5 and 13 interacted strongly to control body weight at 3 weeks. A pleiotropic QTL on chromosome 2 was associated with body weight and some body composition phenotypes. Testis weight was regulated by a QTL on chromosome 13 with a significantly large main effect (2logeBF 15).


By analyzing epistatic interactions, we detected QTL not found in a previous analysis of this mouse population. Hence, the detection of gene–gene interactions may provide new information about the genetic architecture of complex obesity-related traits and may lead to the detection of additional obesity genes.


Body weight and other obesity-related phenotypes are complex traits that are controlled by both genetic and environmental factors.1, 2, 3 The genetic factors controlling growth, body weight and body composition are complex and age-dependent.4, 5, 6, 7, 8, 9, 10 In chickens and mice, for example, different sets of quantitative trait loci (QTL) affect early and late growth. Gene–gene interactions also vary with age and may be more important than main effects during early growth.6, 11 Hence, epistasis plays a significant role in the genetics of growth and body composition.8 Including epistatic interactions in QTL analysis may lead to the detection of QTL with weak marginal but strong interactive effects and thereby improve our understanding of the etiology of obesity as well as the genetic factors that underlie other complex traits.

Traditional statistical methods have been used for detecting epistasis,7, 12 but detecting epistasis becomes increasingly difficult as the number of QTL increases. In addition, conventional methods use two QTL models for detecting gene–gene interactions.13, 14 In contrast, statistical inferences in a Bayesian framework are based on the joint posterior distribution of all unknowns in the model given the observed data.3 These unknowns, which can include the number and locations of QTL as well as their main and epistatic effects, can be estimated by generating posterior samples from the joint posterior distribution. A Bayesian model selection technique for identifying epistatic QTL for complex traits has been developed.15 Bayesian methods provide an efficient and relatively simple way of estimating these effects.

The mouse sample used in this study was derived from parental lines selected for high 3 to 6-week body weight gain (M16i) and low 6-week body weight gain (L6). Initial studies on this sample involved the use of composite interval mapping and focused mainly on detecting main effects.9, 16 Significant QTL effects for growth were observed on chromosomes 1, 2, 3, 6, 10, 11 and 17; chromosomes 2, 7, 15 and 17 were the most important for obesity-related phenotypes. However, few epistatic interactions were detected among main-effect QTL. A recent study used Bayesian techniques for detecting epistasis in a backcross sample derived from other mouse lines.10 QTL with main and epistatic effects were detected for growth and body composition on several chromosomes. Perhaps not surprisingly, no main-effect QTL were present at all ages and the effect of epistasis differed with age. Some QTL had pleiotropic effects on growth and body composition. However, that study used a backcross sample, which does not allow one to distinguish between purely additive and various non-additive effects.

Our objectives were to determine the effect of gene–gene interactions on growth and body composition in an F2 mouse population using Bayesian model selection techniques and to ascertain the changes in these epistatic effects with increases in body weight during the development.

Materials and methods

Mouse sample

Details on the mouse population, marker genotyping and trait phenotypes were provided previously;9, 16 a summary is provided here. A total of 993 mice were bred from two lines of mice selected for increased 3 to 6-week weight gain (M16i) and low 6-week weight (L6). The M16i line was derived from an outbred ICR population, whereas the L6 line was derived from a cross of four inbred lines. L6 males were mated with M16i females; the resulting F1 mice were inter se mated (no full-sib pairings) in two consecutive replicates encompassing a total of 64 full-sib F2 families.9, 16 These mice were reared at 21 °C in a 12:12 h light/dark cycle and 55% relative humidity. Food and water were supplied ad libitum. Purina Mouse Chow 5015 was provided before weaning, and Purina Laboratory Chow 5001 was supplied after weaning. All animals were handled according to the Institutional Animal Care and Use Committee guidelines.

Body weight was recorded for all F2 mice at weeks 3 (WT3wk), 6 (WT6wk) and 10 (WT10wk). Tail length (TAIL) was measured at week 10 as an indicator of skeletal growth; the mice were then euthanized by cervical dislocation. Wet weights of the heart (HRT), liver (LIV), spleen (SPL), right kidney (KID), right testis (TES), right hindlimb subcutaneous fat pad (SCF) and right epididymal fat pad (EPF) were recorded. Empty body weight (EBW), or body weight without ingesta, was also recorded. The trait FAT (the sum of SCF and EPF) was calculated as the sum of SCF and EPF. Body composition data for female mice were used for reproduction phenotyping. Hence, body composition traits were only recorded for males. The SPL was used for DNA extraction.

Marker genotyping

We genotyped 63 fully informative microsatellite markers spanning the 19 autosomes. The marker linkage map covered 1200 cM (Kosambi) with an average spacing of 28 cM. Marker genotypes were determined by PCR and agarose gel electrophoresis. A dominant marker at the Ped locus was genotyped in the F2 mice to determine whether one or two M16i alleles were present. Segregation distortion was evaluated by χ2 testing.17 Detection and correction of genotyping errors was conducted with MAPMAKER.18 Linkage maps were generated with MAPMAKER/EXP, and QTL analysis was carried out after marker distances were estimated.

Statistical analysis

The 13 phenotypes described above were analyzed using the Bayesian model selection method.15, 19 These Bayesian methods were implemented in the freely available package R/qtlbim.20 Our Bayesian procedure proceeded as follows: we partitioned each chromosome into 1-cM grids, resulting in 1200 possible non-overlapping loci across the genome. These preset loci were considered as possible positions of QTL. Before mapping QTL, we calculated the probabilities of particular genotypes at these preset loci given the observed marker data. We placed an upper bound on the number of QTL included in the model for each trait based on the initial results from the traditional interval mapping.15 For most of the traits analyzed, the upper bound was 20. We simultaneously modeled the main (additive–dominance) and epistatic (additive–additive, additive–dominance, dominance–additive and dominance–dominance) effects of each QTL, as well as the effects of the environmental variables (covariates). We used Cockerham's genetic model to construct the main effects of QTL and epistatic interactions between QTL and applied conventional methods used in hierarchical linear models to construct the environmental effects.15, 18 For all the traits, the replicate and the family indicators were included in the model as fixed binary and random covariates, respectively. Besides these two covariates, we also included sex as a fixed covariate, considered gene–sex interactions in the analysis of body weight, and included WT10wk as a fixed covariate for the body composition traits. The Bayesian model selection framework enables us to simultaneously infer the number and positions of multiple QTL and their main effects and interactions.

We followed the methods described in Yi et al.15 and Yi et al.19 to specify the priors for all parameters, briefly described below. The prior number of main-effect QTL lm was set to equal the number of significant QTL detected by the traditional interval mapping and the prior expected number of all QTL (l0) was taken to be lm+3, allowing for some additional interacting QTL with weak main effects. The prior probabilities for the indicators of genetic effects were calculated as described by Yi et al.15. The positions of QTL were uniformly distributed over the preset loci across the genome. We used non-informative prior distributions for the overall mean, residual variance and covariates. The prior for each genetic effect followed a normal distribution, with mean being zero and unknown variance distributed as an inverse χ2 hyperprior. These prior specifications have been shown previously to be reasonable and robust for analysis of real data.15, 19

We fit the models using R/qtlbim,20 which implements the Markov chain Monte Carlo (MCMC) algorithm.19 The MCMC algorithm generates posterior samples from the joint posterior distribution of all parameters in the model, proceeding by sampling each parameter from its conditional posterior distribution using the latest values of all other unknowns and the observed data. Each iteration of the MCMC algorithm cycles through all elements of the unknowns. This process continues for many iterations to obtain random samples from the joint posterior distribution. For each analysis, the MCMC sampler was run for 1.2 × 105 iterations after the first 1000 iterations as burn-in were discarded. To reduce serial correlation in the stored samples, the chain was thinned by one in k=40, yielding 3 × 103 samples for posterior analysis. Convergence diagnostics and mixing behavior assessed using graphical and numerical methods provided by R/qtlbim showed that the chains mixed well and did not indicate a lack of convergence.

We used various methods to graphically and numerically summarize and interpret the posterior samples. The posterior inclusion probability for each locus was estimated as its frequency in the posterior samples. Each locus may be included in the model through its main effects and/or interactions with other loci (epistasis) or environmental effects. The larger the effect size for a locus, the more frequently the locus is sampled. Taking the prior probability into consideration, we used the Bayes factor (BF) to show evidence for inclusion against exclusion of a locus. The BF for a locus is defined as the ratio of the posterior odds to the prior odds for inclusion against exclusion of the locus. A BF threshold of 3 or 2loge (BF)=2.1 supports a claim of significance, according to the recommended guidelines.21 We also separately estimated BFs of main effects and interactions, comparing the models including or excluding a particular effect term. The genetic effects and the proportions of phenotypic variance explained by the different effects (that is, heritabilities) were also estimated. The heritability of an effect was the estimated variance of the effect divided by the phenotypic variance. All these measurements assess the contribution of individual loci while adjusting for effects of all other possible loci.


Main-effect QTL

Bayesian analysis detected significant main-effect QTL for body weight WT3wk, WT6wk, WT10wk (Figure 1) as well as TAIL (not shown) on several chromosomes. Significant main effects for WT3wk each explained 2 to 4% of the phenotypic variance and were detected on chromosomes 2, 3, 6, 8, 11 and 15, among others. Significant main effects on chromosomes 2 and 3 explained the highest proportion of the phenotypic variance for WT6wk. Main effects accounted for 2 to 8% of the variance for body weight at WT10wk (not shown). Age-specific QTL were identified in this work. For example, a QTL on chromosome 15 had marginal effects on WT3wk but had no association with WT6wk and WT10wk (Figure 1). Also, a main-effect QTL on chromosome 6 was associated with WT3wk and WT6wk but not with WT10wk. A pleiotropic QTL on chromosome 2 had significant effects on all growth-related traits. The main and epistatic QTL for TAIL were found on chromosomes 2, 7, 9, 11, 12 and 13 (not shown).

Figure 1

One-dimensional profiles of Bayes factors rescaled as 2logeBF for main (dotted gray lines), epistatic effects (solid black lines) and sex-specific effects (solid gray lines). (a) Body weight at week 3 (WT3wk), (b) body weight at week 6 (WT6wk), (c) body weight at week 10 (WT10wk). The horizontal lines represent the significance threshold of 2logeBF=2.1.

Several QTL with marginal effects on organ and EBW were detected on many chromosomes (not shown). The main effects ranged from 2 to 20% of the variance. Overall, a main-effect QTL for EBW explained the highest proportion of the variance (20%). In addition, a strong main-effect QTL for TES on chromosome 13 explained a large proportion of the variance (15%). When WT10wk was excluded as a covariate from the model, a significant QTL on chromosome 2 had pleiotropic effects on HRT, LIV, SPL and KID.

A number of significant QTL for SCF, EPF and FAT were detected. QTL with pleiotropic main effects on EPF and FAT were located on chromosomes 2 and 18. When adjusted for WT10wk, significant main effects were found on chromosomes 10 and 14 for SCF and EPF, respectively.

QTL with epistatic effects

Epistasis had significant effects on WT3wk on chromosomes 9 and 11 (2logeBF>2.1) (Figure 1). Age-related epistatic effects were observed in this study. For instance, an epistatic QTL on chromosome 9 had significant effects on WT3wk and WT10wk but had no association with WT6wk. Similarly, epistatic QTL on chromosomes 10 and 12 were only associated with WT6wk. Further analysis was conducted to determine the strength of gene–gene interactions among chromosomes. A strong interactive effect was observed between chromosomes 5 and 13 for WT3wk (2logeBF 3.7) (Figure 4).

Epistasis played a significant role in the regulation of EBW, SPL and FAT (Figure 2). Several additive–additive, additive–dominance and dominance–additive effects were detected for EBW. SPL weight was influenced by significant (2logeBF>4) dominance–dominance effects on chromosomes 6, 7, 9 and 10 (Figure 2b). Other interactive effects were identified on chromosomes 1, 2, 7 and 9. The only additive–additive effect for FAT was detected on chromosome 2. In addition, a significant dominance–dominance effect was observed for this trait on chromosome 14. For SPL, correcting for WT10wk resulted in the detection of few epistatic effects (Figure 3a). Also, fat weight was mainly associated with additive–additive effects and dominance–dominance effects (Figure 3b). An interactive effect was observed between QTL on chromosomes 6 and 10 for SPL (Figure 4).

Figure 2

One-dimensional profiles of Bayes factors rescaled as 2logeBF for empty body weight (EBW) (a), spleen (SPL) (b) and FAT (c) (unadjusted for WT10wk) for selected chromosomes for epistatic effects—solid, dashed, dotted and solid-dotted lines represent additive–additive, additive–dominance, dominance–additive and dominance–dominance effects, respectively.

Figure 3

One-dimensional profiles of Bayes factors rescaled as 2logeBF for spleen (SPL) (a), and FAT (b) (adjusted for WT10wk) for selected chromosomes for epistatic effects—solid, dashed, dotted and solid-dotted lines represent additive–additive, additive–dominance, dominance–additive and dominance–dominance effects, respectively.

Figure 4

Two-dimensional profiles of Bayes factors (rescaled as 2logeBF) for WT3wk (top) and spleen (SPL) (bottom) for selected chromosomes. The upper diagonal shows the BF for the model with epistasis compared with no epistasis, and the lower diagonal shows the BF for the full model with main effects and epistasis compared with no quantitative trait loci.

Sex-specific effects

Significant sex-dependent QTL were detected on several chromosomes (Figure 1). A sex-specific QTL on chromosome 11 was detected for all ages and explained 2 to 4% of the phenotypic variance. A significant sex-specific QTL on chromosome 15 was only associated with WT3wk. No sexual dimorphism was observed for body weight on chromosomes 14 and 16.


Growth and body composition are complex traits that are controlled by multiple loci that interact with each other as well as with the environment. The detection of these interrelationships by conventional QTL mapping methods becomes complex as the number of interactions increases. This study used a Bayesian model selection method15 for the joint estimation of the number and positions of QTL and their main and interacting effects.

Growth, age-related body weight and TAIL

Multiple main-effect, epistatic and sex-specific QTL were detected for body weight. A QTL on chromosome 2 had significant marginal effects on body weight at all ages. Other studies showed that chromosome 2 plays a significant role in the genetics of growth, body weight and body composition in many different crosses with varying founding populations, indicating that genetic variation on this chromosome is one of the primary contributors to variation in murine body weight.3, 10, 22, 23, 24

Rocha et al.9 mapped several main-effect QTL for growth by composite interval mapping using the same mouse cross as that used in this study. For main-effect QTL, our present results are consistent with the findings of the previous study. For instance, QTL for WT3wk were identified on chromosomes 1, 2, 3, 4, 6, 7, 8, 11 and 15 in both studies. However, previous studies on this data set using non-Bayesian statistical methods detected few epistatic interactions among main-effect growth QTL.9 The existence of these effects was evident in that work, especially for WT3wk. In addition, some studies have detected strong epistatic effects for growth using other mouse crosses.25, 26 Our Bayesian analysis led to the detection of significant epistatic interactions for WT3wk (2logeBF>2.1) (Figure 1). We detected epistatic QTL with strong effects on chromosomes 5 and 13 (Figure 4), which were not identified in the previous analysis. The epistatic interaction between these two chromosomes was included in the model with high probability (2logeBF 6). The additional growth QTL detected in this study (compared to the study by Rocha et al., 2004) may be the result of our use of more comprehensive methods.

Several studies have reported differences in the genetic control of early and late growth.4, 5, 6 Such differences are not unusual because there is a relatively lower genetic correlation between early and late growth.4, 27 Growth dynamics are made more complex by the significance of gene–gene interactions differing at various ages.4, 6 This phenomenon was also evident in our study. A QTL on chromosome 2 was significantly associated with growth at all ages but epistatic effects were more important for late growth (WT10wk) than early growth (WT3wk and WT6wk) at this locus (Figure 1). These results for chromosome 2 confirm the results by Yi et al.10 who detected a higher level of epistasis in older mice using a backcross that also used M16i as one of the parental strains. Nevertheless, our results generally indicate a stronger effect of epistasis at early ages (WT6wk) than later ages (WT10wk).

Our analyses detected QTL consistent with previous studies. A main-effect QTL on chromosome 6 was associated with WT3wk and WT6wk but not WT10wk. Similarly, a marginal QTL on chromosome 15 was only identified for WT3wk. These were also detected by other studies as separate sets of QTL for early and late growth in mice.5, 10 We also detected QTL that disagreed with some previous results. A previous study identified a QTL that explained 20% of the phenotypic variance for TAIL was observed on chromosome 1,28 but we did not detect any significant QTL on chromosome 1. However, this study identified the main and epistatic QTL for TAIL on chromosomes 2, 3, 7, 9, 11, 12 and 13. These differences could be due to different experimental crosses or methods used.

Organ weights

Many chromosomes were significantly associated with main-effect QTL for organ weights. When organ weights were unadjusted for WT10wk, a QTL on chromosome 2 was significantly associated with HRT, LIV, KID and SPL. However, the inclusion of final body weight as a covariate removed this pleiotropic effect indicating that this QTL likely caused changes in organ weight in proportion to changes in body weight.16 Results from some studies showed that a high phenotypic correlation exists among weights of LIV, HRT, KID and SPL.29 Similar observations were made by other researchers using the same mouse population used here.16 Furthermore, two QTL located at two separate regions on chromosome 2 had pleiotropic effects on all four traits.16 Nevertheless, different genes may be involved in the regulation of these phenotypes.

The mouse population used in this work was previously used to detect main-effect QTL for body composition.16 Our observations for KID were consistent with the results of the previous study. On the other hand, by using Bayesian analysis we identified an additional marginal HRT QTL on chromosome 4. Furthermore, a new QTL for LIV and SPL was detected on chromosome 18. Our use of Bayesian model selection identified several QTL with substantial (2logeBF>2.1) epistatic effects on organ weight. Others also showed the effect of epistasis on organ weight by interval mapping.7 We found a QTL with a very significant effect (2logeBF>12) on TES on chromosome 13 (not shown). Other authors located highly significant16, 30 and suggestive QTL31 for TES weight on the same chromosome.

Fat-related loci

Main-effect and epistatic QTL for fat were detected using the multiple regression method.26 These effects as well as pleiotropy accounted for 63% of the phenotypic variance in an F2 mouse population. QTL with significant main effects on fat-related traits were detected by composite interval mapping in the same population as that used in this study, but no epistatic interactions were detected.16 The inclusion of epistatic effects in this study led to the detection of a new main-effect QTL on chromosome 18 for EPF and SCF. We located several QTL with interactive effects on EPF and FAT in this cross. When adjusted for WT10wk, epistatic QTL on chromosomes 5, 6 and 7 had very large effects on these traits (2logeBF>3). A main-effect QTL for fat traits was observed on chromosome 5 by adjusting for week-12 body weight.10

Chromosome 15 had no significant marginal or epistatic effects on FAT in this work (2logeBF<2.1). These results are surprising because an association between strongly interactive QTL on chromosome 15 and body fat has been observed in several studies.3, 7, 10, 32 QTL with strong marginal effects on body fat have also been detected on this chromosome.16, 33 Some authors indicated that the results obtained from studies on epistasis depend on the statistical method used.7 The differences in our results compared with other findings may also be attributed to differences in the genetic background of the mice and environmental effects.

We observed a number of QTL with pleiotropic effects on body weight and body fat. For example, the QTL on chromosome 2 was associated with all body weight and some fat and organ-related phenotypes. The pleiotropic effect of QTL on body fat and body weight was reported in several studies for diverse mouse populations.22, 26 Body weight and body fat have been found to be highly correlated.16

Obesity among humans often occurs in the context of ready availability of highly palatable, calorie-dense diets. Yet it is not true that we know that all or even most obesity occurs from that per se. This has been nicely described by Drewnowski.34 In reality, obesity is likely due to many and varying factors.35 The QTL we identified were detected in a particular set of environmental circumstances, namely a low-fat, balanced, constant diet of lab chow and with minimum availability in opportunities for physical activity. Given the frequent observations of gene by environment interactions,3 it is most likely that additional and different QTL might be detected where the environment is to be changed. Future research should investigate this possibility.


Using the Bayesian model selection method, we detected several QTL with main, epistatic and sex-specific effects on body weight and obesity-related phenotypes. When this population was used for the detection of QTL for similar traits using the composite interval mapping method, very few epistatic interactions were identified. The use of Bayesian model selection detected many QTL with marginal and epistatic effects as well as epistatic interactions among chromosomes. The detection of epistatic interactions provides new information about the genetic factors underlying body weight and other obesity-related phenotypes. In particular, the discovery that epistatic control of a phenotype such as body weight changes during development adds a new layer of complexity to complex trait analysis.


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This research was partly supported by the National Institutes of Health Grants GM069430, DK056336, DK076050 and HL072757.

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Correspondence to N Yi.

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  • Bayesian methods
  • body weight
  • epistasis
  • quantitative trait loci

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