To describe variation among individuals in the number or distribution of methylated nucleotides at specific gene sequences, a new term, called epialleles, has been coined [16]. Because epiallele phenotypes can have identical underlying DNA sequences, the genetic control mechanisms of these phenotypes are likely to differ from those estimated from traditional models of quantitative genetics. Thus, it is crucial to screen for epiallelic variants within a population and disentangle epigenetic from more standard genetic sources of phenotypic variance, such as additive genetic variance, dominance variance, epistasis and maternal genetic effects [17]. More recently, Johannes et al. [12] developed a panel of epigenetic Recombinant Inbred Lines (epiRILs) in the reference plant Arabidopsis thaliana to identify the genetic variation due to epiallelic variants in flowering time and plant height. Epiallelic variation can also be studied by tracing parent-dependent differences of the same allele. If the same allele functions differently, depending on which parent the allele is derived from, a phenomenon known as genetic imprinting or parent-of-origin effect, this allele may be epigenetic. Previous studies have suggested that genetic imprinting results from an epigenetic mark of differential methylation set during gametogenesis [18]–[20], forming part of the genetic architecture involved in the formation, development, function, and evolution of complex traits and diseases [21]–[25].

The past several years have witnessed an intense interest in mapping and identifying the regions of the genome that contain imprinted sequence variants with genome-wide linkage and association studies. Cheverud et al. [26] and Wolf et al. [27] used a three-generation F design to map genome-wide imprinted quantitative trait loci (iQTLs) that affect body weight and growth in mice, and they found that these traits may be controlled by QTLs with more complex and diverse effect patterns than previously assumed. Li et al. [28] proposed a reciprocal backcross design to estimate the distribution of iQTLs and quantify their effects on physiological traits related to endosperm development in maize. By modeling alleles identical-by-descent in a multi-generational pedigree of canines, Liu et al. [29] derived a linkage-based random effect to genome-wide scan for the existence of iQTLs that affect canine hip dysplasia. However, there is limited knowledge about whether imprinted effects are inherited over generations and, if yes, how imprinting inheritance takes place [19], [30]–[37]. An understanding of these question will help to characterize the impacts of imprinting loci on the genetic diversity of a biological trait or process [38]–[40].

The attempts to characterize imprinting effects are affected by our incapacity to discern the effect of DNA methylation variants from that of DNA sequence variants using a mapping study. This issue was, however, resolved by comparing two reciprocal crosses in which the maternally- or paternally-derived version of the same allele at a gene can be identified [28], [45]. Liu et al. [29] incorporated identical-by-descent (IBD) sharing into a random-effect mapping model, allowing the characterization of the discrepancy of allelic transmission through different parents. Linkage mapping using controlled crosses or pedigrees with known parents has led to the genome-wide identification of imprinted quantitative trait loci (iQTLs) that affect body weight and growth in mice [26], [27], physiological traits related to endosperm development in maize [28], and hip dysplasia in canines [29].

However, to study the precise genetic mechanisms through which chromatin dynamics alter quantitative variation, a simple test of imprinting effects of iQTLs is not adequate. Rather, a detailed understanding of whether and how imprinting effects are transmitted across generations is crucial for determining the contribution of epigenetic modification to heritable phenotypic variation for a complex trait. In this article, we present a new strategy for estimating and testing imprinting effects of iQTLs and their transgenerational transmission through two-generation reciprocal crosses leading to four epigenetically different F families (Figure S1). The new strategy displays two advantages compared with previous models. First, it provides a comprehensive elucidation of the genetic control mechanisms for a complex trait or disease in terms of traditionally defined additive and dominant effects, newly defined imprinted effects, and their interactions. Second, the strategy has power to detect the changes of imprinting effects from generation to generation, thus facilitating the modeling of transgenerational epigenetic variation and inheritance.

We formulated a mixture model-based likelihood for the imprinting effects of iQTLs flanked by markers in four epigenetically different F families. A closed form of the EM algorithm was derived to estimate a high-dimensional set of genetic parameters that define the maternally- and paternally-imprinted genetic effects and their interactions in the F, the additive, dominant, and imprinting effects in the F, and the interactions of different orders between these effects expressed in different generations. The algorithm was tested through simulation studies from which the minimum heritability and sample size for reasonable estimates of each parameter are determined. Additional simulation studies were performed to test the power for the detection of imprinting effects at different levels. In general, the model shows reasonably low false positive rates for the data in which no imprinting effects exist. In an application of the new model for genetic mapping of iQTL in mice, we identified five significant QTLs on chromosomes 1, 4, 9, and 15 for the overall survival time to hyperoxic acute lung injury (HALI). Each of these QTLs displays remarked imprinting effects on HALI. The model was further used to test when and how these imprinting effects are activated to affect the expression of HALI. In general, all the iQTLs trigger marked imprinting effects in the F (see and estimates in Table 2). During transmission into the next generation, these imprinting effects were observed to be shrunk (see estimates in Table 2). But highly significant imprinting effects in the F generation can still be detected (Table 3; see also [46]) when the interactions between the imprinting effects of the F and main effects of the F are jointly tested. This result suggests that imprinting effects detected from pure F generations, as conducted in [46], may have confounded their interactions with other effects formed during transmission. The results from reanalyzing the mouse data with the new model shed light on the new inheritance and aetiology of HALI.

Figure S1

Figure S2

Methods S1