As an epigenetic form of gene regulation, genomic imprinting influences the expression of marked or imprinted genes during gametogenesis and embryonic development in a parent-of-origin-specific manner. Imprinting functions through methylation and histone modifications, which are established in the germline and maintained throughout all somatic cells of an organism. Recent emerging evidence suggests that genetic imprinting may not be transferred between generations through epigenetic remodeling and reprogramming, in order to ensure the totipotency of the zygote and prevent perpetuation of abnormal epigenetic states [
11,
26–29]. To address whether transgenerational epigenetic reprogramming occurs, Wang
et al. [
20] proposed a new mapping model for mapping imprinted quantitative trait loci (
iQTLs) showing the transgenerational inheritance of imprinting effects using a reciprocal F
2 design. By analyzing a published data set of mice [
24], this model identified several
iQTLs for survival time due to HALI. The main result obtained was that, while most of genetic imprinting effects established in the previous generation might be erased, some were still transmitted to the next generations through their interactions with other genetic effects.
The model proposed for a reciprocal backcross design in this article builds upon Wang
et al.’s work to make two key contributions. First, it provides successful inferences about parent-of-origin effects at
iQTLs for HALI survival time from an extensive data analysis of mouse reciprocal backcrosses [
25]. The new model confirms the QTLs (i.e.

and

) discovered by traditional mapping approaches, validating the genetic usefulness of our model. Second, we here put forward a series of new genetic parameters that define the transgenerational inheritance of
iQTLs, greatly facilitating our understanding of the genetic mechanisms of imprinting effects. By linking these definitions with a mapping study, the new model allows the genome-wide scan and discovery of
iQTLs, their number, the type and magnitude of their effects, their genetic interactions and genotype–environment interactions. Although many
iQTLs have been identified for different traits in plants, animals and humans [
3,
10,
17–19], this model will, for the first time, make it possible to study the interplay between
iQTLs and transgenerational epigenetic inheritance. The newly defined parameters for genomic imprinting for HALI survival time will help understand the genetic control mechanisms of this trait in terms of the underlying inheritance, transmission and interactions.
Acute lung injury and adult respiratory distress syndrome, associated with 38.5% mortality or nearly 75

000 deaths/year in the United States [
30], are fatal to any population, especially older people. The genetic control of survival time due to this disease has been studied using the animal model system—mouse. Prows
et al. [
24] detected the two major QTLs (

and

) for HALI survival time in a reciprocal F
2 population derived from sensitive C57BL/6J and resistant 129X1/SvJ inbred mouse strains, and these two QTLs were confirmed by a subsequent mapping study using the reciprocal backcross design produced by the same inbred lines [
25]. All these QTLs were further confirmed by Wang
et al.’s imprinting model [
20] and the model presented here. The new imprinting models provide an explanation about the genetic underpinnings for imprinting inheritance at these QTLs. For example, any identical genotype should be expressed equally under the same condition, but in our study it was found to have different values due to the impact of transgenerational imprinting effects (). In Wang
et al. [
20] and here, we used HALI survival time as an example to assess the usefulness of these models. It can be anticipated that the models can be used to study any other quantitative traits. In other species like maize, similar cross schemes are made [
18], thus the models will find its immediate application in general genetic studies.
Maternal effects may confound the estimation of genomic imprinting. By incorporating Cui’s model [
31] into our four-way reciprocal crosses, it is possible to estimate and eliminate the confounding maternal effect from estimated imprinting effects. In addition, several mechanisms have evolved to erase the epigenetic marks, including germline and somatic reprogramming of DNA methylation and chromatin proteins. However, our previous [
20] and current studies using different designs on the same data set found that at some
iQTLs the epigenetic marks are not cleared across generations. Other examples of this include genomic imprinting in mammals, mating type switching in yeast and paramutation in plants [
11]. The resistance of these imprinted loci to reprogramming may be regarded as part of normal development, but they should not be independent of environmental triggers. Our models can be used to address fundamental issues of what is the extent of resistance to transgenerational epigenetic reprogramming and whether or not epigenetic marks established in response to environmental cues are also resistant [
11]. Further, when the processes of DNA methylation and chromatin proteins are integrated, our model will enable geneticists to predict which type of epigenetic marks will be erased and which will not be erased.