Genomic evaluation of both purebred and crossbred performances

Background

For a two-breed crossbreeding system, Wei and van der Werf presented a model for genetic evaluation using information from both purebred and crossbred animals. The model provides breeding values for both purebred and crossbred performances. Genomic evaluation incorporates marker genotypes into a genetic evaluation system. Among popular methods are the so-called single-step methods, in which marker genotypes are incorporated into a traditional animal model by using a combined relationship matrix that extends the marker-based relationship matrix to non-genotyped animals. However, a single-step method for genomic evaluation of both purebred and crossbred performances has not been developed yet.

Results

An extension of the Wei and van der Werf model that incorporates genomic information is presented. The extension consists of four steps: (1) the Wei van der Werf model is reformulated using two partial relationship matrices for the two breeds; (2) marker-based partial relationship matrices are constructed; (3) marker-based partial relationship matrices are adjusted to be compatible to pedigree-based partial relationship matrices and (4) combined partial relationship matrices are constructed using information from both pedigree and marker genotypes. The extension of the Wei van der Werf model can be implemented using software that allows inverse covariance matrices in sparse format as input.

Conclusions

A method for genomic evaluation of both purebred and crossbred performances was developed for a two-breed crossbreeding system. The method allows information from crossbred animals to be incorporated in a coherent manner for such crossbreeding systems.     

The correlation between relatives on the supposition of genomic imprinting

Standard genetic analyses assume that reciprocal heterozygotes are, on average, phenotypically identical. If a locus is subject to genomic imprinting, however, this assumption does not hold. We incorporate imprinting into the standard quantitative-genetic model for two alleles at a single locus, deriving expressions for the additive and dominance components of genetic variance, as well as measures of resemblance among relatives. We show that, in contrast to the case with Mendelian expression, the additive and dominance deviations are correlated. In principle, this correlation allows imprinting to be detected solely on the basis of different measures of familial resemblances, but in practice, the standard error of the estimate is likely to be too large for a test to have much statistical power. The effects of genomic imprinting will need to be incorporated into quantitative-genetic models of many traits, for example, those concerned with mammalian birthweight.     

The probability density of the total IBD length over a single autosome in unilineal relationships

Several authors have studied identity by descent (IBD) by way of a continuous recombination process along a chromosome. Despite its potential uses in, for example, gene mapping or delineation of biological relationships there has been no exact algebraic result given for the probability density function of the IBD proportion in any familial relationship. Other authors have derived algebraic approximations in the case of half-sibs by way of the Poisson clumping heuristic and used computational methods to compute the distribution function of the IBD sharing for unilineal relationships. Here we provide a general numerical method for finding the density of IBD sharing that could be applied to any unilineal relationship and more importantly we derive algebraically an expression for the density for a grandparent-grandchild relationship. Initially we assume that recombination events occur at random along a chromosome, then go on to show how the method could be extended to incorporate a form of genetic interference.     

Genotypic dispersion and covariance between relatives under linkage disequilibrium

A random mating diploid population under linkage disequilibrium is considered. In the case of two diallelic loci, the problem about condition and joint distributions of genotypes of relatives being in arbitrary genetic relations is solved. Formulae of the partitioning of genotypic variance and covariance between relatives with respect to a polygenic character are inferred (in the case of many characters - of genotypic covariance matrix).     

Parent-of-origin effects cause genetic variation in pig performance traits

In order to assess the relative importance of genomic imprinting for the genetic variation of traits economically relevant for pork production, a data set containing 21 209 records from Large White pigs was analysed. A total of 33 traits for growth, carcass composition and meat quality were investigated. All traits were recorded between 1997 and 2006 at a test station in Switzerland and the pedigree included 15 747 ancestors. A model with two genetic effects for each animal was applied: the first corresponds to a paternal and the second to a maternal expression pattern of imprinted genes. The imprinting variance was estimated as the sum of both corresponding genetic variances per animal minus twice the covariance. The null hypothesis of no imprinting was tested by a restricted maximum likelihood ratio test with two degrees of freedom. Genomic imprinting significantly contributed to the genetic variance of 19 traits. The proportion of the total additive genetic variance that could be attributed to genomic imprinting was of the order between 5% and 19%.     

Estimation of the parameters of the single-locus diallele model of qualitative trait in groups of relations

The method of estimation of parameters of monolocus diallele model (MDM) of qualitative trait on relative group data is described, these parameters being the number of affected and normal proband relatives of the arbitrary family degree and siblings in different matings types. For the case of single ascertainment, the expressions of corresponding probabilities have been taken as functions of MDM parameters using ITO matrixes and genetic transition matrix. Estimation of parameters was obtained by the maximum likelyhood method. Hardy-Weinberg equilibrium is not always necessary for this method; some weak requirement of stationarity is quite enough.     

Two-trait-locus linkage analysis: a powerful strategy for mapping complex genetic traits.

Recent advances in molecular biology have provided geneticists with ever-increasing numbers of highly polymorphic genetic markers that have made possible linkage mapping of loci responsible for many human diseases. However, nearly all diseases mapped to date follow clear Mendelian, single-locus segregation patterns. In contrast, many common familial diseases such as diabetes, psoriasis, several forms of cancer, and schizophrenia are familial and appear to have a genetic component but do not exhibit simple Mendelian transmission. More complex models are required to explain the genetics of these important diseases. In this paper, we explore two-trait-locus, two-marker-locus linkage analysis in which two trait loci are mapped simultaneously to separate genetic markers. We compare the utility of this approach to standard one-trait-locus, one-marker-locus linkage analysis with and without allowance for heterogeneity. We also compare the utility of the two-trait-locus, two-marker-locus analysis to two-trait-locus, one-marker-locus linkage analysis. For common diseases, pedigrees are often bilineal, with disease genes entering via two or more unrelated pedigree members. Since such pedigrees often are avoided in linkage studies, we also investigate the relative information content of unilineal and bilineal pedigrees. For the dominant-or-recessive and threshold models that we consider, we find that two-trait-locus, two-marker-locus linkage analysis can provide substantially more linkage information, as measured by expected maximum lod score, than standard one-trait-locus, one-marker-locus methods, even allowing for heterogeneity, while, for a dominant-or-dominant generating model, one-locus models that allow for heterogeneity extract essentially as much information as the two-trait-locus methods. For these three models, we also find that bilineal pedigrees provide sufficient linkage information to warrant their inclusion in such studies. We also discuss strategies for assessing the significance of the two linkages assumed in two-trait-locus, two-marker-locus models.     

Quantifying genomic imprinting in the presence of linkage

Genomic imprinting decreases the power of classical linkage analysis, in which paternal and maternal transmissions of marker alleles are equally weighted. Several methods have been proposed for taking genomic imprinting into account in the model-free linkage analysis of binary traits. However, none of these methods are suitable for the formal identification and quantification of genomic imprinting in the presence of linkage. In addition, the available methods are designed for use with pure sib-pairs, requiring artificial decomposition in cases of larger sibships, leading to a loss of power. We propose here the maximum likelihood binomial method adaptive for imprinting (MLB-I), which is a unified analytic framework giving rise to specific tests in sibships of any size for (i) linkage adaptive to imprinting, (ii) genomic imprinting in the presence of linkage, and (iii) partial versus complete genomic imprinting. In addition, we propose an original measure for quantifying genomic imprinting. We have derived and validated the distribution of the three tests under their respective null hypotheses for various genetic models, and have assessed the power of these tests in simulations. This method can readily be applied to genome-wide scanning, as illustrated here for leprosy sibships. Our approach provides a novel tool for dissecting genomic imprinting in model-free linkage analysis, and will be of considerable value for identifying and evaluating the contribution of imprinted genes to complex diseases.     

A framework for detecting and characterizing genetic background-dependent imprinting effects

Genomic imprinting, where the effects of alleles depend on their parent-of-origin, can be an important component of the genetic architecture of complex traits. Although there has been a rapidly increasing number of studies of genetic architecture that have examined imprinting effects, none have examined whether imprinting effects depend on genetic background. Such effects are critical for the evolution of genomic imprinting because they allow the imprinting state of a locus to evolve as a function of genetic background. Here we develop a two-locus model of epistasis that includes epistatic interactions involving imprinting effects and apply this model to scan the mouse genome for loci that modulate the imprinting effects of quantitative trait loci (QTL). The inclusion of imprinting leads to nine orthogonal forms of epistasis, five of which do not appear in the usual two-locus decomposition of epistasis. Each form represents a change in the imprinting status of one locus across different classes of genotypes at the other locus. Our genome scan identified two different locus pairs that show complex patterns of epistasis, where the imprinting effect at one locus changes across genetic backgrounds at the other locus. Thus, our model provides a framework for the detection of genetic background-dependent imprinting effects that should provide insights into the background dependence and evolution of genomic imprinting. Our application of the model to a genome scan supports this assertion by identifying pairs of loci that show reciprocal changes in their imprinting status as the background provided by the other locus changes.     

A PEDIGREE OF ONE FAMILY WITH DELAYED SLEEP PHASE SYNDROME

The prevalence of delayed sleep phase syndrome (DSPS) has been estimated to be quite low. Although no genetic inheritance pattern has been described, it has been reported that close to 50% of DSPS patients have biological relatives with similar symptoms. A pedigree of one extended family with symptoms suggestive of DSPS has been identified. Morningnesseveningness questionnaires were administered to all first- and second-degree relatives of a proband identified with DSPS. A total of 51 (86%) questionnaires were returned, and 6 adult biological relatives of 27 (22%) showed a preference for eveningness, which is much higher than reported in the general population. Both the paternal and maternal branches contained affected individuals, suggesting the possibility of a bilineal mode of inheritance. While the trait did not obey simple Mendelian inheritance, the vertical patterns of transmission were consistent with either an autosomal dominant mode of inheritance with incomplete penetrance or a multifactorial mode of inheritance. These data provide some preliminary support to the notion that eveningness, and thus DSPS, may have a genetic component. The prevalence of symptoms suggestive of DSPS is higher in this family than reported in the general population. Case reports such as this support the utility of larger, more systematic studies. It is unclear whether this degree of familiarity is representative of that in the general population. (Chronobiology International, 18(5), 831-840, 2001)     

Genetic conflicts,multiple paternity and the evolution of genomic imprinting.

We present nine diallelic models of genetic conflict in which one allele is imprintable and the other is not to examine how genomic imprinting may have evolved. Imprinting is presumed to be either maternal (i.e., the maternally derived gene is inactivated) or paternal. Females are assumed to be either completely monogamous or always bigamous, so that we may see any effect of multiple paternity. In contrast to previous verbal and quantitative genetic models, we find that genetic conflicts need not lead to paternal imprinting of growth inhibitors and maternal imprinting of growth enhancers. Indeed, in some of our models--those with strict monogamy--the dynamics of maternal and paternal imprinting are identical. Multiple paternity is not necessary for the evolution of imprinting, and in our models of maternal imprinting, multiple paternity has no effect at all. Nevertheless, multiple paternity favors the evolution of paternal imprinting of growth inhibitors and hinders that of growth enhancers. Hence, any degree of multiple paternity means that growth inhibitors are more likely to be paternally imprinted, and growth enhancers maternally so. In all of our models, stable polymorphism of imprinting status is possible and mean fitness can decrease over time. Neither of these behaviors have been predicted by previous models.     

A PEDIGREE OF ONE FAMILY WITH DELAYED SLEEP PHASE SYNDROME

The prevalence of delayed sleep phase syndrome (DSPS) has been estimated to be quite low. Although no genetic inheritance pattern has been described, it has been reported that close to 50% of DSPS patients have biological relatives with similar symptoms. A pedigree of one extended family with symptoms suggestive of DSPS has been identified. Morningnesseveningness questionnaires were administered to all first- and second-degree relatives of a proband identified with DSPS. A total of 51 (86%) questionnaires were returned, and 6 adult biological relatives of 27 (22%) showed a preference for eveningness, which is much higher than reported in the general population. Both the paternal and maternal branches contained affected individuals, suggesting the possibility of a bilineal mode of inheritance. While the trait did not obey simple Mendelian inheritance, the vertical patterns of transmission were consistent with either an autosomal dominant mode of inheritance with incomplete penetrance or a multifactorial mode of inheritance. These data provide some preliminary support to the notion that eveningness, and thus DSPS, may have a genetic component. The prevalence of symptoms suggestive of DSPS is higher in this family than reported in the general population. Case reports such as this support the utility of larger, more systematic studies. It is unclear whether this degree of familiarity is representative of that in the general population. (Chronobiology International, 18(5), 831–840, 2001)     

Frequencies of genotypes of relatives,as determined by stochastic matrices

The ITO method ofLi & Sacks (1954) is extended to simply closed inbreeding systems. Two new matrices I^* and D are introduced. These matrices give the probabilities of descendent genotypes when the ancestor is given and vice versa. The computations of the transition matrices are made less cumbersome by the introduction of an operator-method. The results are extended to multiple alleles (section 2) and to sex-linked loci (section 3). As applications, the computation of genetic correlations (section 4) and of unconditional probabilities (section 6) are considered.     

基因印记与lncRNA

基因印记是一种表观遗传调控机制,在二倍体哺乳动物的发育过程中,基因印记可以调控来自亲代的等位基因差异表达。非编码RNA是不编码蛋白质的RNA,它在RNA水平调控基因表达。研究表明大多数印记基因中存在长非编码RNA（长度>200nt的非编码RNA）的转录,长非编码RNA主要通过顺式的转录干扰作用来实现基因印记。同时基因印记及其相关的长非编码RNA异常表达与许多先天疾病相关,迄今已发现数十种人类遗传疾病与基因印记有关,而lncRNA引起的基因印记在疾病的发生和治疗中起着重要作用。     

PHYLOGENETIC ANALYSIS OF PHENOTYPIC COVARIANCE STRUCTURE. II. RECONSTRUCTING MATRIX EVOLUTION

A modified minimum evolution approach is used to estimate covariance matrices for hypothetical ancestors. Branch lengths are calculated as the mean disparity in corresponding ancestor-descendent covariances. Branches are longest leading to terminal populations and subspecies, while interspecific branches are relatively short, indicating a general conservation of covariance structure among species despite a high degree of intraspecific variability. Absolute deviations in covariance structure are not correlated with phenotypic divergence. Interpreted in light of other studies, the analyses suggest that deviations in covariance structure are most strongly associated with the formation of diagnosably distinct taxa and stochastic sampling of genotypes at the population level. There is no evidence for restructuring of phenotypic covariance structure in association with reproductive isolation. The results suggest that phenotypic covariances are dynamic over short time scales and do not support attempts to extrapolate genetic covariance structure to explain or predict macroevolutionary change. This study further demonstrates that branch lengths, which are not usually analyzed in detail, contain valuable evolutionary information complementary to that residing in the branching pattern.     

Population Genetic Models of Genomic Imprinting

The phenomenon of genomic imprinting has recently excited much interest among experimental biologists. The population genetic consequences of imprinting, however, have remained largely unexplored. Several population genetic models are presented and the following conclusions drawn: (i) systems with genomic imprinting need not behave similarly to otherwise identical systems without imprinting; (ii) nevertheless, many of the models investigated can be shown to be formally equivalent to models without imprinting; (iii) consequently, imprinting often cannot be discovered by following allele frequency changes or examining equilibrium values; (iv) the formal equivalences fail to preserve some well known properties. For example, for populations incorporating genomic imprinting, parameter values exist that cause these populations to behave like populations without imprinting, but with heterozygote advantage, even though no such advantage is present in these imprinting populations. We call this last phenomenon "pseudoheterosis." The imprinting systems that fail to be formally equivalent to nonimprinting systems are those in which males and females are not equivalent, i.e., two-sex viability systems and sex-chromosome inactivation.     

Selective abortion and the evolution of genomic imprinting

Mothers can determine which genotypes of offspring they will produce through selective abortion or selective implantation. This process can, at some loci, favour matching between maternal and offspring genotype whereas at other loci mismatching may be favoured (e.g. MHC, HLA). Genomic imprinting generally renders gene expression monoallelic and could thus be adaptive at loci where matching or mismatching is beneficial. This hypothesis, however, remains unexplored despite evidence that loci known to play a role in genetic compatibility may be imprinted. We develop a simple model demonstrating that, when matching is beneficial, imprinting with maternal expression is adaptive because the incompatible paternal allele is not detected, protecting offspring from selective abortion. Conversely, when mismatching is beneficial, imprinting with paternal expression is adaptive because the maternal genotype is more able to identify the presence of a foreign allele in offspring. Thus, imprinting may act as a genomic ‘cloaking device’ during critical periods in development when selective abortion is possible.     

The Evolution of Genomic Imprinting

In some mammalian genes, the paternally and maternally derived alleles are expressed differently: this phenomenon is called genomic imprinting. Here we study the evolution of imprinting using multivariate quantitative genetic models to examine the feasibility of the genetic conflict hypothesis. This hypothesis explains the observed imprinting patterns as an evolutionary outcome of the conflict between the paternal and maternal alleles. We consider the expression of a zygotic gene, which codes for an embryonic growth factor affecting the amount of maternal resources obtained through the placenta. We assume that the gene produces the growth factor in two different amounts depending on its parental origin. We show that genomic imprinting evolves easily if females have some probability of multiple partners. This is in conflict with the observation that not all genes controlling placental development are imprinted and that imprinting in some genes is not conserved between mice and humans. We show however that deleterious mutations in the coding region of the gene create selection against imprinting.     

THE COMPARISON OF QUANTITATIVE GENETIC PARAMETERS BETWEEN POPULATIONS

A statistical method for comparing matrices of genetic variation and covariation between groups (e.g., species, populations, a single population grown in distinct environments) is proposed. This maximum-likelihood method provides a test of the overall null hypothesis that two covariance component matrices are identical. Moreover, when the overall null hypothesis is rejected, the method provides a framework for isolating the particular components that differ significantly between the groups. Simulation studies reveal that discouragingly large experiments are necessary to obtain acceptable power for comparing genetic covariance component matrices. For example, even in cases of a single trait measured on 900 individuals in a nested design of 100 sires and three dams per sire in each population, the power was only about 0.5 when additive genetic variance differed by a factor of 2.5. Nevertheless, this flexible method makes valid comparison of covariance component matrices possible.     

Theory of genomic imprinting conflict in social insects

Background  

Genomic imprinting refers to the differential expression of genes inherited from the mother and father (matrigenes and patrigenes). The kinship theory of genomic imprinting treats parent-specific gene expression as products of within-genome conflict. Specifically, matrigenes and patrigenes will be in conflict over treatment of relatives to which they are differently related. Haplodiploid females have many such relatives, and social insects have many contexts in which they affect relatives, so haplodiploid social insects are prime candidates for tests of the kinship theory of imprinting.