Equivalence of multibreed animal models and hierarchical Bayes analysis for maternally influenced traits

Background

It has been argued that multibreed animal models should include a heterogeneous covariance structure. However, the estimation of the (co)variance components is not an easy task, because these parameters can not be factored out from the inverse of the additive genetic covariance matrix. An alternative model, based on the decomposition of the genetic covariance matrix by source of variability, provides a much simpler formulation. In this study, we formalize the equivalence between this alternative model and the one derived from the quantitative genetic theory. Further, we extend the model to include maternal effects and, in order to estimate the (co)variance components, we describe a hierarchical Bayes implementation. Finally, we implement the model to weaning weight data from an Angus × Hereford crossbred experiment.

Methods

Our argument is based on redefining the vectors of breeding values by breed origin such that they do not include individuals with null contributions. Next, we define matrices that retrieve the null-row and the null-column pattern and, by means of appropriate algebraic operations, we demonstrate the equivalence. The extension to include maternal effects and the estimation of the (co)variance components through the hierarchical Bayes analysis are then straightforward. A FORTRAN 90 Gibbs sampler was specifically programmed and executed to estimate the (co)variance components of the Angus × Hereford population.

Results

In general, genetic (co)variance components showed marginal posterior densities with a high degree of symmetry, except for the segregation components. Angus and Hereford breeds contributed with 50.26% and 41.73% of the total direct additive variance, and with 23.59% and 59.65% of the total maternal additive variance. In turn, the contribution of the segregation variance was not significant in either case, which suggests that the allelic frequencies in the two parental breeds were similar.

Conclusion

The multibreed maternal animal model introduced in this study simplifies the problem of estimating (co)variance components in the framework of a hierarchical Bayes analysis. Using this approach, we obtained for the first time estimates of the full set of genetic (co)variance components. It would be interesting to assess the performance of the procedure with field data, especially when interbreed information is limited.     

Principal component approach in variance component estimation for international sire evaluation

Background

The dairy cattle breeding industry is a highly globalized business, which needs internationally comparable and reliable breeding values of sires. The international Bull Evaluation Service, Interbull, was established in 1983 to respond to this need. Currently, Interbull performs multiple-trait across country evaluations (MACE) for several traits and breeds in dairy cattle and provides international breeding values to its member countries. Estimating parameters for MACE is challenging since the structure of datasets and conventional use of multiple-trait models easily result in over-parameterized genetic covariance matrices. The number of parameters to be estimated can be reduced by taking into account only the leading principal components of the traits considered. For MACE, this is readily implemented in a random regression model.

Methods

This article compares two principal component approaches to estimate variance components for MACE using real datasets. The methods tested were a REML approach that directly estimates the genetic principal components (direct PC) and the so-called bottom-up REML approach (bottom-up PC), in which traits are sequentially added to the analysis and the statistically significant genetic principal components are retained. Furthermore, this article evaluates the utility of the bottom-up PC approach to determine the appropriate rank of the (co)variance matrix.

Results

Our study demonstrates the usefulness of both approaches and shows that they can be applied to large multi-country models considering all concerned countries simultaneously. These strategies can thus replace the current practice of estimating the covariance components required through a series of analyses involving selected subsets of traits. Our results support the importance of using the appropriate rank in the genetic (co)variance matrix. Using too low a rank resulted in biased parameter estimates, whereas too high a rank did not result in bias, but increased standard errors of the estimates and notably the computing time.

Conclusions

In terms of estimation''s accuracy, both principal component approaches performed equally well and permitted the use of more parsimonious models through random regression MACE. The advantage of the bottom-up PC approach is that it does not need any previous knowledge on the rank. However, with a predetermined rank, the direct PC approach needs less computing time than the bottom-up PC.     

Better Estimates of Genetic Covariance Matrices by “Bending” Using Penalized Maximum Likelihood

Obtaining accurate estimates of the genetic covariance matrix for multivariate data is a fundamental task in quantitative genetics and important for both evolutionary biologists and plant or animal breeders. Classical methods for estimating are well known to suffer from substantial sampling errors; importantly, its leading eigenvalues are systematically overestimated. This article proposes a framework that exploits information in the phenotypic covariance matrix in a new way to obtain more accurate estimates of . The approach focuses on the “canonical heritabilities” (the eigenvalues of ), which may be estimated with more precision than those of because is estimated more accurately. Our method uses penalized maximum likelihood and shrinkage to reduce bias in estimates of the canonical heritabilities. This in turn can be exploited to get substantial reductions in bias for estimates of the eigenvalues of and a reduction in sampling errors for estimates of . Simulations show that improvements are greatest when sample sizes are small and the canonical heritabilities are closely spaced. An application to data from beef cattle demonstrates the efficacy this approach and the effect on estimates of heritabilities and correlations. Penalized estimation is recommended for multivariate analyses involving more than a few traits or problems with limited data.QUANTITATIVE geneticists, including evolutionary biologists and plant and animal breeders, are increasingly dependent on multivariate analyses of genetic variation, for example, to understand evolutionary constraints and design efficient selection programs. New challenges arise when one moves from estimating the genetic variance of a single phenotype to the multivariate setting. An important but unresolved issue is how best to deal with sampling variation and the corresponding bias in the eigenvalues of estimates for the genetic covariance matrix, . It is well known that estimates for the largest eigenvalues of a covariance matrix are biased upward and those for the smallest eigenvalues are biased downward (Lawley 1956; Hayes and Hill 1981). For genetic problems, where we need to estimate at least two covariance matrices simultaneously, this tends to be exacerbated, especially for . In turn, this can result in invalid estimates of , i.e., estimates with negative eigenvalues, and can produce systematic errors in predictions for the response to selection.There has been longstanding interest in “regularization” of covariance matrices, in particular for cases where the ratio between the number of observations and the number of variables is small. Various studies recently employed such techniques for the analysis of high-dimensional, genomic data. In general, this involves a compromise between additional bias and reduced sampling variation of “improved” estimators that have less statistical risk than standard methods (Bickel and Li 2006). For instance, various types of shrinkage estimators of covariance matrices have been suggested that counteract bias in estimates of eigenvalues by shrinking all sample eigenvalues toward their mean. Often this is equivalent to a weighted combination of the sample covariance matrix and a target matrix, assumed to have a simple structure. A common choice for the latter is an identity matrix. This yields a ridge regression type formulation (Hoerl and Kennard 1970). Numerous simulation studies in a variety of settings are available, which demonstrate that regularization can yield closer agreement between estimated and population covariance matrices, less variable estimates of model terms, or improved performance of statistical tests.In quantitative genetic analyses, we attempt to partition observed, overall (phenotypic) covariances into their genetic and environmental components. Typically, this results in strong sampling correlations between them. Hence, while the partitioning into sources of variation and estimates of individual covariance matrices may be subject to substantial sampling variances, their sum, i.e., the phenotypic covariance matrix, can generally be estimated much more accurately. This has led to suggestions to “borrow strength” from estimates of phenotypic components to estimate the genetic covariances. In particular, Hayes and Hill (1981) proposed a method termed “bending” that involved regressing the eigenvalues of the product of the genetic and the inverse of the phenotypic covariance matrix toward their mean. One objective of this procedure was to ensure that estimates of the genetic covariance matrix from an analysis of variance were positive definite. In addition, the authors showed by simulation that shrinking eigenvalues even further than needed to make all values nonnegative could improve the achieved response to selection when using the resulting estimates to derive weights for a selection index, especially for estimation based on small samples. Subsequent work demonstrated that bending could also be advantageous in more general scenarios such as indexes that included information from relatives (Meyer and Hill 1983).Modern, mixed model (“animal model”)-based analyses to estimate genetic parameters using maximum likelihood or Bayesian methods generally constrain estimates to the parameter space, so that—at the expense of introducing some bias—estimates of covariance matrices are positive semidefinite. However, the problems arising from substantial sampling variation in multivariate analyses remain. In spite of increasing applications of such analyses in scenarios where data sets are invariably small, e.g., the analysis of data from natural populations (e.g., Kruuk et al. 2008), there has been little interest in regularization and shrinkage techniques in genetic parameter estimation, other than through the use of informative priors in a Bayesian context. Instead, suggestions for improved estimation have focused on parsimonious modeling of covariance matrices, e.g., through reduced rank estimation or by imposing a known structure, such as a factor-analytic structure (Kirkpatrick and Meyer 2004; Meyer 2009), or by fitting covariance functions for longitudinal data (Kirkpatrick et al. 1990). While such methods can be highly advantageous when the underlying assumptions are at least approximately correct, data-driven methods of regularization may be preferable in other scenarios.This article explores the scope for improved estimation of genetic covariance matrices by implementing the equivalent to bending within animal model-type analyses. We begin with a review of the underlying statistical principles (which the impatient reader might skip), examining the concept of improved estimation, its implementation via shrinkage estimators or penalized estimation, and selected applications. We then describe a penalized restricted maximum-likelihood (REML) procedure for the estimation of genetic covariance matrices that utilizes information from its phenotypic counterparts and present a simulation study demonstrating the effect of penalties on parameter estimates and their sampling properties. The article concludes with an application to a problem relevant in genetic improvement of beef cattle and a discussion.     

Increased genetic gains in sheep,beef and dairy breeding programs from using female reproductive technologies combined with optimal contribution selection and genomic breeding values

Background

Female reproductive technologies such as multiple ovulation and embryo transfer (MOET) and juvenile in vitro embryo production and embryo transfer (JIVET) can boost rates of genetic gain but they can also increase rates of inbreeding. Inbreeding can be managed using the principles of optimal contribution selection (OCS), which maximizes genetic gain while placing a penalty on the rate of inbreeding. We evaluated the potential benefits and synergies that exist between genomic selection (GS) and reproductive technologies under OCS for sheep and cattle breeding programs.

Methods

Various breeding program scenarios were simulated stochastically including: (1) a sheep breeding program for the selection of a single trait that could be measured either early or late in life; (2) a beef breeding program with an early or late trait; and (3) a dairy breeding program with a sex limited trait. OCS was applied using a range of penalties (severe to no penalty) on co-ancestry of selection candidates, with the possibility of using multiple ovulation and embryo transfer (MOET) and/or juvenile in vitro embryo production and embryo transfer (JIVET) for females. Each breeding program was simulated with and without genomic selection.

Results

All breeding programs could be penalized to result in an inbreeding rate of 1 % increase per generation. The addition of MOET to artificial insemination or natural breeding (AI/N), without the use of GS yielded an extra 25 to 60 % genetic gain. The further addition of JIVET did not yield an extra genetic gain. When GS was used, MOET and MOET + JIVET programs increased rates of genetic gain by 38 to 76 % and 51 to 81 % compared to AI/N, respectively.

Conclusions

Large increases in genetic gain were found across species when female reproductive technologies combined with genomic selection were applied and inbreeding was managed, especially for breeding programs that focus on the selection of traits measured late in life or that are sex-limited. Optimal contribution selection was an effective tool to optimally allocate different combinations of reproductive technologies. Applying a range of penalties to co-ancestry of selection candidates allows a comprehensive exploration of the inbreeding vs. genetic gain space.     

Using the realized relationship matrix to disentangle confounding factors for the estimation of genetic variance components of complex traits

Background

In the analysis of complex traits, genetic effects can be confounded with non-genetic effects, especially when using full-sib families. Dominance and epistatic effects are typically confounded with additive genetic and non-genetic effects. This confounding may cause the estimated genetic variance components to be inaccurate and biased.

Methods

In this study, we constructed genetic covariance structures from whole-genome marker data, and thus used realized relationship matrices to estimate variance components in a heterogenous population of ~ 2200 mice for which four complex traits were investigated. These mice were genotyped for more than 10,000 single nucleotide polymorphisms (SNP) and the variances due to family, cage and genetic effects were estimated by models based on pedigree information only, aggregate SNP information, and model selection for specific SNP effects.

Results and conclusions

We show that the use of genome-wide SNP information can disentangle confounding factors to estimate genetic variances by separating genetic and non-genetic effects. The estimated variance components using realized relationship were more accurate and less biased, compared to those based on pedigree information only. Models that allow the selection of individual SNP in addition to fitting a relationship matrix are more efficient for traits with a significant dominance variance.     

Dopaminergic Neuronal Imaging in Genetic Parkinson's Disease: Insights into Pathogenesis

Objectives

To compare the dopaminergic neuronal imaging features of different subtypes of genetic Parkinson''s Disease.

Methods

A retrospective study of genetic Parkinson''s diseases cases in which DaTSCAN (123I-FP-CIT) had been performed. Specific non-displaceable binding was calculated for bilateral caudate and putamen for each case. The right:left asymmetry index and striatal asymmetry index was calculated.

Results

Scans were available from 37 cases of monogenetic Parkinson''s disease (7 glucocerebrosidase (GBA) mutations, 8 alpha-synuclein, 3 LRRK2, 7 PINK1, 12 Parkin). The asymmetry of radioligand uptake for Parkinson''s disease with GBA or LRRK2 mutations was greater than that for Parkinson''s disease with alpha synuclein, PINK1 or Parkin mutations.

Conclusions

The asymmetry of radioligand uptake in Parkinsons disease associated with GBA or LRRK2 mutations suggests that interactions with additional genetic or environmental factors may be associated with dopaminergic neuronal loss.     

Estimating the magnitude of genetic factors by calculating the genetic relative risk of stroke in first-ever lacunar stroke patients

Background

Positive family history of stroke is an independent risk factor for lacunar stroke. However, the magnitude of familial aggregation of a certain disease is better evaluated by the genetic relative risk. This is calculated by dividing the prevalence of specific disease in family members of patients by the prevalence of this disease in the general population. In a cohort of lacunar stroke patients, who were subtyped clinically and radiologically, we determined the genetic relative risk of stroke.

Methods

By questionnaire and additional interview, we obtained a complete first-degree family history of stroke. The prevalence of stroke in first-degree relatives of these lacunar stroke patients was compared to the self-reported prevalence of stroke in a Dutch community based cohort of elderly volunteers. Secondly, the influence of proband characteristics and family composition on parental and sibling history of stroke were evaluated.

Principal Findings

We collected data of 1066 first-degree relatives of 195 lacunar stroke patients. Strokes occurred in 13.5% of first-degree relatives. The genetic relative risk was 2.94 (95%CI 2.45–3.53) for overall first-degree relatives, 4.52 (95%CI 3.61–5.65) for patients'' parents and 2.10 (95%CI 1.63–2.69) for patients'' siblings. Age of proband and proband status for hypertension influenced the chance of having a parent with a history of stroke whereas the likelihood of having a concordant sibling increased with sibship size.

Conclusions

We found an increased genetic relative risk of stroke in first-degree relatives of patients with lacunar stroke. Our data warrant further genomic research in this well-defined high risk population for stroke.     

GVCBLUP: a computer package for genomic prediction and variance component estimation of additive and dominance effects

Background

Dominance effect may play an important role in genetic variation of complex traits. Full featured and easy-to-use computing tools for genomic prediction and variance component estimation of additive and dominance effects using genome-wide single nucleotide polymorphism (SNP) markers are necessary to understand dominance contribution to a complex trait and to utilize dominance for selecting individuals with favorable genetic potential.

Results

The GVCBLUP package is a shared memory parallel computing tool for genomic prediction and variance component estimation of additive and dominance effects using genome-wide SNP markers. This package currently has three main programs (GREML_CE, GREML_QM, and GCORRMX) and a graphical user interface (GUI) that integrates the three main programs with an existing program for the graphical viewing of SNP additive and dominance effects (GVCeasy). The GREML_CE and GREML_QM programs offer complementary computing advantages with identical results for genomic prediction of breeding values, dominance deviations and genotypic values, and for genomic estimation of additive and dominance variances and heritabilities using a combination of expectation-maximization (EM) algorithm and average information restricted maximum likelihood (AI-REML) algorithm. GREML_CE is designed for large numbers of SNP markers and GREML_QM for large numbers of individuals. Test results showed that GREML_CE could analyze 50,000 individuals with 400 K SNP markers and GREML_QM could analyze 100,000 individuals with 50K SNP markers. GCORRMX calculates genomic additive and dominance relationship matrices using SNP markers. GVCeasy is the GUI for GVCBLUP integrated with an existing software tool for the graphical viewing of SNP effects and a function for editing the parameter files for the three main programs.

Conclusion

The GVCBLUP package is a powerful and versatile computing tool for assessing the type and magnitude of genetic effects affecting a phenotype by estimating whole-genome additive and dominance heritabilities, for genomic prediction of breeding values, dominance deviations and genotypic values, for calculating genomic relationships, and for research and education in genomic prediction and estimation.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-270) contains supplementary material, which is available to authorized users.     

Principal component and factor analytic models in international sire evaluation

Background

Interbull is a non-profit organization that provides internationally comparable breeding values for globalized dairy cattle breeding programmes. Due to different trait definitions and models for genetic evaluation between countries, each biological trait is treated as a different trait in each of the participating countries. This yields a genetic covariance matrix of dimension equal to the number of countries which typically involves high genetic correlations between countries. This gives rise to several problems such as over-parameterized models and increased sampling variances, if genetic (co)variance matrices are considered to be unstructured.

Methods

Principal component (PC) and factor analytic (FA) models allow highly parsimonious representations of the (co)variance matrix compared to the standard multi-trait model and have, therefore, attracted considerable interest for their potential to ease the burden of the estimation process for multiple-trait across country evaluation (MACE). This study evaluated the utility of PC and FA models to estimate variance components and to predict breeding values for MACE for protein yield. This was tested using a dataset comprising Holstein bull evaluations obtained in 2007 from 25 countries.

Results

In total, 19 principal components or nine factors were needed to explain the genetic variation in the test dataset. Estimates of the genetic parameters under the optimal fit were almost identical for the two approaches. Furthermore, the results were in a good agreement with those obtained from the full rank model and with those provided by Interbull. The estimation time was shortest for models fitting the optimal number of parameters and prolonged when under- or over-parameterized models were applied. Correlations between estimated breeding values (EBV) from the PC19 and PC25 were unity. With few exceptions, correlations between EBV obtained using FA and PC approaches under the optimal fit were ≥ 0.99. For both approaches, EBV correlations decreased when the optimal model and models fitting too few parameters were compared.

Conclusions

Genetic parameters from the PC and FA approaches were very similar when the optimal number of principal components or factors was fitted. Over-fitting increased estimation time and standard errors of the estimates but did not affect the estimates of genetic correlations or the predictions of breeding values, whereas fitting too few parameters affected bull rankings in different countries.     

Consequences of paternally inherited effects on the genetic evaluation of maternal effects

Background

Mixed models are commonly used for the estimation of variance components and genetic evaluation of livestock populations. Some evaluation models include two types of additive genetic effects, direct and maternal. Estimates of variance components obtained with models that account for maternal effects have been the subject of a long-standing controversy about strong negative estimates of the covariance between direct and maternal effects. Genomic imprinting is known to be in some cases statistically confounded with maternal effects. In this study, we analysed the consequences of ignoring paternally inherited effects on the partitioning of genetic variance.

Results

We showed that the existence of paternal parent-of-origin effects can bias the estimation of variance components when maternal effects are included in the evaluation model. Specifically, we demonstrated that adding a constraint on the genetic parameters of a maternal model resulted in correlations between relatives that were the same as those obtained with a model that fits only paternally inherited effects for most pairs of individuals, as in livestock pedigrees. The main consequence is an upward bias in the estimates of the direct and maternal additive genetic variances and a downward bias in the direct-maternal genetic covariance. This was confirmed by a simulation study that investigated five scenarios, with the trait affected by (1) only additive genetic effects, (2) only paternally inherited effects, (3) additive genetic and paternally inherited effects, (4) direct and maternal additive genetic effects and (5) direct and maternal additive genetic plus paternally inherited effects. For each scenario, the existence of a paternally inherited effect not accounted for by the estimation model resulted in a partitioning of the genetic variance according to the predicted pattern. In addition, a model comparison test confirmed that direct and maternal additive models and paternally inherited models provided an equivalent fit.

Conclusions

Ignoring paternally inherited effects in the maternal models for genetic evaluation can lead to a specific pattern of bias in variance component estimates, which may account for the unexpectedly strong negative direct-maternal genetic correlations that are typically reported in the literature.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0141-5) contains supplementary material, which is available to authorized users.     

DiscML: an R package for estimating evolutionary rates of discrete characters using maximum likelihood

Background

The study of discrete characters is crucial for the understanding of evolutionary processes. Even though great advances have been made in the analysis of nucleotide sequences, computer programs for non-DNA discrete characters are often dedicated to specific analyses and lack flexibility. Discrete characters often have different transition rate matrices, variable rates among sites and sometimes contain unobservable states. To obtain the ability to accurately estimate a variety of discrete characters, programs with sophisticated methodologies and flexible settings are desired.

Results

DiscML performs maximum likelihood estimation for evolutionary rates of discrete characters on a provided phylogeny with the options that correct for unobservable data, rate variations, and unknown prior root probabilities from the empirical data. It gives users options to customize the instantaneous transition rate matrices, or to choose pre-determined matrices from models such as birth-and-death (BD), birth-death-and-innovation (BDI), equal rates (ER), symmetric (SYM), general time-reversible (GTR) and all rates different (ARD). Moreover, we show application examples of DiscML on gene family data and on intron presence/absence data.

Conclusion

DiscML was developed as a unified R program for estimating evolutionary rates of discrete characters with no restriction on the number of character states, and with flexibility to use different transition models. DiscML is ideal for the analyses of binary (1s/0s) patterns, multi-gene families, and multistate discrete morphological characteristics.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-320) contains supplementary material, which is available to authorized users.     

Estimating survival in patients with operable skeletal metastases: an application of a bayesian belief network

Background

Accurate estimations of life expectancy are important in the management of patients with metastatic cancer affecting the extremities, and help set patient, family, and physician expectations. Clinically, the decision whether to operate on patients with skeletal metastases, as well as the choice of surgical procedure, are predicated on an individual patient''s estimated survival. Currently, there are no reliable methods for estimating survival in this patient population. Bayesian classification, which includes Bayesian belief network (BBN) modeling, is a statistical method that explores conditional, probabilistic relationships between variables to estimate the likelihood of an outcome using observed data. Thus, BBN models are being used with increasing frequency in a variety of diagnoses to codify complex clinical data into prognostic models. The purpose of this study was to determine the feasibility of developing Bayesian classifiers to estimate survival in patients undergoing surgery for metastases of the axial and appendicular skeleton.

Methods

We searched an institution-owned patient management database for all patients who underwent surgery for skeletal metastases between 1999 and 2003. We then developed and trained a machine-learned BBN model to estimate survival in months using candidate features based on historical data. Ten-fold cross-validation and receiver operating characteristic (ROC) curve analysis were performed to evaluate the BNN model''s accuracy and robustness.

Results

A total of 189 consecutive patients were included. First-degree predictors of survival differed between the 3-month and 12-month models. Following cross validation, the area under the ROC curve was 0.85 (95% CI: 0.80–0.93) for 3-month probability of survival and 0.83 (95% CI: 0.77–0.90) for 12-month probability of survival.

Conclusions

A robust, accurate, probabilistic naïve BBN model was successfully developed using observed clinical data to estimate individualized survival in patients with operable skeletal metastases. This method warrants further development and must be externally validated in other patient populations.     

Khat use is associated with impaired working memory and cognitive flexibility

Rationale

Khat consumption has increased during the last decades in Eastern Africa and has become a global phenomenon spreading to ethnic communities in the rest of the world, such as The Netherlands, United Kingdom, Canada, and the United States. Very little is known, however, about the relation between khat use and cognitive control functions in khat users.

Objective

We studied whether khat use is associated with changes in working memory (WM) and cognitive flexibility, two central cognitive control functions.

Methods

Khat users and khat-free controls were matched in terms of sex, ethnicity, age, alcohol and cannabis consumption, and IQ (Raven''s progressive matrices). Groups were tested on cognitive flexibility, as measured by a Global-Local task, and on WM using an N-back task.

Result

Khat users performed significantly worse than controls on tasks tapping into cognitive flexibility as well as monitoring of information in WM.

Conclusions

The present findings suggest that khat use impairs both cognitive flexibility and the updating of information in WM. The inability to monitor information in WM and to adjust behavior rapidly and flexibly may have repercussions for daily life activities.     

Spirometry Reference Equations for Central European Populations from School Age to Old Age

Background

Spirometry reference values are important for the interpretation of spirometry results. Reference values should be updated regularly, derived from a population as similar to the population for which they are to be used and span across all ages. Such spirometry reference equations are currently lacking for central European populations.

Objective

To develop spirometry reference equations for central European populations between 8 and 90 years of age.

Materials

We used data collected between January 1993 and December 2010 from a central European population. The data was modelled using “Generalized Additive Models for Location, Scale and Shape” (GAMLSS).

Results

The spirometry reference equations were derived from 118''891 individuals consisting of 60''624 (51%) females and 58''267 (49%) males. Altogether, there were 18''211 (15.3%) children under the age of 18 years.

Conclusion

We developed spirometry reference equations for a central European population between 8 and 90 years of age that can be implemented in a wide range of clinical settings.     

A note on the rationale for estimating genealogical coancestry from molecular markers

Background

Genetic relatedness or similarity between individuals is a key concept in population, quantitative and conservation genetics. When the pedigree of a population is available and assuming a founder population from which the genealogical records start, genetic relatedness between individuals can be estimated by the coancestry coefficient. If pedigree data is lacking or incomplete, estimation of the genetic similarity between individuals relies on molecular markers, using either molecular coancestry or molecular covariance. Some relationships between genealogical and molecular coancestries and covariances have already been described in the literature.

Methods

We show how the expected values of the empirical measures of similarity based on molecular marker data are functions of the genealogical coancestry. From these formulas, it is easy to derive estimators of genealogical coancestry from molecular data. We include variation of allelic frequencies in the estimators.

Results

The estimators are illustrated with simulated examples and with a real dataset from dairy cattle. In general, estimators are accurate and only slightly biased. From the real data set, estimators based on covariances are more compatible with genealogical coancestries than those based on molecular coancestries. A frequently used estimator based on the average of estimated coancestries produced inflated coancestries and numerical instability. The consequences of unknown gene frequencies in the founder population are briefly discussed, along with alternatives to overcome this limitation.

Conclusions

Estimators of genealogical coancestry based on molecular data are easy to derive. Estimators based on molecular covariance are more accurate than those based on identity by state. A correction considering the random distribution of allelic frequencies improves accuracy of these estimators, especially for populations with very strong drift.     

High clonal diversity in threatened peripheral populations of the yellow bird's nest (Hypopitys monotropa; syn. Monotropa hypopitys)

Background and Aims

Peripheral populations of plant species are often characterized by low levels of genetic diversity as a result of genetic drift, restricted gene flow, inbreeding and asexual reproduction. These effects can be exacerbated where range-edge populations are fragmented. The main aim of the present study was to assess the levels of genetic diversity in remnant populations of Hypopitys monotropa (syn. Monotropa hypopitys; yellow bird''s nest) at the edge of the species'' European range in Northern Ireland, since these remnant populations are small and highly fragmented.

Methods

Every plant found through surveys of 21 extant populations was genotyped for eight microsatellite loci to estimate levels and patterns of genetic diversity and clonality.

Key Results

Levels of genetic diversity were relatively high in the populations studied, and the incidence of clonal reproduction was generally low, with a mean of only 14·45 % of clonal individuals. Clones were small and highly spatially structured. Levels of inbreeding, however, were high.

Conclusions

The observed low levels of clonality suggest that the majority of genets in the populations of H. monotropa studied are fertile and that reproduction is predominantly sexual. As the species is highly self-compatible, it is likely that the high levels of inbreeding observed in the populations in the present study are the result of self-pollination, particularly given the small numbers of individuals in most of the patches. Given this extent of inbreeding, further genetic monitoring would be advisable to ensure that genetic diversity is maintained.     

A Novel Approach - The Propensity to Propagate (PTP) Method for Controlling for Host Factors in Studying the Transmission of Mycobacterium Tuberculosis

Rationale

Understanding the genetic variations among Mycobacterium tuberculosis (MTB) strains with differential ability to transmit would be a major step forward in preventing transmission.

Objectives

To describe a method to extend conventional proxy measures of transmissibility by adjusting for patient-related factors, thus strengthening the causal association found with bacterial factors.

Methods

Clinical, demographic and molecular fingerprinting data were obtained during routine surveillance of verified MTB cases reported in the Netherlands between 1993 and 2011, and the phylogenetic lineages of the isolates were inferred. Odds ratios for host risk factors for clustering were used to obtain a measure of each patient''s and cluster''s propensity to propagate (CPP). Mean and median cluster sizes across different categories of CPP were compared amongst four different phylogenetic lineages.

Results

Both mean and median cluster size grew with increasing CPP category. On average, CPP values from Euro-American lineage strains were higher than Beijing and EAI strains. There were no significant differences between the mean and median cluster sizes among the four phylogenetic lineages within each CPP category.

Conclusions

Our finding that the distribution of CPP scores was unequal across four different phylogenetic lineages supports the notion that host-related factors should be controlled for to attain comparability in measuring the different phylogenetic lineages'' ability to propagate. Although Euro-American strains were more likely to be in clusters in an unadjusted analysis, no significant differences among the four lineages persisted after we controlled for host factors.     

Association between Age at Diagnosis of Graves' Disease and Variants in Genes Involved in Immune Response

Background

Graves'' disease (GD) is a complex disease in which genetic predisposition is modified by environmental factors. The aim of the study was to examine the association between genetic variants in genes encoding proteins involved in immune response and the age at diagnosis of GD.

Methods

735 GD patients and 1216 healthy controls from Poland were included into the study. Eight genetic variants in the HLA-DRB1, TNF, CTLA4, CD40, NFKb, PTPN22, IL4 and IL10 genes were genotyped. Patients were stratified by the age at diagnosis of GD and the association with genotype was analysed.

Results

Polymorphism in the HLA-DRB1, TNF and CTLA4 genes were associated with GD. The carriers of the HLA DRB1*03 allele were more frequent in patients with age at GD diagnosis ≤30 years than in patients with older age at GD diagnosis.

Conclusions

HLADRB1*03 allele is associated with young age at diagnosis of Graves'' disease in polish population.     

Estimation of heritability from limited family data using genome-wide identity-by-descent sharing

Background

In classical pedigree-based analysis, additive genetic variance is estimated from between-family variation, which requires the existence of larger phenotyped and pedigreed populations involving numerous families (parents). However, estimation is often complicated by confounding of genetic and environmental family effects, with the latter typically occurring among full-sibs. For this reason, genetic variance is often inferred based on covariance among more distant relatives, which reduces the power of the analysis. This simulation study shows that genome-wide identity-by-descent sharing among close relatives can be used to quantify additive genetic variance solely from within-family variation using data on extremely small family samples.

Methods

Identity-by-descent relationships among full-sibs were simulated assuming a genome size similar to that of humans (effective number of loci ~80). Genetic variance was estimated from phenotypic data assuming that genomic identity-by-descent relationships could be accurately re-created using information from genome-wide markers. The results were compared with standard pedigree-based genetic analysis.

Results

For a polygenic trait and a given number of phenotypes, the most accurate estimates of genetic variance were based on data from a single large full-sib family only. Compared with classical pedigree-based analysis, the proposed method is more robust to selection among parents and for confounding of environmental and genetic effects. Furthermore, in some cases, satisfactory results can be achieved even with less ideal data structures, i.e., for selectively genotyped data and for traits for which the genetic variance is largely under the control of a few major genes.

Conclusions

Estimation of genetic variance using genomic identity-by-descent relationships is especially useful for studies aiming at estimating additive genetic variance of highly fecund species, using data from small populations with limited pedigree information and/or few available parents, i.e., parents originating from non-pedigreed or even wild populations.