Modeling dependency structures in 450k DNA methylation data.

MOTIVATION: DNA methylation has been shown to be spatially dependent across chromosomes. Previous studies have focused on the influence of genomic context on the dependency structure, while not considering differences in dependency structure between individuals. RESULTS: We modeled spatial dependency with a flexible framework to quantify the dependency structure, focusing on inter-individual differences by exploring the association between dependency parameters and technical and biological variables. The model was applied to a subset of the Finnish Twin Cohort study (N = 1611 individuals). The estimates of the dependency parameters varied considerably across individuals, but were generally consistent across chromosomes within individuals. The variation in dependency parameters was associated with bisulfite conversion plate, zygosity, sex and age. The age differences presumably reflect accumulated environmental exposures and/or accumulated small methylation differences caused by stochastic mitotic events, establishing recognizable, individual patterns more strongly seen in older individuals. AVAILABILITY AND IMPLEMENTATION: The twin dataset used in the current study are located in the Biobank of the National Institute for Health and Welfare, Finland. All the biobanked data are publicly available for use by qualified researchers following a standardized application procedure (https://thl.fi/en/web/thl-biobank/for-researchers). A R-script for fitting the dependency structure to publicly available DNA methylation data with the software used in this article is provided in supplementary data. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Spatial modelling improves genetic evaluation in smallholder breeding programs.

BACKGROUND: Breeders and geneticists use statistical models to separate genetic and environmental effects on phenotype. A common way to separate these effects is to model a descriptor of an environment, a contemporary group or herd, and account for genetic relationship between animals across environments. However, separating the genetic and environmental effects in smallholder systems is challenging due to small herd sizes and weak genetic connectedness across herds. We hypothesised that accounting for spatial relationships between nearby herds can improve genetic evaluation in smallholder systems. Furthermore, geographically referenced environmental covariates are increasingly available and could model underlying sources of spatial relationships. The objective of this study was therefore, to evaluate the potential of spatial modelling to improve genetic evaluation in dairy cattle smallholder systems. METHODS: We performed simulations and real dairy cattle data analysis to test our hypothesis. We modelled environmental variation by estimating herd and spatial effects. Herd effects were considered independent, whereas spatial effects had distance-based covariance between herds. We compared these models using pedigree or genomic data. RESULTS: The results show that in smallholder systems (i) standard models do not separate genetic and environmental effects accurately, (ii) spatial modelling increases the accuracy of genetic evaluation for phenotyped and non-phenotyped animals, (iii) environmental covariates do not substantially improve the accuracy of genetic evaluation beyond simple distance-based relationships between herds, (iv) the benefit of spatial modelling was largest when separating the genetic and environmental effects was challenging, and (v) spatial modelling was beneficial when using either pedigree or genomic data. CONCLUSIONS: We have demonstrated the potential of spatial modelling to improve genetic evaluation in smallholder systems. This improvement is driven by establishing environmental connectedness between herds, which enhances separation of genetic and environmental effects. We suggest routine spatial modelling in genetic evaluations, particularly for smallholder systems. Spatial modelling could also have a major impact in studies of human and wild populations.

Flexible modelling of spatial variation in agricultural field trials with the R package INLA.

KEY MESSAGE: Established spatial models improve the analysis of agricultural field trials with or without genomic data and can be fitted with the open-source R package INLA. The objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive ([Formula: see text]) models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the [Formula: see text] and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA.

Prognostic risk models for incident hypertension: A PRISMA systematic review and meta-analysis.

OBJECTIVE: Our goal was to review the available literature on prognostic risk prediction for incident hypertension, synthesize performance, and provide suggestions for future work on the topic. METHODS: A systematic search on PUBMED and Web of Science databases was conducted for studies on prognostic risk prediction models for incident hypertension in generally healthy individuals. Study-quality was assessed using the Prediction model Risk of Bias Assessment Tool (PROBAST) checklist. Three-level meta-analyses were used to obtain pooled AUC/C-statistic estimates. Heterogeneity was explored using study and cohort characteristics in meta-regressions. RESULTS: From 5090 hits, we found 53 eligible studies, and included 47 in meta-analyses. Only four studies were assessed to have results with low risk of bias. Few models had been externally validated, with only the Framingham risk model validated more than thrice. The pooled AUC/C-statistics were 0.82 (0.77-0.86) for machine learning models and 0.78 (0.76-0.80) for traditional models, with high heterogeneity in both groups (I2 > 99%). Intra-class correlations within studies were 60% and 90%, respectively. Follow-up time (P = 0.0405) was significant for ML models and age (P = 0.0271) for traditional models in explaining heterogeneity. Validations of the Framingham risk model had high heterogeneity (I2 > 99%). CONCLUSION: Overall, the quality of included studies was assessed as poor. AUC/C-statistic were mostly acceptable or good, and higher for ML models than traditional models. High heterogeneity implies large variability in the performance of new risk models. Further, large heterogeneity in validations of the Framingham risk model indicate variability in model performance on new populations. To enable researchers to assess hypertension risk models, we encourage adherence to existing guidelines for reporting and developing risk models, specifically reporting appropriate performance measures. Further, we recommend a stronger focus on validation of models by considering reasonable baseline models and performing external validations of existing models. Hence, developed risk models must be made available for external researchers.

Development of risk models of incident hypertension using machine learning on the HUNT study data.

In this study, we aimed to create an 11-year hypertension risk prediction model using data from the Trøndelag Health (HUNT) Study in Norway, involving 17 852 individuals (20-85 years; 38% male; 24% incidence rate) with blood pressure (BP) below the hypertension threshold at baseline (1995-1997). We assessed 18 clinical, behavioral, and socioeconomic features, employing machine learning models such as eXtreme Gradient Boosting (XGBoost), Elastic regression, K-Nearest Neighbor, Support Vector Machines (SVM) and Random Forest. For comparison, we used logistic regression and a decision rule as reference models and validated six external models, with focus on the Framingham risk model. The top-performing models consistently included XGBoost, Elastic regression and SVM. These models efficiently identified hypertension risk, even among individuals with optimal baseline BP (< 120/80 mmHg), although improvement over reference models was modest. The recalibrated Framingham risk model outperformed the reference models, approaching the best-performing ML models. Important features included age, systolic and diastolic BP, body mass index, height, and family history of hypertension. In conclusion, our study demonstrated that linear effects sufficed for a well-performing model. The best models efficiently predicted hypertension risk, even among those with optimal or normal baseline BP, using few features. The recalibrated Framingham risk model proved effective in our cohort.

Sex-dependent selection on an autosomal melanic female ornament promotes the evolution of sex ratio bias.

Sex-dependent selection often leads to spectacularly different phenotypes in males and females. In species in which sexual dimorphism is not complete, it is unclear which benefits females and males derive from displaying a trait that is typical of the other sex. In barn owls (Tyto alba), females exhibit on average larger black eumelanic spots than males but members of the two sexes display this trait in the same range of possible values. In a 12-year study, we show that selection exerted on spot size directly or on genetically correlated traits strongly favoured females with large spots and weakly favoured males with small spots. Intense directional selection on females caused an increase in spot diameter in the population over the study period. This increase is due to a change in the autosomal genes underlying the expression of eumelanic spots but not of sex-linked genes. Female-like males produced more daughters than sons, while male-like females produced more sons than daughters when mated to a small-spotted male. These sex ratio biases appear adaptive because sons of male-like females and daughters of female-like males had above-average survival. This demonstrates that selection exerted against individuals displaying a trait that is typical of the other sex promoted the evolution of specific life history strategies that enhance their fitness. This may explain why in many organisms sexual dimorphism is often not complete.

Utilizing Gaussian Markov random field properties of Bayesian animal models.

In this article, we demonstrate how Gaussian Markov random field properties give large computational benefits and new opportunities for the Bayesian animal model. We make inference by computing the posteriors for important quantitative genetic variables. For the single-trait animal model, a nonsampling-based approximation is presented. For the multitrait model, we set up a robust and fast Markov chain Monte Carlo algorithm. The proposed methodology was used to analyze quantitative genetic properties of morphological traits of a wild house sparrow population. Results for single- and multitrait models were compared.

Hierarchical Modelling of Haplotype Effects on a Phylogeny.

We introduce a hierarchical model to estimate haplotype effects based on phylogenetic relationships between haplotypes and their association with observed phenotypes. In a population there are many, but not all possible, distinct haplotypes and few observations per haplotype. Further, haplotype frequencies tend to vary substantially. Such data structure challenge estimation of haplotype effects. However, haplotypes often differ only due to few mutations, and leveraging similarities can improve the estimation of effects. We build on extensive literature and develop an autoregressive model of order one that models haplotype effects by leveraging phylogenetic relationships described with a directed acyclic graph. The phylogenetic relationships can be either in a form of a tree or a network, and we refer to the model as the haplotype network model. The model can be included as a component in a phenotype model to estimate associations between haplotypes and phenotypes. Our key contribution is that we obtain a sparse model, and by using hierarchical autoregression, the flow of information between similar haplotypes is estimated from the data. A simulation study shows that the hierarchical model can improve estimates of haplotype effects compared to an independent haplotype model, especially with few observations for a specific haplotype. We also compared it to a mutation model and observed comparable performance, though the haplotype model has the potential to capture background specific effects. We demonstrate the model with a study of mitochondrial haplotype effects on milk yield in cattle. We provide R code to fit the model with the INLA package.

Evolutionary dynamics of a sexual ornament in the house sparrow (Passer domesticus): the role of indirect selection within and between sexes.

The relative contribution of sexual and natural selection to evolution of sexual ornaments has rarely been quantified under natural conditions. In this study we used a long-term dataset of house sparrows in which parents and offspring were matched genetically to estimate the within- and across-sex genetic basis for variation and covariation among morphological traits. By applying two-sex multivariate "animal models" to estimate genetic parameters, we estimated evolutionary changes in a male sexual ornament, badge size, from the contribution of direct and indirect selection on correlated traits within males and females, after accounting for overlapping generations and age-structure. Indirect natural selection on genetically correlated traits in males and females was the major force causing evolutionary change in the male ornament. Thus, natural selection on female morphology may cause indirect evolutionary changes in male ornaments. We observed however no directional phenotypic change in the ornament size of one-year-old males during the study period. On the other hand, changes were recorded in other morphological characters of both sexes. Our analyses of evolutionary dynamics in sexual characters require application of appropriate two-sex models to account for how selection on correlated traits in both sexes affects the evolutionary outcome of sexual selection.

Is my study system good enough? A case study for identifying maternal effects.

In this paper, we demonstrate how simulation studies can be used to answer questions about identifiability and consequences of omitting effects from a model. The methodology is presented through a case study where identifiability of genetic and/or individual (environmental) maternal effects is explored. Our study system is a wild house sparrow (Passer domesticus) population with known pedigree. We fit pedigree-based (generalized) linear mixed models (animal models), with and without additive genetic and individual maternal effects, and use deviance information criterion (DIC) for choosing between these models. Pedigree and R-code for simulations are available. For this study system, the simulation studies show that only large maternal effects can be identified. The genetic maternal effect (and similar for individual maternal effect) has to be at least half of the total genetic variance to be identified. The consequences of omitting a maternal effect when it is present are explored. Our results indicate that the total (genetic and individual) variance are accounted for. When an individual (environmental) maternal effect is omitted from the model, this only influences the estimated (direct) individual (environmental) variance. When a genetic maternal effect is omitted from the model, both (direct) genetic and (direct) individual variance estimates are overestimated.

Quantitative genetic modeling and inference in the presence of nonignorable missing data.

Natural selection is typically exerted at some specific life stages. If natural selection takes place before a trait can be measured, using conventional models can cause wrong inference about population parameters. When the missing data process relates to the trait of interest, a valid inference requires explicit modeling of the missing process. We propose a joint modeling approach, a shared parameter model, to account for nonrandom missing data. It consists of an animal model for the phenotypic data and a logistic model for the missing process, linked by the additive genetic effects. A Bayesian approach is taken and inference is made using integrated nested Laplace approximations. From a simulation study we find that wrongly assuming that missing data are missing at random can result in severely biased estimates of additive genetic variance. Using real data from a wild population of Swiss barn owls Tyto alba, our model indicates that the missing individuals would display large black spots; and we conclude that genes affecting this trait are already under selection before it is expressed. Our model is a tool to correctly estimate the magnitude of both natural selection and additive genetic variance.

On estimation and identifiability issues of sex-linked inheritance with a case study of pigmentation in Swiss barn owl (Tyto alba).

Genetic evaluation using animal models or pedigree-based models generally assume only autosomal inheritance. Bayesian animal models provide a flexible framework for genetic evaluation, and we show how the model readily can accommodate situations where the trait of interest is influenced by both autosomal and sex-linked inheritance. This allows for simultaneous calculation of autosomal and sex-chromosomal additive genetic effects. Inferences were performed using integrated nested Laplace approximations (INLA), a nonsampling-based Bayesian inference methodology. We provide a detailed description of how to calculate the inverse of the X- or Z-chromosomal additive genetic relationship matrix, needed for inference. The case study of eumelanic spot diameter in a Swiss barn owl (Tyto alba) population shows that this trait is substantially influenced by variation in genes on the Z-chromosome ([Formula: see text] and [Formula: see text]). Further, a simulation study for this study system shows that the animal model accounting for both autosomal and sex-chromosome-linked inheritance is identifiable, that is, the two effects can be distinguished, and provides accurate inference on the variance components.

Animal models and integrated nested Laplace approximations.

Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian animal models. We analyze animal models for both synthetic case studies and house sparrow (Passer domesticus) population case studies with Gaussian, binomial, and Poisson likelihoods using INLA. Inference results are compared with results using Markov Chain Monte Carlo methods. For model choice we use difference in deviance information criteria (DIC). We suggest and show how to evaluate differences in DIC by comparing them with sampling results from simulation studies. We also introduce an R package, AnimalINLA, for easy and fast inference for Bayesian Animal models using INLA.