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.
Population genetic structure and intra-population levels of genetic variation have important implications for population dynamics and evolutionary processes. Habitat fragmentation is one of the major threats to biodiversity. It leads to smaller population sizes and reduced gene flow between populations and will thus also affect genetic structure. We use a natural system of island and mainland populations of house sparrows along the coast of Norway to characterize the different population genetic properties of fragmented populations. We genotyped 636 individuals distributed across 14 populations at 15 microsatellite loci. The level of genetic differentiation was estimated using F-statistics and specially designed Mantel tests were conducted to study the influence of population type (i.e. mainland or island) and geographic distance on the genetic population structure. Furthermore, the effects of population type, population size and latitude to the level of genetic variation within populations were examined. Our results suggest that genetic processes on islands and mainland differed in two important ways. Firstly, the intra-population level of genetic variation tended to be lower and the occurrence of population bottlenecks more frequent on islands than the mainland. Secondly, although the general level of genetic differentiation was was low to moderate it was higher between island populations than between mainland populations. However, differentiation increased in mainland populations somewhat faster with geographical distance. These results suggest that population bottleneck events and genetic drift have been more important in shaping the genetic composition of island populations compared to populations on the mainland. Such knowledge is relevant for a better understanding of evolutionary processes and conservation of threatened populations.2
Understanding the relative influence of genetic drift and selection is fundamental in evolutionary biology. The theory of neutrality predicts that the genetic differentiation of a quantitative trait (QST) equals the genetic differentiation at neutral molecular markers (FST) if the quantitative trait has not been under selection. Thus, the relative magnitude of observed QST and expected QST under neutral expectations suggests the importance of selection and genetic drift for any observed phenotypic divergence. Because QST is based on additive genetic variance, estimating QST based on phenotypic measurements is problematic due to unknown environmental effects. To account for this, we used a model where the environmental component was allowed to vary when estimating QST. The model was used on data from 14 house sparrow (Passer domesticus) populations in Norway. In accordance with the significant phenotypic inter-population differences our analyses suggested that directional selection may have favoured different optimal phenotypes for some morphological traits across populations. In particular, different body mass and male ornamental phenotypes seemed to have been favoured. The conclusions are, however, dependent on assumptions regarding the proportion of the observed inter-population variation that is due to additive genetic differences, showing the importance of collecting such information in natural populations. By estimating QST, allowing the additive genetic proportion of phenotypic inter-population variation to vary, and by making use of recent statistical methods to compare observed QST with neutral expectations, we can use data that are relatively easy to collect to identify adaptive variation in natural populations.
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 ( and ). 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.
Key messageA novel reparametrization-based INLA approach as a fast alternative to MCMC for the Bayesian estimation of genetic parameters in multivariate animal model is presented.Abstract Multi-trait genetic parameter estimation is a relevant topic in animal and plant breeding programs because multi-trait analysis can take into account the genetic correlation between different traits and that significantly improves the accuracy of the genetic parameter estimates. Generally, multi-trait analysis is computationally demanding and requires initial estimates of genetic and residual correlations among the traits, while those are difficult to obtain. In this study, we illustrate how to reparametrize covariance matrices of a multivariate animal model/animal models using modified Cholesky decompositions. This reparametrization-based approach is used in the Integrated Nested Laplace Approximation (INLA) methodology to estimate genetic parameters of multivariate animal model. Immediate benefits are: (1) to avoid difficulties of finding good starting values for analysis which can be a problem, for example in Restricted Maximum Likelihood (REML); (2) Bayesian estimation of (co)variance components using INLA is faster to execute than using Markov Chain Monte Carlo (MCMC) especially when realized relationship matrices are dense. The slight drawback is that priors for covariance matrices are assigned for elements of the Cholesky factor but not directly to the covariance matrix elements as in MCMC. Additionally, we illustrate the concordance of the INLA results with the traditional methods like MCMC and REML approaches. We also present results obtained from simulated data sets with replicates and field data in rice.
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