Misspecification in mixed-model based association analysis

Additive genetic variance in natural populations is commonly estimated using mixed models, in which the covariance of the genetic effects is modeled by a genetic similarity matrix derived from a dense set of markers. An important but usually implicit assumption is that the presence of any non-additive genetic effect only increases the residual variance, and does not affect estimates of additive genetic variance. Here we show that this is only true for panels of unrelated individuals. In case there is genetic relatedness, the combination of population structure and epistatic interactions can lead to inflated estimates of additive genetic variance

Adaptive Bayesian Density Estimation with Location-Scale Mixtures

We study convergence rates of Bayesian density estimators based on finite location-scale mixtures of a kernel proportional to $\exp\{-|x|^p\}$. We construct a finite mixture approximation of densities whose logarithm is locally $\beta$-Hölder, with squared integrable Hölder constant. Under additional tail and moment conditions, the approximation is minimax for both the Kullback-Leibler divergence. We use this approximation to establish convergence rates for a Bayesian mixture model with priors on the weights, locations, and the number of components. Regarding these priors, we provide general conditions under which the posterior converges at a near optimal rate, and is rate-adaptive with respect to the smoothness of the logarithm of the true density

Adaptive Bayesian density estimation with location-scale mixtures

Abstract: We study convergence rates of Bayesian density estimators based on finite location-scale mixtures of exponential power distributions. We construct approximations of β-Hölder densities be continuous mixtures of exponential power distributions, leading to approximations of the β-Hölder densities by finite mixtures. These results are then used to derive posterior concentration rates, with priors based on these mixture models. The rates are minimax (up to a log n term) and since the priors are independent of the smoothness the rates are adaptive to the smoothness

Natural variation in Arabidopsis thaliana reveals shoot ionome, biomass, and gene expression changes as biomarkers for zinc deficiency tolerance

Zinc (Zn) is an essential nutrient for plants, with a crucial role as a cofactor for many enzymes. Approximately one-third of the global arable land area is Zn deficient, leading to reduced crop yield and quality. To improve crop tolerance to Zn deficiency, it is important to understand the mechanisms plants have adopted to tolerate suboptimal Zn supply. In this study, physiological and molecular aspects of traits related to Zn deficiency tolerance were examined in a panel of 19 Arabidopsis thaliana accessions. Accessions showed a larger variation for shoot biomass than for Zn concentration, indicating that they have different requirements for their minimal Zn concentration required for growth. Accessions with a higher tolerance to Zn deficiency showed an increased expression of the Zn deficiency-responsive genes ZIP4 and IRT3 in comparison with Zn deficiency-sensitive accessions. Changes in the shoot ionome, as a result of the Zn treatment of the plants, were used to build a multinomial logistic regression model able to distinguish plants regarding their Zn nutritional status. This set of biomarkers, reflecting the A. thaliana response to Zn deficiency and Zn deficiency tolerance, can be useful for future studies aiming to improve the performance and Zn status of crop plants grown under suboptimal Zn concentrations

Reconstruction of Networks with Direct and Indirect Genetic Effects

Genetic variance of a phenotypic trait can originate from direct genetic effects, or from indirect effects, i.e., through genetic effects on other traits, affecting the trait of interest. This distinction is often of great importance, for example, when trying to improve crop yield and simultaneously control plant height. As suggested by Sewall Wright, assessing contributions of direct and indirect effects requires knowledge of (1) the presence or absence of direct genetic effects on each trait, and (2) the functional relationships between the traits. Because experimental validation of such relationships is often unfeasible, it is increasingly common to reconstruct them using causal inference methods. However, most current methods require all genetic variance to be explained by a small number of quantitative trait loci (QTL) with fixed effects. Only a few authors have considered the “missing heritability” case, where contributions of many undetectable QTL are modeled with random effects. Usually, these are treated as nuisance terms that need to be eliminated by taking residuals from a multi-trait mixed model (MTM). But fitting such an MTM is challenging, and it is impossible to infer the presence of direct genetic effects. Here, we propose an alternative strategy, where genetic effects are formally included in the graph. This has important advantages: (1) genetic effects can be directly incorporated in causal inference, implemented via our PCgen algorithm, which can analyze many more traits; and (2) we can test the existence of direct genetic effects, and improve the orientation of edges between traits. Finally, we show that reconstruction is much more accurate if individual plant or plot data are used, instead of genotypic means. We have implemented the PCgen-algorithm in the R-package pcgen.</p

Acción : diario de Teruel y su provincia: Año III Número 633 - (11/12/34)

New types of phenotyping tools generate large amounts of data on many aspects of plant physiology and morphology with high spatial and temporal resolution. These new phenotyping data are potentially useful to improve understanding and prediction of complex traits, like yield, that are characterized by strong environmental context dependencies, i.e., genotype by environment interactions. For an evaluation of the utility of new phenotyping information, we will look at how this information can be incorporated in different classes of genotype-to-phenotype (G2P) models. G2P models predict phenotypic traits as functions of genotypic and environmental inputs. In the last decade, access to high-density single nucleotide polymorphism markers (SNPs) and sequence information has boosted the development of a class of G2P models called genomic prediction models that predict phenotypes from genome wide marker profiles. The challenge now is to build G2P models that incorporate simultaneously extensive genomic information alongside with new phenotypic information. Beyond the modification of existing G2P models, new G2P paradigms are required. We present candidate G2P models for the integration of genomic and new phenotyping information and illustrate their use in examples. Special attention will be given to the modelling of genotype by environment interactions. The G2P models provide a framework for model based phenotyping and the evaluation of the utility of phenotyping information in the context of breeding programs.</p

Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors

For a Gaussian time series with long-memory behavior, we use the FEXP-model for semi-parametric estimation of the long-memory parameter $d$. The true spectral density $f_o$ is assumed to have long-memory parameter $d_o$ and a FEXP-expansion of Sobolev-regularity \be > 1. We prove that when $k$ follows a Poisson or geometric prior, or a sieve prior increasing at rate n^{\frac{1}{1+2\be}}, $d$ converges to $d_o$ at a suboptimal rate. When the sieve prior increases at rate n^{\frac{1}{2\be}} however, the minimax rate is almost obtained. Our results can be seen as a Bayesian equivalent of the result which Moulines and Soulier obtained for some frequentist estimators