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The Journal of Agricultural, Biological and Environment Statistics (JABES) special issue on Recent Advances in Design and Analysis of Experiments and Observational Studies in Agriculture covers a select set of topics currently of primary importance in the field. Efficient use of resources in agricultural research, as well as valid statistical inference, requires good designs, and this special issue boasts seven papers providing both review and cutting-edge methodology for the purpose. A broad range of methods for analysis of data arising in different branches agricultural research is covered in another five exciting papers. This special issue highlights the importance of and opportunities for applied statistics in agriculture.

Background Copy number variation (CNV) is an important type of genetic variation contributing to phenotypic differences among mammals and may serve as an alternative molecular marker to single nucleotide polymorphism (SNP) for genome-wide association study (GWAS). Recently, GWAS analysis using CNV has been applied in livestock, although few studies have focused on Holstein cattle. Results We describe 191 CNV detected using intensity data from over 700,000 SNP genotypes generated with the BovineHD Genotyping BeadChip (Illumina, San Diego, CA) in 528 Holstein cows. The CNV were used for GWAS analysis of 10 important production traits of 473 cattle related to feed intake, milk quality, and female fertility, as well as 2 composite traits of net merit and productive life. In total, we detected 57 CNV associated (P

Whole genome prediction (WGP) modeling and genome-wide association (GWA) analyses are big data issues in agricultural quantitative genetics. Both areas require meaningful input from the statistical scholarly community in order to further improve the accuracy of prediction of genetic merit and inference on putative causal variants as well as improving the computational efficiency of existing methods and algorithms. These concerns have become increasingly critical as new sequencing technologies will only exacerbate current model dimensionality problems. We focus primarily on mixed model and hierarchical Bayesian analyses which have been most commonly pursued by animal and plant breeders for WGP thus far. We draw attention to our observation that many such previous analyses have not carefully inferred upon hyperparameters defined at the top levels of the Bayesian model hierarchy, but simply arbitrarily specify their values. We also reassess previous discussions on WGP model dimensionality, believing that useful data augmentation schemes utilized in various Markov Chain Monte Carlo (MCMC) schemes have led to a general misunderstanding that heavy-tailed or variable selection-based WGP models may be highly parameterized relative to more standard mixed model representations. Computational efficiency is addressed with respect to MCMC and competitive, albeit approximate, alternatives. Furthermore, GWA analyses are reassessed, encouraging a greater reliance on shrinkage-based inferences based on critically chosen priors, instead of potentially nonreproducible fixed effects P value-based inference.

Computational efficiency is an increasing concern for whole genome prediction (WGP) based on denser genetic marker panels such that algorithms other than Markov Chain Monte Carlo (MCMC) warrant greater consideration, particularly for hierarchical models that flexibly confer either heavy-tailed (e.g., BayesA) or stochastic search and variable selection (SSVS) instead of Gaussian specifications on marker effect distributions. The expectation maximization (EM) algorithm is one attractive alternative; however, recently proposed hierarchical model implementations of EM have not addressed formal estimation of underlying hyperparameters even though their specifications are known to impact WGP accuracy. Furthermore, EM can be sensitive to starting values. We develop and explore the properties of an empirical Bayes strategy by conditioning EM implementations of BayesA or SSVS WGP models on marginal modal estimation of variance components and other key hyperparameters. These empirical Bayes implementations are compared against their MCMC counterparts for estimation of hyperparameters and WGP accuracy, both within the context of a simulation study and application to a loblolly pine dataset. In all cases, starting values were deemed to be important for EM-based estimates. Starting values based on MCMC posterior means were preferable, whereas those based on setting all marker effects equal to zero generally led to inferior performance. Nevertheless, a recently proposed regularization procedure was useful in alleviating the impact of starting values in the EM implementation of the SSVS model, as was modifying the expectation step in the BayesA model to be based on relative variances rather than on relative precisions.

Multivariate hierarchical Bayesian models provide a flexible framework for comprehensive study of biological systems with more than one outcome. Recent methodological developments facilitate modeling of heterogeneous associations between outcomes by specifying a linear mixed model on (co)variances at different levels of the data structure. Motivated by previous evidence for heterogeneous correlations in animal agriculture, we apply the proposed hierarchical Bayesian models to study the nature of the correlations between key performance outcomes in dairy cattle production systems, namely milk yield and reproduction. That is, the association between these outcomes might depend upon various fixed and random effect sources of heterogeneity both at the individual cow (residual) level as well as the herd (cluster) level. We thus propose a sequential modeling approach based on the deviance information criterion to select relevant explanatory variables on both types of associations. Furthermore, we extend the proposed methodology to accommodate right-censored outcomes, as common for dairy reproduction data, and use it to analyze field data from the Michigan dairy industry. The nature of the associations between milk production and reproduction in dairy cattle was inferred to be strongly heterogeneous and driven by multiple farm management practices and herd attributes, as well as by random clustering effects, at both cow and herd levels, thereby suggesting potential between-herd and within-herd intervention strategies to optimize performance of dairy production systems. Supplementary materials are available online.

Background Recent evidence suggests that some sex differences in brain and behavior might result from direct genetic effects, and not solely the result of the organizational effects of steroid hormones. The present study examined the potential role for sex-biased gene expression during development of sexually dimorphic singing behavior and associated song nuclei in juvenile zebra finches. Results A microarray screen revealed more than 2400 putative genes (with a false discovery rate less than 0.05) exhibiting sex differences in the telencephalon of developing zebra finches. Increased expression in males was confirmed in 12 of 20 by qPCR using cDNA from the whole telencephalon; all of these appeared to be located on the Z sex chromosome. Six of the genes also showed increased expression in one or more of the song control nuclei of males at post-hatching day 25. Although the function of half of the genes is presently unknown, we have identified three as: 17-beta-hydroxysteroid dehydrogenase type IV, methylcrotonyl-CoA carboxylase, and sorting nexin 2. Conclusion The data suggest potential influences of these genes in song learning and/or masculinization of song system morphology, both of which are occurring at this developmental stage.

We propose a general Bayesian approach to heteroskedastic error modeling for generalized linear mixed models (GLMM) in which linked functions of conditional means and residual variances are specified as separate linear combinations of fixed and random effects. We focus on the linear mixed model (LMM) analysis of birth weight (BW) and the cumulative probit mixed model (CPMM) analysis of calving ease (CE). The deviance information criterion (DIC) was demonstrated to be useful in correctly choosing between homoskedastic and heteroskedastic error GLMM for both traits when data was generated according to a mixed model specification for both location parameters and residual variances. Heteroskedastic error LMM and CPMM were fitted, respectively, to BW and CE data on 8847 Italian Piemontese first parity dams in which residual variances were modeled as functions of fixed calf sex and random herd effects. The posterior mean residual variance for male calves was over 40% greater than that for female calves for both traits. Also, the posterior means of the standard deviation of the herd-specific variance ratios (relative to a unitary baseline) were estimated to be 0.60 ± 0.09 for BW and 0.74 ± 0.14 for CE. For both traits, the heteroskedastic error LMM and CPMM were chosen over their homoskedastic error counterparts based on DIC values.