Benchmarking machine learning and parametric methods for genomic prediction of feed efficiency-related traits in Nellore cattle.

Genomic selection (GS) offers a promising opportunity for selecting more efficient animals to use consumed energy for maintenance and growth functions, impacting profitability and environmental sustainability. Here, we compared the prediction accuracy of multi-layer neural network (MLNN) and support vector regression (SVR) against single-trait (STGBLUP), multi-trait genomic best linear unbiased prediction (MTGBLUP), and Bayesian regression (BayesA, BayesB, BayesC, BRR, and BLasso) for feed efficiency (FE) traits. FE-related traits were measured in 1156 Nellore cattle from an experimental breeding program genotyped for ~ 300 K markers after quality control. Prediction accuracy (Acc) was evaluated using a forward validation splitting the dataset based on birth year, considering the phenotypes adjusted for the fixed effects and covariates as pseudo-phenotypes. The MLNN and SVR approaches were trained by randomly splitting the training population into fivefold to select the best hyperparameters. The results show that the machine learning methods (MLNN and SVR) and MTGBLUP outperformed STGBLUP and the Bayesian regression approaches, increasing the Acc by approximately 8.9%, 14.6%, and 13.7% using MLNN, SVR, and MTGBLUP, respectively. Acc for SVR and MTGBLUP were slightly different, ranging from 0.62 to 0.69 and 0.62 to 0.68, respectively, with empirically unbiased for both models (0.97 and 1.09). Our results indicated that SVR and MTGBLUBP approaches were more accurate in predicting FE-related traits than Bayesian regression and STGBLUP and seemed competitive for GS of complex phenotypes with various degrees of inheritance.

Image analysis to automatically classify anemia based on Famacha score in sheep using ocular conjunctiva images.

Haemonchus contortus is the most pathogenic blood-feeding parasitic in sheep, causing anemia and consequently changes in the color of the ocular conjunctiva, from the deep red of healthy sheep to shades of pink to practically white of non-healthy sheep. In this context, the Famacha method has been created for detecting sheep unable to cope with the infection by H. contortus, through visual assessment of ocular conjunctiva coloration. Thus, the objectives of this study were (1) to extract ocular conjunctiva image features to automatically classify Famacha score and compare two classification models (multinomial logistic regression-MLR and random forest-RF) and (2) to evaluate the applicability of the best classification model on three sheep farms. The dataset consisted of 1,156 ocular conjunctiva images from 422 animals. RF model was used to segment the images, i.e., to select the pixels that belong to the ocular conjunctiva. After segmentation, the quantiles (1%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 99%) of color intensity in each image channel (red, blue, and green) were determined and used as explanatory variables in the classification models, and the Famacha scores 1 (non-anemic) to 5 (severely anemic) were the target classes to be predicted (scores 1 to 5, with 162, 255, 443, 266, and 30 images, respectively). For objective 1, the performance metrics (precision and sensitivity) were obtained using MLR and RF models considering data from all farms randomly split. For objective 2, a leave-one-farm-out cross-validation technique was used to assess prediction quality across three farms (farms A, B, and C, with 726, 205, and 225 images, respectively). The RF provided the best performances in predicting anemic animals, as indicated by the high values of sensitivity for Famacha score 3 (80.9%), 4 (46.2%), and 5 (60%) compared to the MLR model. The precision of the RF was 72.7% for Famacha score 1 and 62.5% for Famacha score 2. These results indicate that is possible to successfully predict Famacha score, especially for scores 2 to 4, in sheep via image analysis and RF model using ocular conjunctiva images collected in farm conditions. As expected, model validation excluding entire farms in cross-validation presented a lower prediction quality. Nonetheless, this setup is closer to reality because the developed models are supposed to be used across farms, including new ones, and with different environments and management conditions.

Classification Performance of Machine Learning Methods for Identifying Resistance, Resilience, and Susceptibility to Haemonchus contortus Infections in Sheep.

This study investigated the feasibility of using easy-to-measure phenotypic traits to predict sheep resistant, resilient, and susceptible to gastrointestinal nematodes, compared the classification performance of multinomial logistic regression (MLR), linear discriminant analysis (LDA), random forest (RF), and artificial neural network (ANN) methods, and evaluated the applicability of the best classification model on each farm. The database comprised 3654 records of 1250 Santa Inês sheep from 6 farms. The animals were classified into resistant (2605 records), resilient (939 records), and susceptible (110 records) according to fecal egg count and packed cell volume. A random oversampling method was performed to balance the dataset. The classification methods were fitted using the information of age class, the month of record, farm, sex, Famacha© degree, body weight, and body condition score as predictors, and the resistance, resilience, and susceptibility to gastrointestinal nematodes as the target classes to be predicted considering data from all farms randomly. An additional leave-one-farm-out cross-validation technique was used to assess prediction quality across farms. The MLR and LDA models presented good performances in predicting susceptible and resistant animals. The results suggest that the use of readily available records and easily measurable traits may provide useful information for supporting management decisions at the farm level.

Economic values of reproductive, growth, feed efficiency and carcass traits in Nellore cattle.

A bioeconomic model was developed to calculate the economic value (ev) of reproductive and growth performance, feed efficiency and carcass traits of a seedstock Nellore herd. Data from a full-cycle cattle operation (1,436 dams) located in the Brazilian Cerrado were assessed. The ev was calculated by the difference in profit before and after one-unit improvement in the trait, with others remaining unchanged. The ev was standardized by the phenotypic standard deviation of each trait. Preweaning average daily gain (ADG) was the most economically important trait evaluated (R$ 58.04/animal/year), followed by age at first calving (R$ 44.35), postweaning ADG (R$ 31.43), weight at 450 days (R$ 25.36), accumulated productivity (R$ 21.43), ribeye area (R$ 21.35), calving interval (R$ 19.97), feed efficiency (R$ 15.24), carcass dressing per cent (R$ 8.27), weight at 120 days (R$ 6.22), weight at 365 days (R$ 6.06), weight at weaning (210 days, R$ 5.82), stayability (R$ 5.70) and the probability of early calving (R$ 0.32). The effects of all traits on profits are evidence that their selection may result in the economic and genetic progress of the herd if there is genetic variability.

Enviromics in breeding: applications and perspectives on envirotypic-assisted selection.

KEY MESSAGE: We propose the application of enviromics to breeding practice, by which the similarity among sites assessed on an "omics" scale of environmental attributes drives the prediction of unobserved genotype performances. Genotype by environment interaction (GEI) studies in plant breeding have focused mainly on estimating genetic parameters over a limited number of experimental trials. However, recent geographic information system (GIS) techniques have opened new frontiers for better understanding and dealing with GEI. These advances allow increasing selection accuracy across all sites of interest, including those where experimental trials have not yet been deployed. Here, we introduce the term enviromics, within an envirotypic-assisted breeding framework. In summary, likewise genotypes at DNA markers, any particular site is characterized by a set of "envirotypes" at multiple "enviromic" markers corresponding to environmental variables that may interact with the genetic background, thus providing informative breeding re-rankings for optimized decisions over different environments. Based on simulated data, we illustrate an index-based enviromics method (the "GIS-GEI") which, due to its higher granular resolution than standard methods, allows for: (1) accurate matching of sites to their most appropriate genotypes; (2) better definition of breeding areas that have high genetic correlation to ensure selection gains across environments; and (3) efficient determination of the best sites to carry out experiments for further analyses. Environmental scenarios can also be optimized for productivity improvement and genetic resources management, especially in the current outlook of dynamic climate change. Envirotyping provides a new class of markers for genetic studies, which are fairly inexpensive, increasingly available and transferable across species. We envision a promising future for the integration of enviromics approaches into plant breeding when coupled with next-generation genotyping/phenotyping and powerful statistical modeling of genetic diversity.

Genome-wide scan highlights the role of candidate genes on phenotypic plasticity for age at first calving in Nellore heifers.

Age at first calving (AFC) plays an important role in the economic efficiency of beef cattle production. This trait can be affected by a combination of genetic and environmental factors, leading to physiological changes in response to heifers' adaptation to a wide range of environments. Genome-wide association studies through the reaction norm model were carried out to identify genomic regions associated with AFC in Nellore heifers, raised under different environmental conditions (EC). The SNP effects for AFC were estimated in three EC levels (Low, Medium, and High, corresponding to average contemporary group effects on yearling body weight equal to 159.40, 228.6 and 297.6 kg, respectively), which unraveled shared and unique genomic regions for AFC in Low, Medium, and High EC levels, that varied according to the genetic correlation between AFC in different EC levels. The significant genomic regions harbored key genes that might play an important biological role in controlling hormone signaling and metabolism. Shared genomic regions among EC levels were identified on BTA 2 and 14, harboring candidate genes associated with energy metabolism (IGFBP2, IGFBP5, SHOX, SMARCAL1, LYN, RPS20, MOS, PLAG1, CHCD7, and SDR16C6). Gene set enrichment analyses identified important biological functions related to growth, hormone levels affecting female fertility, physiological processes involved in female pregnancy, gamete generation, ovulation cycle, and age at puberty. The genomic regions highlighted differences in the physiological processes linked to AFC in different EC levels and metabolic processes that support complex interactions between the gonadotropic axes and sexual precocity in Nellore heifers.

Improving genomic prediction accuracy for meat tenderness in Nellore cattle using artificial neural networks.

The goal of this study was to compare the predictive performance of artificial neural networks (ANNs) with Bayesian ridge regression, Bayesian Lasso, Bayes A, Bayes B and Bayes Cπ in estimating genomic breeding values for meat tenderness in Nellore cattle. The animals were genotyped with the Illumina Bovine HD Bead Chip (HD, 777K from 90 samples) and the GeneSeek Genomic Profiler (GGP Indicus HD, 77K from 485 samples). The quality control for the genotypes was applied on each Chip and comprised removal of SNPs located on non-autosomal chromosomes, with minor allele frequency <5%, deviation from HWE (p < 10-6 ), and with linkage disequilibrium >0.8. The FImpute program was used for genotype imputation. Pedigree-based analyses indicated that meat tenderness is moderately heritable (0.35), indicating that it can be improved by direct selection. Prediction accuracies were very similar across the Bayesian regression models, ranging from 0.20 (Bayes A) to 0.22 (Bayes B) and 0.14 (Bayes Cπ) to 0.19 (Bayes A) for the additive and dominance effects, respectively. ANN achieved the highest accuracy (0.33) of genomic prediction of genetic merit. Even though deep neural networks are recognized to deliver more accurate predictions, in our study ANN with one single hidden layer, 105 neurons and rectified linear unit (ReLU) activation function was sufficient to increase the prediction of genetic merit for meat tenderness. These results indicate that an ANN with relatively simple architecture can provide superior genomic predictions for meat tenderness in Nellore cattle.

Genome-Enabled Prediction of Breeding Values for Feedlot Average Daily Weight Gain in Nelore Cattle.

Nelore is the most economically important cattle breed in Brazil, and the use of genetically improved animals has contributed to increased beef production efficiency. The Brazilian beef feedlot industry has grown considerably in the last decade, so the selection of animals with higher growth rates on feedlot has become quite important. Genomic selection (GS) could be used to reduce generation intervals and improve the rate of genetic gains. The aim of this study was to evaluate the prediction of genomic-estimated breeding values (GEBV) for average daily weight gain (ADG) in 718 feedlot-finished Nelore steers. Analyses of three Bayesian model specifications [Bayesian GBLUP (BGBLUP), BayesA, and BayesCπ] were performed with four genotype panels [Illumina BovineHD BeadChip, TagSNPs, and GeneSeek High- and Low-density indicus (HDi and LDi, respectively)]. Estimates of Pearson correlations, regression coefficients, and mean squared errors were used to assess accuracy and bias of predictions. Overall, the BayesCπ model resulted in less biased predictions. Accuracies ranged from 0.18 to 0.27, which are reasonable values given the heritability estimates (from 0.40 to 0.44) and sample size (568 animals in the training population). Furthermore, results from Bos taurus indicus panels were as informative as those from Illumina BovineHD, indicating that they could be used to implement GS at lower costs.

Estimation of genetic parameters for longevity considering the cow's age at last calving.

The aim of this study was to estimate heritability and predict breeding values for longevity among cows in herds of Nellore breed, considering the trait cow's age at last calving (ALC), by means of survival analysis methodology. The records of 11,791 animals from 22 farms were used. The variable ALC has been used by a criterion that made it possible to include cows not only at their first calving but also at their ninth calving. The criterion used was the difference between the date of each cow's last calving and the date of the last calving on each farm. If this difference was greater than 36 months, the cow was considered to have failed and uncensored. If not, this cow was censored, thus indicating that future calving remained possible for this cow. The survival model used for the analyses was the proportional hazards model, and the base risk was given by a Weibull distribution. The heritability estimate obtained was equal to 0.25. It was found that the ALC variable had the capacity to respond to selection for the purpose of increasing the longevity of the cows in the herds.

Bayesian Variable Selection in Multilevel Item Response Theory Models with Application in Genomics.

The goal of this paper is to present an implementation of stochastic search variable selection (SSVS) to multilevel model from item response theory (IRT). As experimental settings get more complex and models are required to integrate multiple (and sometimes massive) sources of information, a model that can jointly summarize and select the most relevant characteristics can provide better interpretation and a deeper insight into the problem. A multilevel IRT model recently proposed in the literature for modeling multifactorial diseases is extended to perform variable selection in the presence of thousands of covariates using SSVS. We derive conditional distributions required for such a task as well as an acceptance-rejection step that allows for the SSVS in high dimensional settings using a Markov Chain Monte Carlo algorithm. We validate the variable selection procedure through simulation studies, and illustrate its application on a study with genetic markers associated with the metabolic syndrome.

Genomic prediction of breeding values for carcass traits in Nellore cattle.

BACKGROUND: The objective of this study was to evaluate the accuracy of genomic predictions for rib eye area (REA), backfat thickness (BFT), and hot carcass weight (HCW) in Nellore beef cattle from Brazilian commercial herds using different prediction models. METHODS: Phenotypic data from 1756 Nellore steers from ten commercial herds in Brazil were used. Animals were offspring of 294 sires and 1546 dams, reared on pasture, feedlot finished, and slaughtered at approximately 2 years of age. All animals were genotyped using a 777k Illumina Bovine HD SNP chip. Accuracy of genomic predictions of breeding values was evaluated by using a 5-fold cross-validation scheme and considering three models: Bayesian ridge regression (BRR), Bayes C (BC) and Bayesian Lasso (BL), and two types of response variables: traditional estimated breeding value (EBV), and phenotype adjusted for fixed effects (Y*). RESULTS: The prediction accuracies achieved with the BRR model were equal to 0.25 (BFT), 0.33 (HCW) and 0.36 (REA) when EBV was used as response variable, and 0.21 (BFT), 0.37 (HCW) and 0.46 (REA) when using Y*. Results obtained with the BC and BL models were similar. Accuracies increased for traits with a higher heritability, and using Y* instead of EBV as response variable resulted in higher accuracy when heritability was higher. CONCLUSIONS: Our results indicate that the accuracy of genomic prediction of carcass traits in Nellore cattle is moderate to high. Prediction of genomic breeding values from adjusted phenotypes Y* was more accurate than from EBV, especially for highly heritable traits. The three models considered (BRR, BC and BL) led to similar predictive abilities and, thus, either one could be used to implement genomic prediction for carcass traits in Nellore cattle.

Using multiple regression, Bayesian networks and artificial neural networks for prediction of total egg production in European quails based on earlier expressed phenotypes.

The prediction of total egg production (TEP) potential in poultry is an important task to aid optimized management decisions in commercial enterprises. The objective of the present study was to compare different modeling approaches for prediction of TEP in meat type quails (Coturnix coturnix coturnix) using phenotypes such as weight, weight gain, egg production and egg quality measurements. Phenotypic data on 30 traits from two lines (L1, n=180; and L2, n=205) of quail were modeled to predict TEP. Prediction models included multiple linear regression and artificial neural network (ANN). Moreover, Bayesian network (BN) and a stepwise approach were used as variable selection methods. BN results showed that TEP is independent from other earlier expressed traits when conditioned on egg production from 35 to 80 days of age (EP1). In addition, the prediction accuracy was much lower when EP1 was not included in the model. The best predictive model was ANN, after feature selection, showing prediction correlations of r=0.792 and r=0.714 for L1 and L2, respectively. In conclusion, machine learning methods may be useful, but reasonable prediction accuracies are obtained only when partial egg production measurements are included in the model.

Liver functional genomics in beef cows on grazing systems: novel genes and pathways revealed.

The adaptation of the liver to periods of negative energy balance is largely unknown in beef cattle on grazing systems. We evaluated liver transcriptome throughout gestation and early lactation of purebred and crossbred beef cows [Angus, Hereford, and their F1 crossbreeds (CR)], grazing high or low herbage allowances (HA) of native grasslands (4 and 2.5 kg dry matter/kg body wt annual mean; n = 16) using an Agilent 4 × 44k bovine array. A total of 4,661 transcripts were affected by days [272 ≥ 2.5-fold difference, false discovery rate (FDR) ≤ 0.10] and 47 pathways were altered during winter gestation (-165 to -15 days relative to calving), when cows experienced decreased body condition score, decreased insulin, and increased nonesterified fatty acid concentrations. Gluconeogenesis and fatty acid oxidation pathways were upregulated, while cell growth, DNA replication, and transcription pathways were downregulated (FDR ≤ 0.25). We observed only small changes in the liver transcriptome during early lactation (+15 to +60 days). A total of 225 genes were differentially expressed (47 ≥ 2-fold difference, FDR ≤ 0.10) between HA. The majority of those were related to glucose and pyruvate metabolism and were upregulated in high HA, reflecting their better metabolic status. Two genes were upregulated in CR cows, but 148 transcripts (74 ≥ 2-fold change difference, FDR ≤ 0.10) were affected by the HA and cow genotype interaction. The transcriptional changes observed indicated a complex and previously unrecognized, hepatic adaptive program of grazing beef cows in different nutritional environments. Novel target candidate genes, metabolic pathways, and regulatory mechanisms were reported.

Searching for phenotypic causal networks involving complex traits: an application to European quail.

BACKGROUND: Structural equation models (SEM) are used to model multiple traits and the casual links among them. The number of different causal structures that can be used to fit a SEM is typically very large, even when only a few traits are studied. In recent applications of SEM in quantitative genetics mixed model settings, causal structures were pre-selected based on prior beliefs alone. Alternatively, there are algorithms that search for structures that are compatible with the joint distribution of the data. However, such a search cannot be performed directly on the joint distribution of the phenotypes since causal relationships are possibly masked by genetic covariances. In this context, the application of the Inductive Causation (IC) algorithm to the joint distribution of phenotypes conditional to unobservable genetic effects has been proposed. METHODS: Here, we applied this approach to five traits in European quail: birth weight (BW), weight at 35 days of age (W35), age at first egg (AFE), average egg weight from 77 to 110 days of age (AEW), and number of eggs laid in the same period (NE). We have focused the discussion on the challenges and difficulties resulting from applying this method to field data. Statistical decisions regarding partial correlations were based on different Highest Posterior Density (HPD) interval contents and models based on the selected causal structures were compared using the Deviance Information Criterion (DIC). In addition, we used temporal information to perform additional edge orienting, overriding the algorithm output when necessary. RESULTS: As a result, the final causal structure consisted of two separated substructures: BW→AEW and W35→AFE→NE, where an arrow represents a direct effect. Comparison between a SEM with the selected structure and a Multiple Trait Animal Model using DIC indicated that the SEM is more plausible. CONCLUSIONS: Coupling prior knowledge with the output provided by the IC algorithm allowed further learning regarding phenotypic causal structures when compared to standard mixed effects SEM applications.

Zero-inflated Poisson regression models for QTL mapping applied to tick-resistance in a Gyr × Holstein F2 population.

Now a days, an important and interesting alternative in the control of tick-infestation in cattle is to select resistant animals, and identify the respective quantitative trait loci (QTLs) and DNA markers, for posterior use in breeding programs. The number of ticks/animal is characterized as a discrete-counting trait, which could potentially follow Poisson distribution. However, in the case of an excess of zeros, due to the occurrence of several noninfected animals, zero-inflated Poisson and generalized zero-inflated distribution (GZIP) may provide a better description of the data. Thus, the objective here was to compare through simulation, Poisson and ZIP models (simple and generalized) with classical approaches, for QTL mapping with counting phenotypes under different scenarios, and to apply these approaches to a QTL study of tick resistance in an F2 cattle (Gyr × Holstein) population. It was concluded that, when working with zero-inflated data, it is recommendable to use the generalized and simple ZIP model for analysis. On the other hand, when working with data with zeros, but not zero-inflated, the Poisson model or a data-transformation-approach, such as square-root or Box-Cox transformation, are applicable.

Zero-inflated Poisson regression models for QTL mapping applied to tick-resistance in a Gyr x Holstein F2 population

Nowadays, an important and interesting alternative in the control of tick-infestation in cattle is to select resistant animals, and identify the respective quantitative trait loci (QTLs) and DNA markers, for posterior use in breeding programs. The number of ticks/animal is characterized as a discrete-counting trait, which could potentially follow Poisson distribution. However, in the case of an excess of zeros, due to the occurrence of several noninfected animals, zero-inflated Poisson and generalized zero-inflated distribution (GZIP) may provide a better description of the data. Thus, the objective here was to compare through simulation, Poisson and ZIP models (simple and generalized) with classical approaches, for QTL mapping with counting phenotypes under different scenarios, and to apply these approaches to a QTL study of tick resistance in an F2 cattle (Gyr x Holstein) population. It was concluded that, when working with zero-inflated data, it is recommendable to use the generalized and simple ZIP model for analysis. On the other hand, when working with data with zeros, but not zero-inflated, the Poisson model or a data-transformation-approach, such as square-root or Box-Cox transformation, are applicable.

Searching for recursive causal structures in multivariate quantitative genetics mixed models.

Biology is characterized by complex interactions between phenotypes, such as recursive and simultaneous relationships between substrates and enzymes in biochemical systems. Structural equation models (SEMs) can be used to study such relationships in multivariate analyses, e.g., with multiple traits in a quantitative genetics context. Nonetheless, the number of different recursive causal structures that can be used for fitting a SEM to multivariate data can be huge, even when only a few traits are considered. In recent applications of SEMs in mixed-model quantitative genetics settings, causal structures were preselected on the basis of prior biological knowledge alone. Therefore, the wide range of possible causal structures has not been properly explored. Alternatively, causal structure spaces can be explored using algorithms that, using data-driven evidence, can search for structures that are compatible with the joint distribution of the variables under study. However, the search cannot be performed directly on the joint distribution of the phenotypes as it is possibly confounded by genetic covariance among traits. In this article we propose to search for recursive causal structures among phenotypes using the inductive causation (IC) algorithm after adjusting the data for genetic effects. A standard multiple-trait model is fitted using Bayesian methods to obtain a posterior covariance matrix of phenotypes conditional to unobservable additive genetic effects, which is then used as input for the IC algorithm. As an illustrative example, the proposed methodology was applied to simulated data related to multiple traits measured on a set of inbred lines.

Selective transcriptional profiling and data analysis strategies for expression quantitative trait loci mapping in outbred F2 populations.

Genetic analysis of transcriptional profiling experiments is emerging as a promising approach for unraveling genes and pathways that underlie variation of complex biological traits. However, these genetical genomics approaches are currently limited by the high cost of microarrays. We studied five different strategies to optimally select subsets of individuals for transcriptional profiling, including (1) maximizing genetic dissimilarity between selected individuals, (2) maximizing the number of recombination events in selected individuals, (3) selecting phenotypic extremes within inferred genotypes of a previously identified quantitative trait locus (QTL), (4) purely random selection, and (5) profiling animals with the highest and lowest phenotypic values within each family-gender subclass. A simulation study was conducted on the basis of a linkage map and marker genotypes were derived from data on chromosome 6 for 510 F2 animals from an existing pig resource population and on a simulated biallelic QTL with pleiotropic effects on performance and gene expression traits. Bivariate analyses were conducted for selected subset sample sizes of 80, 160, and 240 individuals under three different correlation scenarios between the two traits. The genetic dissimilarity and phenotypic extremes within genotype methods had the smallest mean square error on QTL effects and maximum sensitivity on QTL detection, thereby outperforming all other selection strategies, particularly at the smallest proportion of samples selected for gene expression profiling (80/510).

Design of microarray experiments for genetical genomics studies.

Microarray experiments have been used recently in genetical genomics studies, as an additional tool to understand the genetic mechanisms governing variation in complex traits, such as for estimating heritabilities of mRNA transcript abundances, for mapping expression quantitative trait loci, and for inferring regulatory networks controlling gene expression. Several articles on the design of microarray experiments discuss situations in which treatment effects are assumed fixed and without any structure. In the case of two-color microarray platforms, several authors have studied reference and circular designs. Here, we discuss the optimal design of microarray experiments whose goals refer to specific genetic questions. Some examples are used to illustrate the choice of a design for comparing fixed, structured treatments, such as genotypic groups. Experiments targeting single genes or chromosomic regions (such as with transgene research) or multiple epistatic loci (such as within a selective phenotyping context) are discussed. In addition, microarray experiments in which treatments refer to families or to subjects (within family structures or complex pedigrees) are presented. In these cases treatments are more appropriately considered to be random effects, with specific covariance structures, in which the genetic goals relate to the estimation of genetic variances and the heritability of transcriptional abundances.

A Bayesian approach for constructing genetic maps when markers are miscoded.

The advent of molecular markers has created opportunities for a better understanding of quantitative inheritance and for developing novel strategies for genetic improvement of agricultural species, using information on quantitative trait loci (QTL). A QTL analysis relies on accurate genetic marker maps. At present, most statistical methods used for map construction ignore the fact that molecular data may be read with error. Often, however, there is ambiguity about some marker genotypes. A Bayesian MCMC approach for inferences about a genetic marker map when random miscoding of genotypes occurs is presented, and simulated and real data sets are analyzed. The results suggest that unless there is strong reason to believe that genotypes are ascertained without error, the proposed approach provides more reliable inference on the genetic map.