Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data

The use of milk Fourier-transform infrared spectra for predicting cheesemaking traits in Grana Padano Protected Designation of Origin cheese

The prediction of the cheese yield (%CY) traits for curd, solids, and retained water and the amount of fat, protein, solids, and energy recovered from the milk into the curd (%REC) by Bayesian models, using Fourier-transform infrared spectroscopy (FTIR), can be of significant economic interest to the dairy industry and can contribute to the improvement of the cheese process efficiency. The yields give a quantitative measure of the ratio between weights of the input and output of the process, whereas the nutrient recovery allows to assess the quantitative transfer of a component from milk to cheese (expressed in % of the initial weight). The aims of this study were: (1) to investigate the feasibility of using bulk milk spectra to predict %CY and %REC traits, and (2) to quantify the effect of the dairy industry and the contribution of single-spectrum wavelengths on the prediction accuracy of these traits using vat milk samples destined to the production of Grana Padano Protected Designation of Origin cheese. Information from 72 cheesemaking days (in total, 216 vats) from 3 dairy industries were collected. For each vat, the milk was weighed and analyzed for composition (total solids [TS], lactose, protein, and fat). After 48 h from cheesemaking, each cheese was weighed, and the resulting whey was sampled for composition as well (TS, lactose, protein, and fat). Two spectra from each milk sample were collected in the range between 5,011 and 925 cm-1 and averaged before the data analysis. The calibration models were developed via a Bayesian approach by using the BGLR (Bayesian Generalized Linear Regression) package of R software. The performance of the models was assessed by the coefficient of determination (R2VAL) and the root mean squared error (RMSEVAL) of validation. Random cross-validation (CVL) was applied [80% calibration and 20% validation set] with 10 replicates. Then, a stratified cross-validation (SCV) was performed to assess the effect of the dairy industry on prediction accuracy. The study was repeated using a selection of informative wavelengths to assess the necessity of using whole spectra to optimize prediction accuracy. Results showed the feasibility of using FTIR spectra and Bayesian models to predict cheesemaking traits. The R2VAL values obtained with the CVL procedure were promising in particular for the %CY and %REC for protein, ranging from 0.44 to 0.66 with very low RMSEVAL (from 0.16 to 0.53). Prediction accuracy obtained with the SCV was strongly influenced by the dairy factory industry. The general low values gained with the SCV do not permit a practical application of this approach, but they highlight the importance of building calibration models with a dataset covering the largest possible sample variability. This study also demonstrated that the use of the full FTIR spectra may be redundant for the prediction of the cheesemaking traits and that a specific selection of the most informative wavelengths led to improved prediction accuracy. This could lead to the development of dedicated spectrometers using selected wavelengths with built-in calibrations for the online prediction of these innovative traits.

Energy balance of dairy cows predicted by mid-infrared spectra data of milk using Bayesian approaches

Information on dry matter intake (DMI) and energy balance (EB) at the animal and herd level is important for management and breeding decisions. However, routine recording of these traits at commercial farms can be challenging and costly. Fourier-transform mid-infrared (FT-MIR) spectroscopy is a noninvasive technique applicable to a large cohort of animals that is routinely used to analyze milk components and is convenient for predicting complex phenotypes that are typically difficult and expensive to obtain on a large scale. We aimed to develop prediction models for EB and use the predicted phenotypes for genetic analysis. First, we assessed prediction equations using 4,485 phenotypic records from 167 Holstein cows from an experimental station. The phenotypes available were body weight (BW), milk yield (MY) and milk components, weekly-averaged DMI, and FT-MIR data from all milk samples available. We implemented mixed models with Bayesian approaches and assessed them through 50 randomized replicates of a 5-fold cross-validation. Second, we used the best prediction models to obtain predicted phenotypes of EB (EBp) and DMI (DMIp) on 5 commercial farms with 2,365 phenotypic records of MY, milk components and FT-MIR data, and BW from 1,441 Holstein cows. Third, we performed a GWAS and estimated heritability and genetic correlations for energy content in milk (EnM), BW, DMIp, and EBp using the genomic information available on the cows from commercial farms. The highest correlation between the predicted and observed phenotype (ry,y^) was obtained with DMI (0.88) and EB (0.86), while predicting BW was, as anticipated, more challenging (0.69). In our study, models that included FT-MIR information performed better than models without spectra information in the 3 traits analyzed, with increments in prediction correlation ranging from 5% to 10%. For the predicted phenotypes calculated by the prediction equations and data from the commercial farms the heritability ranged between 0.11 and 0.16 for EnM, DMIp and EBp, and 0.42 for BW. The genetic correlation between EnM and BW was -0.17, with DMIp was 0.40 and with EBp was -0.39. From the GWAS, we detected one significant QTL region for EnM, and 3 for BW, but none for DMIp and EBp. The results obtained in our study support previous evidence that FT-MIR information from milk samples contribute to improve the prediction equations for DMI, BW, and EB, and these predicted phenotypes may be used for herd management and contribute to the breeding strategy for improving cow performance.

Exploring the use of NIR and Raman spectroscopy for the prediction of quality traits in PDO cheeses

The aims of this proof of principle study were to compare two different chemometric approaches using a Bayesian method, Partial Least Square (PLS) and PLS-discriminant analysis (DA), for the prediction of the chemical composition and texture properties of the Grana Padano (GP) and Parmigiano Reggiano (PR) PDO cheeses by using NIR and Raman spectra and quantify their ability to distinguish between the two PDO and among their ripening periods. For each dairy chain consortium, 9 cheese samples from 3 dairy industries were collected for a total of 18 cheese samples. Three seasoning times were chosen for each dairy industry: 12, 20, and 36 months for GP and 12, 24, and 36 months for PR. A portable NIR instrument (spectral range: 950-1,650 nm) was used on 3 selected spots on the paste of each cheese sample, for a total of 54 spectra collected. An Alpha300 R confocal Raman microscope was used to collect 10 individual spectra for each cheese sample in each spot for a total of 540 Raman spectra collected. After the detection of eventual outliers, the spectra were also concatenated together (NIR + Raman). All the cheese samples were assessed in terms of chemical composition and texture properties following the official reference methods. A Bayesian approach and PLS-DA were applied to the NIR, Raman, and fused spectra to predict the PDO type and seasoning time. The PLS-DA reached the best performances, with 100% correctly identified PDO type using Raman only. The fusion of the data improved the results in 60% of the cases with the Bayesian and of 40% with the PLS-DA approach. A Bayesian approach and a PLS procedure were applied to the NIR, Raman, and fused spectra to predict the chemical composition of the cheese samples and their texture properties. In this case, the best performance in validation was reached with the Bayesian method on Raman spectra for fat (R2VAL = 0.74). The fusion of the data was not always helpful in improving the prediction accuracy. Given the limitations associated with our sample set, future studies will expand the sample size and incorporate diverse PDO cheeses.

Identification of Milk Adulteration in Camel Milk Using FT-Mid-Infrared Spectroscopy and Machine Learning Models

Camel milk, esteemed for its high nutritional value, has long been a subject of interest. However, the adulteration of camel milk with cow milk poses a significant threat to food quality and safety. Fourier-transform infrared spectroscopy (FT-MIR) has emerged as a rapid method for the detection and quantification of cow milk adulteration. Nevertheless, its effectiveness in conveniently detecting adulteration in camel milk remains to be determined. Camel milk samples were collected from Alxa League, Inner Mongolia, China, and were supplemented with varying concentrations of cow milk samples. Spectra were acquired using the FOSS FT6000 spectrometer, and a diverse set of machine learning models was employed to detect cow milk adulteration in camel milk. Our results demonstrate that the Linear Discriminant Analysis (LDA) model effectively distinguishes pure camel milk from adulterated samples, maintaining a 100% detection rate even at cow milk addition levels of 10 g/100 g. The neural network quantitative model for cow milk adulteration in camel milk exhibited a detection limit of 3.27 g/100 g and a quantification limit of 10.90 g/100 g. The quantitative model demonstrated excellent precision and accuracy within the range of 10-90 g/100 g of adulteration. This study highlights the potential of FT-MIR spectroscopy in conjunction with machine learning techniques for ensuring the authenticity and quality of camel milk, thus addressing concerns related to food integrity and consumer safety.

Cheese yield and nutrients recovery in the curd predicted by Fourier-transform spectra from individual sheep milk samples

The objectives of this study were to explore the use of Fourier-transform infrared (FTIR) spectroscopy on individual sheep milk samples for predicting cheese-making traits, and to test the effect of the farm variability on their prediction accuracy. For each of 121 ewes from 4 farms, a laboratory model cheese was produced, and 3 actual cheese yield traits (fresh cheese, cheese solids, and cheese water) and 4 milk nutrient recovery traits (fat, protein, total solids, and energy) in the curd were measured. Calibration equations were developed using a Bayesian approach with 2 different scenarios: (1) a random cross-validation (80% calibration; 20% validation set), and (2) a leave-one-out validation (3 farms used as calibration, and the remaining one as validation set) to assess the accuracy of prediction of samples from external farms, not included in calibration set. The best performance was obtained for predicting the yield and recovery of total solids, justifying for the practical application of the method at sheep population and dairy industry levels. Performances for the remaining traits were lower, but still useful for the monitoring of the milk processing in the case of fresh curd and recovery of energy. Insufficient accuracies were found for the recovery of protein and fat, highlighting the complex nature of the relationships among the milk nutrients and their recovery in the curd. The leave-one-out validation procedure, as expected, showed lower prediction accuracies, as a result of the characteristics of the farming systems, which were different between calibration and validation sets. In this regard, the inclusion of information related to the farm could help to improve the prediction accuracy of these traits. Overall, a large contribution to the prediction of the cheese-making traits came from the areas known as "water" and "fingerprint" regions. These findings suggest that, according to the traits studied, the inclusion of water regions for the development of the prediction equation models is fundamental to maintain a high prediction accuracy. However, further studies are necessary to better understand the role of specific absorbance peaks and their contribution to the prediction of cheese-making traits, to offer reliable tools applicable along the dairy ovine chain.

Synchronously Predicting Tea Polyphenol and Epigallocatechin Gallate in Tea Leaves Using Fourier Transform-Near-Infrared Spectroscopy and Machine Learning

Tea polyphenol and epigallocatechin gallate (EGCG) were considered as key components of tea. The rapid prediction of these two components can be beneficial for tea quality control and product development for tea producers, breeders and consumers. This study aimed to develop reliable models for tea polyphenols and EGCG content prediction during the breeding process using Fourier Transform-near infrared (FT-NIR) spectroscopy combined with machine learning algorithms. Various spectral preprocessing methods including Savitzky-Golay smoothing (SG), standard normal variate (SNV), vector normalization (VN), multiplicative scatter correction (MSC) and first derivative (FD) were applied to improve the quality of the collected spectra. Partial least squares regression (PLSR) and least squares support vector regression (LS-SVR) were introduced to establish models for tea polyphenol and EGCG content prediction based on different preprocessed spectral data. Variable selection algorithms, including competitive adaptive reweighted sampling (CARS) and random forest (RF), were further utilized to identify key spectral bands to improve the efficiency of the models. The results demonstrate that the optimal model for tea polyphenols calibration was the LS-SVR with R_p = 0.975 and RPD = 4.540 based on SG-smoothed full spectra. For EGCG detection, the best model was the LS-SVR with R_p = 0.936 and RPD = 2.841 using full original spectra as model inputs. The application of variable selection algorithms further improved the predictive performance of the models. The LS-SVR model for tea polyphenols prediction with R_p = 0.978 and RPD = 4.833 used 30 CARS-selected variables, while the LS-SVR model build on 27 RF-selected variables achieved the best predictive ability with R_p = 0.944 and RPD = 3.049, respectively, for EGCG prediction. The results demonstrate a potential of FT-NIR spectroscopy combined with machine learning for the rapid screening of genotypes with high tea polyphenol and EGCG content in tea leaves.

Dry Matter Intake Prediction from Milk Spectra in Sarda Dairy Sheep

Individual dry matter intake (DMI) is a relevant factor for evaluating feed efficiency in livestock. However, the measurement of this trait on a large scale is difficult and expensive. DMI, as well as other phenotypes, can be predicted from milk spectra. The aim of this work was to predict DMI from the milk spectra of 24 lactating Sarda dairy sheep ewes. Three models (Principal Component Regression, Partial Least Squares Regression, and Stepwise Regression) were iteratively applied to three validation schemes: records, ewes, and days. DMI was moderately correlated with the wavenumbers of the milk spectra: the largest correlations (around ±0.30) were observed at ~1100-1330 cm^-1 and ~2800-3000 cm^-1. The average correlations between real and predicted DMI were 0.33 (validation on records), 0.32 (validation on ewes), and 0.23 (validation on days). The results of this preliminary study, even if based on a small number of animals, demonstrate that DMI can be routinely estimated from the milk spectra.

Prediction of fresh and ripened cheese yield using detailed milk composition and udder health indicators from individual Brown Swiss cows

The composition of raw milk is of major importance for dairy products, especially fat, protein, and casein (CN) contents, which are used worldwide in breeding programs for dairy species because of their role in human nutrition and in determining cheese yield (%CY). The aim of the study was to develop formulas based on detailed milk composition to disentangle the role of each milk component on %CY traits. To this end, 1,271 individual milk samples (1.5 L/cow) from Brown Swiss cows were processed according to a laboratory model cheese-making procedure. Fresh %CY (%CY_CURD), total solids and water retained in the fresh cheese (%CY_SOLIDS and %CY_WATER), and 60-days ripened cheese (%CY_RIPENED) were the reference traits and were used as response variables. Training-testing linear regression modeling was performed: 80% of observations were randomly assigned to the training set, 20% to the validation set, and the procedure was repeated 10 times. Four groups of predictive equations were identified, in which different combinations of predictors were tested separately to predict %CY traits: (i) basic composition, i.e., fat, protein, and CN, tested individually and in combination; (ii) udder health indicators (UHI), i.e., fat + protein or CN + lactose and/or somatic cell score (SCS); (iii) detailed protein profile, i.e., fat + protein fractions [CN fractions, whey proteins, and nonprotein nitrogen (NPN) compounds]; (iv) detailed protein profile + UHI, i.e., fat + protein fractions + NPN compounds and/or UHI. Aside from the positive effect of fat, protein, and total casein on %CY, our results allowed us to disentangle the role of each casein fraction and whey protein, confirming the central role of β-CN and κ-CN, but also showing α-lactalbumin (α-LA) to have a favorable effect, and β-lactoglobulin (β-LG) a negative effect. Replacing protein or casein with individual milk protein and NPN fractions in the statistical models appreciably increased the validation accuracy of the equations. The cheese industry would benefit from an improvement, through genetic selection, of traits related to cheese yield and this study offers new insights into the quantification of the influence of milk components in composite selection indices with the aim of directly enhancing cheese production.

Phenotypic and genetic characterization of the occurrence of noncoagulating milk in dairy sheep

Milk coagulation ability is of central importance for the sheep dairy industry because almost all sheep milk is destined for cheese processing. The occurrence of milk with impaired coagulation properties is an obstacle to cheese processing and, in turn, to the profitability of the dairy companies. In this work, we investigated the causes of noncoagulation of sheep milk; specifically, we studied the effect of milk physicochemical properties on milk coagulation status [coagulating and noncoagulating (NC) milk samples, which do or do not coagulate within 30 min, respectively], and whether mid-infrared spectroscopy (MIR) could be used to assess variability in coagulation status. We also investigated the genetic background of milk coagulation ability. Individual milk samples were collected from 996 Sarda ewes farmed in 47 flocks located in Sardinia (Italy). Considered traits were daily milk yield, milk composition traits, and milk coagulation properties (rennet coagulation time, curd firming time, and curd firmness), and MIR spectra were acquired. About 9% of samples did not coagulate within 30 min. A logistic regression approach was used to test the effect of milk-related traits on milk coagulation status. A principal component (PC) analysis was carried out on the milk MIR spectra, and PC scores were then used as covariates in a logistic regression model to assess their relationship with milk coagulation status. Results of the present work demonstrated that the probability of having NC samples increases as milk contents of proteins and chlorides and somatic cell score increase. The analysis of PC extracted from milk spectra that influenced coagulation status highlighted key regions associated with lactose and protein concentrations, and others not associated with routinely collected milk composition traits. These results suggest that the occurrence of NC is mostly related to damage of the epithelium secretory mammary cells, which occurs with the advancement of a lactation or due to unhealthy mammary gland status. Genetic analysis of milk coagulation status and of the extracted PC confirmed the genetic background of the milk coagulability of sheep milk.

Multivariate and Genome-Wide Analysis of Mid-Infrared Spectra of Non-Coagulating Milk of Sarda Sheep Breed

Milk coagulation ability is crucial for the dairy sheep industry since the whole amount of milk is processed into cheese. Non-coagulating milk (NCM) is defined as milk not forming a curd within the testing time. In sheep milk, it has been reported in literature that up to 20% of milk is NCM. Although the clotting properties of individual milk have been widely studied, little attention has been given to NCM and genomic dissection of this trait. Mid-infrared (MIR) spectra can be exploited both to predict cheese-making aptitude and to discriminate between coagulating milk and NCM. The main goals of this work were (i) to assess the predictivity of MIR spectra for NCM classification and (ii) to conduct a genome-wide association study on coagulation ability. Milk samples from 949 Sarda ewes genotyped and phenotyped for milk coagulation properties (MCPs) served as the training dataset. The validation dataset included 662 ewes. Three classical MCPs were measured: rennet coagulation time (RCT), curd firmness (a30), and curd firming time (k20). Moreover, MIR spectra were acquired and stored in the region between 925.92 and 5,011.54 cm−1. The probability of a sample to be NCM was modeled by step-wise logistic regression on milk spectral information (LR-W), logistic regression on principal component (LR-PC), and canonical discriminant analysis of spectral wave number (DA-W). About 9% of the samples did not coagulate at 30 min. The use of LR-W gave a poorer classification of NCM. The use of LR-PC improved the percentage of correct assignment (45 ± 9%). The DA-W method allows us to reach 75.1 ± 10.3 and 76.5 ± 18.4% of correct assignments of the inner and external validation datasets, respectively. As far as GWA of NCM, 458 SNP associations and 45 candidate genes were detected. The genes retrieved from public databases were mostly linked to mammary gland metabolism, udder health status, and a milk compound also known to affect the ability of milk to coagulate. In particular, the potential involvement of CAPNs deserves further investigation.

Phenomic Selection: A New and Efficient Alternative to Genomic Selection

Recently, it has been proposed to switch molecular markers to near-infrared (NIR) spectra for inferring relationships between individuals and further performing phenomic selection (PS), analogous to genomic selection (GS). The PS concept is similar to genomic-like omics-based (GLOB) selection, in which molecular markers are replaced by endophenotypes, such as metabolites or transcript levels, except that the phenomic information obtained for instance by near-infrared spectroscopy (NIRS ) has usually a much lower cost than other omics. Though NIRS has been routinely used in breeding for several decades, especially to deal with end-product quality traits, its use to predict other traits of interest and further make selections is new. Since the seminal paper on PS , several publications have advocated the use of spectral acquisition (including NIRS and hyperspectral imaging) in plant breeding towards PS , potentially providing a scope of what is possible. In the present chapter, we first come back to the concept of PS as originally proposed and provide a classification of selected papers related to the use of phenomics in breeding. We further provide a review of the selected literature concerning the type of technology used, the preprocessing of the spectra, and the statistical modeling to make predictions. We discuss the factors that likely affect the efficiency of PS and compare it to GS in terms of predictive ability. Finally, we propose several prospects for future work and application of PS in the context of plant breeding.

Heritable Variation of Foliar Spectral Reflectance Enhances Genomic Prediction of Hydrogen Cyanide in a Genetically Structured Population of Eucalyptus

Plants produce a wide diversity of specialized metabolites, which fulfill a wide range of biological functions, helping plants to interact with biotic and abiotic factors. In this study, an integrated approach based on high-throughput plant phenotyping, genome-wide haplotypes, and pedigree information was performed to examine the extent of heritable variation of foliar spectral reflectance and to predict the leaf hydrogen cyanide content in a genetically structured population of a cyanogenic eucalyptus (Eucalyptus cladocalyx F. Muell). In addition, the heritable variation (based on pedigree and genomic data) of more of 100 common spectral reflectance indices was examined. The first profile of heritable variation along the spectral reflectance curve indicated the highest estimate of genomic heritability ( h g 2 =0.41) within the visible region of the spectrum, suggesting that several physiological and biological responses of trees to environmental stimuli (ex., light) are under moderate genetic control. The spectral reflectance index with the highest genomic-based heritability was leaf rust disease severity index 1 ( h g 2 =0.58), followed by the anthocyanin reflectance index and the Browning reflectance index ( h g 2 =0.54). Among the Bayesian prediction models based on spectral reflectance data, Bayes B had a better goodness of fit than the Bayes-C and Bayesian ridge regression models (in terms of the deviance information criterion). All models that included spectral reflectance data outperformed conventional genomic prediction models in their predictive ability and goodness-of-fit measures. Finally, we confirmed the proposed hypothesis that high-throughput phenotyping indirectly capture endophenotypic variants related to specialized metabolites (defense chemistry), and therefore, generally more accurate predictions can be made integrating phenomics and genomics.

Invited review: A comprehensive review of visible and near-infrared spectroscopy for predicting the chemical composition of cheese

Substantial research has been carried out on rapid, nondestructive, and inexpensive techniques for predicting cheese composition using spectroscopy in the visible and near-infrared radiation range. Moreover, in recent years, new portable and handheld spectrometers have been used to predict chemical composition from spectra captured directly on the cheese surface in dairies, storage facilities, and food plants, removing the need to collect, transport, and process cheese samples. For this review, we selected 71 papers (mainly dealing with prediction of the chemical composition of cheese) and summarized their results, focusing our attention on the major sources of variation in prediction accuracy related to cheese variability, spectrometer and spectra characteristics, and chemometrics techniques. The average coefficient of determination obtained from the validation samples ranged from 86 to 90% for predicting the moisture, fat, and protein contents of cheese, but was lower for predicting NaCl content and cheese pH (79 and 56%, respectively). There was wide variability with respect to all traits in the results of the various studies (standard deviation: 9-30%). This review draws attention to the need for more robust equations for predicting cheese composition in different situations; the calibration data set should consist of representative cheese samples to avoid bias due to an overly specific field of application and ensure the results are not biased for a particular category of cheese. Different spectrometers have different accuracies, which do not seem to depend on the spectrum extension. Furthermore, specific areas of the spectrum-the visible, infrared-A, or infrared-B range-may yield similar results to broad-range spectra; this is because several signals related to cheese composition are distributed along the spectrum. Small, portable instruments have been shown to be viable alternatives to large bench-top instruments. Last, chemometrics (spectra pre-treatment and prediction models) play an important role, especially with regard to difficult-to-predict traits. A proper, fully independent, validation strategy is essential to avoid overoptimistic results.

Foundations of Bayesian Learning in Clinical Neuroscience

There is an increasing interest in using prediction models to forecast clinical outcomes within the fields of neurosurgery and clinical neuroscience. The present chapter outlines the foundations of Bayesian learning and introduces Bayes theorem and its use in machine learning methodology. The use of Bayesian networks to structure and define associations between outcome predictors and final outcomes is highlighted and Naïve Bayes classifiers are outlined for use in predicting neurosurgical outcomes, where the understanding of underlying causes is less important. The present work aims to orient researchers in Bayesian machine learning methods and when and how to use them. When used correctly, these tools have the potential to improve the understanding of factors influencing neurosurgical outcomes, aid in structuring the relationships between them, and provide reliable machine learning classification models for predicting neurosurgical outcomes.

Effects of breed, farm intensiveness, and cow productivity level on cheese-making ability predicted using infrared spectral data at the population level

Fourier-transform infrared (FTIR) spectra collected during milk recording schemes at population level can be used for predicting novel traits of interest for farm management, cows' genetic improvement, and milk payment systems. The aims of this study were as follows. (1) To predict cheese yield traits using FTIR spectra from routine milk recordings exploiting previously developed calibration equations. (2) To compare the predicted cheese-making abilities of different dairy and dual-purpose breeds. (3) To analyze the effects of herds' level of intensiveness (HL) and of the cow's level of productivity (CL). (4) To compare the patterns of predicted cheese yields with the patterns of milk composition in different breeds to discern the drivers of cheese-making efficiency. The major sources of variation of FTIR predictions of cheese yield ability (fresh cheese or cheese solids produced per unit milk) of individual milk samples were studied on 115,819 cows of 4 breeds (2 specialized dairy breeds, Holstein and Brown Swiss, and 2 dual-purpose breeds, Simmental and Alpine Grey) from 6,430 herds and exploiting 1,759,706 FTIR test-day spectra collected over 7 yr of milk sampling. Calibration equations used were previously developed on 1,264 individual laboratory model cheese procedures (cross-validation R² 0.85 and 0.95 for fresh and solids cheese yields, respectively). The linear model used for statistical analysis included the effects of parity, lactation stage, year of calving, month of sampling, HL, CL, breed of cow, and the interactions breed × HL and breed × CL. The HL and CL stratifications (5 classes each) were based on average daily secretion of milk net energy per cow. All effects were highly significant (P < 0.001). The major conclusions were as follows. (1) The FTIR-based prediction of cheese yield of milk goes beyond the knowledge of fat and protein content, partially explaining differences in cheese-making ability in different cows, breeds and herds. (2) Differences in cheese yields of different breeds are only partially explained by milk fat and protein composition, and less productive breeds are characterized by a higher milk nutrient content as well as a higher recovery of nutrients in the cheese. (3) High-intensive herds not only produce much more milk, but the milk has a higher nutrient content and a higher cheese yield, whereas within herds, compared with less productive cows, the more productive cows have a much greater milk yield, milk with a greater content of fat but not of protein, and a moderate improvement in cheese yield, differing little from expectations based on milk composition. Finally, (4) the effects of HL and CL on milk quality and cheese-making ability are similar but not identical in different breeds, the less productive ones having some advantage in terms of cheese-making ability. We can obtain FTIR-based prediction of cheese yield from individual milk samples retrospectively at population level, which seems to go beyond the simple knowledge of milk composition, incorporating information on nutrient retention ability in cheese, with possible advantages for management of farms, genetic improvement of dairy cows, and milk payment systems.

Prediction of fatty acid composition using milk spectral data and its associations with various mid-infrared spectral regions in Michigan Holsteins

Fatty acid composition in milk is not only reflective of nutritional quality but also potentially predictive of other attributes (e. g. including the cow's energy balance and its relative output of methane emissions). Furthermore, a higher ratio of long-chain to short-chain fatty acids or mean carbon number has been associated with negative energy balance in dairy cows, whereas enhanced nutritional properties have been generally associated with higher levels of unsaturation. We set out to directly compare Bayesian regression strategies with partial least squares for the prediction of various milk fatty acids using Fourier-transform infrared spectrum data on 777 milk samples taken from 579 cows on 4 Michigan dairy herds between 5 and 90 d in milk. We also set out to identify those spectral regions that might be associated with fatty acids and whether carbon number or level of unsaturation might contribute to the strength of these associations. These associations were based on adaptively clustered windows of wavenumbers to mitigate the distorting effects of severe multicollinearity on marginal associations involving individual wavenumbers. In general, Bayesian regression methods, particularly the variable selection method BayesB, outperformed partial least squares regression for cross-validation prediction accuracy for both individual fatty acids and fatty acid groups. Strong signals for wavenumber associations using BayesB were well distributed throughout the mid-infrared spectrum, particularly between 910 and 3,998 cm^-1. Carbon number appeared to be linearly related to strength of wavenumber associations for 38 moderately to highly predicted fatty acids within the spectral regions of 2,286 to 2,376 and 2,984 to 3,100 cm^-1, whereas nonlinear associations were determined within 1,141 to 1,205; 1,570 to 1,630; and 1,727 to 1,768 cm^-1. However, no such associations were detected with level of unsaturation. Spectral regions where there were significant relationships between strength of association and carbon number may be useful targets for inferring the relative proportion of long-chain to short-chain fatty acids, and hence energy balance.

Genetic parameters of differential somatic cell count, milk composition, and cheese-making traits measured and predicted using spectral data in Holstein cows

Mastitis is one of the most prevalent diseases in dairy cattle and is the cause of considerable economic losses. Alongside somatic cell count (SCC), differential somatic cell count (DSCC) has been recently introduced as a new indicator of intramammary infection. The DSCC is expressed as a count or a proportion (%) of polymorphonuclear neutrophils plus lymphocytes (PMN-LYM) in milk somatic cells. These numbers are complemented to total somatic cell count or to 100 by macrophages (MAC). The aim of this study was to investigate the genetic variation and heritability of DSCC, and its correlation with milk composition, udder health indicators, milk composition, and technological traits in Holstein cattle. Data used in the analysis consisted in single test-day records from 2,488 Holstein cows reared in 36 herds located in northern Italy. Fourier-transform infrared (FTIR) spectroscopy was used to predict missing information for some milk coagulation and cheese-making traits, to increase sample size and improve estimation of the genetic parameters. Bayesian animal models were implemented via Gibbs sampling. Marginal posterior means of the heritability estimates were 0.13 for somatic cell score (SCS); 0.11 for DSCC, MAC proportion, and MAC count; and 0.10 for PMN-LYM count. Posterior means of additive genetic correlations between SCS and milk composition and udder health were low to moderate and unfavorable. All the relevant genetic correlations between the SCC traits considered and the milk traits (composition, coagulation, cheese yield and nutrients recovery) were unfavorable. The SCS showed genetic correlations of -0.30 with the milk protein proportion, -0.56 with the lactose proportion and -0.52 with the casein index. In the case of milk technological traits, SCS showed genetic correlations of 0.38 with curd firming rate (k₂₀), 0.45 with rennet coagulation time estimated using the curd firming over time equation (RCT_eq), -0.39 with asymptotic potential curd firmness, -0.26 with maximum curd firmness (CF_max), and of -0.31 with protein recovery in the curd. Differential somatic cell count expressed as proportion was correlated with SCS (0.60) but had only 2 moderate genetic correlations with milk traits: with lactose (-0.32) and CF_max (-0.33). The SCS was highly correlated with the log PMN-LYM count (0.79) and with the log MAC count (0.69). The 2 latter traits were correlated with several milk traits: fat (-0.38 and -0.43 with PMN-LYM and MAC counts, respectively), lactose percentage (-0.40 and -0.46), RCT_eq (0.53 and 0.41), t_max (0.38 and 0.48). Log MAC count was correlated with k₂₀ (+0.34), and log PMN-LYM count was correlated with CF_max (-0.26) and weight of water curd as percentage of weight of milk processed (-0.26). The results obtained offer new insights into the relationships between the indicators of udder health and the milk technological traits in Holstein cows.

Phenotypic and genetic variation of ultraviolet-visible-infrared spectral wavelengths of bovine meat

Spectroscopic predictions can be used for the genetic improvement of meat quality traits in cattle. No information is however available on the genetics of meat absorbance spectra. This research investigated the phenotypic variation and the heritability of meat absorbance spectra at individual wavelengths in the ultraviolet-visible and near-infrared region (UV-Vis-NIR) obtained with portable spectrometers. Five spectra per instrument were taken on the ribeye surface of 1185 Piemontese young bulls from 93 farms (13,182 Herd-Book pedigree relatives). Linear animal model analyses of 1481 single-wavelengths from UV-Vis-NIRS and 125 from Micro-NIRS were carried out separately. In the overlapping regions, the proportions of phenotypic variance explained by batch/date of slaughter (14 ± 6% and 17 ± 7%,), rearing farm (6 ± 2% and 5 ± 3%), and the residual variances (72 ± 10% and 72 ± 5%) were similar for the UV-Vis-NIRS and Micro-NIRS, but additive genetics (7 ± 2% and 4 ± 2%) and heritability (8.3 ± 2.3% vs 5.1 ± 0.6%) were greater with the Micro-NIRS. Heritability was much greater for the visible fraction (25.2 ± 11.4%), especially the violet, blue and green colors, than for the NIR fraction (5.0 ± 8.0%). These results allow a better understanding of the possibility of using the absorbance of visible and infrared wavelengths correlated with meat quality traits for the genetic improvement in beef cattle.

Evaluating the performance of machine learning methods and variable selection methods for predicting difficult-to-measure traits in Holstein dairy cattle using milk infrared spectral data

Fourier-transform infrared (FTIR) spectroscopy is a powerful high-throughput phenotyping tool for predicting traits that are expensive and difficult to measure in dairy cattle. Calibration equations are often developed using standard methods, such as partial least squares (PLS) regression. Methods that employ penalization, rank-reduction, and variable selection, as well as being able to model the nonlinear relations between phenotype and FTIR, might offer improvements in predictive ability and model robustness. This study aimed to compare the predictive ability of 2 machine learning methods, namely random forest (RF) and gradient boosting machine (GBM), and penalized regression against PLS regression for predicting 3 phenotypes differing in terms of biological meaning and relationships with milk composition (i.e., phenotypes measurable directly and not directly in milk, reflecting different biological processes which can be captured using milk spectra) in Holstein-Friesian cattle under 2 cross-validation scenarios. The data set comprised phenotypic information from 471 Holstein-Friesian cows, and 3 target phenotypes were evaluated: (1) body condition score (BCS), (2) blood β-hydroxybutyrate (BHB, mmol/L), and (3) κ-casein expressed as a percentage of nitrogen (κ-CN, % N). The data set was split considering 2 cross-validation scenarios: samples-out random in which the population was randomly split into 10-folds (8-folds for training and 1-fold for validation and testing); and herd/date-out in which the population was randomly assigned to training (70% herd), validation (10%), and testing (20% herd) based on the herd and date in which the samples were collected. The random grid search was performed using the training subset for the hyperparameter optimization and the validation set was used for the generalization of prediction error. The trained model was then used to assess the final prediction in the testing subset. The grid search for penalized regression evidenced that the elastic net (EN) was the best regularization with increase in predictive ability of 5%. The performance of PLS (standard model) was compared against 2 machine learning techniques and penalized regression using 2 cross-validation scenarios. Machine learning methods showed a greater predictive ability for BCS (0.63 for GBM and 0.61 for RF), BHB (0.80 for GBM and 0.79 for RF), and κ-CN (0.81 for GBM and 0.80 for RF) in samples-out cross-validation. Considering a herd/date-out cross-validation these values were 0.58 (GBM and RF) for BCS, 0.73 (GBM and RF) for BHB, and 0.77 (GBM and RF) for κ-CN. The GBM model tended to outperform other methods in predictive ability around 4%, 1%, and 7% for EN, RF, and PLS, respectively. The prediction accuracies of the GBM and RF models were similar, and differed statistically from the PLS model in samples-out random cross-validation. Although, machine learning techniques outperformed PLS in herd/date-out cross-validation, no significant differences were observed in terms of predictive ability due to the large standard deviation observed for predictions. Overall, GBM achieved the highest accuracy of FTIR-based prediction of the different phenotypic traits across the cross-validation scenarios. These results indicate that GBM is a promising method for obtaining more accurate FTIR-based predictions for different phenotypes in dairy cattle.

Performance of different portable and hand-held near-infrared spectrometers for predicting beef composition and quality characteristics in the abattoir without meat sampling

The availability of portable and handheld NIR instruments on the market opens up new possibilities in meat analysis. However, there is lack of research comparing different NIR instruments for evaluating beef characteristics from spectra obtained directly on the meat surface. Our aim, therefore, was to build and test calibration and prediction models for predicting beef characteristics, and to compare the performances of three NIR instruments differing in size and characteristics: a transportable visible-NIR spectrometer (Vis-NIRS), a portable (NIRS), and a hand-held Micro-NIRS. Spectra were collected from 178 beef samples (Longissimus thoracis muscle) from the meat surface in the abattoir. The spectra were subjected to different mathematical pretreatments then partial least square regressions. The results showed that all instruments predicted dry matter, protein and lipids with R²_VAL 0.23 to 0.70; pH and cooking loss R²_VAL 0.19 to 0.25; and color R²_VAL 0.35 to 0.77. Overall, the prediction performances of the three instruments were similar, although Micro-NIRS performed better in some respects.

Integrating genomic and infrared spectral data improves the prediction of milk protein composition in dairy cattle

Background

Over the past decade, Fourier transform infrared (FTIR) spectroscopy has been used to predict novel milk protein phenotypes. Genomic data might help predict these phenotypes when integrated with milk FTIR spectra. The objective of this study was to investigate prediction accuracy for milk protein phenotypes when heterogeneous on-farm, genomic, and pedigree data were integrated with the spectra. To this end, we used the records of 966 Italian Brown Swiss cows with milk FTIR spectra, on-farm information, medium-density genetic markers, and pedigree data. True and total whey protein, and five casein, and two whey protein traits were analyzed. Multiple kernel learning constructed from spectral and genomic (pedigree) relationship matrices and multilayer BayesB assigning separate priors for FTIR and markers were benchmarked against a baseline partial least squares (PLS) regression. Seven combinations of covariates were considered, and their predictive abilities were evaluated by repeated random sub-sampling and herd cross-validations (CV).

Results

Addition of the on-farm effects such as herd, days in milk, and parity to spectral data improved predictions as compared to those obtained using the spectra alone. Integrating genomics and/or the top three markers with a large effect further enhanced the predictions. Pedigree data also improved prediction, but to a lesser extent than genomic data. Multiple kernel learning and multilayer BayesB increased predictive performance, whereas PLS did not. Overall, multilayer BayesB provided better predictions than multiple kernel learning, and lower prediction performance was observed in herd CV compared to repeated random sub-sampling CV.

Conclusions

Integration of genomic information with milk FTIR spectral can enhance milk protein trait predictions by 25% and 7% on average for repeated random sub-sampling and herd CV, respectively. Multiple kernel learning and multilayer BayesB outperformed PLS when used to integrate heterogeneous data for phenotypic predictions.

Prediction of meat quality traits in the abattoir using portable near-infrared spectrometers: heritability of predicted traits and genetic correlations with laboratory-measured traits

Background

The possibility of assessing meat quality traits over the meat chain is strongly limited, especially in the context of selective breeding which requires a large number of phenotypes. The main objective of this study was to investigate the suitability of portable infrared spectrometers for phenotyping beef cattle aiming to genetically improving the quality of their meat. Meat quality traits (pH, color, water holding capacity, tenderness) were appraised on rib eye muscle samples of 1,327 Piemontese young bulls using traditional (i.e., reference/gold standard) laboratory analyses; the same traits were also predicted from spectra acquired at the abattoir on the intact muscle surface of the same animals 1 d after slaughtering. Genetic parameters were estimated for both laboratory measures of meat quality traits and their spectra-based predictions.

Results

The prediction performances of the calibration equations, assessed through external validation, were satisfactory for color traits (R² from 0.52 to 0.80), low for pH and purge losses (R² around 0.30), and very poor for cooking losses and tenderness (R² below 0.20). Except for lightness and purge losses, the heritability estimates of most of the predicted traits were lower than those of the measured traits while the genetic correlations between measured and predicted traits were high (average value 0.81).

Conclusions

Results showed that NIRS predictions of color traits, pH, and purge losses could be used as indicator traits for the indirect genetic selection of the reference quality phenotypes. Results for cooking losses were less effective, while the NIR predictions of tenderness were affected by a relatively high uncertainty of estimate. Overall, genetic selection of some meat quality traits, whose direct phenotyping is difficult, can benefit of the application of infrared spectrometers technology.

Structural equation modeling for unraveling the multivariate genomic architecture of milk proteins in dairy cattle

The aims of this study were to investigate potential functional relationships among milk protein fractions in dairy cattle and to carry out a structural equation model (SEM) GWAS to provide a decomposition of total SNP effects into direct effects and effects mediated by traits that are upstream in a phenotypic network. To achieve these aims, we first fitted a mixed Bayesian multitrait genomic model to infer the genomic correlations among 6 milk nitrogen fractions [4 caseins (CN), namely κ-, β-, α_S1-, and α_S2-CN, and 2 whey proteins, namely β-lactoglobulin (β-LG) and α-lactalbumin (α-LA)], in a population of 989 Italian Brown Swiss cows. Animals were genotyped with the Illumina BovineSNP50 Bead Chip v.2 (Illumina Inc.). A Bayesian network approach using the max-min hill-climbing (MMHC) algorithm was implemented to model the dependencies or independence among traits. Strong and negative genomic correlations were found between β-CN and α_S1-CN (-0.706) and between β-CN and κ-CN (-0.735). The application of the MMHC algorithm revealed that κ-CN and β-CN seemed to directly or indirectly influence all other milk protein fractions. By integrating multitrait model GWAS and SEM-GWAS, we identified a total of 127 significant SNP for κ-CN, 89 SNP for β-CN, 30 SNP for α_S1-CN, and 14 SNP for α_S2-CN (mostly shared among CN and located on Bos taurus autosome 6) and 15 SNP for β-LG (mostly located on Bos taurus autosome 11), whereas no SNP passed the significance threshold for α-LA. For the significant SNP, we assessed and quantified the contribution of direct and indirect paths to total marker effect. Pathway analyses confirmed that common regulatory mechanisms (e.g., energy metabolism and hormonal and neural signals) are involved in the control of milk protein synthesis and metabolism. The information acquired might be leveraged for setting up optimal management and selection strategies aimed at improving milk quality and technological characteristics in dairy cattle.

Near-infrared spectroscopy outperforms genomics for predicting sugarcane feedstock quality traits

The main objectives of this study were to evaluate the prediction performance of genomic and near-infrared spectroscopy (NIR) data and whether the integration of genomic and NIR predictor variables can increase the prediction accuracy of two feedstock quality traits (fiber and sucrose content) in a sugarcane population (Saccharum spp.). The following three modeling strategies were compared: M1 (genome-based prediction), M2 (NIR-based prediction), and M3 (integration of genomics and NIR wavenumbers). Data were collected from a commercial population comprised of three hundred and eighty-five individuals, genotyped for single nucleotide polymorphisms and screened using NIR spectroscopy. We compared partial least squares (PLS) and BayesB regression methods to estimate marker and wavenumber effects. In order to assess model performance, we employed random sub-sampling cross-validation to calculate the mean Pearson correlation coefficient between observed and predicted values. Our results showed that models fitted using BayesB were more predictive than PLS models. We found that NIR (M2) provided the highest prediction accuracy, whereas genomics (M1) presented the lowest predictive ability, regardless of the measured traits and regression methods used. The integration of predictors derived from NIR spectroscopy and genomics into a single model (M3) did not significantly improve the prediction accuracy for the two traits evaluated. These findings suggest that NIR-based prediction can be an effective strategy for predicting the genetic merit of sugarcane clones.

Breed of goat affects the prediction accuracy of milk coagulation properties using Fourier-transform infrared spectroscopy

The prediction of traditional goat milk coagulation properties (MCP) and curd firmness over time (CF_t) parameters via Fourier-transform infrared (FTIR) spectroscopy can be of significant economic interest to the dairy industry and can contribute to the breeding objectives for the genetic improvement of dairy goat breeds. Therefore, the aims of this study were to (1) explore the variability of milk FTIR spectra from 4 goat breeds (Camosciata delle Alpi, Murciano-Granadina, Maltese, and Sarda), and to assess the possible discriminant power of milk FTIR spectra among breeds, (2) assess the viability to predict coagulation traits by using milk FTIR spectra, and (3) quantify the effect of the breed on the prediction accuracy of MCP and CF_t parameters. In total, 611 individual goat milk samples were used. Analysis of variance of measured MCP and CF_t parameters was carried out using a mixed model including the farm and pendulum as random factors, and breed, parity, and days in milk as fixed factors. Milk spectra for each goat were collected over the spectral range from wavenumber 5,011 to 925 × cm^-1. Discriminant analysis of principal components was used to assess the ability of FTIR spectra to identify breed of origin. A Bayesian model was used to calibrate equations for each coagulation trait. The accuracy of the model and the prediction equation was assessed by cross-validation (CRV; 80% training and 20% testing set) and stratified CRV (SCV; 3 breeds in the training set, one breed in the testing set) procedures. Prediction accuracy was assessed by using coefficient of determination of validation (R²_VAL), the root mean square error of validation (RMSE_VAL), and the ratio performance deviation. Moreover, measured and FTIR predicted traits were compared in the SCV procedure by assessing their least squares means for the breed effect, Pearson correlations, and variance heteroscedasticity. Results showed the feasibility of using FTIR spectra and multivariate analyses to correctly assign milk samples to their breeds of origin. The R²_VAL values obtained with the CRV procedure were moderate to high for the majority of coagulation traits, with RMSE_VAL and ratio performance deviation values increasing as the coagulation process progresses from rennet addition. Prediction accuracy obtained with the SCV were strongly influenced by the breed, presenting general low values restricting a practical application. In addition, the low Pearson correlation coefficients of Sarda breed for all the traits analyzed, and the heteroscedastic variances of Camosciata delle Alpi, Murciano-Granadina, and Maltese breeds, further indicated that it is fundamental to consider the differences existing among breeds for the prediction of milk coagulation traits.

Fourier Transform Infrared Spectroscopy as a Tool to Study Milk Composition Changes in Dairy Cows Attributed to Housing Modifications to Improve Animal Welfare

Animal welfare status is assessed today through visual evaluations requiring an on-farm visit. A convenient alternative would be to detect cow welfare status directly in milk samples, already routinely collected for milk recording. The objective of this study was to propose a novel approach to demonstrate that Fourier transform infrared (FTIR) spectroscopy can detect changes in milk composition related to cows subjected to movement restriction at the tie stall with four tie-rail configurations varying in height and position (TR1, TR2, TR3 and TR4). Milk mid-infrared spectra were collected on weekly basis. Long-term average spectra were calculated for each cow using spectra collected in weeks 8–10 of treatment. Principal component analysis was applied to spectral averages and the scores of principal components (PCs) were tested for treatment effect by mixed modelling. PC7 revealed a significant treatment effect (p = 0.01), particularly for TR3 (configuration with restricted movement) vs. TR1 (recommended configuration) (p = 0.03). The loading spectrum of PC7 revealed high loadings at wavenumbers that could be assigned to biomarkers related to negative energy balance, such as β-hydroxybutyrate, citrate and acetone. This observation suggests that TR3 might have been restrictive for cows to access feed. Milk FTIR spectroscopy showed promising results in detecting welfare status and housing conditions in dairy cows.

Association between days open and milk spectral data in dairy cows

Data on 19,489 Brown Swiss cows reared in northeastern Italy were used to associate absorbances of individual wavenumbers within the mid-infrared range with days open (DO). Different postcalving days in milk (DIM) intervals were studied to determine the most informative milk sampling periods for predicting DO. Milk samples were analyzed using a MilkoScan (Foss Electric, Hillerød, Denmark) Fourier-transform infrared (FTIR) spectrometer for 1,060 wavenumbers (wn) ranging from 5,011 to 925 cm^-1. To determine DO, we considered an insemination to lead to conception when there was no return of heat (i.e., no successive insemination) and the cow had a subsequent calving date whereby gestation length was required to be within ±30 d of 290 d. Only milk records within the first 90 DIM were considered. Associations were inferred by (1) fitting linear regression models between the DO and each individual wavenumber or milk component, and (2) fitting a Bayesian regression model that included the complete FTIR spectral data. The effects of including systematic effects (parity number, year-season, herd) in the model on these associations were also studied. These analyses were performed for the complete data (5-90 DIM) and for data stratified by DIM period (5 to 30, 31 to 60, and 61 to 90 DIM). Overall, regions of wavenumbers of the milk FTIR spectra that were associated with DO included wn 2,973 to 2,830 cm^-1 [related to fat-B (C-H stretch)], wn 2,217 to 1,769 cm^-1 [related to fat-A (C = O stretch)], wn 1,546 cm^-1 (related to protein), wn 1,465 cm^-1 (related to urea and fat), wn 1,399 to 1,245 cm^-1 (related to acetone), and wn 1,110 cm^-1 (related to lactose). Estimated effects depended on the DIM period, with milk samples drawn during DIM intervals 31 to 60 d and 61 to 90 d being most strongly associated with DO. These DIM intervals are also typically most associated with negative energy balance and peak lactation.

Integration of Wet-Lab Measures, Milk Infrared Spectra, and Genomics to Improve Difficult-to-Measure Traits in Dairy Cattle Populations

The objective of this study was to evaluate the contribution of Fourier-transformed infrared spectroscopy (FTIR) data for dairy cattle breeding through two different approaches: (i) estimating the genetic parameters for 30 measured milk traits and their FTIR predictions and investigating the additive genetic correlation between them and (ii) evaluating the effectiveness of FTIR-derived phenotyping to replicate a candidate bull’s progeny testing or breeding value prediction at birth. Records were available from 1,123 cows phenotyped using gold standard laboratory methodologies (LAB data). This included phenotypes related to fine milk composition and milk technological characteristics, milk acidity, and milk protein fractions. The dataset used to generate FTIR predictions comprised 729,202 test-day records from 51,059 Brown Swiss cows (FIELD data). A first approach consisted of estimating genetic parameters for phenotypes available from LAB and FIELD datasets. To do so, a set of bivariate animal models were run, and genetic correlations between LAB and FIELD phenotypes were estimated using FIELD information obtained at the population level. Heritability estimates were generally higher for FIELD predictions than for the corresponding LAB measures. The additive genetic correlations (r_a) between LAB and FIELD phenotypes had different magnitudes across traits but were generally strong. Overall, these results demonstrated the potential of using FIELD information as indicator traits for the indirect genetic improvement of LAB measures. In the second approach, we included genotype information for 1,011 cows from the LAB dataset, 1,493 cows from the FIELD dataset, 181 sires with daughters in both LAB and FIELD datasets, and 540 sires with daughters in the FIELD dataset only. Predictions were obtained using the single-step GBLUP method. A four fold cross-validation was used to assess the predictive ability of the different models, assessed as the ability to predict masked LAB records from daughters of progeny testing bulls. The correlation between observed and predicted LAB measures in validation was averaged over the four training-validation sets. Different sets of phenotypic information were used sequentially in cross-validation schemes: (i) LAB cows from the training set; (ii) FIELD cows from the training set; and (iii) FIELD cows from the validation set. Models that included FIELD records showed an improvement for the majority of traits. This study suggests that breeding programs for difficult-to-measure traits could be implemented using FTIR information. While these programs should use progeny testing, acceptable values of accuracy can be achieved also for bulls without phenotyped progeny. Robust calibration equations are, deemed as essential.

Genetic Parameters of Different FTIR-Enabled Phenotyping Tools Derived from Milk Fatty Acid Profile for Reducing Enteric Methane Emissions in Dairy Cattle

This study aimed to infer the genetic parameters of five enteric methane emissions (EME) predicted from milk infrared spectra (13 models). The reference values were estimated from milk fatty acid profiles (chromatography), individual model-cheese, and daily milk yield of 1158 Brown Swiss cows (85 farms). Genetic parameters were estimated, under a Bayesian framework, for EME reference traits and their infrared predictions. Heritability of predicted EME traits were similar to EME reference values for methane yield (CH₄/DM: 0.232-0.317) and methane intensity per kg of corrected milk (CH₄/CM: 0.177-0.279), smaller per kg cheese solids (CH₄/SO: 0.093-0.165), but greater per kg fresh cheese (CH₄/CU: 0.203-0.267) and for methane production (dCH₄: 0.195-0.232). We found good additive genetic correlations between infrared-predicted methane intensities and the reference values (0.73 to 0.93), less favorable values for CH₄/DM (0.45-0.60), and very variable for dCH₄ according to the prediction method (0.22 to 0.98). Easy-to-measure milk infrared-predicted EME traits, particularly CH₄/CM, CH₄/CU and dCH₄, could be considered in breeding programs aimed at the improvement of milk ecological footprint.

Infrared Spectrometry as a High-Throughput Phenotyping Technology to Predict Complex Traits in Livestock Systems

High-throughput phenotyping technologies are growing in importance in livestock systems due to their ability to generate real-time, non-invasive, and accurate animal-level information. Collecting such individual-level information can generate novel traits and potentially improve animal selection and management decisions in livestock operations. One of the most relevant tools used in the dairy and beef industry to predict complex traits is infrared spectrometry, which is based on the analysis of the interaction between electromagnetic radiation and matter. The infrared electromagnetic radiation spans an enormous range of wavelengths and frequencies known as the electromagnetic spectrum. The spectrum is divided into different regions, with near- and mid-infrared regions being the main spectral regions used in livestock applications. The advantage of using infrared spectrometry includes speed, non-destructive measurement, and great potential for on-line analysis. This paper aims to review the use of mid- and near-infrared spectrometry techniques as tools to predict complex dairy and beef phenotypes, such as milk composition, feed efficiency, methane emission, fertility, energy balance, health status, and meat quality traits. Although several research studies have used these technologies to predict a wide range of phenotypes, most of them are based on Partial Least Squares (PLS) and did not considered other machine learning (ML) techniques to improve prediction quality. Therefore, we will discuss the role of analytical methods employed on spectral data to improve the predictive ability for complex traits in livestock operations. Furthermore, we will discuss different approaches to reduce data dimensionality and the impact of validation strategies on predictive quality.

Regularized selection indices for breeding value prediction using hyper-spectral image data

High-throughput phenotyping (HTP) technologies can produce data on thousands of phenotypes per unit being monitored. These data can be used to breed for economically and environmentally relevant traits (e.g., drought tolerance); however, incorporating high-dimensional phenotypes in genetic analyses and in breeding schemes poses important statistical and computational challenges. To address this problem, we developed regularized selection indices; the methodology integrates techniques commonly used in high-dimensional phenotypic regressions (including penalization and rank-reduction approaches) into the selection index (SI) framework. Using extensive data from CIMMYT's (International Maize and Wheat Improvement Center) wheat breeding program we show that regularized SIs derived from hyper-spectral data offer consistently higher accuracy for grain yield than those achieved by standard SIs, and by vegetation indices commonly used to predict agronomic traits. Regularized SIs offer an effective approach to leverage HTP data that is routinely generated in agriculture; the methodology can also be used to conduct genetic studies using high-dimensional phenotypes that are often collected in humans and model organisms including body images and whole-genome gene expression profiles.

Structural equation modeling for investigating multi-trait genetic architecture of udder health in dairy cattle

Mastitis is one of the most prevalent and costly diseases in dairy cattle. It results in changes in milk composition and quality which are indicators of udder inflammation in absence of clinical signs. We applied structural equation modeling (SEM) - GWAS aiming to explore interrelated dependency relationships among phenotypes related to udder health, including milk yield (MY), somatic cell score (SCS), lactose (%, LACT), pH and non-casein N (NCN, % of total milk N), in a cohort of 1,158 Brown Swiss cows. The phenotypic network inferred via the Hill-Climbing algorithm was used to estimate SEM parameters. Integration of multi-trait models-GWAS and SEM-GWAS identified six significant SNPs for SCS, and quantified the contribution of MY and LACT acting as mediator traits to total SNP effects. Functional analyses revealed that overrepresented pathways were often shared among traits and were consistent with biological knowledge (e.g., membrane transport activity for pH and MY or Wnt signaling for SCS and NCN). In summary, SEM-GWAS offered new insights on the relationships among udder health phenotypes and on the path of SNP effects, providing useful information for genetic improvement and management strategies in dairy cattle.

The evolving role of Fourier-transform mid-infrared spectroscopy in genetic improvement of dairy cattle

Over the last 100 years, significant advances have been made in the characterisation of milk composition for dairy cattle improvement programs. Technological progress has enabled a shift from labour intensive, on-farm collection and processing of samples that assess yield and fat levels in milk, to large-scale processing of samples through centralised laboratories, with the scope extended to include quantification of other traits. Fourier-transform mid-infrared (FT-MIR) spectroscopy has had a significant role in the transformation of milk composition phenotyping, with spectral-based predictions of major milk components already being widely used in milk payment and animal evaluation systems globally. Increasingly, there is interest in analysing the individual FT-MIR wavenumbers, and in utilising the FT-MIR data to predict other novel traits of importance to breeding programs. This includes traits related to the nutritional value of milk, the processability of milk into products such as cheese, and traits relevant to animal health and the environment. The ability to successfully incorporate these traits into breeding programs is dependent on the heritability of the FT-MIR predicted traits, and the genetic correlations between the FT-MIR predicted and actual trait values. Linking FT-MIR predicted traits to the underlying mutations responsible for their variation can be difficult because the phenotypic expression of these traits are a function of a diverse range of molecular and biological mechanisms that can obscure their genetic basis. The individual FT-MIR wavenumbers give insights into the chemical composition of milk and provide an additional layer of granularity that may assist with establishing causal links between the genome and observed phenotypes. Additionally, there are other molecular phenotypes such as those related to the metabolome, chromatin accessibility, and RNA editing that could improve our understanding of the underlying biological systems controlling traits of interest. Here we review topics of importance to phenotyping and genetic applications of FT-MIR spectra datasets, and discuss opportunities for consolidating FT-MIR datasets with other genomic and molecular data sources to improve future dairy cattle breeding programs.

Genomic Analysis of Milk Protein Fractions in Brown Swiss Cattle

Simple Summary

Milk protein fractions are hugely important in the dairy industry because of the key role they play in milk technological properties. The selection of cows for milk protein fractions may, therefore, improve both the nutritional and technological characteristics of milk, and, consequently, the processing efficiency and value of the dairy product. This study estimated the genetic parameters of the major milk protein fractions (four caseins, and two whey proteins) determined variously as: (i) milk content (g/100g milk), (ii) percentage of milk nitrogen (%N) and (iii) daily yield (g/d) in Brown Swiss dairy cattle. The results showed that the (co)variances and genetic parameter estimates differed according to how the proteins were measured. These results provide useful information for developing selection strategies in dairy cattle breeding programs aimed at improving both the nutritional and technological properties of milk.

Abstract

Depending on whether milk protein fractions are evaluated qualitatively or quantitatively, different genetic outcomes may emerge. In this study, we compared the genetic parameters for the major milk protein fractions—caseins (α_S1-, α_S2-, β-, and к-CN), and whey proteins (β-lactoglobulin, β-LG; α-lactalbumin, α-LA)—estimated using the multi-trait genomic best linear unbiased prediction method and expressed variously as milk content (g/100g milk), percentage of milk nitrogen (%N) and daily yield per cow (g/d). The results showed that the genetic parameter estimates varied according to how the milk protein fractions were expressed. Heritability estimates for the caseins and whey protein fractions expressed as daily yields were lower than when they were expressed as proportions and contents, revealing important differences in genetic outcomes. The proportion and the content of β-CN were negatively correlated with the proportions and contents of α_S1-CN, α_S2-CN, and к-CN, while the daily yield of β–CN was negatively correlated with the daily yields of α_S1-CN and α_S2-CN. The Spearman’s rank correlations and the coincidence rates between the various predicted genomic breeding values (GEBV) for the milk protein fractions expressed in different ways indicated that these differences had a significant effect on the ranking of the animals. The results suggest that the way milk protein fractions are expressed has implications for breeding programs aimed at improving milk nutritional and technological characteristics.

Prediction of meat quality traits in the abattoir using portable and hand-held near-infrared spectrometers

The use of near-infrared spectrometers (NIRS) for predicting meat quality traits directly in the abattoir was tested with three trials. For the calibration trial, spectra were acquired from the cross-cut surface of the Longissimus thoracis muscle on 1166 carcasses of Piemontese young bulls with a portable visible-near-infrared spectrometer (Vis-NIRS) and with a small hand-held instrument (Micro-NIRS). A sample of the same muscle was analyzed to provide the reference. Validation statistics of the two instruments were similar. Predictabilities of meat color and purge loss were good, whereas for the other traits they were less promising. The repeatability trial showed that post-slaughter factors, not predictable by NIR spectra collected in the abattoir, affect reference meat quality values. A trial under operative conditions showed that both spectrometers were able to capture the major sources of variation in most of the meat quality traits. Overall, NIRS could be used to predict the animals' "native" characteristics exploitable for genetic improvement of meat quality traits.

Prediction of Milk Coagulation Properties and Individual Cheese Yield in Sheep Using Partial Least Squares Regression

Simple Summary

Considered that all sheep milk in Italy is destined for cheese processing, traits describing rennet coagulation aptitude should be among the most important selection goals for dairy breeds. To reduce the costs and logistics related to the large-scale recording of these traits, mid-infrared (MIR) spectroscopy could be conveniently used to generate reliable predictions without any additional cost. The aims of this research were to predict the milk coagulation properties (MCP) and individual cheese yield (ILCY) in sheep by MIR spectrometry using partial least squares regression (PLS), and to compare different data pre-treatment procedures. The prediction results observed in the present study, although moderate, suggest the possibility of adding novel phenotypes (e.g., MCP and ILCY) in breeding schemes for dairy sheep breeds. Mid-infrared spectroscopy coupled with PLS regression could allow the prediction of phenotypes at the population level without additional costs.

Abstract

The objectives of this study were (i) the prediction of sheep milk coagulation properties (MCP) and individual laboratory cheese yield (ILCY) from mid-infrared (MIR) spectra by using partial least squares (PLS) regression, and (ii) the comparison of different data pre-treatments on prediction accuracy. Individual milk samples of 970 Sarda breed ewes were analyzed for rennet coagulation time (RCT), curd-firming time (k20), and curd firmness (a30) using the Formagraph instrument; ILCY was measured by micro-manufacturing assays. An Furier-transform Infrared (FTIR) milk-analyzer was used for the estimation of the milk gross composition and the recording of MIR spectrum. The dataset (n = 859, after the exclusion of 111 noncoagulating samples) was divided into two sub-datasets: the data of 700 ewes were used to estimate prediction model parameters, and the data of 159 ewes were used to validate the model. Four prediction scenarios were compared in the validation, differing for the use of whole or reduced MIR spectrum and the use of raw or corrected data (locally weighted scatterplot smoothing). PLS prediction statistics were moderate. The use of the reduced MIR spectrum yielded the best results for the considered traits, whereas the data correction improved the prediction ability only when the whole MIR spectrum was used. In conclusion, PLS achieves good accuracy of prediction, in particular for ILCY and RCT, and it may enable increasing the number of traits to be included in breeding programs for dairy sheep without additional costs and logistics.

Chemometric authentication of farming systems of origin of food (milk and ripened cheese) using infrared spectra, fatty acid profiles, flavor fingerprints, and sensory descriptions

Milk samples from 1264 cows in 85 farms were authenticated for different farming-systems using a 10-fold cross-validated linear-discriminant-analysis using Fourier-transform infrared spectra (FTIRS) and gas-chromatographic fatty-acid (FA) profiles. FTIRS gave correct classification greater than FAs (97.4% vs. 81.1%) during calibration, but slightly worse in validation (73.5% vs 77.3%) and their combination improved the results. All milk samples were processed into ripened model-cheeses, and analyzed by near-infrared-spectrometry (NIRS), by proton-transfer-reaction time-of-flight mass-spectrometry for their volatile organic compound (VOCs) fingerprint and by panel sensory profiling (SENS). Farming-system authentication on cheese samples was less efficient than on milk, but still possible. The instrumental methods yielded similar validation results, better than SENS, and their combination improved the correct classification rate. The efficiency of the different technics was affected by specific farming systems. In conclusion, dairy products could be discriminated for farming-systems with acceptable accuracy, but the methods tested differ in sampling procedure, rapidity and costs.

Accuracy and biases in predicting the chemical and physical traits of many types of cheeses using different visible and near-infrared spectroscopic techniques and spectrum intervals

Near-infrared spectroscopy (NIRS) has been widely used to determine various composition traits of many dairy products in the industry. In the last few years, near-infrared (NIR) instruments have become more and more accessible, and now, portable devices can be easily used in the field, allowing the direct measurement of important quality traits. However, the comparison of the predictive performances of different NIR instruments is not simple, and the literature is lacking. These instruments may use different wavelength intervals and calibration procedures, making it difficult to establish whether differences are due to the spectral interval, the chemometric approach, or the instrument's technology. Hence, the aims of this study were (1) to evaluate the prediction accuracy of chemical contents (5 traits), pH, texture (2 traits), and color (5 traits) of 37 categories of cheese; (2) to compare 3 instruments [2 benchtop, working in reflectance (R) and transmittance (T) mode (NIRS-R and NIRS-T, respectively) and 1 portable device (VisNIRS-R)], using their entire spectral ranges (1100-2498, 850-1048, and 350-1830 nm, respectively, for NIRS-R, NIRS-T and VisNIRS-R); (3) to examine different wavelength intervals of the spectrum within instrument, comparing also the common intervals among the 3 instruments; and (4) to determine the presence of bias in predicted traits for specific cheese categories. A Bayesian approach was used to develop 8 calibration models for each of 13 traits. This study confirmed that NIR spectroscopy can be used to predict the chemical composition of a large number of different cheeses, whereas pH and texture traits were poorly predicted. Color showed variable predictability, according to the trait considered, the instrument used, and, within instrument, according to the wavelength intervals. The predictive performance of the VisNIRS-R portable device was generally better than the 2 laboratory NIRS instruments, whether with the entire spectrum or selected intervals. The VisNIRS-R was found suitable for analyzing chemical composition in real time, without the need for sample uptake and processing. Our results also indicated that instrument technology is much more important than the NIR spectral range for accurate prediction equations, but the visible range is useful when predicting color traits, other than lightness. Specifically for certain categories (i.e., caprine, moldy, and fresh cheeses), dedicated calibrations seem to be needed to obtain unbiased and more accurate results.

Comparison of Bayesian and partial least squares regression methods for mid-infrared prediction of cheese-making properties in Montbéliarde cows

Assessing the cheese-making properties (CMP) of milks with a rapid and cost-effective method is of particular interest for the Protected Designation of Origin cheese sector. The aims of this study were to evaluate the potential of mid-infrared (MIR) spectra to estimate coagulation and acidification properties, as well as curd yield (CY) traits of Montbéliarde cow milk. Samples from 250 cows were collected in 216 commercial herds in Franche-Comté with the objectives to maximize the genetic diversity as well as the variation in milk composition. All coagulation and CY traits showed high variability (10 to 43%). Reference analyses performed for soft (SC) and pressed cooked (PCC) cheese technology were matched with MIR spectra. Prediction models were built on 446 informative wavelengths not tainted by the water absorbance, using different approaches such as partial least squares (PLS), uninformative variable elimination PLS, random forest PLS, Bayes A, Bayes B, Bayes C, and Bayes RR. We assessed equation performances for a set of 20 CMP traits (coagulation: 5 for SC and 4 for PCC; acidification: 5 for SC and 3 for PCC; laboratory CY: 3) by comparing prediction accuracies based on cross-validation. Overall, variable selection before PLS did not significantly improve the performances of the PLS regression, the prediction differences between Bayesian methods were negligible, and PLS models always outperformed Bayesian models. This was likely a result of the prior use of informative wavelengths of the MIR spectra. The best accuracies were obtained for curd yields expressed in dry matter (CY_DM) or fresh (CY_FRESH) and for coagulation traits (curd firmness for PCC and SC) using the PLS regression. Prediction models of other CMP traits were moderately to poorly accurate. Whatever the prediction methodology, the best results were always obtained for CY traits, probably because these traits are closely related to milk composition. The CY_DM predictions showed coefficient of determination (R²) values up to 0.92 and 0.87, and RS_y,x values of 3 and 4% for PLS and Bayes regressions, respectively. Finally, we divided the data set into calibration (2/3) and validation (1/3) sets and developed prediction models in external validation using PLS regression only. In conclusion, we confirmed, in the validation set, an excellent prediction for CY_DM [R² = 0.91, ratio of performance to deviation (RPD) = 3.39] and a very good prediction for CY_FRESH (R² = 0.84, RPD = 2.49), adequate for analytical purposes. We also obtained good results for both PCC and SC curd firmness traits (R² ≥ 0.70, RPD ≥1.8), which enable quantitative prediction.

Predicting soil microplastic concentration using vis-NIR spectroscopy

Microplastic accumulation in soil may have a detrimental impact on soil biota. The lack of standardized methods to identify and quantify microplastics in soils is an obstacle to research. Existing techniques are time-consuming and field data are seldom collected. To tackle the problem, we explored the possibilities of using a portable spectroradiometer working in the near infrared range (350-2500 nm) to rapidly assess microplastic concentrations in soils without extraction. Four sets of artificially polluted soil samples were prepared. Three sets had only one polymer polluting the soil (low-density polyethylene (LDPE), polyethylene terephthalate (PET), or polyvinyl chloride (PVC)). The fourth set contained random amounts of the three polymers (Mix). The concentrations of microplastics were regressed on the reflectance observed for each of the 2150 wavelengths registered by the instrument, using a Bayesian approach. For a measurement range between 1 and 100 g kg^-1, results showed a root-mean-squared-deviation (RMSD) of 8, 18, and 10 g kg^-1 for LDPE, PET, and PVC. The Mix treatment presented an RMSD of 8, 10, and 5 g kg^-1 for LDPE, PET, and PVC. The repeatability of the proposed method was 0.2-8.4, 0.1-5.1, and 0.1-9.0 g kg^-1 for LDPE, PET, and PVC, respectively. Overall, our results suggest that vis-NIR techniques are suitable to identify and quantify LDPE, PET, and PVC microplastics in soil samples, with a 10 g kg^-1 accuracy and a detection limit ≈ 15 g kg^-1. The method proposed is different than other approaches since it is faster because it avoids extraction steps and can directly quantify the amount of plastic in a sample. Nevertheless, it seems to be useful only for pollution hotspots.

Application of visible and near-infrared spectroscopy for evaluation of ewes milk with different feeds

Rapid measurement optical techniques have the advantage over traditional methods of being faster and non-destructive. In this work visible and near-infrared spectroscopy (vis-NIRS) was used to investigate differences between measured values of key milk properties (e.g. fat, protein and lactose) in 30 samples of ewes milk according to three feed systems; faba beans, field peas and control diet. A mobile fibre-optic vis-NIR spectrophotometer (350–2500 nm) was used to collect reflectance spectra from milk samples. Principal component analysis was used to explore differences between milk samples according to the feed supplied, and a partial least-squares regression and random forest regression were adopted to develop calibration models for the prediction of milk properties. Results of the principal component analysis showed clear separation between the three groups of milk samples according to the diet of the ewes throughout the lactation period. Milk fat, protein and lactose were predicted with good accuracy by means of partial least-squares regression (R2 = 0.70–0.83 and ratio of prediction deviation, which is the ratio of standard deviation to root mean square error of prediction = 1.85–2.44). However, the best prediction results were obtained with random forest regression models (R2 = 0.86–0.90; ratio of prediction deviation = 2.73–3.26). The adoption of the vis-NIRS coupled with multivariate modelling tools can be recommended for exploring to differences between milk samples according to different feed systems, and to predict key milk properties, based particularly on the random forest regression modelling technique.

A landscape of the heritability of Fourier-transform infrared spectral wavelengths of milk samples by parity and lactation stage in Holstein cows

Fourier-transform near- and mid-infrared (FTIR) milk spectral data are routinely collected in many countries worldwide. Establishing an optimal strategy to use spectral data in genetic evaluations requires knowledge of the heritabilities of individual FTIR wavelength absorbances. Previous FTIR heritability estimates have been based on relatively small sample sizes and have not considered the possibility that heritability may vary across parities and stages of the lactation. We used data from ∼370,000 test-day records of Canadian Holstein cows to produce a landscape of the heritability of FTIR spectra, 1,060 wavelengths in the near- and mid-infrared spectrum (5,011-925 cm^-1), by parity and month of the lactation (mo 1 to 3 and mo 1 to 6, respectively). The 2 regions of the spectrum associated with absorption of electromagnetic energy by water molecules were estimated to have very high phenotypic variances, very low heritabilities, and very low proportion of variance explained by herd-year-season (HYS) subclasses. The near- or short-wavelength infrared (SWIR: 5,066-3,672 cm^-1) region was also characterized by low heritability estimates, whereas the estimated proportion of the variance explained by HYS was high. The mid-wavelength infrared region (MWIR: 3,000-2,500 cm^-1) and the transition between mid and long-wavelength infrared region (MWIR-LWIR: 1,500-925 cm^-1) harbor several waves characterized by moderately high (≥0.4) heritabilities. Most of the high-heritability regions contained wavelengths that are reported to be associated with important milk metabolites and components. Interestingly, these 2 same regions tended to show more variability in heritabilities between parity and lactation stage. Second parity showed heritability patterns that were distinctly different from those of the first and third parities, whereas the first 2 mo of the lactation had clearly distinct heritability patterns compared with mo 3 to 6.

Bayesian functional regression as an alternative statistical analysis of high-throughput phenotyping data of modern agriculture

BACKGROUND

Modern agriculture uses hyperspectral cameras with hundreds of reflectance data at discrete narrow bands measured in several environments. Recently, Montesinos-López et al. (Plant Methods 13(4):1-23, 2017a. 10.1186/s13007-016-0154-2; Plant Methods 13(62):1-29, 2017b. 10.1186/s13007-017-0212-4) proposed using functional regression analysis (as functional data analyses) to help reduce the dimensionality of the bands and thus decrease the computational cost. The purpose of this paper is to discuss the advantages and disadvantages that functional regression analysis offers when analyzing hyperspectral image data. We provide a brief review of functional regression analysis and examples that illustrate the methodology. We highlight critical elements of model specification: (i) type and number of basis functions, (ii) the degree of the polynomial, and (iii) the methods used to estimate regression coefficients. We also show how functional data analyses can be integrated into Bayesian models. Finally, we include an in-depth discussion of the challenges and opportunities presented by functional regression analysis.

RESULTS

We used seven model-methods, one with the conventional model (M1), three methods using the B-splines model (M2, M4, and M6) and three methods using the Fourier basis model (M3, M5, and M7). The data set we used comprises 976 wheat lines under irrigated environments with 250 wavelengths. Under a Bayesian Ridge Regression (BRR), we compared the prediction accuracy of the model-methods proposed under different numbers of basis functions, and compared the implementation time (in seconds) of the seven proposed model-methods for different numbers of basis. Our results as well as previously analyzed data (Montesinos-López et al. 2017a, 2017b) support that around 23 basis functions are enough. Concerning the degree of the polynomial in the context of B-splines, degree 3 approximates most of the curves very well. Two satisfactory types of basis are the Fourier basis for period curves and the B-splines model for non-periodic curves. Under nine different basis, the seven method-models showed similar prediction accuracy. Regarding implementation time, results show that the lower the number of basis, the lower the implementation time required. Methods M2, M3, M6 and M7 were around 3.4 times faster than methods M1, M4 and M5.

CONCLUSIONS

In this study, we promote the use of functional regression modeling for analyzing high-throughput phenotypic data and indicate the advantages and disadvantages of its implementation. In addition, many key elements that are needed to understand and implement this statistical technique appropriately are provided using a real data set. We provide details for implementing Bayesian functional regression using the developed genomic functional regression (GFR) package. In summary, we believe this paper is a good guide for breeders and scientists interested in using functional regression models for implementing prediction models when their data are curves.