Leveraging Breeding Values Obtained from Random Regression Models for Genetic Inference of Longitudinal Traits

Leveraging genomics and temporal high-throughput phenotyping to enhance association mapping and yield prediction in sesame

Sesame (Sesamum indicum) is an important oilseed crop with rising demand owing to its nutritional and health benefits. There is an urgent need to develop and integrate new genomic-based breeding strategies to meet these future demands. While genomic resources have advanced genetic research in sesame, the implementation of high-throughput phenotyping and genetic analysis of longitudinal traits remains limited. Here, we combined high-throughput phenotyping and random regression models to investigate the dynamics of plant height, leaf area index, and five spectral vegetation indices throughout the sesame growing seasons in a diversity panel. Modeling the temporal phenotypic and additive genetic trajectories revealed distinct patterns corresponding to the sesame growth cycle. We also conducted longitudinal genomic prediction and association mapping of plant height using various models and cross-validation schemes. Moderate prediction accuracy was obtained when predicting new genotypes at each time point, and moderate to high values were obtained when forecasting future phenotypes. Association mapping revealed three genomic regions in linkage groups 6, 8, and 11, conferring trait variation over time and growth rate. Furthermore, we leveraged correlations between the temporal trait and seed-yield and applied multi-trait genomic prediction. We obtained an improvement over single-trait analysis, especially when phenotypes from earlier time points were used, highlighting the potential of using a high-throughput phenotyping platform as a selection tool. Our results shed light on the genetic control of longitudinal traits in sesame and underscore the potential of high-throughput phenotyping to detect a wide range of traits and genotypes that can inform sesame breeding efforts to enhance yield.

Maize green leaf area index dynamics: genetic basis of a new secondary trait for grain yield in optimal and drought conditions

KEY MESSAGE

Green Leaf Area Index dynamics is a promising secondary trait for grain yield and drought tolerance. Multivariate GWAS is particularly well suited to identify the genetic determinants of the green leaf area index dynamics. Improvement of maize grain yield is impeded by important genotype-environment interactions, especially under drought conditions. The use of secondary traits, that are correlated with yield, more heritable and less prone to genotype-environment interactions, can increase breeding efficiency. Here, we studied the genetic basis of a new secondary trait: the green leaf area index (GLAI) dynamics over the maize life cycle. For this, we used an unmanned aerial vehicle to characterize the GLAI dynamics of a diverse panel in well-watered and water-deficient trials in two years. From the dynamics, we derived 24 traits (slopes, durations, areas under the curve), and showed that six of them were heritable traits representative of the panel diversity. To identify the genetic determinants of GLAI, we compared two genome-wide association approaches: a univariate (single-trait) method and a multivariate (multi-trait) method combining GLAI traits, grain yield, and precocity. The explicit modeling of correlation structure between secondary traits and grain yield in the multivariate mixed model led to 2.5 times more associations detected. A total of 475 quantitative trait loci (QTLs) were detected. The genetic architecture of GLAI traits appears less complex than that of yield with stronger-effect QTLs that are more stable between environments. We also showed that a subset of GLAI QTLs explains nearly one fifth of yield variability across a larger environmental network of 11 water-deficient trials. GLAI dynamics is a promising grain yield secondary trait in optimal and drought conditions, and the detected QTLs could help to increase breeding efficiency through a marker-assisted approach.

Longitudinal genome-wide association analysis using a single-step random regression model for height in Japanese Holstein cattle

Growth traits, such as body weight and height, are essential in the design of genetic improvement programs of dairy cattle due to their relationship with feeding efficiency, longevity, and health. We investigated genomic regions influencing height across growth stages in Japanese Holstein cattle using a single-step random regression model. We used 72,921 records from birth to 60 mo of age with 4,111 animals born between 2000 and 2016. The analysis included 1,410 genotyped animals with 35,319 single nucleotide polymorphisms, consisting of 883 females with records and 527 bulls, and 30,745 animals with pedigree information. A single genomic region at the 58.4 megabase pair on chromosome 18 was consistently identified across 6 age points of 10, 20, 30, 40, 50, and 60 mo after multiple testing corrections for the significance threshold. Twelve candidate genes, previously reported for longevity and gestation length, were found near the identified genomic region. Another location near the identified region was also previously associated with body conformation, fertility, and calving difficulty. Functional Gene Ontology enrichment analysis suggested that the candidate genes regulate dephosphorylation and phosphatase activity. Our findings show that further study of the identified candidate genes will contribute to a better understanding of the genetic basis of height in Japanese Holstein cattle.

Genome-wide association study of multiyear dynamic growth traits in hybrid Liriodendron identifies robust genetic loci associated with growth trajectories

The genetic factors underlying growth traits differ over time points or stages. However, most current studies of phenotypes at single time points do not capture all loci or explain the genetic differences underlying growth trajectories. Hybrid Liriodendron exhibits obvious heterosis and is widely cultivated, although its complex genetic mechanism underlying growth traits remains unknown. A genome-wide association study (GWAS) is an effective method for elucidating the genetic architecture by identifying genetic loci underlying complex quantitative traits. In the present study, using a GWAS, we identified robust loci associated with growth trajectories in hybrid Liriodendron populations. We selected 233 hybrid progenies derived from 25 crosses for resequencing, and measured their tree height (H) and diameter at breast height (DBH) for 11 consecutive years; 192 972 high-quality single nucleotide polymorphisms (SNPs) were obtained. The dynamics of the multiyear single-trait GWAS showed that year-specific SNPs predominated, and only five robust SNPs for DBH were identified in at least three different years. Multitrait GWAS analysis with model parameters as latent variables also revealed 62 SNPs for H and 52 for DBH associated with the growth trajectory, displaying different biomass accumulation patterns, among which four SNPs exerted pleiotropic effects. All identified SNPs also exhibited temporal variations in effect sizes and inheritance patterns potentially related to different growth and developmental stages. The haplotypes resulting from these significant SNPs might pyramid favorable loci, benefitting the selection of superior genotypes. The present study provides insights into the genetic architecture of dynamic growth traits and lays a basis for future molecular-assisted breeding.

Random regression for modeling soybean plant response to irrigation changes using time-series multispectral data

Plant response to drought is an important yield-related trait under abiotic stress, but the method for measuring and modeling plant responses in a time series has not been fully established. The objective of this study was to develop a method to measure and model plant response to irrigation changes using time-series multispectral (MS) data. We evaluated 178 soybean (Glycine max (L.) Merr.) accessions under three irrigation treatments at the Arid Land Research Center, Tottori University, Japan in 2019, 2020 and 2021. The irrigation treatments included W5: watering for 5 d followed by no watering 5 d, W10: watering for 10 d followed by no watering 10 d, D10: no watering for 10 d followed by watering 10 d, and D: no watering. To capture the plant responses to irrigation changes, time-series MS data were collected by unmanned aerial vehicle during the irrigation/non-irrigation switch of each irrigation treatment. We built a random regression model (RRM) for each of combination of treatment by year using the time-series MS data. To test the accuracy of the information captured by RRM, we evaluated the coefficient of variation (CV) of fresh shoot weight of all accessions under a total of nine different drought conditions as an indicator of plant's stability under drought stresses. We built a genomic prediction model (MT RRM   model ) using the genetic random regression coefficients of RRM as secondary traits and evaluated the accuracy of each model for predicting CV. In 2020 and 2021,the mean prediction accuracies of MT RRM   models built in the changing irrigation treatments (r = 0.44 and 0.49, respectively) were higher than that in the continuous drought treatment (r = 0.34 and 0.44, respectively) in the same year. When the CV was predicted using the MT RRM   model across 2020 and 2021 in the changing irrigation treatment, the mean prediction accuracy (r = 0.46) was 42% higher than that of the simple genomic prediction model (r =0.32). The results suggest that this RRM method using the time-series MS data can effectively capture the genetic variation of plant response to drought.

Prediction of heading date, culm length, and biomass from canopy-height-related parameters derived from time-series UAV observations of rice

Unmanned aerial vehicles (UAVs) are powerful tools for monitoring crops for high-throughput phenotyping. Time-series aerial photography of fields can record the whole process of crop growth. Canopy height (CH), which is vertical plant growth, has been used as an indicator for the evaluation of lodging tolerance and the prediction of biomass and yield. However, there have been few attempts to use UAV-derived time-series CH data for field testing of crop lines. Here we provide a novel framework for trait prediction using CH data in rice. We generated UAV-based digital surface models of crops to extract CH data of 30 Japanese rice cultivars in 2019, 2020, and 2021. CH-related parameters were calculated in a non-linear time-series model as an S-shaped plant growth curve. The maximum saturation CH value was the most important predictor for culm length. The time point at the maximum CH contributed to the prediction of days to heading, and was able to predict stem and leaf weight and aboveground weight, possibly reflecting the association of biomass with duration of vegetative growth. These results indicate that the CH-related parameters acquired by UAV can be useful as predictors of traits typically measured by hand.

Leveraging spatiotemporal genomic breeding value estimates of dry matter yield and herbage quality in ryegrass via random regression models

Joint modeling of correlated multienvironment and multiharvest data of perennial crop species may offer advantages in prediction schemes and a better understanding of the underlying dynamics in space and time. The goal of the present study was to investigate the relevance of incorporating the longitudinal dimension of within-season multiple measurements of forage perennial ryegrass (Lolium perenne L.) traits in a reaction-norm model setup that additionally accounts for genotype × environment (G × E) interactions. Genetic parameters and accuracy of genomic estimated breeding value (gEBV) predictions were investigated by fitting three genomic random regression models (gRRMs) using Legendre polynomial functions to the data. Genomic DNA sequencing of family pools of diploid perennial ryegrass was performed using DNA nanoball-based technology and yielded 56,645 single-nucleotide polymorphisms, which were used to calculate the allele frequency-based genomic relationship matrix. Biomass yield's estimated additive genetic variance and heritability values were higher in later harvests. The additive genetic correlations were moderate to low in early measurements and peaked at intermediates with fairly stable values across the environmental gradient except for the initial harvest data collection. This led to the conclusion that complex (G × E) arises from spatial and temporal dimensions in the early season with lower reranking trends thereafter. In general, modeling the temporal dimension with a second-order orthogonal polynomial improved the accuracy of gEBV prediction for nutritive quality traits, but no gain in prediction accuracy was detected for dry matter yield (DMY). This study leverages the flexibility and usefulness of gRRM models for perennial ryegrass breeding and can be readily extended to other multiharvest crops.

Proximal and remote sensing in plant phenomics: 20 years of progress, challenges, and perspectives

Plant phenomics (PP) has been recognized as a bottleneck in studying the interactions of genomics and environment on plants, limiting the progress of smart breeding and precise cultivation. High-throughput plant phenotyping is challenging owing to the spatio-temporal dynamics of traits. Proximal and remote sensing (PRS) techniques are increasingly used for plant phenotyping because of their advantages in multi-dimensional data acquisition and analysis. Substantial progress of PRS applications in PP has been observed over the last two decades and is analyzed here from an interdisciplinary perspective based on 2972 publications. This progress covers most aspects of PRS application in PP, including patterns of global spatial distribution and temporal dynamics, specific PRS technologies, phenotypic research fields, working environments, species, and traits. Subsequently, we demonstrate how to link PRS to multi-omics studies, including how to achieve multi-dimensional PRS data acquisition and processing, how to systematically integrate all kinds of phenotypic information and derive phenotypic knowledge with biological significance, and how to link PP to multi-omics association analysis. Finally, we identify three future perspectives for PRS-based PP: (1) strengthening the spatial and temporal consistency of PRS data, (2) exploring novel phenotypic traits, and (3) facilitating multi-omics communication.

AirMeasurer: open-source software to quantify static and dynamic traits derived from multiseason aerial phenotyping to empower genetic mapping studies in rice

Low-altitude aerial imaging, an approach that can collect large-scale plant imagery, has grown in popularity recently. Amongst many phenotyping approaches, unmanned aerial vehicles (UAVs) possess unique advantages as a consequence of their mobility, flexibility and affordability. Nevertheless, how to extract biologically relevant information effectively has remained challenging. Here, we present AirMeasurer, an open-source and expandable platform that combines automated image analysis, machine learning and original algorithms to perform trait analysis using 2D/3D aerial imagery acquired by low-cost UAVs in rice (Oryza sativa) trials. We applied the platform to study hundreds of rice landraces and recombinant inbred lines at two sites, from 2019 to 2021. A range of static and dynamic traits were quantified, including crop height, canopy coverage, vegetative indices and their growth rates. After verifying the reliability of AirMeasurer-derived traits, we identified genetic variants associated with selected growth-related traits using genome-wide association study and quantitative trait loci mapping. We found that the AirMeasurer-derived traits had led to reliable loci, some matched with published work, and others helped us to explore new candidate genes. Hence, we believe that our work demonstrates valuable advances in aerial phenotyping and automated 2D/3D trait analysis, providing high-quality phenotypic information to empower genetic mapping for crop improvement.

A Bayesian random regression method using mixture priors for genome-enabled analysis of time-series high-throughput phenotyping data

The recent advancement in image-based phenotyping platforms enables the acquisition of large-scale nondestructive crop phenotypes measured at frequent intervals. To further understand the underlying genetic basis over a physiological process and improve plant breeding programs, the question of how to efficiently utilize these time-series measurements in genome-enabled analysis including genomic prediction and genome-wide association studies (GWASs) should be considered. In this paper, a Bayesian random regression model with mixture priors is developed to introduce more meaningful biological assumptions to the analysis of longitudinal traits. The mixture prior for marker effects in Bayes Cπ is implemented in our developed model (RR-BayesC) for demonstration purpose. The estimation of single-nucleotide polymorphism-specific effects that are related to the dynamic performance of crops and the accuracy of genomic prediction by RR-BayesC were studied through both simulated and real rice (Oryza sativa L.) data. For genomic prediction, three predictive scenarios were studied. In the simulated study, RR-BayesC showed a significantly higher prediction accuracy than that obtained by single-trait analysis, especially for days when heritability were low. In real data analysis, RR-BayesC showed relatively high prediction accuracy when forecast is required for phenotypes at later period (e.g., from 0.94 to 0.98 for lines with observations at an earlier period and from 0.65 to 0.67 for lines without any observations). For GWASs, inference of single markers and inference of genomic windows were conducted. In the simulated study, RR-BayesC showed its promising ability to distinguish quantitative trait loci (QTL) that are invariant to temporal covariates and QTL that interact with time. An association study of real data was also presented to demonstrate the application of RR-BayesC in real data analysis. In this paper, we develop a Bayesian random regression model that is able to incorporate mixture priors to marker effects and show improved performance of genomic prediction and GWASs for longitudinal data analysis based on both simulated and real data. The software tool JWAS offers routines to perform our proposed random regression analysis.

Prospectus of Genomic Selection and Phenomics in Cereal, Legume and Oilseed Breeding Programs

The last decade witnessed an unprecedented increase in the adoption of genomic selection (GS) and phenomics tools in plant breeding programs, especially in major cereal crops. GS has demonstrated the potential for selecting superior genotypes with high precision and accelerating the breeding cycle. Phenomics is a rapidly advancing domain to alleviate phenotyping bottlenecks and explores new large-scale phenotyping and data acquisition methods. In this review, we discuss the lesson learned from GS and phenomics in six self-pollinated crops, primarily focusing on rice, wheat, soybean, common bean, chickpea, and groundnut, and their implementation schemes are discussed after assessing their impact in the breeding programs. Here, the status of the adoption of genomics and phenomics is provided for those crops, with a complete GS overview. GS’s progress until 2020 is discussed in detail, and relevant information and links to the source codes are provided for implementing this technology into plant breeding programs, with most of the examples from wheat breeding programs. Detailed information about various phenotyping tools is provided to strengthen the field of phenomics for a plant breeder in the coming years. Finally, we highlight the benefits of merging genomic selection, phenomics, and machine and deep learning that have resulted in extraordinary results during recent years in wheat, rice, and soybean. Hence, there is a potential for adopting these technologies into crops like the common bean, chickpea, and groundnut. The adoption of phenomics and GS into different breeding programs will accelerate genetic gain that would create an impact on food security, realizing the need to feed an ever-growing population.

Advanced high-throughput plant phenotyping techniques for genome-wide association studies: A review

Linking phenotypes and genotypes to identify genetic architectures that regulate important traits is crucial for plant breeding and the development of plant genomics. In recent years, genome-wide association studies (GWASs) have been applied extensively to interpret relationships between genes and traits. Successful GWAS application requires comprehensive genomic and phenotypic data from large populations. Although multiple high-throughput DNA sequencing approaches are available for the generation of genomics data, the capacity to generate high-quality phenotypic data is lagging far behind. Traditional methods for plant phenotyping mostly rely on manual measurements, which are laborious, inaccurate, and time-consuming, greatly impairing the acquisition of phenotypic data from large populations. In contrast, high-throughput phenotyping has unique advantages, facilitating rapid, non-destructive, and high-throughput detection, and, in turn, addressing the shortcomings of traditional methods. Aim of Review: This review summarizes the current status with regard to the integration of high-throughput phenotyping and GWAS in plants, in addition to discussing the inherent challenges and future prospects. Key Scientific Concepts of Review: High-throughput phenotyping, which facilitates non-contact and dynamic measurements, has the potential to offer high-quality trait data for GWAS and, in turn, to enhance the unraveling of genetic structures of complex plant traits. In conclusion, high-throughput phenotyping integration with GWAS could facilitate the revealing of coding information in plant genomes.

High-Throughput Phenotyping and Random Regression Models Reveal Temporal Genetic Control of Soybean Biomass Production

Understanding temporal accumulation of soybean above-ground biomass (AGB) has the potential to contribute to yield gains and the development of stress-resilient cultivars. Our main objectives were to develop a high-throughput phenotyping method to predict soybean AGB over time and to reveal its temporal quantitative genomic properties. A subset of the SoyNAM population (n = 383) was grown in multi-environment trials and destructive AGB measurements were collected along with multispectral and RGB imaging from 27 to 83 days after planting (DAP). We used machine-learning methods for phenotypic prediction of AGB, genomic prediction of breeding values, and genome-wide association studies (GWAS) based on random regression models (RRM). RRM enable the study of changes in genetic variability over time and further allow selection of individuals when aiming to alter the general response shapes over time. AGB phenotypic predictions were high (R 2 = 0.92-0.94). Narrow-sense heritabilities estimated over time ranged from low to moderate (from 0.02 at 44 DAP to 0.28 at 33 DAP). AGB from adjacent DAP had highest genetic correlations compared to those DAP further apart. We observed high accuracies and low biases of prediction indicating that genomic breeding values for AGB can be predicted over specific time intervals. Genomic regions associated with AGB varied with time, and no genetic markers were significant in all time points evaluated. Thus, RRM seem a powerful tool for modeling the temporal genetic architecture of soybean AGB and can provide useful information for crop improvement. This study provides a basis for future studies to combine phenotyping and genomic analyses to understand the genetic architecture of complex longitudinal traits in plants.

Hierarchical mixed-model expedites genome-wide longitudinal association analysis

A hierarchical random regression model (Hi-RRM) was extended into a genome-wide association analysis for longitudinal data, which significantly reduced the dimensionality of repeated measurements. The Hi-RRM first modeled the phenotypic trajectory of each individual using a RRM and then associated phenotypic regressions with genetic markers using a multivariate mixed model (mvLMM). By spectral decomposition of genomic relationship and regression covariance matrices, the mvLMM was transformed into a multiple linear regression, which improved computing efficiency while implementing mvLMM associations in efficient mixed-model association expedited (EMMAX). Compared with the existing RRM-based association analyses, the statistical utility of Hi-RRM was demonstrated by simulation experiments. The method proposed here was also applied to find the quantitative trait nucleotides controlling the growth pattern of egg weights in poultry data.

Estimation of dynamic SNP-heritability with Bayesian Gaussian process models

Motivation

Improved DNA technology has made it practical to estimate single-nucleotide polymorphism (SNP)-heritability among distantly related individuals with unknown relationships. For growth- and development-related traits, it is meaningful to base SNP-heritability estimation on longitudinal data due to the time-dependency of the process. However, only few statistical methods have been developed so far for estimating dynamic SNP-heritability and quantifying its full uncertainty.

Results

We introduce a completely tuning-free Bayesian Gaussian process (GP)-based approach for estimating dynamic variance components and heritability as their function. For parameter estimation, we use a modern Markov Chain Monte Carlo method which allows full uncertainty quantification. Several datasets are analysed and our results clearly illustrate that the 95% credible intervals of the proposed joint estimation method (which ‘borrows strength’ from adjacent time points) are significantly narrower than of a two-stage baseline method that first estimates the variance components at each time point independently and then performs smoothing. We compare the method with a random regression model using MTG2 and BLUPF90 software and quantitative measures indicate superior performance of our method. Results are presented for simulated and real data with up to 1000 time points. Finally, we demonstrate scalability of the proposed method for simulated data with tens of thousands of individuals.

Availability and implementation

The C++ implementation dynBGP and simulated data are available in GitHub: https://github.com/aarjas/dynBGP. The programmes can be run in R. Real datasets are available in QTL archive: https://phenome.jax.org/centers/QTLA.

Supplementary information

Supplementary data are available at Bioinformatics online.

Adaptability and stability analyses of plants using random regression models

The evaluation of cultivars using multi-environment trials (MET) is an important step in plant breeding programs. One of the objectives of these evaluations is to understand the genotype by environment interaction (GEI). A method of determining the effect of GEI on the performance of cultivars is based on studies of adaptability and stability. Initial studies were based on linear regression; however, these methodologies have limitations, mainly in trials with genetic or statistical unbalanced, heterogeneity of residual variances, and genetic covariance. An alternative would be the use of random regression models (RRM), in which the behavior of the genotypes is characterized as a reaction norm using longitudinal data or repeated measurements and information regarding a covariance function. The objective of this work was the application of RRM in the study of the behavior of common bean cultivars using a MET, based on Legendre polynomials and genotype-ideotype distances. We used a set of 13 trials, which were classified as unfavorable or favorable environments. The results revealed that RRM enables the prediction of the genotypic values of cultivars in environments where they were not evaluated with high accuracy values, thereby circumventing the unbalanced of the experiments. From these values, it was possible to measure the genotypic adaptability according to ideotypes, according to their reaction norms. In addition, the stability of the cultivars can be interpreted as variation in the behavior of the ideotype. The use of ideotypes based on real data allowed a better comparison of the performance of cultivars across environments. The use of RRM in plant breeding is a good alternative to understand the behavior of cultivars in a MET, especially when we want to quantify the adaptability and stability of genotypes.

Integrating High-Throughput Phenotyping and Statistical Genomic Methods to Genetically Improve Longitudinal Traits in Crops

The rapid development of remote sensing in agronomic research allows the dynamic nature of longitudinal traits to be adequately described, which may enhance the genetic improvement of crop efficiency. For traits such as light interception, biomass accumulation, and responses to stressors, the data generated by the various high-throughput phenotyping (HTP) methods requires adequate statistical techniques to evaluate phenotypic records throughout time. As a consequence, information about plant functioning and activation of genes, as well as the interaction of gene networks at different stages of plant development and in response to environmental stimulus can be exploited. In this review, we outline the current analytical approaches in quantitative genetics that are applied to longitudinal traits in crops throughout development, describe the advantages and pitfalls of each approach, and indicate future research directions and opportunities.

Smoothing and extraction of traits in the growth analysis of noninvasive phenotypic data

BACKGROUND

Non-destructive high-throughput plant phenotyping is becoming increasingly used and various methods for growth analysis have been proposed. Traditional longitudinal or repeated measures analyses that model growth using statistical models are common. However, often the variation in the data is inappropriately modelled, in part because the required models are complicated and difficult to fit. We provide a novel, computationally efficient technique that is based on smoothing and extraction of traits (SET), which we compare with the alternative traditional longitudinal analysis methods.

RESULTS

The SET-based and longitudinal analyses were applied to a tomato experiment to investigate the effects on plant growth of zinc (Zn) addition and growing plants in soil inoculated with arbuscular mycorrhizal fungi (AMF). Conclusions from the SET-based and longitudinal analyses are similar, although the former analysis results in more significant differences. They showed that added Zn had little effect on plants grown in inoculated soils, but that growth depended on the amount of added Zn for plants grown in uninoculated soils. The longitudinal analysis of the unsmoothed data fitted a mixed model that involved both fixed and random regression modelling with splines, as well as allowing for unequal variances and autocorrelation between time points.

CONCLUSIONS

A SET-based analysis can be used in any situation in which a traditional longitudinal analysis might be applied, especially when there are many observed time points. Two reasons for deploying the SET-based method are (i) biologically relevant growth parameters are required that parsimoniously describe growth, usually focussing on a small number of intervals, and/or (ii) a computationally efficient method is required for which a valid analysis is easier to achieve, while still capturing the essential features of the exhibited growth dynamics. Also discussed are the statistical models that need to be considered for traditional longitudinal analyses and it is demonstrated that the oft-omitted unequal variances and autocorrelation may be required for a valid longitudinal analysis. With respect to the separate issue of the subjective choice of mathematical growth functions or splines to characterize growth, it is recommended that, for both SET-based and longitudinal analyses, an evidence-based procedure is adopted.

Multi-trait random regression models increase genomic prediction accuracy for a temporal physiological trait derived from high-throughput phenotyping

Random regression models (RRM) are used extensively for genomic inference and prediction of time-valued traits in animal breeding, but only recently have been used in plant systems. High-throughput phenotyping (HTP) platforms provide a powerful means to collect high-dimensional phenotypes throughout the growing season for large populations. However, to date, selection of an appropriate statistical genomic framework to integrate multiple temporal traits for genomic prediction in plants remains unexplored. Here, we demonstrate the utility of a multi-trait RRM (MT-RRM) for genomic prediction of daily water usage (WU) in rice (Oryza sativa) through joint modeling with shoot biomass (projected shoot area, PSA). Three hundred and fifty-seven accessions were phenotyped daily for WU and PSA over 20 days using a greenhouse-based HTP platform. MT-RRMs that modeled additive genetic and permanent environmental effects for both traits using quadratic Legendre polynomials were used to assess genomic correlations between traits and genomic prediction for WU. Predictive abilities of the MT-RRMs were assessed using two cross-validation (CV) scenarios. The first scenario was designed to predict genetic values for WU at all time points for a set of accessions with unobserved WU. The second scenario was designed to forecast future genetic values for WU for a panel of known accessions with records for WU at earlier time periods. In each scenario we evaluated two MT-RRMs in which PSA records were absent or available for time points in the testing population. Weak to strong genomic correlations between WU and PSA were observed across the days of imaging (0.29-0.870.38-0.80). In both CV scenarios, MT-RRMs showed better predictive abilities compared to single-trait RRM, and prediction accuracies were greatly improved when PSA records were available for the testing population. In summary, these frameworks provide an effective approach to predict temporal physiological traits that are difficult or expensive to quantify in large populations.

Predicting Longitudinal Traits Derived from High-Throughput Phenomics in Contrasting Environments Using Genomic Legendre Polynomials and B-Splines

Recent advancements in phenomics coupled with increased output from sequencing technologies can create the platform needed to rapidly increase abiotic stress tolerance of crops, which increasingly face productivity challenges due to climate change. In particular, high-throughput phenotyping (HTP) enables researchers to generate large-scale data with temporal resolution. Recently, a random regression model (RRM) was used to model a longitudinal rice projected shoot area (PSA) dataset in an optimal growth environment. However, the utility of RRM is still unknown for phenotypic trajectories obtained from stress environments. Here, we sought to apply RRM to forecast the rice PSA in control and water-limited conditions under various longitudinal cross-validation scenarios. To this end, genomic Legendre polynomials and B-spline basis functions were used to capture PSA trajectories. Prediction accuracy declined slightly for the water-limited plants compared to control plants. Overall, RRM delivered reasonable prediction performance and yielded better prediction than the baseline multi-trait model. The difference between the results obtained using Legendre polynomials and that using B-splines was small; however, the former yielded a higher prediction accuracy. Prediction accuracy for forecasting the last five time points was highest when the entire trajectory from earlier growth stages was used to train the basis functions. Our results suggested that it was possible to decrease phenotyping frequency by only phenotyping every other day in order to reduce costs while minimizing the loss of prediction accuracy. This is the first study showing that RRM could be used to model changes in growth over time under abiotic stress conditions.

Utilizing trait networks and structural equation models as tools to interpret multi-trait genome-wide association studies

BACKGROUND

Plant breeders seek to develop cultivars with maximal agronomic value, which is often assessed using numerous, often genetically correlated traits. As intervention on one trait will affect the value of another, breeding decisions should consider the relationships among traits in the context of putative causal structures (i.e., trait networks). While multi-trait genome-wide association studies (MTM-GWAS) can infer putative genetic signals at the multivariate scale, standard MTM-GWAS does not accommodate the network structure of phenotypes, and therefore does not address how the traits are interrelated. We extended the scope of MTM-GWAS by incorporating trait network structures into GWAS using structural equation models (SEM-GWAS). Here, we illustrate the utility of SEM-GWAS using a digital metric for shoot biomass, root biomass, water use, and water use efficiency in rice.

RESULTS

A salient feature of SEM-GWAS is that it can partition the total single nucleotide polymorphism (SNP) effects acting on a trait into direct and indirect effects. Using this novel approach, we show that for most QTL associated with water use, total SNP effects were driven by genetic effects acting directly on water use rather that genetic effects originating from upstream traits. Conversely, total SNP effects for water use efficiency were largely due to indirect effects originating from the upstream trait, projected shoot area.

CONCLUSIONS

We describe a robust framework that can be applied to multivariate phenotypes to understand the interrelationships between complex traits. This framework provides novel insights into how QTL act within a phenotypic network that would otherwise not be possible with conventional multi-trait GWAS approaches. Collectively, these results suggest that the use of SEM may enhance our understanding of complex relationships among agronomic traits.