Pedigree‐management‐flight interaction for temporal phenotype analysis and temporal phenomic prediction

Unoccupied aerial systems (UAS, aka drones) provide high dimensional temporal phenotype data for predictive plant breeding and genetic dissection. Methods to assess temporal phenotype data are an emerging need to predict temporal breeding values of genotypes. Here a novel interaction design was developed and evaluated to include drone flight dates as a component into the mixed model; allowing the temporal changes of drone image derived traits of maize hybrids across different flight dates as well as different management conditions to be monitored. Across 2017 and 2019 respectively, 228 and 100 maize hybrids were grown under two types of management (optimal and late plantings). Seven drone surveys were conducted over each management in 2017 while five drone surveys were conducted over each management in 2019. Temporal plant height (canopy height measurements, CHM) and normalized green‐red difference index (NGRDI) were extracted from each drone survey and used as phenotype data to evaluate the interaction design. Day of flight effects explained the highest amount of total variation for grain yield in the interaction model, meaning the majority of phenotypic variation of CHM and NGRDI occurred across growth with a unique temporal trajectory in each management system. Temporal repeatability values remained higher than 0.5 for CHM and NGRDI in each year. Temporal CHM and NGRDI breeding values of maize hybrids were combined in ridge and lasso regression prediction models. Yield prediction ability of untested genotypes in untested environments were predicted higher by using pedigree × management × flight (PMF) and pedigree× management (PM) interaction results (∼0.34 and 0.52 in 2017 and 2019). Combining environment specific phenomic data (PMF plus PM) gave a larger improvement in yield prediction when the tested and untested environments were less similar. Overall, combined temporal phenomic data could moderately predict grain yield under the most challenging predictive breeding scenario, untested and unrelated genotypes in untested environments.


INTRODUCTION
High throughput phenotyping (HTP) platforms allow researchers to examine phenotypes of complex traits in plants at high temporal resolution.Unoccupied aerial systems (UAS) systems are used in field-based research where a large number of plants (such as in a plant breeding nursery) can be phenotyped at high resolution with minimal labor, cost, and high functionality (Shi et al., 2016).Importantly, repetitive UAS surveys over plant breeding nurseries enable examination of temporal phenotypic variation occurring across plant growth, impractical and overlooked in traditional phenotyping so far (Araus & Cairns, 2014).
The majority of current literature pertaining to UAS derived plant height and reflectance band estimates has focused on the extraction of breeding values (i.e., genetic means or best linear unbiased predictors/estimates) per individual flight dates in maize (Zea mays L.) hybrids (Anderson et al., 2020;Anderson et al., 2019;Pugh et al., 2018;Tirado et al., 2020).Several optimization related studies regarding the implementation of field based HTP platforms were proposed in agricultural field-based research plots (Anderson et al., 2019;Chu et al., 2018;Geipel et al., 2014;Han et al., 2019;Han et al., 2018;Malambo et al., 2018;Pugh et al., 2018;Shi et al., 2016;Tirado et al., 2020).UAS based predictions require plot-based data extraction pipelines from the outputs of UAS flights (e.g.3D point clouds and geographically corrected images) which are still being developed and improved (Anderson & Murray, 2020;Matias et al., 2020;Morales et al., 2020).Extraction pipelines are important for

Core Ideas
• Three-way interaction model reveals temporal genotypic values and phenotypic plasticity.• Phenomic data accurately predicted yield in untested environments and was improved by incorporating three-way interactions.• Maize plant height increased in the later planting faster than in optimal planting until the flowering period.
plant breeding nurseries and trials to estimate breeding values of tested genetic materials (e.g.hybrids or inbreds) from their temporal reactions under different environmental conditions and managements (Araus & Cairns, 2014;Sankaran et al., 2015;Shi et al., 2016;Tirado et al., 2020).Genotype-by-environment interaction is important in crop science to understand plasticity of complex traits, such as plant height in maize (Peiffer et al., 2014;Wallace et al., 2016).However, understanding the underlying causes of plasticity for measures like plant height and yield remains limited, in part because they are cumulative of environmental interactions over growth which cannot be disambiguated.Monitoring of genotypes throughout all growth stages, especially early growth, is needed to understand plasticity.Temporal phenotypic information of plant height and reflectance bands revealed that various loci govern variation in the temporal phenotypes of plant height and reflectance bands at different time points in genome wide association studies and that these can become masked by other loci by the terminal growth period (Adak, Murray & Anderson, 2021;Adak, Murray, Anderson, et al., 2021;Anderson et al., 2020;Pauli et al., 2016;J. Wang et al., 2021;Xavier et al., 2017).Thus, over growth, genome wide markers predicted temporal plant height and reflectance bands with varying prediction abilities and varying effect sizes; demonstrating sources of variation change over growth periods in terms of temporal plant heights and reflectance bands (Adak, Murray & Anderson, 2021;Adak, Murray, Anderson, et al., 2021;Anderson et al., 2020;J. Wang et al., 2021;X. Wang et al., 2019;Wu et al., 2019).This is important where temporal plant height and reflectance bands data should be analyzed jointly to better scrutinize their plasticity within growth stages.
Previous field based HTP studies have evaluated temporal plant heights or reflectance bands nested within individual flight dates to predict the breeding values for each flight date independently.Here we further advance this approach by analyzing UAS derived temporal data in an interaction based statistical model, where the genetic model term has interactions of pedigrees and flight dates to obtain the temporal breeding values.These temporal breeding values can be used to dissect the plasticity along with different levels of management conditions (e.g., late and optimal planting) and populations (e.g., diverse hybrids population in maize).To test this interaction model, a set of 228 and 100 maize hybrids grown in 2017 and 2019, managed as both optimal and late plantings, were used.From this experiment, seven and five drone surveys were conducted over 2017 and 2019 trials respectively, with specific drone flights the same across plantings in each year.
Combining two years of data also forced addressing one of the other major barriers of UAS based phenotyping and predictions, connecting data across environments where both flight dates and plant growth stages differ.Having the ability to build models that predict from data collected across different years or environment is critical for predictive breeding, as well as for agronomic management.Previously, it was found that the penalized linear model outperformed ensemble methods in prediction of yield in maize (Adak, Murray, Božinović, et al., 2021), ridge and lasso algorithms were preferred to predict yield using main effect of genotype with their temporal phenomic data across different managements in both years.
The objectives of this study were to (a) develop and evaluate an interaction based statistical design to predict the temporal breeding values over flights, here using both a structural (CHM) and a vegetation index (normalized greenred difference index [NGRDI]) measure; (b) evaluate maize hybrids across flight dates, managements, and environments; (c) predict maize grain yield using temporal phenotypes of CHM and NGRDI in each year through cross validation to test the predictive ability of temporal phenotype data for grain yield in each year; and finally (d) evaluate if phenomic data derived from three way interaction component can improve predictions across environments

Genetic materials and management conditions
Two different populations were used in this study separately in two years (2017 and 2019) and each was grown under optimal planting with irrigation (OI) and late planting with irrigation (LP).So optimal and late plantings in 2017 and 2019 were abbreviated as 17-OI, 17-LP, 19-OI and 19-LP respectively.The LP trials was expected to experience increased heat stress.The 2017 trials were a subset of the Genomes to Field (https://www.genomes2fields.org/)project genotypeby-environment trial containing 228 hybrids.The 17-OI and 17-LP trials were planted on 3 March 2017 and 6 April 2017 respectively.The 2019 trial contained 100 advanced diverse maize hybrids developed by the Texas A&M maize breeding program, unrelated and genetically distant by pedi-gree from the Genomes to Field set.The 19-OI and 19-LP trial were planted on 20 March 2019 and 12 April 2019, respectively.

Field based high throughput phenotyping and data extraction
Red-green-blue (RGB) field images were collected using a UAS (an unoccupied aerial vehicle [UAV] fit with sensors and other technology to collect data), DJI Phantom 4 Pro V2.0, outfitted with a 1-inch 20MP CMOS sensor with a mechanical shutter (SZ DJI Technology Co., Ltd., Shenzhen, China).The RGB sensor was used in this study due to its more affordable price than the multispectral sensor, so RGB sensor will probably have a wider range of use in the near future.Using the DJI GS Pro application, flight missions were planned with 25 m elevation (above ground), 90% forward and side overlaps, flight speed of 1.2 m/s, and a shutter interval of 2.0s.The resultant ground sampling distance was 0.7 cm/pix for individual images.
Geotagged images were processed using Agisoft Metashape (Agisoft LLC, St. Petersburg, Russia) and orthomosaics were constructed using the software's structure from motion with multi-view stereo methodology.Ground control points were measured using a V-map Dual Frequency L1/L2 PPK GNSS Receiver (Micro Aerial Projects).An overview of the workflow to generate orthomosaics was follows: (a) raw RGB images were loaded into a new Agisoft project; (b) coordinate system/projection was set (most commonly WGS84); (c) photos were aligned using referenced preselection, key point limit 40,000, tie point limit 4,000; (d) initial bundle adjustment: optimized camera calibration using the following distortion parameters: f, cx/cy, k1, k2, k3, p1, and p2; (e) tightened tie point accuracy value by setting marker accuracy at 0.5 pix and tie point accuracy at 0.1 pix; (f) imported ground control points as a .csvfile and performed a manual alignment; (g) unchecked all images in the reference pane.Optimized camera alignment using all available camera distortion parameters (h) adjusted bounding box to include the entire sparse cloud; (i) built dense cloud; (j) calibrated colors, including white balance; (k) built a digital elevation map; and (l) built orthomosaics (with digital elevation map as surface).
The UAS was flown over 2017 and 2019 trials to collect temporal plant heights and NGRDI ( Green−Red Green+Red ) (Tucker, 1979).Seven (2017) and five (2019) UAS surveys were conducted over both managements (Table 1).Plant heights in the 99 th percentile were estimated from the densified point cloud following the procedures set forth by (Anderson et al., 2019) using a hierarchical robust interpolation approach.The R/UAStools::plotshpcreate (Anderson & Murray, 2020) function was used to create the polygons shapefiles (.shp) for each two row plots since each maize hybrid were planted two row plots in each replication.Resulting shapefiles were used within the R/FIELDimageR (Matias, Caraza-Harter & Endelman, 2020) to extract the NGRDI (Tucker, 1979) for each row plot of both populations.Grain yield (t ha -1 ) was collected using a research plot combine.Flowering times were collected as the number days after sowing at which approximately 50% of each plot expressed extruded silks (days till silking) and 50% expressed tassels extruded anthers (days to anthesis [DTA]).Three types of terminal plant heights were measured at the end of reproductive stage once manually using a ruler.These were plant height (from ground to tip of tassel), flag leaf height (from ground to flag leaf), and ear height (from ground to closest ear to ground).

Experimental design and statistical analysis
Each trial was grown as a randomized complete block design with spatial variation partitioned into ranges and rows with two replications (Eq.1).Each plot consisted of two consecutive row plots in each replication.Each row was ∼7.62 m, including a 1.22 m alley, and row spacing was 0.76 m.Variance components and yield (t ha -1 ) of maize hybrids were estimated in each year using the Eq. 1 below: where   is the yield value (t ha -1 ) of the ith two row planted maize hybrid belonging to jth management, kth range, lth row, and mth replication; μ = grand mean; pedigree i is the random effect of ith maize hybrid with pedigree   ∼ (0, σ 2 pedigree ); management j is the random effect of jth management with management   ∼ (0, σ 2 management  ); pedigree × management i×j is the random effect of interaction between ith maize hybrid and jth management with (pedigree * management)   ∼ (0, σ 2 (pedigree × management)  ); range k and row l are the random effects of th range, th row with range   ∼ (0, σ 2 range  ),    ∼ (0, σ 2 row  ), which did not need nesting as they were unique locations in the field, rep m is the random effect of mth replication nested within jth management with ). Error ijklm is the residual error containing unexplained variation by any components in Eq. 1.
Repeatability of yield was calculated in each year using the below formula (Eq.2).
(2) where  is the number of managements (late and optimal plantings), and  is the number of replications (two reps) in each year.
To predict the temporal phenotype data (CHM and NGRDI) of maize hybrids, we here propose a three-way interaction design (Eq.2) across flight dates and managements for each year as follows: where   is the CHM or NGRDI values of two rows of the th maize hybrid belonging to th flight date, th management, th range, th row and th replication nested within th management; μ = grand mean; pedigree  is the random effect of th maize hybrid with pedigree   ∼ (0, σ 2 pedigree  ); f light  is the random effect of th flight with f light   ∼ (0, σ 2 f light  ); management k is the random effect of th management with management   ∼ (0, σ 2 management  ); (pedigree * f light)  is the random effect of interaction between th maize hybrid and th flight date with (pedigree × f light)   ∼ (0, σ ( pedigree × f light) 2  ); (pedigree × management)  is the random effect of interaction between th maize hybrid and th management with (pedigree × management)   ∼ (0, σ 2 (pedigree × management)  ); (f light × management)  is the random effect of interaction between th flight and th management with ); error  is the residual error containing unexplained variation after fitting components in Eq. 3.
Temporal repeatability (Eq.4) for each temporal phenotype was calculated as follows: where a, b, and c are the numbers of managements (late and optimal plantings), flight times (seven in 2017 and five in 2019) and replications (two reps) in 2017 and 2019 trials.All equations were run using the lme4 package in R with restricted maximum likelihood (REML) approach (Bates et al., 2014).The codes of equation 3 and 4 are available at https://github.com/alperadak/pedigree-flight-management.

UAS prediction model
Breeding values of grain yield (genotypic best linear unbiased predictors from Eq. 1) were used as dependent variables in prediction models.two prediction models were run as folows: (a) results of only three-way interaction in Eq. 3 PMF of CHM and NGRDI were used to predict yield, and (b) results of two-way (PM) and three-way (PMF) interactions of CHM and NGRDI were used to predict grain yield.NGRDI was previously nominated by lasso as one of the important vegetation index in prediction the maize grain yield (Adak, Murray, Božinović, et al., 2021).Prediction was conducted between managements in 2017 and 2019.OI trials were used for training as tested environments while LP trials were used as untested (validation) environments in each year.Before prediction, temporal phenomic data was preprocessed using the scaling function and then used in training the ridge and lasso models in caret package.The R/caret package (Bates et al., 2014) was used to construct the prediction models with 200 iterations; each iteration contained the random data split where 60 percent of maize hybrids were used as tested genotypes while the remaining hold-out 40 percent were used as untested genotypes.Five-fold cross validation with three repeats were used in each iteration.One iteration of the prediction models is briefly explained here.First, a random data split was conducted as 60:40 percent ratio as training and test data set respectively.Second ridge, and lasso regressions were trained using training data set (60 percent split data), where model was set "glmnet" for both ridge and lasso regressions, alpha level was set as "0" and "1" for ridge and lasso regressions respectively, "lambda" values were also searched between 0 and 1(0, .1,.2,.3,.4,.5, .6,.7,.8,.9 and 1) to tune the ridge and lasso regressions.Third, correlation between actual breeding values (predicted by Eq. 1) of yield and predicted breeding values of yield (by lasso and ridge regressions) were calculated as a merit of prediction ability.
In here, four different prediction abilities were calculated as follows:

Results of interaction design and temporal repeatability
Temporal phenomic data of CHM and NGRDI were predicted by an interaction design (Eq. 3) containing three-way interactions of maize hybrids (pedigree), drone flights (flights), and managements (optimal and late plantings).Overall, the flight variance component explained the highest percent variation of total variation for CHM and NGRDI (Figure 1).Interaction based design for temporal phenotype enabled calculation of the temporal repeatability of CHM and NGRDI by equation 4 (Eq.4).Temporal repeatability was 0.87 and 0.55 for CHM in 2017 and 2019, and 0.56 and 0.68 for NGRDI in 2017 and 2019 respectively (Figure 1).
The temporal variation of the maize hybrids were scrutinized across management by demonstrating the (  *  ℎ * ) and ( ℎ * ) interactions for CHM (Figure 2) and NGRDI (Figure 3).
Temporal plant heights (CHM) were taller in late planting than optimal planting across flight dates in both years con-sistently, except durring later growth in 2017 where the late planting, due to a compressed growth period, was senescing (Figure 2).Terminal UAS heights were in agrement with manually measured plant heights (plant height, flag leaf flight, and ear height) (Figure 4).Maize hybrids flowered earlier in late plantings, when measured in days after planting, than in optimal plantings in both year consistently (Figure 4).Normalized green-red difference index (NGRDI) always scored higher in late planting than optimal planting up to the end of flowering times in both years consistently, however this shifted where NGRDI scores were lower in late planting than optimal planting after flowering times in both year consistently, showing the earlier senesence of this planting (Figure 3).Grain yield was lower in late platings than in the optimal plantings, as typically is observed (Figure 4).Comparing genotypes, correaltions between NGRDI and grain yield within a planting date were consistently positive belonging to early flight dates in both years, and reached up to ∼0.5 in 2019 and ∼0.6 in 2017; however, the correaltions became weaker and sometimes turned non-significant during late flights in both years (Figure 5).Correlations between CHM and grain yield were more stable than correlations between NGRDI and grain yield, and reached up to ∼ 0.5 in both years (Figure 5).

Prediction model
The predictions of grain yield were conducted based on four different prediction abilities and two phenomic data in cross validation (see the prediction model in Material and Methods).It was found that when the results of three-(PMF) and two-(PM) way interactions were used together, the prediction ability was higher than using only the results of the three-way interaction (PMF) in both ridge and lasso regressions.Ridge regression mostly performed better than lasso in prediction the grain yield in untested environments (CV3 and CV4) in both years (Figure 6).When only the results of PMF were used, prediction ability were ∼0.23 in CV3 and CV4 of 2017 by lasso regression; however, prediction abilities were higher (∼0.33 in CV3 and CV4) by ridge regression (Figure 6).Similar results were observed in 2019; lasso predicted grain yield with a prediction ability of ∼0.52 in CV3 and ∼0.49 in CV4, less than the prediction ability of ridge regression (∼0.53 in CV3 and ∼0.50 in CV4) (Figure 6).Remarkably, combined phenomic data derived from PMF plus PM interactions predicted grain yield greater than phenomic data derived from only PMF in both years by ridge regression (Figure 6).Combined phenomic data predicted grain yield in the 2017 with a prediction accuracy of ∼0.35 in CV3 and ∼0.34 in CV4 by ridge regression, which were substantially higher than prediction accuracies (∼0.28 in CV3 and ∼0.26 in CV4) obtained when phenomic data derived from only PMF was used (Figure 6).Similarly, combined phenomic data predicted grain yield in the 2019 with the prediction accuracy of ∼0.53 in CV3 and ∼0.52 in CV4 by ridge regression, marginally higher than the prediction accuracies (∼0.52 in CV3 and CV4) obtained when only phenomic data was used; across 200 iterations (Figure 6)

The importance of interaction designs in temporal data analysis
In crop science, statistical model selection is an important step when evaluating temporal traits collected from various time points of crop growth.UAS high throughput F I G U R E 3 Shows the results of pedigree × flight × management and flight × management interactions for the normalized green-red difference index (NGRDI).A and C are the results of pedigree × flight × management for 2017 and 2019 trials respectively; A and D are the results of flight × management interaction for the 2017 and 2019 trials respectively.Temporal variation of NGRDI showed that the late plating had greater overall values there was an interaction after flowering times in both years consistently.Vertical dashed lines show the means of flowering time (days to anthesis; DTA) of each management in 2017 and 2019.LP and OI are the late and optimal planting managements respectively phenotyping application provide a vast amount of temporal data for complex traits.A need for statistical and biologically meaningful data assessment to predict genetic performance has emerged as a major concern.This study proposed a novel interaction model design to integrate UAS across different trials, containing a three-way interaction of pedigree (maize hybrids), drone surveys (flight) and managements (optimal and late plantings).Thus, temporal breeding values of maize hybrids temporal traits (e.g., CHM and NGRDI) can be estimated and visualized through flight times as a result of three-way interaction components in the mixed model (Eq.1).Visualizing temporal breeding values, the phenotypic plasticity of traits was dissected within growth stages (Figures 2 and 3).
Utilizing the interaction component (pedigree × flight × management [PMF] component in Equation 1), the temporal trajectories of CHM and NGRDI per genotype occurring at any time of growth can be evaluated within the given time level using the interaction factor; that is meaningful in bio-logical interpretation of crop growth as compared to single time point derived phenotype.

Prediction of grain yield
Temporal changes in the CHM and NGRDI had unique trajectories for late and optimal plantings in both years (Figure 2 and 3); these trajectories were positively correlated with low and high grain yield in late and optimal planting managements in both years (Figure 5).In other words, these temporal trajectories of CHM and NGRDI became early predictors of grain yield, across diverse management (optimal vs late plantings).Phenomic data derived from three-and two-way interactions improved the predictions of grain yield (Figure 6).In this study, for presentation simplicity, CHM was chosen as a single structural phenotype and NGRDI a single spectral phenotype.Past studies have shown that prediction power for yield is substantially increased by adding additional structural and spectral phenotypes (Adak, Murray, Božinović, et al., 2021; The explained percent variation by each variance component of equation 1 for grain yield, plant heights and flowering times.A, B and C show the explained percent variances by each component for grain yield, three types of manually measured plant heights and flowering times respectively.White diamonds are the repeatability values (calculated by Equation 2) of yield, plant heights and flowering times; white rectangles are the R-squared of the models.Ear height (EHT), flag leaf height (FHT), plant height (PHT) are manually measured plant heights from ground to first ear, to flag leaf and to tip of tassel respectively; DTA and DTS are days to anthesis and silking, respectively.D, E and F are the breeding values of maize hybrids for grain yield, three types of manually measured plant heights and flowering times respectively; breeding values were obtained from pedigree × management component in each year Aguate et al., 2017;Danilevicz et al., 2021;Krause, González-Pérez, Crossa, Pérez-Rodríguez, Montesinos-López, Singh, Dreisigacker, Poland, Rutkoski, Sorrells, et al., 2019).Additional phenotypes correlated to the trait of interest (here grain yield) but not perfectly correlated to any other variables may contain additional information for prediction (Figure 5).However, too many additional measured spectral or structural phenotypes can increase risks of correlation and multicollinearity among variables.However, in the largest study of field collected phenotypes to date, collecting 89 multispectral VIs with 12 flight times leading to 1,068 phenomic temporal variables, showed levels of correlation between VI predictors was similar to genotyping with ∼153,000 SNPs (Adak, Murray & Anderson, 2021).This suggests we have not yet saturated the field-collected phenome's with VIs.Additional bands, such as those collected by hyperspectral cameras, open magnitude more VIs.There are also new possible measures that can be taken using UAS, like plant texture, which could be predictive (Fu et al., 2021).
In addition to other measures of segregating variation in the plant, variation descriptive of the growing environment, such as weather parameters can improve prediction models and be useful.Weather parameters have previously been incorporated with genomic markers to predict the grain yield of maize hybrids (Costa-Neto et al., 2021;Jarquin et al., 2021;Jarquín et al., 2014;Rogers & Holland, 2021;Technow et al., 2015), these weather effects boosted grain yield prediction ability.However, prediction ability was also found to depend on similarity in levels between tested and untested environments.During growth, plants change their phenotypes in response to changing weather parameters; an example of this has been shown here for temporal plant height (CHM) and NGRDI as a result of the three-way interaction in Eq 3 (Figure 2 and 3).From a predictive plant breeding standpoint, temporally varying phenotype data under different environmental conditions have a potential to serve as new predictors across different environments.Temporal phenomic data will change depending on the environment which does not require a similarity between environments like weather data to predict best.Therefore, it is notable that results of three-and two-way interactions together boosted the prediction ability to be greater in 2017 than in 2019 (Figure 6) for the grain yield prediction of unknown genotypes in unknown environment.This was likely because variation in temporal phenotypes caused by changing environmental parameters across growth were captured by the temporal phenotypes of each genotype in each environment allowing prediction between diverse environments.Temporal phenotype data captured by UAS results from each genotypes biological interaction with changing environmental parameters occurring across growth.It is logical therefore that temporal variation captured in UAS derived traits can improve the link between training and test environments.Environmental predictors cannot be perfectly replicated in a field environment, and are distinct between one another, unlike genomic data.Temporal phenotype data are manipulated by a suite of segregating loci for each temporally measured trait; some that change effect sizes over multiple time points, while other segregating loci change temporal phenotypes only at single time points (Adak, Conrad, et al., 2021;Adak, Murray & Anderson, 2021;Adak, Murray, Anderson, et al., 2021;Anderson et al., 2020;Pauli et al., 2016;J. Wang et al., 2021;X. Wang et al., 2019).Towards understanding temporal effects of the segregating loci, what we can heritably select in plant breeding, temporal UAS phenotyping data combined can potentially better predict grain yield across tested environments than genomic markers alone.Temporal phenomic data is different for each plant and environment, however, genomic data is the same for each plant across environments.Therefore, phenomic complement derived from two-and three way interactions in Eq 3 complement each other and have emerged as promising predictors compared to genomic data in prediction models between different environments, however combination of phenomic, weather and genomic data would be best but has yet to be reported.
F I G U R E 6 Prediction abilities calculated for grain yield using phenomic data.The results of pedigree × management × flight (PMF in Eq. 3) interaction was used as predictors in first prediction scenario, and the combination of results of pedigree × management × flight (PMF in Eq. 3) interaction and results of pedigree × management (PM in Eq. 3) interaction results were used in second prediction scenario.Ridge and lasso regressions were used in 2017 and 2019.Combined data boosted the prediction accuracies in prediction of grain yield of maize hybrids in untested environments.CV1 (cross validation 1) is the prediction accuracy of tested genotypes (60% maize hybrids) in tested environment (optimal planting, OI); CV2 is the prediction accuracy of tested genotypes (60% maize hybrids) in untested environment (late planting, LP); CV3 is the prediction accuracy of untested genotypes (40% maize hybrids) in tested environment (optimal planting, OI) and CV4 is the prediction accuracy of untested genotypes (40% maize hybrids) in untested environment (late planting, LP) in both years.RMSE, root mean square Previous prediction studies considering both genomic and environmental data together demonstrated prediction accuracies are increased by modeling genotype by environmental interaction effects.However, prediction models were found to be most successful when similarity was high between training and test environments (Bandeira e Sousa et al., 2017;Cuevas et al., 2018;Monteverde et al., 2018).Our results here indicate that temporal phenotype data can predict grain yield better when the similarity between training and test environment is lower (Figure 6; 2017 trials).Using weather data and temporal phenomic data, is an obvious extension to improve temporal phenomic predictions, in segregating plant breeding populations (Adak, Murray & Anderson, 2021).Temporal phenomic prediction might provide greater ability to predict grain yield between unrelated environments but requires many more predictors than this study presents.

CONCLUSION
With the advent of field based high throughput phenotyping, temporal data extraction from multiple time points via multi-ple UAS surveys provides novel temporal measurements for use in predictive plant breeding, physiological and biological understanding.This study demonstrated a novel, efficient interaction based mixed model to evaluate temporal data, with drone flights and their interactions added as novel variance components.Thus, pedigrees monitored across multiple time points and environments dissected the temporal plasticity that occurred across growth.Temporal phenomic prediction was previously introduced where drone derived temporal phenotypic data was used to predict yield across diverse managements in maze that yielded equal to or better than genomic prediction (Adak, Murray & Anderson, 2021).This study extended temporal phenomic prediction by using different genotypes and environments and leveraging PMF component derived phenomic data to train machine learning based prediction models.

A C K N O W L E D G M E N T S
(a) cross validation 1 (CV1) is based on the correlation between actual yield values of the 60 percent selected genotypes (also known as tested genotype used in training model) and predicted yield values of same 60 percent selected genotype in OI (also known as tested environment); (b) cross validation 2 (CV2) is based on the correlation between actual yield values of the 40 percent of remaining held out genotypes in OI (also known as untested genotypes) and predicted yield values of same 40 percent; (c) cross validation 3 (CV3) is based on the correlation between actual yield values of the 60 percent selected genotype and predicted yield values of same 60 percent selected genotype in LP (also known as F I G U R E 1 Explained percent variation by each variance component of Equation 3 (Eq.3) for temporal plant height (canopy height measurement; CHM) and normalized green-red difference index (NGRDI).Left axis shows the percentages explained by the variance components; right axis shows the temporal repeatability values of the temporal traits (white diamond), R-squared (white triangle) and root mean square error (RMSE, white square) of the models.The flight effect and interactions explained the highest proportion of total variation untested environment); (d) cross validation 4 (CV4) is based on the correlation between actual yield values of the 40 percent of remaining held-out genotypes in LP and predicted yield values of same 40 percent.Prediction codes are available at https://github.com/alperadak/pedigree-flightmanagement.

F
Shows the results of pedigree × flight × management and flight × management interactions for the temporal plant height (canopy height measurement; CHM).A and C are the results of pedigree × flight × management for 2017 and 2019 trials, respectively; A and D are the results of flight × management interaction for the 2017 and 2019 trials, respectively.Temporal variation of CHM showed that late plating had higher overall values until flowering times in both years consistently.Vertical dashed lines show the means of flowering time (days to anthesis; DTA) of each management in 2017 and 2019.LP and OI are the late and optimal planting managements, respectively

F
I G U R E 5 Correlation coefficients of temporal phenomic data belonging to 2017 (left) and 2019 (right) and yield.LP and OI indicate late and optimal planting management respectively in both years Quantitative Genetic and Maize Breeding Program in Texas A&M university would like to thank Dr. Sorin Popescu, Dr. Lonesome Malambo, Dr. Dale Cope and Dr Scott Wilde for their expert assistance in conducting UAV surveys equipped with RGB and multispectral sensors.A.A. was supported by a fellowship from Republic of Turkey, Ministry of National Education and Ministry of Agriculture and Forestry.The authors would like to thank Dr. Don Conlee who supplied the weather data containing 10-minute increments from Texas A&M Research Farm Mesonet weather station.The authors would also like to thank David Rooney, Jacob Pekar, and Stephen Labar for their agronomic and technical support, and graduate students and undergraduate/high school employees for their hard work and effort maintaining fields and recording phenotypic data.AU T H O R C O N T R I B U T I O N SAlper Adak: Conceptualization; Data curation; Formal analysis; Investigation; Methodology; Software; Supervision; Validation; Visualization; Writing-original draft.Steven L. Anderson: Conceptualization; Data curation; Formal analysis; Investigation; Methodology; Software; Writing-review & editing.Seth C. Murray: Conceptualization; Funding acquisition; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Writingreview & editing.C O N F L I C T O F I N T E R E S TThe authors declare no conflict of interest.O R C I DAlper Adak https://orcid.org/0000-0002-2737-8041RE F E R E N C E S Flights as days after planting (DAP) and their corresponding days in optimal and late plantings in 2017 and 2019 T A B L E 1 ; range  and row  are the random effects of th range, th row with range   ∼ (0, σ 2 [] is the random effect of th replication nested within th management with rep[management] []  ∼ (0, σ 2 rep[management] [] )