Soybeans

The seeds were derived from introgressing G. soja (PI468916) into G. max (A81-356022). Specifically, the BC₅F₅ plant P-C609-45-2-2 was heterozygous for the LG I protein QTL introgression from G. soja. These seeds were planted directly into pots containing Bradyrhizobium japonicum-inoculated soil and supplemented with full nutrient fertilizer (Osmocote 14-14-14) in growth chambers at the University of Minnesota. Chambers were set initially to a photoperiod of 14/10 and thermocycle of 22°C/10°C and monitored to mimic Illinois field growing conditions. Relative humidity settings were 50-60%, and light intensity was measured at 550-740 μE m^-2 sec^-1. All harvests occurred at 1400 hours and consisted of samples pooled from a minimum of three plants [52 (link)]. Samples were harvested from plants in parallel and flash frozen in liquid nitrogen before storage at -80°C. Open flowers and young leaf tissue samples were collected simultaneously. Pods and seeds were harvested by seed weight and pod lengths that correspond to approximated Days After Flowering (DAF) as specified. The one-cm pod was processed intact (approximately 7-DAF), while the four and five cm pods (approximately 10-13 DAF and 14-17 DAF) were divided into seed and pod-shell components. Seed 21-DAF, Seed 25-DAF, Seed 28-DAF and Seed 35-DAF had seed weights between 10 and 25 milligrams, 25 and 50 milligrams, 50 and 100 milligrams, 100 and 200 milligrams, and greater than 200 milligrams, respectively.
Root and nodule tissues were harvested from plants grown in growth chambers set to 16-hr photoperiods with light intensities ranging from 310-380 μE m^-2 sec^-1. Seeds were imbibed for three days, planted in quartz sand and fertilized with a full nutrient solution. Root tissue was harvested after 12 days. Nodules were harvested at 20-25 days after inoculation; for these samples, plants were fertilized for the first seven days with nutrient solution containing 3.5 mM NO₃ and subsequently fertilized every other day with a full nutrient solution lacking nitrogen.
Soybean tissue samples were ground with liquid nitrogen by mortar and pestle. Total RNA was isolated by a modified TRIzol^® (Invitrogen) protocol [53 (link)]. DNA was removed by digest with on-column RNase-free DNase (Qiagen), and RNA was purified and concentrated by RNeasy column (Qiagen). RNA quality was evaluated by gel electrophoresis, spectrophotometer and Agilent 2100 bioanalyzer.

Hy-Line Brown laying hens were fed with a regular diet (corn-soybean meal-based; containing 0.32% non-phytate phosphorus (NPP); Table 1) start from 35 weeks of age. On the last day of age 40 weeks, a total of 60 hens that laid eggs between 07:30−08:30 were randomly selected to evaluate the daily phosphorus rhythms. Of them, 45 hens were euthanized for sample collection, and the other 15 hens were used to study the feed intake and calcium/phosphorus excretion rhythms. For sample collection, the 45 hens were sampled according the oviposition cycle: at oviposition, at 6, 12, 18 h post-oviposition, and at the next oviposition, respectively, with 9 hens sampled at each of the time point. The following samples were collected: blood (for serum), uterine (stored at −80 ℃, for Western-blotting analysis), femur (in 4% paraformaldehyde, for histological analysis) and kidney (stored at −80 ℃, for Western-blotting analysis). For the other 15 hens, the feed intake was recoded and the excreta was collected at the following intervals: from oviposition to 6 h post-oviposition, from 7 to 12 h post-oviposition, from 13 to 18 h post-oviposition, from 19 h post-oviposition to the next oviposition.Table 1

Composition and nutrient concentrations of basal diet (%, unless noted, as-is basis)

Item	Low phosphorus	Regular phosphorus
Ingredients
Corn	56.69	56.69
Soybean meal	25.77	25.77
Distillers dried grains with solubles	4.00	4.00
Calcium carbonate	9.73	9.04
Dicalcium phosphate	-	1.15
Soybean oil	1.51	1.51
Sodium chloride	0.26	0.26
DL-Methionine	0.18	0.18
Choline chloride	0.15	0.15
Montmorillonite	0.71	0.25
Premix1	1	1
In total	100.00	100.00
Nutrient levels
Metabolizable energy, kcal/kg (calculated)	2,600	2,600
Crude protein (calculated)	16.5	16.5
Total phosphorus (calculated/analyzed)	0.34/0.34	0.53/0.49
Non-phytate phosphorus (calculated)	0.14	0.32
Calcium (calculated/analyzed)	3.50/3.47	3.50/3.52

¹Provided per kilogram of diet: manganese 60 mg, copper 8 mg, zinc 80 mg, iodine 0.35 mg, selenium 0.3 mg, vitamin A 8000 IU, vitamin E 30 mg, vitamin K₃ 1.5 mg, thiamine 4 mg, riboflavin 13 mg, pantothenic acid 15 mg, nicotinamide 20 mg, pyridoxine 6 mg, biotin 0.15 mg, folic acid 1.5 mg, and cobalamin 0.02 mg

The previously explained evaluation criteria used for the optimization of the training set composition were also employed to optimize its size due to their ability to function as an evaluation metric for a given training set. The criteria tested in this role were Avg_GRM_self in the untargeted scenario, Avg_GRM_MinMax for targeted optimization, and CDmean and Rscore in both scenarios. To this end, the first step was evaluating the training set obtained during the cross-validation using the aforementioned criteria. For instance, the value of Avg_GRM_self was calculated for the training set obtained through optimization with Avg_GRM_self for all the tested training set sizes (10, 20, 40, 60, 80 and 100 % of the candidate set) in the 40 iterations of the cross-validation. Next, the value of the evaluation metric was plotted against the training set size (supplementary materials, Figures S25–S30) and the following function was fitted to it: $$\begin{array}{c}\hfill evaluation\_metric=\frac{ln(size-d)}{m{(size-d)}^p}+n\end{array}$$ where d, m, p and n are the parameters used to fit the function to the observed data, size is the size of the training set and ln is the natural logarithm. Equation 3 was chosen for its ability to fit the 3 types of curve observed (Ratkowsky 1993 (link)): rapid growth followed by slower growth ( $p<0.5$ ), fast growth followed by a plateau ( $0.5<p<1$ ) and rapid growth followed by a slow decline ( $p>1$ ) (Figures S25 - S30). Optimization per se was only possible in the latter type of curve, as it is the only one with a maximum within the range of tested training set sizes. For the rest, the fitted function was always increasing, which makes actual optimization impossible. Instead, we selected the training set size that would result in an acceptable accuracy loss. To that end, we used the fitted function (Eq. 3) to select the training set sizes for which the evaluation metric reached 95% and 99% of the value it had for the entire candidate set, aiming to find a training set able to generate a GS model with a target accuracy of 95% and 99% of the maximum accuracy obtained when the entire candidate set is the training set. This assumes that the evaluation metric and the actual accuracy are correlated, and this assumption had to be validated using the cross-validation results to interpolate the accuracy that would have been obtained with the selected training set sizes. This analysis was performed in all datasets except for the soybean data, as we do not have the complete information across the entire range of training set sizes due to the preselection step as explained in the cross-validation section.