## 2 Results
### Large Phenotypic Variability  
The data analysis of the field trials involved fitting single-trait and single-environment linear mixed models to estimate adjusted means. Overall, large phenotypic variability was observed in the CGN population in both years. Most traits had a coefficient of variation (CV%) greater than 10%, with particularly high values for tannins, phenolic acids, flavonoids, and lipid-derived products (Table 2). The only exception to the large CVs was C18:2, with a coefficient of variation (CV%) of \(\sim\)2.7%. Notably, some accessions showed (phenotypically) simultaneous low levels of complex tannins (procyanidin B1 and B2) and flavonoids (myricetin and quercetin) in both years, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Trait 1a**} & \multicolumn{2}{c}{**Cross-Validation**} \\ \cline{2-4}  & **Tuning Parameter LVs 2b **c** \\ \hline Protein 2021–2022 & 12 & 0.99 \\ Oil 2021–2022 & 10 & 0.97 \\ C18:1 2021–2022 & 11 & 0.87 \\ C18:2 2021–2022 & 11 & 0.82 \\ C18:3 2021–2022 & 11 & 0.94 \\ Catechin 2021 & 6 & 0.78 \\ Catechin 2022 & 5 & 0.80 \\ Epicatechin 2021 & 5 & 0.76 \\ Epicatechin 2022 & 5 & 0.81 \\ Procyanidin B1 2021 & 6 & 0.86 \\ Procyanidin B1 2022 & 5 & 0.84 \\ Procyanidin B2 2021 & 5 & 0.72 \\ Procyanidin B2 2022 & 5 & 0.82 \\ \hline \hline \end{tabular}  
* For protein, oil, fatty acids, a multi-year model was developed. b LVs indicates the number of latent variables (known as “terms” in WinIISTIM 4 software). The optimal number of variables was the one minimizing CV errors in WinIISTIM. c\({}^{*}\)\(\tau_{\text{cv}}\) represents the average value across the 10 rounds of CV.  
\end{table} 
Table 1: Person correlation between predicted and actual chemical values (\(\tau_{\text{cv}}\)) of the 10-fold cross-validation (CV). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**2021**} & \multicolumn{3}{c}{**2022**} \\ \cline{3-10}
**Chemical Class** & **Trait 1a** ** & **Min** & **Mean** & **Max** & **CV\%** & **Min** & **Mean** & **Max** & **CV\%** \\ \hline Oil & Oil & 1.37 & 1.69 & 2.14 & 7.93 & 1.23 & 1.49 & 1.84 & 7.07 \\ Protein & Protein & 18.70 & 25.14 & 30.66 & 7.91 & 22.02 & 29.29 & 35.15 & 7.04 \\ Fatty acid & C18:1 & 15.74 & 21.17 & 27.11 & 11.19 & 1481 & 20.05 & 25.12 & 9.23 \\ Fatty acid & C18:2 & 48.68 & 52.73 & 56.60 & 2.77 & 48.51 & 52.97 & 58.83 & 2.88 \\ C18:3 & 2.50 & 4.79 & 7.37 & 15.15 & 2.57 & 52.0 & 7.40 & 12.60 \\ Catechin & 1.04 & 41.93 & 80.17 & 38.28 & 0.28 & 7.22 & 15.51 & 42.20 \\ Tannin & Epicatechin & 0.15 & 37.04 & 70.01 & 39.69 & 1.23 & 11.76 & 21.63 & 37.58 \\ Procyanidin B1 & 1.81 & 77.85 & 212.08 & 33.10 & 0.51 & 16.14 & 31.30 & 37.33 \\  & Procyanidin B2 & 0.22 & 90.60 & 224.26 & 32.37 & 1.42 & 32.20 & 60.16 & 37.16 \\  & p-counterar acid & 0.05 & 7.16 & 27.45 & 71.03 & 0.01 & 0.06 & 0.17 & 53.00 \\ Phenolic acid & Caffe acid & 0.04 & 1.46 & 5.58 & 72.98 & 0.02 & 0.56 & 1.97 & 61.30 \\  & Ferulic acid & 0.12 & 5.01 & 8.64 & 34.36 & - & - & - & - \\ Flavonoid & Myricetin & 0.01 & 14.98 & 62.09 & 96.12 & 0.06 & 4.92 & 18.84 & 86.01 \\  & Quercetin & 0.13 & 6.19 & 32.00 & 90.06 & 0.30 & 2.63 & 6.62 & 55.37 \\  & Hexanal & 16.67 & 984.70 & 2797.92 & 62.36 & - & - & - \\ Lipid oxidation product & 1-Linecolor glycerol & - & - & - & - & 0.01 & 0.19 & 0.62 & 65.84 \\  & 2-Hydroxyoleic acid (OHOA) & - & - & - & 2.37 & 7.18 & 10.87 & 27.08 \\ Alkaloid & Convicine & - & - & - & - & 2.31 & 16.67 & 28.42 & 27.90 \\ \hline \hline \end{tabular}  
* Oil, protein, and fatty acids are expressed as a percentage of dry weight (%), while the other compounds are expressed in ppm.  
\end{table} 
Table 2: Summary statistics for the adjusted phenotypic data of 245 faba bean (_Vicia faba_ L.) accessions. The table details the minimum (min), maximum (max), mean, and coefficient of variation in percentage (CV%) in 2021 and 2022.  
including CGN12310 (Canadian landrace), CGN13511 (Pakistani landrace), CGN15623 (Dutch variety), CGN15630 (Finnish variety), and CGN18933 (Israeli variety).