Fig. 5

Hierarchical clustering heatmap illustrating the interrelationships between nitrogen-potassium fertilization treatment combinations (N1K1, N1K2, N1K3, N2K1, N2K2, N2K3, N3K1, N3K2, and N3K3) and yield and quality traits across five sugar beet cultivars (C1: Indira, C2: Carma, C3: Mallak, C4: Melodia, and C5: Shantala). The heatmap depicts the clustering patterns of the treatment combinations based on their associations with traits such as root yield (RY), biological yield (BY), total soluble solids (TSS), sugar yield (SY), sugar yield efficiency (SYE), SC (S), alkaline coefficient (AC), purity, sugar loss to molasses (SLM), and recoverable sugar yield (RSY). The color scale represents the strength of the associations, with red indicating positive relationships and blue representing negative relationships. The dendrogram on the left side illustrates the hierarchical clustering of the treatment combinations based on their similarity in trait associations across cultivars.