Leaf-Shape Variation Affects the Validity of the Square-Law Relationship Between Leaf Area and Leaf Length: Evidence from 12 Malus Cultivars

The Montgomery equation (ME), A = kLW, provides a simple and non-destructive approach for estimating leaf area (A) from leaf length (L) and width (W), whereas the square-law equation (SLE) assumes that A∝L2. This study evaluated and compared the goodness of fit of the ME and SLE across 12 Malus cultivars and examined whether variation in leaf shape was associated with SLE performance. A total of 3679 leaves were analyzed, and the coefficient of variation in the width-to-length ratio was used to quantify within-cultivar leaf-shape variation. The ME provided a good fit for all 12 cultivars, with root-mean-square error (RMSE) values not exceeding 0.0285. For the pooled dataset, the estimated Montgomery parameter was 0.6641, with a 95% confidence interval of 0.6632–0.6650, and fell within the theoretical range of 1/2 to π/4. The ME consistently showed lower RMSE than the SLE, with the relative reduction in RMSE exceeding 49% for all cultivars. In addition, variation in the ratio of width to length was strongly positively correlated with the RMSE of the SLE. These findings suggest that variation in leaf shape is closely associated with the goodness of fit of the SLE and support the use of both leaf dimensions for more reliable leaf-area estimation. This study provides a practical basis for rapid and non-destructive estimation of leaf area in Malus.