Applying Some Mathematical Models to Estimate Leaf Area of Christ’s-thorn Jujube trees (Ziziphus spina-christi L.) Based on Leaf Morphometric Measurements in the Koya District

Abstract

The Christ’s-thorn jujube (Ziziphus spina-christi L.) is an important agricultural, medicinal, and ecological plant. Understanding photosynthetic capability, biomass buildup, transpiration, and ecological modeling all depend on accurate estimates of leaf area. In this study, 610 mature leaves of Z. spina-christi were collected in Koya district, Iraqi Kurdistan Region, Erbil, and measured for leaf length (L), width (W), and area (LA) in October 2025. Leaf area was estimated using regression-based models, which were statistically validated using the Statistical Package for the Social Sciences software. Simple linear, multiple linear, and exponential regression models were developed to predict leaf area from their dimensions. Although simple linear regressions based on L or W individually were statistically significant (P < 0.001), they accounted for only 78–85% of the observed variation in leaf area (R2 = 0.783–0.849); greater predictive performance was achieved by models using the product of leaf dimensions (LW). Among all models evaluated, the simple linear regression model LA = 0.082 + 0.69 (LW) emerged as the most effective, providing the highest precision for its type (R2 = 0.972, mean square error = 0.1). The more complex multiple linear regression model, LA = 0.15 + 8.28 L2 + 0.41 W2 (R2 = 0.96), and the exponential model, LA = 0.89e0.31(L + W) (R2 = 0.94), also displayed high accuracy but with increased computational complexity. The model LA = a + b (LW) is suggested as the best method, taking into account both practical simplicity and predicted accuracy. It provides a dependable, effective, and non-destructive instrument for physiological and agronomic studies on Z. spina-christi.