A mathematical model to estimate seedling vigor index (SVI) of sunflower (Helianthus annuus L.) seeds in soils contaminated with heavy metals was developed. This model was used to quantitatively describe the complex effects of heavy metal concentrations in soils (C_s) on seed germination and seedling growth. Negative linear regressions between relative seed germination percentage (GP), root length (L_r), and shoot length (L_s) versus log C_s varied as a function of soil properties and type and concentration of heavy metals. With an increase in the heavy metal concentration in soils, the predicted SVI values decreased and reasonably described the experimental SVI values within an 80% prediction band. This demonstrates that SVI values can be predicted, a priori, using SVI-soil models. Based on the sensitivity analysis, root elongation was more significantly affected by the external environment than shoot elongation. Consequently, the SVI-soil model developed in this study can explain heavy metal phytotoxicity to sunflower in complex soil systems. Further research using a diverse range of hyperaccumulator plants and soils is required to render SVI-soil model more available for complex systems in predictions of heavy metal phytotoxicity and hyperaccumulating behaviors of hyperaccumulator plants in various soil systems.

建立了估算重金属污染土壤中向日葵种子幼苗活力指数的数学模型。该模型用于定量描述土壤中重金属浓度（C _s）对种子发芽和幼苗生长的复杂影响。相对种子发芽率（GP），根长（L _r）和苗长（L _s）与log C _s之间的负线性回归随土壤特性，重金属的类型和浓度而变化。随着土壤中重金属浓度的增加，预测的SVI值降低，并在80％的预测范围内合理地描述了实验SVI值。这表明可以先验地预测SVI值，使用SVI-soil模型。根据敏感性分析，根部伸长受外部环境的影响比枝条伸长的影响更大。因此，在这项研究中开发的SVI-土壤模型可以解释重金属对复杂土壤系统中向日葵的植物毒性。为了使SVI-土壤模型更适用于复杂系统，需要对各种不同类型的超蓄积植物和土壤进行进一步研究，以预测重金属植物毒性和各种土壤系统中超蓄积植物的超蓄积行为。