[Modification and its application of generalized Schumacher model]

Area of Science:

• Ecology
• Mathematical Biology
• Forestry

Context:

• Accurate modeling of plant growth is crucial for conservation and understanding population dynamics.
• Existing growth equations, such as the Schumacher and Logistic models, have limitations in self-adaptability and practicality.
• Analyzing the growth patterns of endangered species like Tsuga longibracteata and Platycladus orientalis requires robust mathematical frameworks.

Purpose:

• To propose a modified Schumacher growth equation incorporating Gompertz function, generalized Schumacher equation, and Schumacher equation.
• To analyze the mathematical characteristics and adaptability of the proposed modified Schumacher equation.
• To validate the efficacy of the modified Schumacher equation using genetic algorithms for fitting growth data of endangered plants.

Summary:

• A modified Schumacher growth equation was developed by integrating the Gompertz function and generalized Schumacher equation.
• The modified equation demonstrated superior self-adaptability and practicality compared to traditional models.
• Genetic algorithms were employed to fit the growth data of Tsuga longibracteata and Platycladus orientalis, confirming the modified equation's effectiveness.

Impact:

• The modified Schumacher equation significantly outperformed the original Schumacher equation, generalized Schumacher equation, Logistic model, and Li's self-adaptive model.
• This enhanced model provides a more accurate tool for the dynamics simulation of tree growth.
• The findings contribute to a better understanding of population growth dynamics, particularly for endangered plant species.