Dynamic assessment of the ecological value of cultivated land based on the Gompertz curve model: A case study of Lezhi County, China

Abstract

With the continuous advancement of ecological compensation mechanisms, there is an urgent need to refine the dynamic evaluation of the ecological value of cultivated land (EVCL). This study constructs a dynamic assessment model for the EVCL based on the Gompertz curve, selecting Lezhi County in Sichuan Province, China, as the study area. The impact of the evolution of ecological compensation policies on the EVCL is examined. Using the functional value method, the study quantifies four key ecosystem services: agricultural product supply, water conservation, carbon sequestration and oxygen release, and soil and water conservation. It estimates that the ecological value per hectare of cultivated land reached CNY 704,250 in 2022, expressed in constant 1990 prices using the official GDP deflator published by the National Bureau of Statistics of China. A Gompertz curve linear equation was developed through logarithmic linearization, and parameter estimation was supported by the GDP growth rate as a proxy variable. This approach ensured statistical consistency and avoided overfitting. The model was compared with the traditional Pearl curve using quantitative indicators such as the coefficient of determination (R²) and root mean square error (RMSE). These measures highlight the superior correction capacity and fitting stability of the Gompertz model. To ensure temporal consistency, all monetary values were harmonized by converting nominal series into constant 1990 prices before integration with historical data (1979–2022) and GM(1,1) forecasts up to 2052. This integration provided a coherent time series for calculating development stage coefficients and projecting EVCL. The results indicate that the ecological value follows an asymmetric S-shaped growth trajectory as development stages advance, aligning with the gradual evolution of ecological compensation policies and increasing institutional maturity. By linking quantitative model validation with policy evolution, the study not only estimates the EVCL from 1979 to 2052 but also provides a methodological reference for evaluating ecological compensation policies across regions.