Symbiotic Evolution of Rural Settlements and Traditional Agricultural Water Conservancy Facilities Based on the Lotka-Volterra Model

Agricultural water conservancy facilities serve as the foundation and lifeline for the development of sustainable agriculture in a nation. In response to the evolving natural environment and food security demands, ancient agricultural water conservancy facilities coexist with rural areas, establishing a harmonious and sustainable symbiotic coordination mechanism. This study constructs a theoretical framework for the symbiosis between rural areas and ancient agricultural water conservancy facilities based on symbiotic theory. The Lotka-Volterra model is employed to validate the symbiotic evolutionary relationship between rural areas and ancient agricultural water conservancy facilities and to explore the mechanistic patterns of their symbiotic evolution process. Additionally, numerical simulations are conducted using MATLAB software to investigate the optimal solutions for the symbiotic relationship model between rural areas and ancient agricultural water conservancy facilities. The research findings indicate that: (1) The symbiotic model between rural areas and ancient agricultural water conservancy facilities undergoes evolutionary stages, including commensalism, parasitism, competitive symbiosis, and asymmetric mutualism. (2) The evolutionary pattern of their symbiotic relationship is influenced by the symbiotic coefficients of their interactions. (3) The results demonstrate that symmetric mutualism represents the most stable and effective symbiotic model. Therefore, governments and relevant authorities should adopt appropriate measures to guide the evolution of rural areas and agricultural water conservancy facilities toward the symmetric mutualism model. This approach provides a scientific basis for the future development strategies of rural areas and agricultural water conservancy facilities.