Modeling and Solving Population Survival of Species with Variable Sex Ratios Based on An Improved Lotka-Volterra Model

Abstract The survival of species and changes in sex ratios have a significant impact on population dynamics. This paper proposes a population survival analysis method based on an improved Lotka-Volterra model, aiming to explore how changes in sex ratios affect population viability. First, the model incorporates sex ratio as a dynamic variable and establishes an interaction model between predators and prey. Second, by introducing environmental factors and interspecies competition, the analysis examines the effects of these factors on reproductive rates and population stability. Then, the stability of the model is verified using Jacobi determinants, enhancing the model’s reliability. Finally, the results indicate that adaptive sex ratios can improve the population’s resilience to environmental fluctuations, providing theoretical support for ecological management.