The Mystery Hidden in the Sex Ratio

Abstract

In order to unravel the secrets hidden within the gender ratio of lampreys, we proposed several models to simulate the cascade of effects on ecosystems. Firstly, we established a Logistic model-based food chain model. We found that as the gender ratio increases, the predator population rises while environmental resource levels decline, and the lamprey population initially increases before decreasing. Simultaneously, habitat utilization rate was considered as an indicator affecting the ecosystem. Through modeling, we discovered a positive correlation between habitat utilization rate and the gender ratio of lampreys. Secondly, we developed a Game Evolution Model based on the Moran process. We defined a payoff matrix to simulate competition between male and female lampreys. We assumed that gender ratio and environmental resource levels influence reproductive success, finding that an intermediate gender ratio results in higher reproductive success, considered an advantage. When the gender ratio approaches 0 or 1, reproductive success decreases, considered a disadvantage. We also defined a function for resource utilization rate concerning gender ratio, concluding that higher gender ratios lead to higher resource utilization rates.Thirdly, we defined an ecosystem evolution model based on the Logistic model. Three interaction modes between organisms and lampreys were established: competition, independent coexistence, and parasitism. We discovered that when the gender ratio approaches 0.64, the stability of the ecosystem is highest.Through entropy weight method, we determined the weights of each factor, and observed the stability of the comprehensive index at different gender ratios, finding that a gender ratio closer to 0.64 corresponds to a more stable ecosystem. Finally, utilizing the previously established game evolution model, we introduced parasites. In this model, by reducing the punishment for parasites choosing betrayal and increasing the probability of parasites choosing betrayal. Ultimately, we found that deviating from a gender ratio of 0.64 provides an advantage for parasites.