Why aphids are not pests in cacao? An approach based on a predator-prey model with aging
Abstract
We studied a mean-field predator-prey model with aging to simulate the interaction between aphids (Toxoptera aurantii) and syrphid larvae in cacao farms in Ilheus, Bahia. Based on the classical predator-prey model, we propose a system of differential equations with three rate equations. Unlike the original Lotka-Volterra model, our model includes two aphid population classes: juveniles (non-breeding) and adult females (asexually breeding). We obtained steady-state solutions for juvenile and adult populations by analyzing the stability of the fixed points as a function of model parameters. The results show that the absorbing state (zero prey population) is always possible, but not consistently stable. A nonzero stationary solution is achievable with appropriate parameter values. Using phase diagrams, we analyzed the stationary solution, providing a comprehensive understanding of the dynamics involved. Simulations on complete graphs yielded results closely matching the differential equations. We also performed simulations on random networks to highlight the influence of network topology on system behavior. Our findings highlight the critical role of life-stage structure, predation, and spatial variation in stabilizing predator-prey systems. This emphasizes the importance of network effects in population dynamics and refines the framework for biological pest control in agriculture. Ultimately, our research contributes to sustainable agricultural practices.
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