Starvation-recovery dynamics: insights via a nutritional state-structured model

This paper presents a nutritional state-structured model (NSM) to explore the dynamics of starvation and recovery in consumer-resource systems, focusing on full consumers ( $F$), hungry consumers ( $H$), and resources ( $R$). The model employs a system of differential equations to capture ecological processes such as reproduction, starvation, and resource regeneration. Through bifurcation analysis, we identified critical thresholds, notably the starvation rate ( $\sigma$) relative to the reproduction rate ( $\lambda$), that dictate system stability, transitioning between extinction and coexistence equilibria. Parameter sensitive and numerical simulations revealed how parameter variations influence population persistence and resource sustainability, with $\sigma >\lambda$ promoting balanced ecosystems and $\lambda >\sigma$ leading to potential overexploitation. The analogue of the basic reproduction number ( ${\mathcal{R}}_{\mathrm{e}}$) was derived using the next-generation matrix method, providing insights into the invasion dynamics and stability conditions of the system. This framework serves as a robust tool for analyzing eco-evolutionary interactions and assessing population persistence under resource-limited conditions. Finally, we demonstrated how higher fat reserves enhance competitive advantage, thereby driving the evolutionary trend toward larger body sizes as predicted by Cope's rule.