Complex Dynamics of a Lotka–Volterra Food Chain Model with Allee Effect in Prey and Discrete Delay in Predation

Grasping how factors like the Allee effect, resource limits, and developmental delays interact is key to forecasting an ecosystem’s long-term persistence and stability. Here, we present and examine a prey-dependent, three-level food-chain model that embeds an Allee effect in the prey, a finite carrying capacity for resource limitation, and a discrete gestation delay in the top predator — capturing real-world phenomena such as survival thresholds at low prey densities, restricted environmental resources, and time lags in predator reproduction. Following nondimensionalization, we carry out a thorough analytical study, establishing positivity and boundedness of solutions, exploring both local and global stability, and performing Hopf and transcritical bifurcation analyses. When delays are included, we derive stability criteria that depend on the length of the gestation period and pinpoint critical delay values that trigger oscillatory behavior. Finally, numerical simulations paired with global sensitivity analysis corroborate our theoretical results. Together, these findings shed light on how the interplay among Allee effects, carrying capacity, and time delays can drive population dynamics toward stability, sustained oscillations, or collapse — insights that are vital for effective biodiversity management and conservation planning.