The Moran–Ricker model with time delay: Managing population dynamics in species with non-overlapping generations

This study investigates a model of population dynamics for a regulated homogeneous population with non-overlapping generations. It assumes a reduction in resource availability due to consumption by the previous generation, implementing delayed density-dependent regulation. Additionally, an annual removal of a proportion of the population is introduced as a control measure. The proposed model was analyzed both analytically and numerically. It was demonstrated that when the population growth rate exceeds $e$, the model exhibits the Hydra effect: increased removal intensity paradoxically leads to population growth due to reduced intraspecific competition for resources. The system displays multistability, where identical demographic parameters can result in distinct dynamic regimes – stable equilibrium, periodic oscillations, or irregular fluctuations. While population removal expands the stability domain of the non-trivial equilibrium, variations in the removal rate under multistable conditions can trigger dynamic shifts by moving the population into the basin of attraction of an oscillatory regime. Using empirical data from the larch budmoth (Zeiraphera griseana), it was shown that annual removal reduces the oscillation period, while higher removal intensity decreases oscillation amplitude, leading to more frequent but smaller-scale population outbreaks. A significant reduction in amplitude occurs near the bifurcation threshold of the control parameter, where the invariant curve collapses, transitioning the system to stable dynamics. The model-based analysis explores population scenarios under varying control intensities for the larch budmoth, with results generalizable to species sharing similar demographic traits. These findings emphasize the importance of balancing removal strategies to avoid unintended regime shifts while stabilizing population dynamics.