Dynamics of discrete-time larch budmoth population models

The larch budmoth (LBM) population in the Swiss Alps is well known for its periodic outbreaks and regular oscillations over several centuries. The ecological mechanisms that drive these oscillations, however, have not been unambiguously identified, although a number of hypotheses have been proposed. In this article, we investigate several LBM resulting from these different ecological hypotheses. We first study a leaf quality-moth population model and then two moth–parasitoid models. Existence and stability of equilibria are investigated and sufficient conditions for which populations can persist are derived. We then provide conclusions based on our analysis.