When does population collapse happen suddenly versus gradually?

Population models often assume birth and death scale smoothly with density, but real species face Allee effects: they struggle when too sparse. This work studies a map combining logistic growth with tunable Allee effects, finding that at a specific parameter combination (the tricritical point), the system exhibits unusual symmetry-breaking behavior. The model connects population dynamics to physics concepts like phase transitions and chaos suppression, with potential applications to conservation biology.