Population Limits with Multiple Habitats and Mechanisms: I. Age-Independent Periodic Breeders

We provide generalizations of the conventional logistic population dynamics models suitable for periodic breeders, such as migratory birds, occupying varied habitats during the breeding cycle. These models require separate density dependencies for the birth and death rates, which may be habitat specific. Some analytical functional forms for the density dependencies are discussed where the population controlling mechanisms are each characterized by a distinct carrying capacity and saturation power. Multiple mechanisms might be operative simultaneously with the smallest carrying capacity usually dominating, but subject to influence from the others. We compare the dynamics and applicability for corresponding continuous differential and discrete difference population models. Generally, the differential models are stable, but exhibit repetitive seasonal variations for periodic breeders. The inherent delays in the discrete models may yield instabilities for large birth rates, as is known for single habitats, and may lead to significant discrepancies from the differential models for periodic breeders. The discrete models are also applicable to the life cycles of metamorphic and spawning species with non-overlapping generations. Threshold effects are also considered.