Single-class orbits in nonlinear Leslie matrix models for semelparous populations

Area of Science:

• Population Dynamics
• Mathematical Biology
• Ecology

Background:

• Leslie matrix models are crucial for understanding population dynamics.
• Semelparous populations reproduce once and then die, presenting unique demographic challenges.
• The stability of population states, particularly single-class states, is key to predicting population persistence.

Purpose of the Study:

• To investigate the dynamics of a general nonlinear Leslie matrix model for semelparous populations.
• To determine the conditions under which the single-class state is attractive or repelling.
• To explore the relationship between competition (inter- and intra-class) and population state stability.

Main Methods:

• Development of a general nonlinear Leslie matrix model.
• Analysis of the attractivity of the single-class state.
• Numerical simulations to investigate population dynamics under varying competition levels.

Main Results:

• The single-class state is attractive when inter-class competition is severe.
• The single-class state is repelling when intra-class competition is severe.
• Numerical results indicate that not all cohorts necessarily coexist, even when the single-class state is repelling.

Conclusions:

• Competition structure significantly influences the stability of population states in semelparous populations.
• Severe inter-class competition can lead to simplified population structures (single-class states).
• Severe intra-class competition can destabilize single-class states, potentially leading to complex dynamics or extinction.