Demographic variation and survival in discrete population models

Area of Science:

• Mathematical Biology
• Dynamical Systems
• Population Ecology

Background:

• Discrete population models are crucial for understanding population dynamics.
• Analyzing long-term persistence and extinction is fundamental in ecological studies.
• Nonlinear difference equations exhibit complex behaviors relevant to population survival.

Purpose of the Study:

• To explore persistence and extinction attributes of a discrete population model.
• To classify conditions for population extinction at specific time points (N).
• To analyze population survival on finite and infinite time horizons.

Main Methods:

• Analysis of a first-order autonomous nonlinear difference equation.
• Investigation of population trajectories over time.
• Decomposition of initial population sizes based on persistence and extinction outcomes.

Main Results:

• A classification of extinction times for population trajectories was established.
• Dynamic complexity inherent in difference equations was observed in survival analyses.
• Initial population sizes were decomposed into persistent and extinction intervals.

Conclusions:

• The study provides a detailed understanding of population model extinction and persistence.
• The findings highlight the intricate relationship between initial conditions and long-term population viability.
• The research contributes to the analysis of complex dynamical systems in ecological contexts.