Attraction to equilibria in discrete population models with delayed feedbacks: stage-structure versus age-structure

Area of Science:

• Population Dynamics
• Mathematical Biology
• Ecology

Background:

• Biological populations commonly exhibit time delays and distinct life stages.
• Understanding these features is crucial for accurate population modeling and ecological predictions.

Purpose of the Study:

• To investigate the influence of time delays and stage structure on population dynamics using simple models.
• To differentiate population dynamics based on when intraspecific competition occurs relative to reproduction.
• To analyze the role of adult recruitment patterns in population stability.

Main Methods:

• Development and analysis of simple mathematical models for biological populations.
• Comparison of population dynamics under different timing scenarios for intraspecific competition.
• Investigation of the impact of adult recruitment shapes on population stability.
• Derivation of mathematical criteria for global attraction in discrete, non-monotone systems.

Main Results:

• Time delays, particularly when intraspecific competition occurs outside the reproduction period, can lead to long-term population oscillations.
• The pattern of adult recruitment significantly affects population dynamics; contest-type competition does not typically generate long-term oscillations.
• Two general criteria for global attraction in discrete, non-monotone systems were established.

Conclusions:

• The timing of intraspecific competition relative to reproduction is a critical factor in generating population oscillations.
• Stage structure, specifically the nature of adult recruitment, plays a key role in population stability.
• The study provides novel mathematical criteria for analyzing the stability of discrete dynamical systems.