Population growth and competition models with decay and competition consistent delay.

Area of Science:

• Mathematical Biology
• Population Dynamics
• Theoretical Ecology

Background:

• The logistic equation is a fundamental model for population growth.
• Previous models often simplified or omitted time delays and intraspecific competition.
• Understanding these factors is crucial for accurate ecological predictions.

Purpose of the Study:

• To derive and analyze a novel delayed logistic equation accounting for intraspecific competition.
• To investigate the global dynamics, stability, and extinction/survival thresholds of the model.
• To extend the model to a two-species competition system and explore evolutionary dynamics.

Main Methods:

• Derivation of an alternative expression for the delayed logistic equation.
• Global analysis using the theory of chain transitive sets and comparison theorems for delay differential equations.
• Analysis of a two-species competition model including local stability, bifurcation diagrams, and adaptive dynamics.

Main Results:

• The modified model shows no possibility of sustained population oscillations.
• A clear threshold determining population extinction versus survival was identified based on model parameters.
• Interspecific competition dynamics revealed evolutionary trends in reproductive delays.

Conclusions:

• The derived delayed logistic equation provides a more realistic framework for population dynamics.
• Intraspecific competition and time delays significantly influence population stability and evolutionary trajectories.
• The model offers insights into species coexistence and adaptation in competitive environments.