Dispersal-induced growth in time-periodic two-patch environments with asymmetric migration

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Population persistence is crucial for ecosystem stability.
• Dispersal-induced growth (DIG) is a phenomenon where migration prevents extinction.
• Understanding DIG requires analyzing population dynamics under varying spatial and temporal conditions.

Purpose of the Study:

• To investigate the mechanisms driving dispersal-induced growth (DIG).
• To explore how asymmetric migration and environmental oscillations influence population persistence.
• To identify key factors enabling population survival through migration.

Main Methods:

• Utilized a time-periodic two-patch mathematical model.
• Incorporated asymmetric migration matrices to simulate population movement.
• Analyzed the principal eigenvalue's qualitative properties (monotonicity, asymptotic behaviors, level set topology) concerning migration rate and frequency.

Main Results:

• Characterized the critical factors influencing DIG under environmental oscillations.
• Demonstrated that specific migration rates can induce population persistence where isolation or even mixing leads to extinction.
• Revealed the complex interplay between spatial connectivity and temporal environmental variation.

Conclusions:

• The study provides new insights into population persistence mechanisms.
• Dispersal-induced growth is a significant factor in population dynamics under fluctuating environments.
• Mathematical modeling is essential for understanding complex ecological phenomena like DIG.