Loading...

Effect of Time Fluctuation in Migration Probability in a Simple Evolution Model

Masoumi, Mohammad Amin | 2025

0 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58338 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Ejtehadi, Mohammad Reza; Kaveh, Kamran
  7. Abstract:
  8. Understanding the complex dynamics of species populations in response to environmental and migratory pressures is essential for ecological and evolutionary studies. This study employs the Moran model to precisely analyze the population dynamics of mutant and native species on two interconnected islands under periodic migration. We examine three distinct migration scenarios: symmetric periodic migration, where migration probabilities between islands are equal; in-phase oscillatory migration with varying amplitudes, allowing for independent migration rates; and out-of-phase oscillatory migration, introducing phase-shifted migration patterns. Each scenario integrates unique migration probabilities and mutant reproduction rates, while the death rates and native reproduction rates remain uniform. Utilizing the Moran birth-death process, we derive the master and mean equations to track the temporal evolution of mutant populations and quantify phase differences between islands. Our findings reveal that the period and amplitude of migration profoundly shape population dynamics. In symmetric migration, phase differences peak at moderate migration amplitudes and increase with longer periods. In-phase and out-of-phase oscillatory migrations exhibit nonlinear population trends driven by specific migration patterns and reproductive rate disparities, leading to either population stabilization or decline. Notably, out-of-phase migration reduces phase differences by allowing extended residence on islands with higher growth, resulting in more synchronized population behaviors across islands. These results highlight the critical interaction between migration dynamics, period, and intrinsic growth rates, offering valuable insights into evolutionary adaptations and population stability in fluctuating environment
  9. Keywords:
  10. Population Dynamics ; Evolutionary Graphs Theory ; Phase Difference Method ; Moran Model ; Periodic Migration

 Digital Object List

 Bookmark

...see more