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Effect of Migration on Moran’s Evolutionary Dynamics

Gorgi, Melika | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56582 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Ejtehadi, Mohammad Reza; Kaveh, Kamran
  7. Abstract:
  8. Natural selection in structured populations is considered a crucial subject in evolutionary and population genetics. There is no explicit relationship between discrete-time stochastic models such as the Moran process and continuous-time models such as the Fisher-Kolmogorov equation. However, under specific conditions and within the limits of natural selection and weak selection, a connection can be found between these two models. To gain a better understanding of the specific relationship between these two models, we obtain partial differential equations for the spatiotemporal dynamics of natural selection by extending the birthdeath and death-birth processes of the Moran process to a continuous environment. The growth rate in the system consists of two components: the birth rate, s, and the death rate, q. In this study, we have shown that the wave speed for the birth-death, death-birth, and Fisher-Kolmogorov dynamics is significantly different. When q = 0, the wave speed in the deathbirth process is greater than that of the Fisher-Kolmogorov process, and the Fisher-Kolmogorov wave has a higher speed than the birth-death process. To further investigate the dynamics of the system, weighted one-dimensional and two-dimensional graphs are used, demonstrating the applicability of the coherence theorem to continuous environments. Here, the coherence condition is equivalent to the stability of the internal flow in each graph vertex. This coherence creates a symmetry similar to the symmetry of numerical potential and vector potential in electromagnetism. In this context, we have derived a general equation for the average growth rate in a coherent environment
  9. Keywords:
  10. Natural Selection ; Migration ; Mobility ; Evolutionary Graphs Theory ; Isothermal ; Birth-Death Process ; Death-Birth Process

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