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Area of Science:

  • Evolutionary Biology
  • Population Dynamics
  • Mathematical Modeling

Background:

  • Adaptation relies on the spread of novel traits.
  • Dispersal behavior significantly influences spread dynamics, especially with long-range jumps.
  • Predicting evolutionary spread with long-range dispersal remains a challenge.

Purpose of the Study:

  • To develop a predictive model for evolutionary spread considering long-range dispersal.
  • To quantify the impact of dispersal kernel tails on spread dynamics.
  • To describe the time-dependent convergence to asymptotic spread behavior.

Main Methods:

  • Iterative scaling approximation.
  • Computer simulations.
  • Rigorous mathematical bounds.

Main Results:

  • Evolutionary spread is determined by a trade-off between frequency and effectiveness of long-distance jumps.
  • Asymptotic spatial growth follows power laws or stretched exponentials, depending on dispersal kernel tails.
  • Anomalously slow, time-dependent convergence to asymptotic behavior is described.

Conclusions:

  • The developed approximation accurately predicts evolutionary spread with long-range dispersal.
  • Findings contrast with deterministic mean-field predictions, offering a more nuanced understanding.
  • Results are applicable to epidemic spread on networks with long-range connections.