The Acceleration of Evolutionary Spread by Long-Range Dispersal

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A lattice contact-process model with power-law dispersal kernel (tail ~ r^{-μ-d}) and stochastic birth-death rules shows three concrete growth regimes: when μ<d log-diameter grows as a stretched exponential, for d<μ<d+1 radius follows a superlinear power law, and for μ>d+2 growth is linear like a Fisher wave. A self-consistent saddle-point recurrence linking l(t) to l(t/2) predicts the scalings and matches simulations (runs up to ~10^7 sites, stopping at ~70% occupancy) and explains very slow crossovers.

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" chapters (11)

1. 0:00Spatial models in evolution
2. 1:50Processes of biological spread
3. 4:26Long-range dispersal dynamics
4. 8:14Simulating growth regimes
5. 11:52Historical models and noise
6. 15:26Mathematical frameworks
7. 19:05Simulation and growth analysis
8. 22:34Theoretical derivation
9. 30:28Asymptotic regimes and theory
10. 36:10Validating the dynamic model
11. 40:07Future directions and queries