The acceleration of evolutionary spread by long-range dispersal

Abstract

The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also on the dispersal behavior of the species. Spreading at a constant speed is generally predicted when dispersal is sufficiently short-ranged. However, the case of long-range dispersal is unresolved: While it is clear that even rare long-range jumps can lead to a drastic speedup, it has been difficult to quantify the ensuing stochastic growth process. Yet such knowledge is indispensable to reveal general laws for the spread of modern human epidemics, which is greatly accelerated by aviation. We present a simple iterative scaling approximation supported by simulations and rigorous bounds that accurately predicts evolutionary spread for broad distributions of long distance dispersal. In contrast to the exponential laws predicted by deterministic "mean-field" approximations, we show that the asymptotic growth is either according to a power-law or a stretched exponential, depending on the tails of the dispersal kernel. More importantly, we provide a full time-dependent description of the convergence to the asymptotic behavior which can be anomalously slow and is needed even for long times. Our results also apply to spreading dynamics on networks with a spectrum of long-range links under certain conditions on the probabilities of long distance travel and are thus relevant for the spread of epidemics.

References in corpus (14)

• Understanding individual human mobility patterns
• The scaling laws of human travel
• Front propagation into unstable states
• Gene surfing
• Mixing structures in the Mediterranean Sea from Finite-Size Lyapunov Exponents
• Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach
• Parallel adaptation: One or many waves of advance of an advantageous allele?
• On the scaling of the chemical distance in long-range percolation models
• Truncation effects in superdiffusive front propagation with Lévy flights
• Population dynamics at high Reynolds number
• Superfast front propagation in reactive systems with anomalous diffusion
• Two-dimensional SIR epidemics with long range infection
• SIR epidemics with long range infection in one dimension
• When Knowing Early Matters: Gossip, Percolation and Nash Equilibria

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