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2018 ; 115
(16
): E3645-E3654
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Fluctuations uncover a distinct class of traveling waves
#MMPMID29610340
Birzu G
; Hallatschek O
; Korolev KS
Proc Natl Acad Sci U S A
2018[Apr]; 115
(16
): E3645-E3654
PMID29610340
show ga
Epidemics, flame propagation, and cardiac rhythms are classic examples of
reaction-diffusion waves that describe a switch from one alternative state to
another. Only two types of waves are known: pulled, driven by the leading edge,
and pushed, driven by the bulk of the wave. Here, we report a distinct class of
semipushed waves for which both the bulk and the leading edge contribute to the
dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant
fluctuations similar to pulled waves. The transitions between pulled, semipushed,
and fully pushed waves occur at universal ratios of the wave velocity to the
Fisher velocity. We derive these results in the context of a species invading a
new habitat by examining front diffusion, rate of diversity loss, and
fluctuation-induced corrections to the expansion velocity. All three quantities
decrease as a power law of the population density with the same exponent. We
analytically calculate this exponent, taking into account the fluctuations in the
shape of the wave front. For fully pushed waves, the exponent is -1, consistent
with the central limit theorem. In semipushed waves, however, the fluctuations
average out much more slowly, and the exponent approaches 0 toward the transition
to pulled waves. As a result, a rapid loss of genetic diversity and large
fluctuations in the position of the front occur, even for populations with
cooperative growth and other forms of an Allee effect. The evolutionary outcome
of spatial spreading in such populations could therefore be less predictable than
previously thought.
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