This paper is an introductory review of the problem of front propagation into unstable states.
Our presentation is centered around the concept of the asymptotic linear spreading velocity …

Natural systems are undeniably subject to random fluctuations, arising from either
environmental variability or thermal effects. The consideration of those fluctuations supposes …

Propagating fronts are seen in varieties of nonequilibrium pattern forming systems in
Physics, Chemistry and Biology. In the last two decades, many researchers have contributed …

We propose a phenomenological description for the effect of a weak noise on the position of
a front described by the Fisher-Kolmogorov-Petrovsky-Piscounov equation or any other …

Ecological and evolutionary dynamics are intrinsically entwined. On short timescales,
ecological interactions determine the fate and impact of new mutants, while on longer …

Including the effect of thermal fluctuations in traditional computational fluid dynamics
requires developing numerical techniques for solving the stochastic partial differential …

In growing populations, the fate of mutations depends on their competitive ability against the
ancestor and their ability to colonize new territory. Here we present a theory that integrates …

Traveling fronts describe the transition between two alternative states in a great number of
physical and biological systems. Examples include the spread of beneficial mutations …

In this review, we provide a concise summary of several important mathematical results for
stochastic travelling waves generated by monostable and bistable reaction-diffusion …

The position of propagating population fronts fluctuates because of the discreteness of the
individuals and stochastic character of processes of birth, death, and migration. Here we …