Gene Expression

Waves of stationary shape:

Over at Scienceblogs, people are talking about waves. Of course, everyone thinks that waves are in the domain of physics, and people always forget about one of my favorite subjects: waves of advance. Way back in the day, RA Fisher wondered what might happen if genes had to spread not just locally but across space, and he published his findings in a landmark article called The Wave of Advance of Advantageous Genes. This paper was not just important for its contributions to population genetics, but because of fundamental contributions to applied mathematics. As far as I can tell, Fisher and the great mathematician Kolmogorov published similar findings on this same subject in the same year. To that end, these kinds of waves of advance are often referred to as “Fisherian” waves.

What was Fisher’s model, what did he find, and how has it been extended?


  1. #1 Bob O'H
    May 24, 2009

    It’s now known as the KPP-Fisher equation.

    The dynamics depend on the shape of the dispersal distribution: it has to be exponentially bounded (Denis Mollison proved this in the 80s. It’s an amazing result). Some of the UEA guy followed Nick Barton’s work to see what happens when the distribution isn’t exponentially bounded: I can’t dig out the references now, but check Kamal Ibrahim and Richard Nichols.

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