  Spatially resolved genetic data is increasingly used to reconstruct the
migrational history of species. To assist such inference, we study, by means of
simulations and analytical methods, the dynamics of neutral gene frequencies in
a population undergoing a continual range expansion in one dimension. During
such a colonization period, lineages can fix at the wave front by means of a
``surfing'' mechanism [Edmonds C.A., Lillie A.S. & Cavalli-Sforza L.L. (2004)
Proc Natl Acad Sci USA 101: 975-979]. We quantify this phenomenon in terms of
(i) the spatial distribution of lineages that reach fixation and, closely
related, (ii) the continual loss of genetic diversity (heterozygosity) at the
wave front, characterizing the approach to fixation. Our simulations show that
an effective population size can be assigned to the wave that controls the
(observable) gradient in heterozygosity left behind the colonization process.
This effective population size is markedly higher in pushed waves than in
pulled waves, and increases only sub-linearly with deme size. To explain these
and other findings, we develop a versatile analytical approach, based on the
physics of reaction-diffusion systems, that yields simple predictions for any
deterministic population dynamics.
