Thus, for this test case we choose $\nu=1$. At both ends, all derivatives of $S(z(t))$ in $t$ vanish. Also notice the forward/backward symmetry $S(z(t_{H}-t)) = 1 - S(z(t))$ for $t_{L}
\leq t \leq t_{H}$ [@eriksson2012].

Population dispersal
--------------------

We set up the initial population density at $t=50$ kya as shown in the top left panel of Figure \[fig:outofafrica0\]. The integration units are scaled following Tab. \[tab:scalings\] such that $\lambda =
1.67\cdot10^{-3}$ ky$^{-1}$ and $c=208$ km$^2$/ky (consistent with those used in [@young1995]). The solver is then run using time frame $\mathcal K$ maps described above, down to 1 kya. The remaining plots (Figures \[fig:outofafrica1\],\[fig:outofafrica2\]) display the resulting population dispersal simulation on unsmoothed $\mathcal{K}$ maps, regularized by (\[eq:regularizer0\]). Using population parameters consistent with the literature, the gross features of the late (50-60 kya) out-of-Africa dispersal of [*Homo sapiens*]{} are reproduced [@forster2004], e.g. the colonization of Western Europe by $\sim 40$ kya and that of South America before 14 kya. Using the solver with the same initial conditions but on a smooth NPP map, like the one shown in right panel of Figure \[fig:siberiaCCrawvssmooth\], [*without*]{} the regularizer (\[eq:regularizer0\]), yields the same wavefront propagation speed.

Conclusions
===========

In this paper, we presented a novel 