Section \[sec:fisherkpp\] and shown in Figure \[fig:mapsegmentation\]. However, the regularization scheme (Section \[sec:noisyNPPmaps\]) should be used with caution. A $u=0$ boundary condition region is not the same as one with low $\mathcal{K}$, which can pass a tiny population into a subequent region where it may well flourish. For example, historically known falling sea levels opened passages across Bab al Mandeb to open South Asia for human dispersal [@siddall2003], and the retreat of the North American ice sheet opened a passage on the Bering strait around 12 kya (kilo-years ago).

World-wide hominin dispersal {#sec:dispersal}
============================

We now turn to a sample application of the methods presented above: the world-wide dispersal of *Homo sapiens* out of Africa.

Capacity maps
-------------

Our construction of a time-dependent $\mathcal{K}$ uses Net Primary Productivity (NPP) as a proxy [@eriksson2012]. The Miami model [@grieser2006] was originally formulated in 1972 to estimate NPP (in grams (of carbon) in dry organic matter/m$^2$/day) from annual temperature and rainfall [@lieth1975]. In order to compute our NPP maps, we obtained the temperature and precipitation data from simulations by the [bridge]{} program [@bridgeproj] organized at the University of Bristol [@bigelow2003; @harrison2001; @pickett2004; @prentice2000]. The simulation data that we used were computed on a 