Table 1.
Variables in left column are scaled versions of those in right column.
Fig 1.
Left: Godunov vs. pdepe at t = 2. Right: same at time t = 20. Only x > 0 data are shown. The time step h = 1/12 and Δx = 1/5. Initial data: u(x) = 1 if |x| < 1, zero otherwise.
Fig 2.
Time frame interpolation methods.
The interpolation maps at different times: sigmoids Eq (12) for ν = 1/2 and ν = 1, straight line, and Eriksson’s f(f(f(t))) model [1]. Time scaling is s = (t − tL)/(tH − tL).
Table 2.
Predicted arrival times for 10 sites [29–31].
The furthest apart American sites†, Meadowcroft and Fell’s Cave, were used for optimization. Error estimates give approximate sensitivities to the coarse r steps in the left-hand plot of Fig 3. Entry NA means the half-filling wave did not arrive. All values are in kilo—years before present.
Fig 3.
Diffusion and growth parameters optimization.
Left: the RMS value of simulation compared to earliest known populations of Meadowcroft and Fell’s Cave. The approximate optimal value of D is 190km2/yr. The minimum RMS value is shallow in D but sensitive to r = λ, showing we are probing both the traveling wave and diffusion tail. Right: a detailed minr(RMS) optimization in D and in r at D = 190: λmin = rmin = 2.04 × 10−3 yr−1.
Fig 4.
Color-coding and labeling for all of out-of-Africa dispersal plots.
Dark blue shows water, with . Growth rate is λ = 2.04 ⋅ 10−3 y−1, and diffusion coefficient D = 190km2/y. The initial distribution at Ts = 45 kya is denoted by a small dark red spot in Eritrea, west of the Bab al Mandab straight: a σ = 3 pixel Gaussian with peak u = local
, color scale 2.1.
Fig 5.
log(1 + 10u) plot for out-of-Africa dispersal population distribution at t = 39 kya.
Fig 6.
log(1 + 10u) plot for out-of-Africa dispersal population distribution at t = 31 kya.
Fig 7.
log(1 + 10u) plot for out-of-Africa dispersal population distribution at t = 20 kya.
Notice that the bridge across the Bering Straight is not yet closed.
Fig 8.
log(1 + 10u) plot for out-of-Africa dispersal population distribution at t = 10 kya.
The bridge across the Bering Straight is now closed.
Fig 9.
log(1 + 10u) plot for out-of-Africa dispersal population distribution at t = 1 kya.
Fig 10.
Land is set to 1 (light blue) and water 0 (dark blue) on a low-resolution Nx = 100, Ny = 50 grid. Row 26 has 4 habitable segments (cyan), column 87 has 5 segments (yellow).