Although widely used in the analysis of spatial movement, the Fisher equation incorporates some biologically and anthropologically unrealistic assumptions (19), perhaps most importantly, that individual dispersal begins at birth, and so dispersal is continuous through life.
This measure, the mean squared displacement of an individual, is then adjusted by random dispersal in two dimensions, and generation time .
For the pre-Clovis origin model, we centered the colonizing wave on Meadowcroft Rockshelter (11) in Pennsylvania, and Cactus Hill (12) in Virginia, two of the earliest, and most prominent pre-Clovis candidates in North America.
To model the wave of advance, we follow procedures outlined by Fort and colleagues (13–18) in their recent studies of other human prehistoric expansions.
A third hypothesis, which has been raised recently is that the initial colonists could have rapidly skirted the western coast of North America and established their first substantial occupations in South America (4).
In this hypothesis, colonists would then have moved north through the Isthmus of Panama colonizing North America from the south.
They show the velocity of the time-delayed traveling wave is then = 0), Eq. 3 with ethnographic data on maximum population growth rates γ, mean generation times is ≈20 years, and maximum annual population growth rates γ is ≈0.04 (20).