The wave-of-advance model was introduced to describe the spread of advantageous genes in a population. It can be adapted to model the uptake of any advantageous technology through a population, such as the arrival of neolithic farmers in Europe, the domestication of the horse, and the development of the wheel, iron tools, political organization, or advanced weaponry. Any trait that preexists alongside the advantageous one could be carried along with it, such as genetics or language, regardless of any intrinsic superiority. Decoupling of the advantageous trait from other ''hitchhiking'' traits depends on its adoption by the preexisting population. Here, we adopt a similar wave-of-advance model based on food production on a heterogeneous landscape with multiple populations. Two key results arise from geographic inhomogeneity: the ''subsistence boundary,'' land so poor that the wave of advance is halted, and the temporary ''diffusion boundary'' where the wave cannot move into poorer areas until its gradient becomes sufficiently large. At diffusion boundaries, farming technology may pass to indigenous people already in those poorer lands, allowing their population to grow and resist encroachment by farmers. Ultimately, this adoption of technology leads to the halt in spread of the hitchhiking trait and establishment of a permanent ''cultural boundary'' between distinct cultures with equivalent technology.farming ͉ neolithic ͉ population I n a seminal work, Ammerman and Cavalli-Sforza (1) analyzed the spread of farming technology through Europe in terms of a diffusive flow or displacement of population that they termed a demic flow. Earlier work (2) had considered ''cultural'' diffusion where technology was passed without significant movement of population. A quantitative model (3) of this ''wave-ofadvance'' theory made use of the Fisher equation (4) with a wave speed of Ϸ1 km per year.Demic flow (5, 6) raises the possibility that cultural, genetic (7,8), and linguistic traits (6, 9) with no intrinsic advantage may ''hitchhike,'' i.e., spread with the advancing farmers. The IndoEuropean languages and the genetic distribution of European people (10) have been advanced as prime examples. Other processes, such as contact-induced language evolution (6) and other advancing technologies, such as horse husbandry, the wheel, and iron, are also claimed to be examples. A quantitative model of cultural hitchhiking is therefore of interest for determining how much common understanding of the general phenomenon can be gained by such a simple mechanism.Hitchhiking is well studied in the genetic literature (11, 12), and loss of genetic diversity through culture is known in whales (13); however, little has been done with continuous geography. Here, we incorporate inhomogeneous geography and the competing mechanisms of demic and cultural diffusion into a model (14) that can give either wave of advance or diffusion and growth scenarios.Although a deterministic model ignores crucial rare events, it should be regarded as a historical nu...