I’ve talked here before how history can be seen as a sequence of periods of steady exponential growth, separated by a few sudden jumps to new modes.  A new paper in Science offers a nice concrete model of how a new mode can be triggered by an old mode reaching a particular level.   In this case the new mode is humans using culture to share and improve complex behavior like art and tool construction.   The model says the new mode was not possible until humans were dense enough so that skill improvements from groups copying each other could overcome the tendency of a lone group’s skills to devolve.  From Science Daily:

“Our paper proposes a new model for why modern human behaviour started at different times in different regions of the world, why it disappeared in some places before coming back, and why in all cases it occurred more than 100,000 years after modern humans first appeared.  By modern human behaviour, we mean a radical jump in technological and cultural complexity, which makes our species unique. This includes symbolic behavior, such as abstract and realistic art, and body decoration using threaded shell beads, ochre or tattoo kits; musical instruments; bone, antler and ivory artefacts; stone blades; and more sophisticated hunting and trapping technology, like bows, boomerangs and nets.” …

[They] found that complex skills learnt across generations can only be maintained when there is a critical level of interaction between people. Using computer simulations of social learning, they showed that high and low-skilled groups could coexist over long periods of time and that the degree of skill they maintained depended on local population density or the degree of migration between them. Using genetic estimates of population size in the past, the team went on to show that density was similar in sub-Saharan Africa, Europe and the Middle-East when modern behaviour first appeared in each of these regions.

From the Science paper:

The origins of modern human behavior are marked by increased symbolic and technological complexity in the archaeological record. In western Eurasia this transition, the Upper Paleolithic, occurred about 45,000 years ago, but many of its features appear transiently in southern Africa about 45,000 years earlier. We show that demography is a major determinant in the maintenance of cultural complexity and that variation in regional subpopulation density and/or migratory activity results in spatial structuring of cultural skill accumulation. Genetic estimates of regional population size over time show that densities in early Upper Paleolithic Europe were similar to those in sub-Saharan Africa when modern behavior first appeared. Demographic factors can thus explain geographic variation in the timing of the first appearance of modern behavior without invoking increased cognitive capacity.

While this transition clearly let humans more quickly grow their tech abilities, it is not clear that this translated immediately into an ability to more quickly grow the number of humans.  That didn’t clearly happen until the farming revolution of about 10,000 years ago.   So did the efficient exchange of farming innovations require a different higher density threshold, or did farming require a certain minimum accumulation of tech abillities, or what?