If everyone in a group traded resources with every other member of the community, I hypothesize that the number of movements of resources (and the total distance traveled in a given period of time) would be proportional to the square of the population of the group. As the population increased, the average attainable speed would need to keep pace (its value proportional to the square of the population). If the speed was unable to keep pace, the number of transactions would be limited; perhaps to the point of affecting the size of the population itself by reducing the amount of survival related resources available to each individual.
Two pieces of evidence seem to support this hypothesis. The number of trips from the National Household Travel Survey’s Summary of Travel Trends is linearly correlated with the square of the number of travelers in the United States, and more so than just the number of travelers alone. Projections of travel speed for the world’s population since 0 A.D. appear reasonable; beginning at one mile per hour, by the 1960s aircraft speeds of 200-plus miles per hour would have been attained.
To continue the expected trend in speed, resources would need to be transported at more than 900 miles per hour into supersonic speeds during the next decade. The unlikelihood of this happening given the record of non-military the supersonic aircraft suggests that the world may be near or at its maximum speed of resource acquisition, meaning that the population will be forced to stop growing exponentially.