This phenomenon is explained by the pattern of colonization of the United States. Sparsely populated interior of the country allowed ample room to accommodate all the "excess" people, counteracting mechanisms (spread of communicable diseases due to overcrowding, low real wages and insufficient calories per capita due to the limited amount of available agricultural land) which led to high mortality in the Old World. With low mortality but stage 1 birth rates, the United States necessarily experienced exponential population growth (from less than 4 million people in 1790, to 23 million in 1850, to 76 million in 1900.)
