Within the framework of the article, we assess regions and countries that in the future may become new foci of economic and civilizational activity. This issue is relevant because many countries are now witnessing the exhaustion of demographic growth opportunities, which in turn will hinder intensive economic growth in them. To address the issue, we propose a two–stage econometric modeling procedure. The first econometric dependence links population growth rate with total fertility rate, and the second dependence reveals the impact of economic, institutional and cultural factors on fertility rate. Empirical testing of models was performed for a sample of 15 countries (Russia, Ukraine, Kazakhstan, Kyrgyzstan, France, Germany, Iran, Japan, China, Mexico, Egypt, Great Britain, USA, Canada and Australia) and showed high productivity and invariance of the proposed model scheme. Based on the constructed models, we put forward several quantitative characteristics of national demographic regimes. The most important of them is the long–term demographic effect of scale, taking into account the reaction of the population to the growth of per capita welfare. Applied calculations show that the U.S. still has the potential to maintain its growth regime for quite a long time, while China, Japan and Germany have almost exhausted this resource. The most likely foci of a new round of development of human civilization may be Russia, Kazakhstan and Iran, which, taking into account neighboring countries, form a kind of regional cluster in the center of Eurasia. It is in this area of the planet that we should expect the greatest economic and political activity in the next two to three decades.