Taken from here, this chart shows the effects of differential population change over the 1950-2100 period, using United Nations data from 2010. The site's summation merits sharing.
The population of the United States of America is projected to grow continuously for many decades to come. By the end of the century the US population will be approximately the same size as that of the 27 states that make up the European Union.
China's population, on the other hand will only slightly grow (due to its momentum effect) until around 2025. Then it will start to decline significantly until it will reach a bit more than 900 million.
For comparison: India's population will outgrow that of China by 2020 and then further increase to more than 1.7 billion around 2065. Only then it is projected to start declining.
A most dramatic demographic change is projected for the most populous country in Africa: Nigeria. While its population was only around 38 million in 1950, it has now increased to about 150 million and is projected to reach almost 750 million by the end of the century. Shortly after 2050 Nigeria's population will become larger than the (growing) population of the United States; and by 2065 Nigeria's population will outgrow the population of the 27 states of the European Union combined. In fact, around 2070 Nigeria's population will be as large as China's population in 1950.
India is another country with remarkable population growth: By 1950 India's population was almost exactly the same size as that of the 27 countries of the European Union combined. Today India has four times as many people and by around 2060, India's population will be 3.4 times that of Europe. Within about one century, India's population has outgrown Europe's population by 1.2 billion people.
These fundamental discrepancies in population growth will shift the geo-strategic weight away from Europe towards Asia and Africa.
A glance at Wikipedia's list of the populations of the countries of the world over time confirms this. In 1950, the United States' 151.9 million would have been outnumbered two-to-one by the 68.4 million of Germany, 50.1 million of the United Kingdom, 47.1 million of Italy, 42.5 million of France, and 28.1 million of Spain. Looking outside of the North Atlantic area, there were barely more Brazilians than there were Britons and Italians, war-devastated Poland's 24.8 millions comfortably outnumbered Egypt's 21.9 million inhabitants, the Netherlands had 30-40% fewer inhabitants than Canada or South Africa, Singapore had barely a million residents, and the populations of the smaller Persian Gulf states were measurable in hundreds of thousands or even tens of thousands.
Europe's populations grew absolutely, and quite substantially, but declined relative to the rest of the world as the demographic transition took hold, with greater effect owing to the superior medical technology and sharply reduced infant mortality available in our time, as opposed to a century ago. This decline manifested even relative to other high- and middle-income continents and countries. On Tuesday, Slate noted that day was "Pi Day", that shortly after 2:29 pm Eastern Standard Time United States Census Bureau's population clock hit 314 159 265--"pi times 10 to the eighth", as Slate notes--according to a press release. On that day, it should be noted, the five European countries that together outnumbered the United States two-to-one sixty-two years ago now lead the United States by just a couple million people. Soon, these five countries' lead will disappear; soon, the United States will lead.
Looking at the simple crude metric of total population says nothing about other, arguably more important factors, like (say) age composition. (To name a single example, Nigeria is going to be so much younger than China in 2050.) By themselves, these population totals don't mean anything. It's imaginable that Nigerian economic weight wouldn't equal its demographic weight, arguably likely given its problems and current leadership. But having a population on the order of China's and Europe's, and younger than either, makes the chances of such growth that much more likely.