Which countries are affected?
More economically developed countries including most of Europe, the US, South Korea and Australia have lower fertility rates.
It does not mean the number of people living in these countries is falling, at least not yet as the size of a population is a mix of the fertility rate, death rate and migration.
It can also take a generation for changes in fertility rate to take hold.
But Prof Murray said: “We will soon be transitioning to a point where societies are grappling with a declining population.”
Half the world’s nations are still producing enough children to grow, but as more countries advance economically, more will have lower fertility rates.