Jeff Wise in Slate has an essay about "World population may actually start declining, not exploding".
A somewhat more arcane milestone, meanwhile, generated no media coverage at all: It took humankind 13 years to add its 7 billionth. That’s longer than the 12 years it took to add the 6 billionth—the first time in human history that interval had grown. (The 2 billionth, 3 billionth, 4 billionth, and 5 billionth took 123, 33, 14, and 13 years, respectively.) In other words, the rate of global population growth has slowed. And it’s expected to keep slowing. Indeed, according to experts’ best estimates, the total population of Earth will stop growing within the lifespan of people alive today.
In other words, the global population has crossed the zero point of the Great Second Derivative of population growth. This is not news as UN and other projections have long predicted a "hump" in human population during the next century, but the article goes to an extreme: What if, once it stops growing and begins shrinking, the human population shrinks down to some very small number?
That might sound like an outrageous claim, but it comes down to simple math. According to a 2008 IIASA report, if the world stabilizes at a total fertility rate of 1.5—where Europe is today—then by 2200 the global population will fall to half of what it is today. By 2300, it’ll barely scratch 1 billion. (The authors of the report tell me that in the years since the initial publication, some details have changed—Europe’s population is falling faster than was previously anticipated, while Africa’s birthrate is declining more slowly—but the overall outlook is the same.) Extend the trend line, and within a few dozen generations you’re talking about a global population small enough to fit in a nursing home.
Notice how so many people who comment on the global population assume that human growth is a homogeneous process? That is, they understand that nations presently have different rates of growth, but conceive of them as being at different places in a process of Westernization. They treat the nations themselves as homogeneous entities.
That's not the right way to think about the future. We have heterogeneous national populations, with subgroups that have very high fertility rates. The largest contrast in terms of proportion of the population in most countries is rural/urban, where rural people have larger family sizes than city-dwellers. One of the biggest contributors to the decline in population growth has been urbanization, as city-dwellers tend to have kids later and have fewer of them. So as the populations of most countries make the transition to urban majorities, their growth rate slows.
There are many other factors, some cultural and others more broadly environmental. Religion is a key factor, and countries with diverse religious populations, like the U.S., have large variance in family sizes among different religious groups. The effect of religion on family size isn't absolute, as urbanization, education, and economic constraints lead to lower family sizes even among religious groups that encourage a "quiver-full" family size. However, I suspect that the variance among cultural groups within countries will persist, and that persistence in the face of a global reduction in growth will tend to increase the proportion of the population represented by fast-growing groups. As fast-growing groups increase in proportion, the overall growth rate of the population increases. So modeling a steady future decline in population assumes a uniform cultural effect on these heterogenous groups, which I doubt.
I also consider it an open question whether family size will be positively selected moving forward in time. All else being equal, bigger families will represent more and more of the population, and any genes that correlate with larger family size will increase in numbers. At present, we are seeing the large effect of environmental factors on reducing family size, just as environmental factors during the last 200 years have massively increased survival within populations with large family sizes. But as we equalize the environment in various ways, any effect of genes will become relatively more important in their contribution to variance in family size.
As Malcolm reminds us in Jurassic Park, "life finds a way"...