Today, the Sahara Desert is a vast, nearly lifeless expanse of sand and rock. But ancient cave paintings tell of a time when it was fertile grassland and bands of human hunters chased aurochs and antelope.

The shift from grassland to desert happened, geologically speaking, overnight. About 5,500 years ago, a wobble in Earth’s orbit catalyzed ecosystem changes that caused the Sahara to go from green to brown in a matter of centuries or even decades.

Environmental change, scientists have learned, is not always gradual and linear. Instead, a series of small modifications can push a system to a “tipping point,” where it flips, quite suddenly, from one state to another. And many believe that human population dynamics are an increasingly important variable in environmental change, at local, regional, and global scales.

In previous millennia, the Earth was transformed by massive forces of nature – volcanic eruptions, solar flares, the clash of continents. Today, human beings may be the most powerful force of environmental change. Our numbers more than quadrupled over the last century, hitting seven billion in 2011. Resource consumption, at least in the affluent countries, has skyrocketed. More people are living in  environmentally fragile regions, such as coastal areas. Together, these dynamics are reshaping natural systems as never before.

Of course, there are vast disparities in environmental impact among humans. But, collectively, we have altered the biosphere to the point that some have named our era the Anthropocene, or “age of man.” According to some measures, more than 80 percent of the Earth’s land is under direct human control, and we appropriate a fifth of the planet’s biomass for our use. Human emissions of carbon dioxide and other heat-trapping gases are warming the planet and acidifying the oceans. And, because of human activity, we are now in the midst of the biggest wave of extinctions since the end of the dinosaurs.

Beyond IPAT

What is the relationship between population dynamics and environmental change – and what does that connection bode for the future?

Generations of environmental studies students learned that environmental impact (I) is the sum of population size (P) times per capita affluence level (A) times the impact of technologies (T). This is the “IPAT” equation: I = P x A x T.

Today, however, we know it’s not that simple. IPAT is a useful reminder that population, consumption, and technology all help shape our environmental footprint. But it is misleading if taken too literally, writes University of California, Berkeley, ecologist John Harte in A Pivotal Moment.  As Harte observes, “[IPAT] conveys the notion that population is a linear multiplier….In reality, population plays a much more dynamic and complex role in shaping environmental quality.”

Non-linear effects, including thresholds and feedbacks, can amplify the environmental impact of human numbers, writes Harte. For example, a species may depend on a certain amount of intact habitat to survive. As human settlements encroach, a threshold is eventually crossed, and the species will, sometimes quite suddenly (within a generation or two), collapse.

Feedback loops can also fast-forward environmental damage. A classic example is the loss of “albedo”: on a warming planet, there is less ice and snow to reflect heat back to space, so more sunlight is absorbed by the Earth’s surface, which intensifies warming. Harte observes that many feedbacks are fueled by population dynamics. For example, warming accelerates the decomposition of organic matter in cultivated soil. That decomposition, in turn, releases carbon dioxide into the atmosphere, which speeds even more warming. Because more people generally means more cultivated land, population growth affects the intensity of this feedback effect.

Tipping Points: Global and Local

Could the growing human presence on the planet – both in terms of numbers and consumption – trigger global tipping points, with disastrous consequences? Some observers think so.

In 2009, a team of scientists led by Johan Rockström, executive director of the Stockholm Resilience Center, set out to delineate a “safe operating space for humanity.” They identified10 biophysical boundaries that must not be transgressed if we wish to preserve a habitable planet. Rockström and his colleagues found that three of the boundaries – for climate change, biodiversity loss, and global nitrogen – have already been crossed.

Last year, University of California, Berkeley, paleoecologist Anthony Barnosky and colleagues warned of an approaching “state shift” in the Earth’s biosphere. As Barnosky told Science Daily, “the data suggest that there will be a reduction in biodiversity and severe impacts on much of what we depend on to sustain our quality of life, including, for example, fisheries, agriculture, forest products, and clean water. This could happen within just a few generations.”

Others remain skeptical. A study led by Barry Brook, director of climate science at the University of Adelaide, found that global-scale ecological tipping points are unlikely – in part because ecosystems on different continents are not strongly connected. And a paper by the Breakthrough Institute charged that the global boundaries set by Rockström and colleagues are somewhat arbitrary.

But while the notion of global tipping points remains controversial, there is no doubt that such thresholds exist at the local and regional levels. Across the planet, human activity is pushing many natural systems beyond the point of no return.

For example, the Mato Grosso region of the Amazon rainforest may soon be “on a one-way route to becoming a dry and relatively barren savannah,” according to the New Scientist. And record-breaking declines in the extent and volume of sea ice signal that an ice-free summer Arctic may be near.

Such local and regional shifts could have grim implications for human well-being. New research shows that human-induced climate change could dramatically reduce crop yields in many parts of the world, at a time when global food production must increase by 70 percent to keep pace with demand. Tufts University economists Frank Ackerman and Elizabeth A. Stanton found that “global warming is now causing unprecedentedly rapid changes in the climate conditions that affect agriculture – much faster than crops can evolve on their own, and probably too fast for the traditional processes of trial-and-error adaptation by farmers….Within a few decades, business as usual climate change would reach levels at which adaptation is no longer possible.”

Hans Joachim Schellnhuber, director of the Potsdam Institute for Climate Impact Research, has identified a series of regional climate tipping points that, together or separately, could shift the global climate into a new – and inhospitable – state.

The Time Is Now

It is not too late to step back from the brink. Authors of the tipping-point studies call for a range of interventions: limiting climate change, low-carbon approaches to development, better ecosystem management, and measures to voluntarily slow population growth where it is still rapid, such as encouraging girls’ education and universal access to family planning and reproductive health.

If we fail to scale back our impact, the cumulative effect of many small changes could be a planet that is virtually unrecognizable. “What features establish the identity of a face?” asks Schellnhuber. “What distortions erase that identity beyond recognition?”

Back when the Sahara was a green and fertile grassland, its human inhabitants had no way of knowing their world was about to change. Today, we have an increasingly sophisticated set of tools with which to survey our environment and measure our own impact. While our capacity to predict the future remains imperfect, we should consider ourselves warned.