For decades, it has been an open secret among conservationists. An elegant equation widely used to calculate how many species will go extinct from deforestation and habitat destruction -- one of the "laws" of ecological theory -- was a little shaky.
More often than not, unless carefully calibrated, the equation seemed to overestimate extinction rates.
Early threats of mass global extinctions by 2000, based on the algorithm, failed to materialize. Exploring why, ecologists developed ideas like the "extinction debt." Species found in reduced habitats may not go extinct immediately, they said, but inexorably, their numbers would at some point decline. While the timing was not clear, the law, if modified, held true.
But still many wondered: Where are the extinct species? Where are the bodies?
A controversial study published today in Nature proposes an answer, arguing that scientists have made a fundamental mistake in how they reverse engineer this law, known as the species-area relationship, to extinction estimates. Given this mistake, it suggests, extinction debts could be little more than statistical noise, and the extinction estimates in reports like the "Millennium Ecosystem Assessment" could be overstated by double or more.
"This is welcome news in that we have bought a little time for saving species," said Stephen Hubbell, a co-author of the study and ecologist at the University of California, Los Angeles. "But we have to redo a whole lot of research that was done incorrectly."
But several prominent ecologists are challenging the paper's evidence and conclusions, including Michael Rosenzweig of the University of Arizona. Rosenzweig, one of the field's authorities, reviewed the paper for Nature and found it deeply flawed. He suggested the journal's editors reject the study and said he was shocked they published it.
"I was desperately upset by it," Rosenzweig said. "I can't begin to tell you."
Stuart Pimm at Duke University called the study's title -- "Species-area relationships always overestimate extinction rates from habitat loss" -- an outrage. Their portrayal of the equation bordered on a straw man, he said, except that "it's not even that structured."
"They say they've got a recipe for baking bread," he said. "What they've done is bake cookies."
Pimm and Rosenzweig feel the study's sweeping conclusions are not supported by its data. While Hubbell and his co-author, Fangliang He of China's Sun Yat-sen University, raise an important theoretical point for estimating extinctions -- a notion echoed by several other ecologists -- they do not shake the foundations of ecology, they said.
"What Steve has done is an incremental contribution" to research conducted over the past decade, Pimm said. "That's fine, but if it didn't have this inflammatory title, it probably wouldn't have been published in Nature."
No ecologist disagrees that humanity has started, or will soon start, the Earth's sixth great wave of extinction, a process largely driven by destruction of natural habitats.
Fossil studies and current extinction rates, free of theoretical morass, show that the world is losing species at about 100 times the normal rate. If Hubbell and He are correct, their work is about future projections -- whether this rate escalates even higher, as some have warned.
"Does it really matter if it's 100 times or 1,000 times?" said Daniel Simberloff, an ecologist at the University of Tennessee, Knoxville, and one of the first people to experimentally test the species-area relationship. Either way, he said, "it's still a huge, huge problem."
Still, even if estimates based on the species-area relationship are a crude tool -- they explain half of extinction rates, according to Simberloff -- they are widely used to gauge the loss of species not known to science. While many notice when a charismatic animal like the ivory-billed woodpecker goes extinct, there will probably never be a data-rich map, say, for beetle diversity, let alone bacteria, Hubbell said.
It is this lack of empirical data, the ebb and tide of unknown bugs, shrubs and grubs, that theoretical ecologists have attempted to fill with mathematics for the past century.
Going back to the 1800s, as naturalists skittered about cataloging the world's fauna and flora, researchers like Alexander von Humboldt noted that, as a forest or pasture increased in size, the number of species also rose.
Diversity and area seemed deeply related, almost like one of Isaac Newton's physical laws. And since the mid-20th century, scientists have sought to define, in the language of math, this law, dubbed the species-area relationship, or SAR.
Modern work on the relationship began with the amateur scientist Frank Preston, and was given credibility by the ecologists Robert MacArthur and E.O. Wilson in their 1967 book, "The Theory of Island Biogeography." As the title implies, their theories stemmed from mental models of islands: chop an island in half and, eventually, the equilibrium of species the spit could support would dwindle according to a sort of golden ratio between species and area.
Scientists like Simberloff, Wilson's graduate student, gathered data that supported the math fitted to the species-area relationship. A rule-of-thumb emerged: If habitat drops by 90 percent, half the species are lost.
By the late 1970s, scientists used the law to estimate how many species would be lost to deforestation of the Amazon River Basin, or across the entire world. Up to half the world's species could go extinct by 2000, they warned.
These broad estimates were pure speculation, said He, the Nature co-author. Appearing in the "gray literature," studies produced by governments and NGOs that often do not face peer review, the figures crept into the mass media and peer-reviewed research.
"These numbers get into the popular culture and get into the scientific culture and stop being challenged at some point," Hubbell said.
Many of these simple estimates have persisted, or been repeated by newer reports like the "Millennium Ecosystem Assessment," a report by the United Nations published in 2005, which Hubbell and He criticized in their paper. That report states that future extinction rates could rise to 1,000 or 10,000 the typical rate, noting only in its marginalia that the 10,000 rate was "speculative," stemming solely from work in the early 1990s.
Most ecologists, though, remained well aware of problems with early extinction estimates and continued to build up the theoretical models and data surrounding the species-area relationship, according to Ann Kinzig, an ecologist at Arizona State University whose work a decade ago with John Harte, at the University of California, Berkeley, provided a theoretical backbone for the He and Hubbell study.
Kinzig and Harte focused on "endemic" species, populations that exist only within the area being modeled. Given such a limit, they proposed an "endemics-area relationship" -- yes, an EAR -- that better predicted immediate extinctions, with lower estimates. This refinement seems natural: If the entire range of a species begins to disappear, their numbers may dwindle in a more immediate, predictable way.
In principle, SAR and EAR should yield the same answer, Harte added in an email.
"They are not inconsistent or mutually exclusive," Harte said. "Most extinction misestimates arise because the SAR is assumed to be a power law" -- a type of mathematical equation -- "when in fact it isn't, or because the shape of lost habitat, or the shape of remaining good habitat, is complicated by habitat fragmentation."
'Ecology's great laws'
The Nature paper published today stems from a simple idea. Both SAR and EAR can be pictured as circles spreading over a forest from a fixed point. When building a SAR, the diversity count rises by one for each new species encountered -- say, a white pine -- as the circle expands; each additional white pine won't increase this count. By contrast, an EAR counts up only at the last white pine found in its circumference.
If the pines were randomly distributed across a forest, then the SAR and EAR would be identical. But that is not how nature works. Animals and plants clump together, and when that is the case, extinction estimates derived from SAR methods will, as He and Hubbell boldly put it, "always" be above EAR estimates. Using precisely mapped forest and bird data, they then showed that their EAR-based estimates rang true, with some of their SAR models overshooting actual losses by up to two-and-a-half times.
These are the study's important contributions, said Jessica Green, an ecologist at the University of Oregon, another devotee of endemics-based models. Hubbell and He's EAR theory seems to fit results for a California serpentine grassland, she added.
"So much emphasis has been placed on the species-area relationship," Green said. "But from a conservation standpoint, the endemics-area relationship is where it's at."
According to Duke's Pimm, though, the Nature study used a drastically simplified version of the species-area relationship, one that seems ignorant of recent research, to make a blanket statement about SAR-based estimates, one reinforced through the study's blunt language, such as "the most widely used method of estimating species extinction rates ... is not correct."
One of Pimm's own studies, from 1995, is cited as a SAR-based overestimate, a take Pimm called "unambiguously false." It is part of what gets him exercised about the study. If they had "actually read the damn papers," he said, "they'd have seen that the numbers match."
There is a sturdy list of studies published since 1995 that show similar fits, Pimm added. If Hubbell and He had followed the proper recipe for creating their SAR-based estimate, they may have seen very different results, he added.
Even if some SAR-based estimates do not overestimate species loss, Hubbell said, the paper's central mathematical proof holds. "It doesn't matter if the SAR curve fits the data," he said. "The [issue] is the sampling problem is completely different."
Arizona's Rosenzweig has a broader concern. Many talk about the species-area relationship being ecology's great law. But it is not one law. "It's ecology's great laws," emphasis on the plural, he said. He and Hubbell excised one small part of the species-area relationship, modeled it, then pretended "that's all there is," he said.
Their focus was solely on the immediate extinction of endemic species -- an important point for conservation estimates, perhaps, but only part of the story, Rosenzweig said. Endemic extinctions are like money borrowed from a loan shark, but the species-area relationship also describes, say, your car loan and 30-year mortgage, he said.
"In essence, they say if I can estimate the money that I owe the loan sharks, then I can say forget about those mortgage and car payments," Rosenzweig said.
There is a vast body of literature, spanning decades, showing that the loss of diversity is governed by the species-area relationship, Rosenzweig added. For example, over millions of years, the amount of land available to forests was governed by the rise and fall of sea levels, and these expansions and contractions, evident in the fossil record, are explained precisely by SAR-based models, he said.
"That's about 210 million years of good track record," Rosenzweig said.
'Let's try and get it right'
Simberloff, who did not find the Nature study to be an important advance, warned that the paper could be misused by those politically driven to minimize the damage done by habitat loss. "This sounds like a major argument against preserving large areas," he said, "and in practical terms it shouldn't be."
Still, it benefits no one to exaggerate extinction risks, either, Arizona State's Kinzig said.
"There's enough going on in the world that we shouldn't be over-alarmist about this," she said. "Let's try and get it right."
It seems likely that the proof proposed by He and Hubbell will be an important contribution to refining extinction estimates, though one of many. Some ecologists have proposed models that begin to tackle the notion that "lost" habitat is not always paved over -- what happens to species when prairie is turned to farmland, for example. Others are working on edge effects, how a forest's interior may change when newly exposed as fringe terrain.
Truly, predictions are a mug's game.
In 2004, Chris Thomas, a biologist at the University of York, published a study, also in Nature, that used the species-area relationship to estimate extinctions driven by climate change. Many challenged Thomas' study then, and He and Hubbell also critique his conclusions in their paper.
Even with reduced estimates, though, the massive uncertainties encountered in projections like Thomas' can swing both ways, he warned, invoking a truism of scientists: a quote, possibly apocryphal, attributed to Niels Bohr, a pioneer of quantum mechanics.
"Remember that uncertainty can be either better or worse than we currently think," Thomas said. "As Niels Bohr said, 'Prediction is very difficult, especially about the future.'"
Reporter Allison Winter contributed.
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