The Best American Science and Nature Writing Part 8

"We want our great-grandchildren to be shrimpers a hundred and fifty years from now," she said.

"Go," shouted Joe Skinner, releasing brakes that governed two winches. Squeals, grinds, the sounds of cable and rope under stress on the throbbing bed of a major diesel smothered the splash of green nets on the water. As cables let out, the nets disappeared behind the boat. At six A.M. at the start of the 2005 Alabama shrimp season, the A. S. Skinner was trawling.

We were in Mobile Bay. A rising sun, barely burning through haze, added a band of pink to a formless horizon. Around us a circus of boatsa"trawls, skiffs, outboardsa"were out for opening day. "It's a madhouse," said Mike Skinner, Joe's brother at the helm. A black radar screen set at one-mile resolution was dotted with forty or fifty green moving spots. "I'll be glad when this day is over."

A. S. Skinner, for whom the boat was named, had been a jeweler, as was his son. But grandson Gary left gold in the showcase to seek his fortune with shrimp. Great-grandsons Mike and Joe joined him at age five. By high school, the last formal education they sought, they were taking boats out by themselves. "When I came out of high school, we done good," said Mike, tall and angular, dressed in blue-jean shorts and a white T-s.h.i.+rt. The first year they grossed $200,000. "We didn't work that hard. Dad had two good years and then it started dropping."

The Skinners, aged thirty-two and thirty, each with a one-year-old son, reminded me of cowboys I'd known out West, still pining for pastures before barbed wire. Their dreams of a commons, free to exploit, had once been our dream, so woven into our national DNA that we, like they, mourned its pa.s.sing. Each spring they rode out after a myth, only to find that the world had changed.

The sea stopped giving in the 1980s. Catches flattened worldwide. There were, in fact, only so many shrimp in the sea. And because of overfis.h.i.+ng for half a century, the average shrimp size caught in the gulf had shrunk from "50" to "75."

There was also growing dismay that shrimpers wasted more than they caught. Down below, in the channel made famous by the Union admiral David Farragut's cry, "d.a.m.n the torpedoes. Full speed ahead," was a kind of "fis.h.i.+ng" that was nothing short of marine clear-cutting.

In the gold rush days, before Joe and Mike were born, shrimpers killed ten pounds of sea life for every pound of harvested shrimpa"waste that reached one billion pounds a year in the gulf. Once called "trash," now called "by-catch," this sea life included sea turtles driven to the brink of extinction and juvenile red snapper, a good eating fish. Under environmental regulations requiring escape hatches in nets, the ratio of by-catch to shrimp has been reduced to four to one, still a startling sight when the Skinners dumped their twin nets on deck. Using grain shovels, they transferred this squirming pile into a large wooden box of seawater mixed with Cargil Boat and Boil salt. The shrimp sank to the bottom, and the by-catch, mostly dead, floated to the surface. This they skimmed and threw overboard.

Gulf shrimpers, the last cowboys of the sea, were corralled in 2006 when the U.S. government, trying to balance the gulf's ecosystem with a sustainable supply of shrimp for a viable commercial fishery, capped the federal-waters shrimp fleet at 2,700 boats, down from a gold rush high of 7,500, and ordered federal clerks to be randomly stationed aboard to record by-catch. The goal was a "maximum sustainable yield," roughly 110 million pounds a year, which left 22 billion shrimp to reproduce, according to modeling by Dr. Jim Nance, head of the NOAA Fisheries Service Galveston Laboratory. This figure was half the natural shrimp population before the arrival of the trawl, estimated Bill Hogarth, the former head of the agency.

The Skinners grossed $1,000 on opening daya"not a bad haul, I thought, until I learned that it was half the price they got when they were teenagers. They made a living but not a killing selling their shrimp to their father, who ran a roadside stand on Dauphin Island. "The last few years, we're just paying for fuel," said Joe, sitting below their federal license framed on the Masonite wall of their boat's dinette. "If it weren't for the shop..." His voice trailed off.

What really ended the Skinners' dreams, what really brought shrimpers to their knees and tears in Mobile Bay, Brownsville, New Orleans, Biloxi, and Bayou la Batrea"all along the Gulf Coasta"was not regulation or lack of shrimp but good old global supply and demand. "Because of imported, farmed shrimp from the Far East," said Joe Skinner, "wholesale shrimp prices in the U.S. are the same as when Dad started thirty years ago."

The story of farmed shrimp begins with a j.a.panese dish called "dancing shrimp," a ca.s.serole that arrives at your table with the unmistakable sound of something inside striking the cover. Jumping about on a bed of hot rice are Kuruma prawnsa"live. The object is to grab one between chopsticks and pop it wiggling into your mouth. Kuruma, large, meaty shrimp found in limited quant.i.ties in the Sea of j.a.pan, sell for a hundred dollars a pound. Seventy-five years ago this rarity prompted an ichthyology student at Tokyo University to try growing Kuruma in captivity.

Until 1933, when Motosaku Fujinaga first sp.a.w.ned and hatched shrimp in a lab, aquaculture had been an ancient artisa.n.a.l practice. Tides swept fish and shrimp into estuaries, and weirs were built to prevent their escape. The shrimp grew to eating size in naturally replenished waters.

Out of their element, though, shrimp proved to be finicky eaters, fragile and p.r.o.ne to diseases. It took Fujinaga twenty-five years of trying, interrupted by World War II, to be able to grow ten kilograms of shrimp to adulthood. In 1967, when he spoke to the United Nations Food and Agriculture Organization's first world conference on shrimp culture in Mexico City, Fujinaga envisioned a world where capitalism and altruism could coexist in the "vast and boundless marshes, swamps, or jungles in the tropics." Shrimp farms, he predicted, "will greatly contribute toward the increased supply of animal protein to the human race."

It was a lovely thought. A Blue Revolution. But his success fueled a global grab in which protein and profits flowed one waya"north toward the moneyed. One year after his speech, a group of j.a.pa nese businessmen bought Fujinaga's technology, won a U.S. patent, and approached DuPont for money. DuPont declined, but two officials who heard the pitch, Paul Bente and John Rutledge Ches.h.i.+re, were so excited they quit their jobs, put up $200,000 of Ches.h.i.+re's family money, and opened Marifarms in a bay near Panama City, Florida.

Aided by research at the U.S. lab in Galveston, Marifarms harvested a disappointing 6,000 pounds in 1970, according to Ches.h.i.+re's book, Memoir of a Shrimp Farmer. The same year another venture, Sea Farms, was digging ca.n.a.ls in a Florida key to grow shrimp.

Because of environmental issuesa"Marifarms scooped up pregnant white shrimp and confined them in a public bay, while Sea Farms flew in nonindigenous shrimp from Central America, a practice Florida soon prohibiteda"shrimp farming moved south. Supported by USAID, World Bank loans, and willing developing-world officials, the corporate giants United Fruit, Armour, Conagra, and Ralston Purina launched shrimp farms in Honduras, Brazil, Panama, and Ecuador, according to oral histories collected by Bob Rosenberry of Shrimp News International. Learning as they went, the farmed-shrimp industry laid waste to mangroves, fis.h.i.+ng communities, and ecosystems. The word "plundering" comes to mind.

A shrimp farm is a salt.w.a.ter feedlot. There can be as many as 170,000 shrimp larvae in a one-acre pond that is one to two meters deep. So-called intensive ponds can yield 6,000 to 18,000 pounds of shrimp in that acre in three to six months. (A good wheat yield is 3,600 pounds per acre.) Because of this density, the waste they swim in, and their susceptibility to disease, most farmed shrimp are treated with antibiotics, only some of them legal in the United States. A wide array of poisons is used to kill unwanted sea life and cleanse ponds for reuse, creating what Public Citizen calls a "chemical c.o.c.ktail." In random sampling of imported shrimp, health officials in the United States, j.a.pan, and the European Union have found chloramphenicol, a dangerous antibiotic banned in food.

The industry acknowledges that 5 percent of the world's mangroves, hundreds of thousands of acres, have been destroyed creating shrimp ponds. In some estuaries 80 percent of the mangroves are gone. A commons was privatized, ruining artisa.n.a.l fis.h.i.+ng and driving indigenous fishermen to work raising shrimp. By removing the thick coastal barrier of trees, shrimp farms have undoubtedly aggravated damage from hurricanes and tsunamis. And salt intrusion has sterilized once fertile estuaries.

Even in the best-run farms, two to four pounds of sea life is caught and ground up as feed for every pound of shrimp raised. Mortality rates of 30 percent are common. The dead shrimp, shrimp excrement, and chemical additives are often flushed into coastal waters.

By the mid-1970s, farmed shrimp from South and Central America, at less than half the cost of gulf shrimp, began arriving at Red Lobster restaurantsa"and everywhere else. All-you-can-eat shrimp dinners became a standard, filling both waistlines and Red Lobster's coffers. That box of shrimp I retrieved from the dumpster cost $2.50 a pound and sold, in my case, for $25 a pound, a markup that bettered the beer's.

Quietly, farmed shrimp took over the market, its source hidden behind the motif of a picturesque but actually sinking shrimp fleet. By 1980 half of America's shrimp consumption came from foreign farms. By 2001 shrimp pa.s.sed canned tuna as America's favorite seafood. Today, 90 percent of our shrimpa"more than 1 billion pounds a yeara"come from foreign farms. Virtually every restaurant chain, from Captain D's to Red Lobster, serves farmed shrimp. Foreign farmed shrimp were peddled for years by vendors at the National Shrimp Festival in Alabamaa"until they were caughta"and at happy hour for the Gulf of Mexico Fishery Management Council meeting in Birmingham, Alabama, in March 2005, where government officials finalized a ten-year freeze on 2,700 shrimp boat licenses. The sight of government biologists slurping Vietnamese shrimp after reining in American shrimpers was an irony sharper than c.o.c.ktail sauce. Even in New Orleans, where a handful of high-end chefs brag about their Louisiana shrimp, imported shrimp are the norm in most restaurants. A new Louisiana law requires restaurateurs to tell the trutha"if asked.

To get a sense of the pink tsunami on U.S. sh.o.r.es, I flew to Long Beach, California, the single largest shrimp port, where among the 5 million containers arriving each year are several thousand filled with shrimp, 265 million pounds of it in a year.

On the day I visited, five s.h.i.+ps were docking with nine containersa"412,000 poundsa"of shrimp from Peru, Ecuador, Venezuela, and China. One container, a semitrailer load, holds an astounding amount. Laid out in a customs warehouse, boxes holding 30,000 pounds of shrimp covered a 12-by-100-foot area chest high. Based on our average consumption, this one container held a year's supply of shrimp for 12,000 Americans.

The container in question had been seized and opened because of suspicions that the beautiful bags of store-ready "26/30" frozen raw shrimp, labeled "farm raised in Indonesia," may, in fact, have come from China and been relabeled in Singapore, a common cat-and-mouse game that customs officials call "transs.h.i.+pment." A bag was dispatched to a government lab in Savannah, Georgia, to try a new sniffing tool that might determine its source. Transs.h.i.+pping is used to evade special import taxes or restrictions, such as one imposed on Chinese shrimp and four other species in 2007 after malachite green, gentian violet, and other carcinogens were found in farmed fish.

"It's very, very difficult to prove a transs.h.i.+pment issue," said Jeff DeHaven, the deputy director of fines, penalties, and forfeitures. So great is their volume of business that importers just walk away from seized containers, he said. Moreover, U.S. customs is concerned primarily with duty issues, not food safety. "We don't look at that much shrimp," admitted an enforcement chief.

The Food and Drug Administration, responsible for imported food safety, samples less than 1 percent of the 1 billion pounds, a "sorry" record, according to U.S. Representative John Dingell, who in 2007 chaired food safety hearings before the House Energy and Commerce Committee. Mindful of consumer fears fanned by poisoned seafood arriving from China, the Global Aquaculture Alliancea"an industry group underwritten by Wal-Mart, Red Lobster, and multinational seafood importersa"has written standards that, if enforced, could produce clean, safe shrimp without damaging people or the environment. But that will take years, admitted GAA president George Chamberlain. Only 45 shrimp farms are certified by the alliancea"out of more than 100,000 worldwide.

Today, if you live more than a hundred miles from the Gulf Coast, the shrimp you eat most likely come from a foreign farm. You can tour these farms while standing at your supermarket seafood freezer and reading labels. The top ten countries exporting to the United States are Thailand, Indonesia, Ecuador, China, Vietnam, Malaysia, Mexico, India, Bangladesh, and Guyana. The wholesale value of their shrimp is $4 billion a year.

Despite that income, citizens in the developing world have protested shrimp farmsa"and have been killed for doing so. The Blues of a Revolution, a book published in 2003 by a consortium of environmental and indigenous groups, described Honduran shrimp farms ringed by barbed wire and watchtowers and armed guards. Between 1992 and 1998, in the Bay of Fonseca near large shrimp farms, "11 fishermen have been found dead by shooting or by machete injuries ... no one has been brought to justice."

One story from the book I cannot shake involved Korunamoyee Sardar, a Banglades.h.i.+ woman who, on November 7, 1990, joined a protest against a new shrimp farm near Harin Khola. She was shot in the head, cut into pieces, and thrown into a Bangladesh river. A monument stands where she was murdered. It reads: "Life is struggle, struggle is life."

Red Lobster, which buys 5 percent of the world's shrimp, is Bangladesh's biggest U.S. customer. The restaurant did not respond to repeated requests for an interview.

FELIX SALMON A Formula for Disaster.

FROM Wired.

A YEAR AGO, it was hardly unthinkable that a math wizard like David X. Li might someday earn a n.o.bel Prize. After all, financial economistsa"even Wall Street quantsa"have received the n.o.bel in economics before, and Li's work on measuring risk has had more impact, more quickly, than previous n.o.bel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He took a notoriously tough nuta"determining correlation, or how seemingly disparate events are relateda"and cracked it wide open with a simple and elegant mathematical formula, one that would become ubiquitous in finance worldwide.

For five years, Li's formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quant.i.ties of new securities, expanding financial markets to unimaginable levels.

His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrencheda"and was making people so much moneya"that warnings about its limitations were largely ignored.

Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li's formula hadn't expected. The cracks became full-fledged canyons in 2008a"when ruptures in the financial system's foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.

David X. Li, it's safe to say, won't be getting that n.o.bel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.

How could one formula pack such a devastating punch? The answer lies in the bond market, the mult.i.trillion-dollar system that allows pension funds, insurance companies, and hedge funds to lend trillions of dollars to companies, countries, and home buyers.

A bond, of course, is just an IOU, a promise to pay back money with interest by certain dates. If a companya"say, IBMa"borrows money by issuing a bond, investors will look over its accounts very closely to make sure it has the wherewithal to repay them. The higher the perceived riska"and there's always some riska"the higher the interest rate the bond must carry.

Bond investors are very comfortable with the concept of probability. If there's a 1 percent chance of default but they get an extra 2 percentage points in interest, they're ahead of the game overalla"like a casino, which is happy to lose big sums every so often in return for profits most of the time.

Bond investors also invest in pools of hundreds or even thousands of mortgages. The potential sums involved are staggering: Americans now owe more than $11 trillion on their homes. But mortgage pools are messier than most bonds. There's no guaranteed interest rate, since the amount of money homeowners collectively pay back every month is a function of how many have refinanced and how many have defaulted. There's certainly no fixed maturity date: money shows up in irregular chunks as people pay down their mortgages at unpredictable timesa"for instance, when they decide to sell their house. And most problematically, there's no easy way to a.s.sign a single probability to the chance of default.

Wall Street solved many of these problems through a process called tranching, which divides a pool and allows for the creation of safe bonds with a risk-free triple-A credit rating. Investors in the first tranche, or slice, are first in line to be paid off. Those next in line might get only a double-A credit rating on their tranche of bonds but will be able to charge a higher interest rate for bearing the slightly higher chance of default. And so on.

The reason that ratings agencies and investors felt so safe with the triple-A tranches was that they believed there was no way hundreds of homeowners would all default on their loans at the same time. One person might lose his job, another might fall ill. But those are individual calamities that don't affect the mortgage pool much as a whole: everybody else is still making their payments on time.

But not all calamities are individual, and tranching still hadn't solved all the problems of mortgage-pool risk. Some things, like falling house prices, affect a large number of people at once. If home values in your neighborhood decline and you lose some of your equity, there's a good chance your neighbors will lose theirs as well. If, as a result, you default on your mortgage, there's a higher probability they will default, too. That's called correlationa"the degree to which one variable moves in line with anothera"and measuring it is an important part of determining how risky mortgage bonds are.

Investors like risk, as long as they can price it. What they hate is uncertaintya"not knowing how big the risk is. As a result, bond investors and mortgage lenders desperately want to be able to measure, model, and price correlation. Before quant.i.tative models came along, the only time investors were comfortable putting their money in mortgage pools was when there was no risk whatsoevera"in other words, when the bonds were guaranteed implicitly by the federal government through Fannie Mae or Freddie Mac.

Yet during the nineties, as global markets expanded, there were trillions of new dollars waiting to be put to use lending to borrowers around the worlda"not just mortgage seekers but also corporations and car buyers and anybody running a balance on their credit carda"if only investors could put a number on the correlations between them. The problem is excruciatingly hard, especially when you're talking about thousands of moving parts. Whoever solved it would earn the eternal grat.i.tude of Wall Street and quite possibly the attention of the n.o.bel committee as well.

To understand the mathematics of correlations better, consider something simple, like a kid in an elementary schoola"let's call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the cla.s.s spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than onea"not just Alice but also the girl she sits next to, Britney. If Britney's parents get divorced, what are the chances that Alice's parents will get divorced, too? Still about 5 percent: the correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percenta"which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: it could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the cla.s.s spelling bee, the chance of Alice winning it is zero, which means the correlation is negative:a"1.

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

But it's a very inexact science. Just measuring those initial 5 percent probabilities involves collecting lots of disparate data points and subjecting them to all manner of statistical and error a.n.a.lysis. Trying to a.s.sess the conditional probabilitiesa"the chance that Alice will get head lice if Britney gets head licea"is an order of magnitude harder, since those data points are much rarer. As a result of the scarcity of historical data, the errors there are likely to be much greater.

In the world of mortgages, it's harder still. What is the chance that any given home will decline in value? You can look at the past history of housing prices to give you an idea, but surely the nation's macroeconomic situation also plays an important role. And what is the chance that if a home in one state falls in value, a similar home in another state will fall in value as well?

Enter Li, a star mathematician who grew up in rural China in the mid-1960s. He excelled in school and eventually got a master's degree in economics from Nankai University before leaving the coun try to get an MBA from Laval University in Quebec. That was followed by two more degrees: a master's in actuarial science and a Ph.D. in statistics, both from Ontario's University of Waterloo. In 1997 he landed at Canadian Imperial Bank of Commerce, where his financial career began in earnest; he later moved to Barclays Capital and by 2004 was charged with rebuilding its quant.i.tative a.n.a.lytics team.

Li's trajectory is typical of the quant era, which began in the mid-1980s. Academia could never compete with the enormous salaries that banks and hedge funds were offering. At the same time, legions of math and physics Ph.D.'s were required to create, price, and arbitrage Wall Street's ever more complex investment structures.

In 2000, while working at JPMorgan Chase, Li published a paper in the Journal of Fixed Income t.i.tled "On Default Correlation: A Copula Function Approach." (In statistics, a copula is used to couple the behavior of two or more variables.) Using some relatively simple matha"by Wall Street standards, anywaya"Li came up with an elegant way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.

If you're an investor, you have a choice these days: you can either lend directly to borrowers or sell investors credit default swaps, insurance against those same borrowers defaulting. Either way, you get a regular income streama"interest payments or insurance paymentsa"and either way, if the borrower defaults, you lose a lot of money. The returns on either strategy are nearly identical, but because an unlimited number of credit default swaps can be sold against each borrower, the supply of swaps isn't constrained the way the supply of bonds is, so the CDS market managed to grow extremely rapidly. Though credit default swaps were relatively new when Li's paper came out, they soon became a bigger and more liquid market than the bonds on which they were based.

When the price of a credit default swap goes up, that indicates that default risk has risen. Li's breakthrough was that instead of waiting to a.s.semble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market. It's hard to build a historical model to predict Alice's or Britney's behavior, but anybody could see whether the price of credit default swaps on Britney tended to move in the same direction as that on Alice. If it did, then there was a strong correlation between Alice's and Britney's default risks, as priced by the market. Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit a.s.sumption that financial markets in general, and CDS markets in particular, can price default risk correctly).

It was a brilliant simplification of an intractable problem. And Li didn't just radically dumb down the difficulty of working out correlations; he decided not to even bother trying to map and calculate all of the nearly infinite relations.h.i.+ps between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation numbera"one clean, simple, all-sufficient figure that sums up everything else.

The effect on the securitization market was electric. Armed with Li's formula, Wall Street's quants saw a new world of possibilities. And the first thing they did was start creating a huge number of brand-new triple-A securities. Using Li's copula approach meant that ratings agencies like Moody'sa"or anybody wanting to model the risk of a tranchea"no longer needed to puzzle over the underlying securities. All they needed was that correlation number, and out would come a rating telling them how safe or risky the tranche was.

As a result, just about anything could be bundled and turned into a triple-A bonda"corporate bonds, bank loans, mortgage-backed securities, whatever you liked. The resulting pools were often known as collateralized debt obligations, or CDOs. You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A. You could even take lower-rated tranches of other CDOs, put them in a pool, and tranche thema"an instrument known as a CDO-squared, which at that point was so far removed from any actual underlying bond or loan or mortgage that no one really had a clue what it included. But it didn't matter. All you needed was Li's copula function.

The CDS and CDO markets grew together, feeding on each other. At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrock eted to more than $62 trillion. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.

At the heart of it all was Li's formula. When you talk to market partic.i.p.ants, they use words like beautiful, simple, and, most commonly, tractable. It could be applied anywhere, for anything, and was quickly adopted not only by banks originating new bonds but also by traders and hedge funds dreaming up complex trades between those bonds.

"The corporate CDO world relied almost exclusively on this copula-based correlation model," says Darrell Duffie, a Stanford University finance professor who served on Moody's Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world's financial vocabulary that brokers started quoting prices based on their correlations. "Correlation trading has spread through the psyche of the financial markets like a highly infectious thought virus," wrote the derivatives guru Janet Tavakoli in 2006.

The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented the copula function, Paul Wilmott wrote that "the correlations between financial quant.i.ties are notoriously unstable." Wilmott, a quant.i.tative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. And he wasn't alone. During the boom years, everybody could reel off reasons why the Gaussian copula function wasn't perfect. Li's approach made no allowance for unpredictability: it a.s.sumed that correlation was a constant rather than something mercurial. Investment banks would regularly phone Stanford's Duffie and ask him to come in and talk to them about exactly what Li's copula was. Every time he would warn them that it was not suitable for use in risk management or valuation.

In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn't understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.

In finance, you can never reduce risk outright; you can only try to set up a market in which people who don't want risk sell it to those who do. But in the CDO market, people used the Gaussian copula model to convince themselves they didn't have any risk at all, when in fact they just didn't have any risk 99 percent of the time. The other 1 percent of the time they blew up. Those explosions may have been rare, but they could destroy all previous gains, and then some.

Li's copula function was used to price hundreds of billions of dollars' worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared.

Bankers securitizing mortgages knew that their models were highly sensitive to house-price appreciation. If it ever turned negative on a national scale, a lot of bonds that had been rated triple-A, or risk-free, by copula-powered computer models would blow up. But no one was willing to stop the creation of CDOs, and the big investment banks happily kept on building more, drawing their correlation data from a period when real estate only went up.

"Everyone was pinning their hopes on house prices continuing to rise," says Kai Gilkes of the credit research firm CreditSights, who spent ten years working at ratings agencies. "When they stopped rising, pretty much everyone was caught on the wrong side, because the sensitivity to house prices was huge. And there was just no getting around it. Why didn't rating agencies build in some cus.h.i.+on for this sensitivity to a house-price-depreciation scenario? Because if they had, they would have never rated a single mortgage-backed CDO."

Bankers should have noted that very small changes in their underlying a.s.sumptions could result in very large changes in the correlation number. They also should have noticed that the results they were seeing were much less volatile than they should have beena"which implied that the risk was being moved elsewhere. Where had the risk gone?

They didn't know, or didn't ask. One reason was that the outputs came from "black box" computer models and were hard to subject to a commonsense smell test. Another was that the quants, who should have been more aware of the copula's weaknesses, weren't the ones making the big a.s.set-allocation decisions. Their managers, who made the actual calls, lacked the math skills to understand what the models were doing or how they worked. They could, however, understand something as simple as a single correlation number. That was the problem.

"The relations.h.i.+p between two a.s.sets can never be captured by a single scalar quant.i.ty," Wilmott says. For instance, consider the share prices of two sneaker manufacturers: when the market for sneakers is growing, both companies do well and the correlation between them is high. But when one company gets a lot of celebrity endors.e.m.e.nts and starts stealing market share from the other, the stock prices diverge and the correlation between them turns negative. And when the nation morphs into a land of flip-flop-wearing couch potatoes, both companies decline and the correlation becomes positive again. It's impossible to sum up such a history in one correlation number, but CDOs were invariably sold on the premise that correlation was more of a constant than a variable.

No one knew all of this better than David X. Li: "Very few people understand the essence of the model," he told the Wall Street Journal way back in fall 2005.

"Li can't be blamed," says Gilkes of CreditSights. After all, he just invented the model. Instead, we should blame the bankers who misinterpreted it. And even then, the real danger was created not because any given trader adopted it but because every trader did. In fi nancial markets, everybody doing the same thing is the cla.s.sic recipe for a bubble and inevitable bust.

Na.s.sim Nicholas Taleb, hedge fund manager and author of The Black Swan, is particularly harsh when it comes to the copula. "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked," he says. "Co-a.s.sociation between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."

Li has been notably absent from the current debate over the causes of the crash. In fact, he is no longer even in the United States. Several months ago, he moved to Beijing to head up the risk-management department of China International Capital Corporation. In a recent conversation, he seemed reluctant to discuss his paper and said he couldn't talk without permission from the PR department. In response to a request, CICC's press office sent an e-mail saying that Li was no longer doing the kind of work he did in his previous job and therefore would not be speaking to the press.

In the world of finance, too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can take a few years' worth of data and come up with probabilities for things that models say should happen only once every 10,000 years. Then people invest on the basis of those probabilities, without stopping to wonder whether the numbers make any sense.

As Li himself said of his own model: "The most dangerous part is when people believe everything coming out of it."

DAWN STOVER Not So Silent Spring.

FROM Conservation Magazine.

A MALE EUROPEAN BLACKBIRD was terrorizing the neighborhood. For several months, he started singing at around 5 A.M. each day, but this was no ordinary song. The bird imitated the sounds of ambulance sirens and car alarms at a jarringly lifelike volume. It even produced cell-phone ring tones that went unanswered for hours.

The tale of the annoying blackbird in Somerset, United Kingdom, was not unique. Hans Slabbekoorn, an a.s.sistant professor of behavioral biology at Leiden University in the Netherlands, had heard similar storiesa"but he was skeptical that such bizarre reports could be true. So he started asking people to send him recordings of the off-kilter blackbirds. Sure enough, what he got back was pitch-perfect imitations of urban noises, including not just sirens and car alarms but even the distinctive sound of a golf cart backing upa"mimicked by blackbirds living near a golf course.

While the sounds seemed artificial, the reason birds were making them was surprisingly natural. Living amid a growing cacophony of man-made noises, the blackbirds started incorporating human sounds into their repertoire. And Slabbekoorn says the unusual strategy might actually help the birds: song variety indicates matur ity in male blackbirds, and female blackbirds prefer older guys.

Blackbirds aren't the only animals changing their tunes. As human noise intrudes on naturea"from freeway traffic noise to jets screaming over the rainforesta"scientists are starting to believe that the acoustic environment is far more intricate and fragile than they ever imagined. Long regarded as a random collection of bird songs and animal cries, the natural soundscape might actually be a coordinated symphony, with animal calls spread carefully across the acoustic spectrum. Now researchers are getting the first glimpses of what happens when humanity's choir drowns out whole sections of that spectrum. Animals ranging from blackbirds to beluga whales are changing their calls or switching them to new frequencies. Others are adapting in ways so powerful that they may be triggering the first steps in an evolutionary shakeup. And some animals are disappearing altogether.

Scientists have traditionally studied animal sounds by focusing on individual species and their vocalizations. Bernie Krause, a bioacoustician who has spent forty years recording the calls of the wild, has hatched a radically different approach and, in turn, a revolutionary vision of the relations.h.i.+p between animals, their environment, and the sounds they emit.

It all started in 1968 when Krause, then a musician, was having lunch with Van d.y.k.e Parks of the Beach Boys. Parks suggested that Krause "do an alb.u.m on ecology." Krause and his musical partner had introduced the Moog synthesizer to pop music and had contributed to hundreds of alb.u.ms and movie soundtracks, but Krause knew little about ecology beyond his recent reading of Rachel Carson's Silent Spring. Intrigued by Parks's suggestion, Krause went alone with his equipment to Muir Woods, north of San Francisco. "I was so intrigued by what I heard that I made a decision that this was what I wanted to do for the rest of my life," he recalls.

Overtaken by his newfound pa.s.sion for ecology, Krause eventually sold his music company, enrolled in graduate school, and got his doctorate in bioacoustics. But his musical training never left him. In fact, it helped sp.a.w.n a startling notion that came to him early one morning while camping in Kenya's Masai Mara reserve. Krause had been up for thirty hours, recording the sounds of insects, owls, hyenas, bats, and elephants. Exhausted and "completely out of it," Krause was suddenly struck by the idea that the animal sounds around him were ... orchestral. "These critters are vocalizing in relations.h.i.+p to one another," he thought to himself.

Back in his studio, Krause examined sonograms of the recording session. It was clear to him that what he had heard was a sequence of sounds so carefully part.i.tioned that they read like a musical score. Different species vocalize at specific frequencies or times so they can be heard above the other animalsa"in the same way you can make out the individual sounds of the trumpets, violins, and clarinets as Beethoven's Fifth builds to a crescendo. Krause dubbed the spectrum of animal sounds "biophony" and distinguishes them from human sounds, which he calls "anthrophony."

Krause wasn't alone in his conclusions. More than a decade later, in a laboratory far away from Krause's California headquarters, Hans Slabbekoorn picked up on the same distinction. And, taking Krause's work a step further, he started piecing together its startling implications.

Before studying blackbirds, Slabbekoorn worked in the tropics of Cameroon, testing a theory that habitat constraints can drive birds to sing at different frequencies. Sounds that mask birdcalls may cause difficulty or ambiguity in communication, and Slabbekoorn thought he could get to the bottom of this by comparing the songs of birds living in dense rainforest with those in more open habitats.

His test subject was a bird called the little greenbul. He discovered that little greenbuls in the dense forest sang more often at lower frequencies than their relatives living in open areas, probably because lower frequencies transmit more effectively through thick vegetationa"and also because the dense forest is filled with the sounds of high-pitched insects. "It was often so noisy in these habitats that I could hardly make good recordings," Slabbekoorn recalls.

After returning to the Netherlands, Slabbekoorn suspected a similar dynamic was taking place in the city. Most urban noise comes from cars, trucks, buses, and trains, whose sounds are concentrated at low frequencies. If the rainforest's high-frequency noise drives birds to use lower frequencies, Slabbekoorn reasoned, then the low-frequency sounds of the city should pressure birds to use higher frequencies. As his research progressed, Slabbekoorn found that great t.i.ts and European blackbirds are indeed switching to higher frequencies to be heard.