The northernmost point of mainland Britain is a piece of land called Dunnet Head, which sticks off the Scottish coast like a big toe testing the cold waters of the North Sea. Atop cliffs at the tip of the toe sits a squat lighthouse, built in 1831 by Robert Stevenson, the grandfather of the author Robert Louis Stevenson. The lighthouse is popular with shutterbugs, but none is here on this early-July afternoon. Blame the wind. It jostles you, roughs you up, rips the breath from your nose.

Not that the wind has driven everything away: Dunnet Head hosts one of the largest seabird colonies in Scotland. From an overlook near the lighthouse, you can peer down at thousands of murres and razorbills bunched five birds deep on narrow shelves of rock; the wind carries their churlish growls. From their nests among the cliffs’ many nooks and crannies, northern fulmars croak and wheeze, but above the general clamor rings a high cry that is both insistent and becoming more and more rare: Kit-ti-waake! Kit-ti-waake! Kit-ti-waake!

The United Kingdom is home to almost half of the seabirds that breed in Europe. Of those, nearly three-quarters are in Scotland. Seabirds all over the world are declining, but few more so than the kittiwake in this part of the North Sea. Where it was once one of the most common birds here, in places its numbers have dropped by more than 90 percent. Colonies in the Orkneys and the Shetlands that rang with the calls of tens of thousands of kittiwakes now have just a few hundred pairs, or a few dozen, or none at all. But to save the kittiwake, biologists must extract the cause of its decline from a system rife with uncertainties and beset by change.

The kittiwake is a small gull about 15 inches in length, with a wingspan a little more than twice that. Adults have a typical gull’s white head and gray wings, but while they may be known for their voice—many of their common names are onomatopoeic in some way—kittiwakes truly distinguish themselves in the air. They have an almost ethereal buoyancy, their movements so graceful and fluid that when they flap, they seem to be trying not so much to generate lift as to hold themselves down.

This affinity for motion may seem total, but like all seabirds, kittiwakes must come ashore to breed. This they do in the spring. Even then, they seem loath to touch too much ground, nesting on the most precipitous of coastal cliffs. Their nests, built of grass and mud and spaced neatly apart, barely accommodate their two or three eggs, much less their body; the birds cling to the edges with their tiny toe claws. Once finished breeding, they return to the sea. Some might not come within sight of land until the next year.

This out-of-sight-ness is part of what makes kittiwakes so hard to protect. Cordoning off their terrestrial haunts is helpful—the Royal Society for the Protection of Birds recently added Dunnet Head to its list of reserves—but it is not enough. Kittiwakes also must eat, and in the North Sea, the creature they prefer is a slender silver fish called the lesser sand eel.

In the 1990s, when biologists first noted the kittiwake’s decline, a story started to piece itself together. Kittiwakes were in trouble, it was suggested, because they could not find enough sand eels to feed their chicks. Sand-eel stocks were low, in turn, because of two main factors: warmer sea-surface temperatures brought on by climate change, and a fishing industry that caught hundreds of thousands of tons of sand eel each year, in part to feed salmon and hake in Scandinavian fish farms. The solution seemed straightforward, conceptually if not politically: Close the sand-eel fishery off the eastern Scottish coast. The European Commission did just that in 2000, but while there was some initial promise, kittiwake numbers kept dropping.

Something else was clearly afoot. Scientists did not know what it was, and they knew they did not have long to figure it out. “In the old days, you did an experiment or a study, and then you analyzed the data, and then you wrote the manuscript, and then it was reviewed, and eventually it was published, and all of that could take 10 years,” says Neil Banas, a mathematical ecologist at the University of Strathclyde. “But the ocean is changing faster than our ability to complete the scientific cycle. We’re being shown just how quickly we have to work. The seabirds are disappearing now, and so we have to understand it now.”

Banas works out of a small office on the eighth floor of one of Strathclyde’s buildings in downtown Glasgow. He is in his mid-40s, with a curly jumble of brown hair and a bright, inquisitive disposition. On his bookshelves—always check a person’s bookshelves—are titles that testify to his diverse interests: statistics and fluid dynamics, Haida epics, novels, travelogues, an anthology of writings on the sea. He is originally from New Jersey and has a doctorate in oceanography, but he majored in physics and religion as an undergraduate and has a master’s degree in religious studies. “The biological world is neither exactly logical nor a chaos; neither a ball of warm sentiments nor cold and aloof,” he wrote in his master’s thesis. “It runs on other principles: a musky, tactless intimacy, and a meandering logic, full of reversals.”

Banas came to the North Sea ecosystem five years ago, as a visiting researcher at Strathclyde from the University of Washington, and he was hired on faculty at Strathclyde shortly thereafter. Ever since, he has been enmeshed in the ecosystem’s details and dynamics. You could say that he is part of a group working to help the kittiwake, but that would not be wholly accurate; his role is both deeper and more distanced. To understand the kittiwake’s decline, he does not focus on the kittiwake. He hardly looks at the kittiwake at all. Instead, he looks at plankton, of which there are two kinds. Phytoplankton are single-celled plants that form the base of the food web. The tiny organisms that feed on phytoplankton are called zooplankton. Plankton is derived from the Greek word planktos, which means “wanderer” or “drifter,” and both phytoplankton and zooplankton live mostly at the mercy of ocean currents. Their movements drive marine productivity: Where there are a lot of phytoplankton, there tend to be a lot of zooplankton. Where there are zooplankton, there are small fish, such as sand eel. Where there are a lot of small fish, there are a lot of seabirds, such as kittiwakes, or larger fish or whales or humans.

In the North Sea, the links from phytoplankton to zooplankton to sand eel to kittiwake look simple enough when sketched out, like a string of beads, one after the other. That is the purpose of the model of plankton dynamics that Banas is building: to strip a complex system down to its essential components, rendering it as something people can wrap their mind around and, perhaps, manage. A facsimile of the thing, if not the thing itself.

Models are everywhere. Almost all the environmental stories you read or hear, be they about melting glaciers or the fate of some endangered animal or the path of a hurricane, have a model in them somewhere. Whether they are straightforward statistical tests or elaborate meta-worlds, models at their best help explain what we saw, what we are seeing now, and what we might see in the future. They are, as one pair of modelers have written, a “toy version of nature.”

Models are also not new. The famous Fibonacci sequence from the 13th century, for instance, is a population model. The golden ratio may be all anyone remembers, but Fibonacci conceived of 1, 1, 2, 3, 5, 8, 13, etc., as a way to account for proliferating rabbits.

One of the first modern ecological models, the Lotka-Volterra equations—named for the two ecologists who devised them independently in the 1920s—describes the theoretical relationship between a predator and its prey. Predators gorge on prey until the prey population declines. Once prey numbers drop, the predator population drops, since it no longer has enough food. When that happens, the predation pressure on the prey decreases, and its numbers start to rise. Now predators have more to eat and their population rises. The prey start to drop again, and thereafter, predators and prey oscillate in perpetuity in boom-and-bust cycles.

Like the Fibonacci sequence, Lotka-Volterra has an elegant simplicity. As a model, it has been described as sublime. The one proviso, and it is admittedly a big one, is that the phenomenon Lotka-Volterra depicts has never been found anywhere. Approximations of it occur—the best known is between lynx and hares in far northern climes—but inevitably, some other factor interrupts the cycle. Other animals eat the hares. Someone cuts down the forest in which the lynx live. The world of Lotka-Volterra, in other words, does not exist.

How can a pristine abstract world be all that informative about the messy real one? More broadly, how are models used not just to make sense of that messy real world, but also to make meaning? In this environmental moment, these are contentious questions. Toy versions of nature they may be, but most models are so complicated that for someone untrained in the statistical arts, they can be hard to understand, and therefore hard to trust. Well-known models, such as the Intergovernmental Panel on Climate Change’s projections of sea-level rise, start to double as political shibboleths. Do you believe what the model is saying? Are you willing to go where it leads you? Acceptance of a model’s mathematical output is, for most of us, an act of faith, and one confounded still more by the contradiction that lies at the heart of modeling: “Essentially all models are wrong,” the British statistician George Box once wrote, “but some are useful.”

The first model of plankton population dynamics was published in 1939 by Richard Fleming, a biologist at the Scripps Institution of Oceanography, in San Diego, California. Fleming reduced a sea of variables to a straightforward process: The rate of change of phytoplankton density in a given place at a given time will be a function of their growth (through reproduction by cell division) minus their death (through grazing by zookplankton). With this equation, Fleming could predict with reasonable accuracy the influx of phytoplankton in the English Channel during a period of seasonal bounty known as the spring bloom.

As a model, this was remarkably simple—rate of population change equals births minus deaths, in essence—but its implications were profound. It gave biologists a new way to think about how plankton moved through the ocean, a new means of explaining why they were where they were. Within two years, two biologists working at Georges Bank, off the New England coast, had expanded Fleming’s model to include turbulence as a parameter. Turbulence, or the mixing of water, influences the amount of phytoplankton available to zooplankton. This expanded plankton model was the first to couple biological phenomena with the environment’s physical properties.

Then, in the 1950s, John Steele, a British researcher at the Woods Hole Oceanographic Institution, in Massachusetts, made a crucial innovation when he developed a nutrient-phytoplankton-zooplankton food-chain model in a two-layer sea. Where earlier models were forced to assume that the ocean existed in a steady state, Steele’s model added spatial structure and time, which allowed it to represent the seasonal exchange between deep and shallow water. Other researchers added more details, and as computers became more powerful and their use widespread, Steele and his colleagues were able to incorporate even more complexity into their models.

The spread of what one biologist called “in silico research”—as opposed to the in vitro (outside a living organism) and in vivo (in a living organism) approaches of old—came with a risk. In 2012, Roger Cropp and John Norbury, a pair of mathematical biologists, wrote a paper titled “Modelling Plankton Ecosystems and the Library of Lotka.” They took their cue from the Jorge Luis Borges story “The Library of Babel,” about a library that holds an immense number of 410-page books, which together contain all possible combinations of 25 characters, sensical and nonsensical.

Likewise the Library of Lotka. Cropp and Norbury calculated that absent any real data, a plankton-population model that makes “reasonable” assumptions about a generic system “contains at least 10151 predictions, only one of which is correct, but all of which are plausible.” They estimated that even with the world’s most powerful computer, running the model through all its permutations would take longer than the universe has existed.

In his office, or sometimes at a coffee shop, Banas works to “slash the Library of Lotka exponent,” shrinking the 10151 possibilities by confronting models with real data. “It’s a bit like a bonsai,” he told me. “The model possibilities want to grow wild and bushy, but with every data point, you can make a little snip.

Banas and his colleagues are building a chain of models that attempts to connect the changes in the ocean to the zooplankton to the sand eel to the kittiwake. “You explain the sand eel, and you begin to explain a lot of what is happening with the birds,” Banas said.

As with the kittiwake, the way to a sand eel’s heart is through its stomach. In the North Sea, the sand eel’s principal prey is Calanus finmarchicus, a copepod about a tenth of an inch long that may be the most abundant and best-studied zooplankton on the planet. C. finmarchicus lives not just in the North Sea, but across the whole of the North Atlantic and up into the High Arctic. There, it has, per Banas, “a real Jack London life history,” fattening up on phytoplankton during the spring bloom before descending thousands of feet to overwinter in a dormant state.

An illustration of sand eels and kittiwake feathers
Leonardo Santamaria

Most C. finmarchicus in the North Sea come from the Norwegian Sea, a place of such awesome primary productivity, Banas said, that a tiny fraction of its output is enough to drive extensive food webs. In a typical year, or in what biologists used to think of as a typical year, tremendous amounts of C. finmarchicus would rise from the depths in the spring and be borne into the North Sea via surface currents. Once in the North Sea, sand-eel larvae would feed on them and grow to a size delectable to a number of seabirds, kittiwakes among them.

Since the 1960s, though, C. finmarchicus biomass in the North Sea has declined by 70 percent. The decline accelerated in the 1980s, when the North Sea warmed, and the currents from the Norwegian Sea were no longer as strong or predictable. The puzzle was that, despite the loss of C. finmarchicus due to the regime shift, the overall biomass of zooplankton in the North Sea stayed about the same.

Still, the sand eel were declining. The reason appears to lie in a regional reorganization of the Calanus genus, and the displacement of C. finmarchicus in the North Sea by another species from the south, C. helgolandicus. As the southern limit for C. finmarchicus and the northern limit for C. helgolandicus, Banas explains, the North Sea is a boundary between two copepod lifestyles. On the one hand, C. finmarchicus, which inhabits cold, deep water, can live for more than one year and must store fat for the winter. It is enormous (as copepods go). C. helgolandicus, on the other hand, comes from warmer, shallower coastal seas. It can cycle through multiple generations in a single year and is smaller and less fatty.

Although the conventional wisdom holds that the inherent size disparity between the two species is responsible for the sand eel’s predicament, modeling work by Banas’s colleagues suggests that a difference in the timing of the two species’ peak abundances may be more crucial. The hordes of C. finmarchicus carried into the North Sea every spring have hatched the previous year and are fully grown; the sand-eel larvae that eat them get big quickly. But when the C. helgolandicus arrive, they have not reached their full size. The sand eel that eat them do not get as large as quickly, and so are less calorific in May, when the kittiwakes arrive to snap them up for the hungry chicks back on the cliffs.

What this means for the kittiwakes is still open to interpretation. “The story about kittiwakes and sand eels has been told so many times, and lots of those articles say that as sand eel go up or down, kittiwakes go up or down,” says Agnes Olin, one of Banas’s graduate students. “There are certainly a few big papers where you see a relationship between sand-eel abundance and seabird success, but there are also papers where you don’t see that relationship.” Sometimes, when sand eel are abundant in the North Sea, seabirds do poorly, or they do well in one region but not another.

The problem, Olin thinks, is that many researchers tend to conceive of sand eels as a single entity. “It’s rare that you have data on sand eels at a scale that’s relevant to a seabird,” she told me. “You can have an estimate of sand-eel abundance for the whole North Sea, but you need fine-scale information to see sand eel the way kittiwakes do.”

From a kittiwake’s perspective, for example, fat sand eels would seem to be ideal; but, Olin cautions, not too fat. If a year is too good and the sand eel do too well, then they might hibernate early. They do this by burying themselves in the sand, which is how they get their name. Once the sand eels are buried, the kittiwakes get nothing. “So the end result is the same as sand eel having a poor year,” Olin said, “except it happened when they were having a good year.”

Such details of sand-eel natural history may be key to the kittiwake story. With Banas and Ruedi Nager, Olin recently finished a cluster analysis of kittiwake colonies along the east coast of the U.K., from the Shetlands and Orkneys down to southern England. They looked at how colonies’ reproductive success compared with area sand-eel stocks. While some groups were declining steeply, they found, some were ticking along reasonably well. Declines were not uniform, in other words, but tied in part to the state of local sand-eel performance. “That’s why models are useful,” Olin said. “You can start to explain why you might find a correlation in one area in one time but not in another place at another time.”

To account for all these nuances, Olin is building a model that will produce more detailed maps of sand-eel size and survival. For this, she read everything she could find about the species. “I approached the problem more like a biologist than a modeler,” she said. She looked at how water temperature affects sand eels’ rates of ingestion, and how well the little fish can see under different light conditions. She noted that when foraging, a sand eel swims one body length per second (about five inches or so), and in that time it can eat one or two copepods. Listening to her enumerate her bibliography, which includes a thesis in its original Danish, it becomes clear that she is not turning the sand eel into a generic cog for her model. Instead, she is turning her intimate understanding of the sand eel into the most accurate possible abstraction of the species.

The difficulty lies in moving from that abstraction back to the mess of the entire North Sea. “It’s a mistake to think there is one model for everything,” says Michael Heath, a marine scientist at the University of Strathclyde and the head of Banas’s marine modeling group. His labor of love is a nutrient budget for the North Sea, of which Banas’s and Olin’s models are just one small part. In this “big-picture, large-scale view,” as Heath calls it, huge amounts of energy move from bottom sediments to the deep ocean to the surface, where zooplankton can access it. Zookplankton’s performance, after some minor adjustments, then helps predict fish numbers.

While Banas and Olin dwell in the details of copepod and sand-eel natural history, Heath comes at the task from a wry distance. “I don’t really focus on how the kittiwake is doing,” he told me. “I just have a box that says Birds and Mammals.” The North Sea ecosystem, he goes on, has rules but no purpose, and so no central state to which it longs to return. “That’s a human wish,” he said.

Humans have already bent the North Sea ecosystem to their wishes. Kittiwakes, Heath pointed out, may not have always been so dependent on sand eel. “There was massive overexploitation of piscivorous fish in the 1980s, which led to the rise of sand eels in the 1990s,” he said. “That led to the massive expansion in the sand-eel fishery.” But subsequent closures of fisheries for species that ate sand eel may have contributed in part to a decline in sand-eel stocks. “Humans aren’t always so good at thinking about things being in complex networks,” Heath said. “Not everything is a linear response. Not at all.”

These ripples of human acts past and present can be some of the hardest things to account for in a model. Heath mentions fisheries’ discards, the undersize or otherwise unusable fish that are tossed over the side of a fishing boat. For decades, kittiwakes and other gulls benefited from the discard subsidy, so much so that most biologists believe their populations were artificially inflated. When management targets for seabirds were set in the early 1970s, those enhanced numbers were declared the natural baseline. Now discards are forbidden, and some gull populations are plunging as a result. “Self-correcting might be another way to put it,” Heath told me. “It’s not even clear there should be that many kittiwakes.”

Heath had a kind of trickster grin when he said this, so I assumed he was kidding. He was, sort of. “Obviously there is a difference between poor accounting methods, bad assumptions, and legitimately worrying declines,” he said. He put the kittiwake somewhere among the three, leaning toward the last. Even if the sharp decreases since the 1990s are a kind of correction, that hardly means everything is A-okay. “What we’re seeing now probably reflects roughly what the system can support in its current state,” Heath said. “But that is not what it should be able to support.” It sounds almost like a human wish.

Models stack atop models, sifting through streams of information until they arrive at what looks like a cause: the warming North Sea, one microscopic animal displacing another, a small fish that stays small longer than it used to, a bird that cannot breed. Once the links leading to the kittiwake’s decline are uncovered, what can be done about them? Some of these phenomena were set in motion ages ago; scientists are proposing to address their effects just as they build in momentum and hurtle away.

Often, when trying to keep track of all the models and their different layers of meaning, I thought of the kittiwakes at Dunnet Head. Olin did not include that colony in her cluster analysis—no one monitors it regularly, so it has no recorded history—but since it sits across the Pentland Firth from the Orkney colonies, I assume its numbers are also trending downward. Then again, I saw chicks in the nests. Some had juvenile plumage, others were flapping to strengthen their flight muscles. I mentioned this to one biologist and he perked up. “That’s great news!” he said.

Banas had talked of the North Sea system having a “knife-edge quality, an edge-of-chaos quality,” as huge variances butt up against underlying stabilities—which is how it can fluctuate, sometimes wildly, without collapsing. At Dunnet Head, I looked for stabilities that might forestall collapse. There seemed to be few: the walls of rock, the sea pounding them, maybe the wind. Little else. Certainly not the kittiwakes. Most were far off, trying to find food, a flurry of white specks near the horizon. Even with my binoculars, I could not see them well; at times I was not sure if they were birds or spume from the waves.

Back in Glasgow in his office (or at a coffee shop), I knew this was how Banas was seeing the kittiwakes too, in a way: as dots dancing across his visual plane. Through all these dots, he was trying to fit a line that he hoped would show something like the truth—or, failing that, would at least be useful. But there was no guarantee. “Even when you’re right in the middle of it, staring at the details, you’re not completely sure what you should be talking about,” he told me. “The complexity is in the silence, when we lapse into silence. Sometimes when Heath and I are talking, we’ll work down and down, and then we think, Have we made it to the bottom? To the most critical level? Or is this just another side channel? And then silence.”

Dunnet Head is not silent in that depthless way—at least not yet—but underneath the cacophony of the colony, it has a quality of remove, of stillness. I put down my binoculars and watched the birds in front of me. Some balanced on the edges of their impossible nests, but a few were airborne. They whipped about the cliff face, buffeted by the wind, by forces that have changed the seas and their fortunes. Against these forces they whirled, crying out their name.