I.
In ecology, the species diversity of an ecosystem can be described using Shannon’s entropy. Shannon’s entropy is typically expressed as:
H′ = −∑ pi ln(pi)
where pi is the relative abundance of species i.
This approach, borrowed from information theory, considers the complexity of a forest, coral reef, puddle in the sand, etc., in terms of how much new information is gained when a single organism is sampled from the ecosystem at random. Richer ecosystems with a balanced abundance of many different species have higher entropy. The entropy of a system with exactly one species is zero.
II.
The cavern was 220 feet deep at its lowest point, and possibly much deeper, its full extent having never been mapped. Julia hung around 60 feet, breathing slowly to keep her buoyancy neutral, gazing over an outcropping into the depths. Limestone fingers jabbed into the murky water, curled as if to beckon her downward. But the fish she’d come to study kept mostly to the shallows, they liked the sunlight, the seasonal algal blooms, the constant temperature of 91 degrees, the bounty of diatoms and tiny crustaceans to round out their diet. She kicked over to a ledge where a scattering of little blue eggs sat on a bed of green algae. A predaceous diving beetle aimed its mandibles at one and Julia swatted it away, then began collecting the eggs one by one in a glass pipette.
It was a slow forage, the eggs barely a millimeter in diameter and strewn widely throughout the spring. Julia moved methodically, running a spiral from the outer perimeter of the spring around towards the center. By the time her pressure gauge was in the red she had scoured the large majority of the sampling area and had twenty-two eggs in her jar.
Her advisor stood waiting as she hauled herself out of the water. Craig had designed the project and served as both principal investigator and field work supervisor. He had brought Julia on for her expertise in the study of extremophiles, as demonstrated by her Master’s thesis on acidophilic eukaryotes, and not at all because she was an attractive woman 20 years his junior and new to the field. Her job was to do the grunt work. And to personally manage all phases of the data collection, and carry out the statistical analysis, and interpret the results, and write the research paper, in which his name would appear before hers. He seemed professional, so far. A little hard to talk to.
While Julia disassembled her gear, Craig examined the sample. “You’re short,” he said. “The study design is for thirty.”
“I couldn't find thirty,” she said.
It shouldn’t have been surprising. The population of Burial Spring pupfish (Cyprinodon sepultus) was at its lowest level since the species was discovered. C. sepultus was limited to a single fissure-ridge cavern in the limestone where Badwater Basin meets the Owlshead Mountains. Like other pupfishes of the Great Basin, it had evolved under extremely specific conditions as the pluvial lakes of the last glaciation receded, leaving behind tiny pockets of barely habitable water. The ability of pupfishes to adapt to such a punishing environment was unique among vertebrates and made them a promising candidate for ecological and biomedical research. But their specialized genome also made them highly susceptible to disruptions. An earthquake just a few months prior had produced a standing wave that killed all the algae in Burial Spring, and in turn the population of C. sepultus died off in large numbers. The most recent survey counted only 47 individuals. Though the species reproduces quickly, the level of genetic diversity and spawning potential following such a shock was likely to be critically low.
Craig’s study proposed to transport a small number of eggs into an ex situ facility and hatch them into a captive “lifeboat population,” which could then be bred, maintained, and returned to the wild to mitigate future population shocks. It would be difficult to establish the captive stock with so few eggs. But they would have to make do with what they had.
They loaded the eggs and the scuba equipment onto the bed of Craig’s truck and drove northeast over the playa. The fish conservation facility stood a few miles from Burial Spring. Most of the construction budget had gone to the wet lab and the refugium, a huge concrete tank built to replicate the natural features of Burial Spring. The living quarters consisted of a tiny kitchen with bar seating and a fire extinguisher that was always in the way, a single bedroom with two bunks, and an unpleasant bathroom. The satellite internet was spotty at best, but at least the air conditioning worked.
When they arrived they brought the eggs to a breeding tank where a trio of males, recovered from Burial Spring during the last population survey, swam unassumingly. C. sepultus was a small species, about the size of Julia’s thumb, with metallic blue scales and violet-black fins (if you looked closely, the fins shined with a dull iridescence she found quite beautiful). She carefully placed the eggs around the tank, just underneath a thin plastic mesh intended to make sure the males fertilized them instead of eating them. By morning, if they were lucky, at least some would have embryos inside.
She and Craig ate a dinner of microwaved ramen, which he slurped aggressively while largely avoiding her attempts at conversation. The only way to get him talking, it seemed, was to prompt him to complain: He resented the project’s lack of funding in particular, his budget so meager he could only afford to hire a single temporary research assistant (as if to imply Julia was somehow inadequate), not to mention the immense annoyance of having to appease the various state and federal conservation bureaucracies who ruled over the Death Valley ecosystem. After dinner she changed into sweats in the bathroom, holding her breath against the smell of the sump pit below. She climbed into one of the bunks. On the other one, Craig snored like a tortured pig. It took a long time to fall asleep.
III.
Drowning. Back in the Burial Spring, gasping for air and getting hot, silty, clay-tasting water. Above: a vague tear of sunlight, very far away. She flailed for her regulator, which was nowhere, then went for her second stage, also missing. Not even a tank on her back. Where was her gear? What was she doing this deep? She must have blacked out. Woken up just in time to die. There had been an idea, something she’d picked up from a poem or a song, that drowning, in spite of the terror, would be a surprisingly peaceful way to die. This notion had been incorrect. There were no surprises here, only panic, the pounding of a heart that was losing its fuel, the searing heat in her lungs as they started to take in water, disgusting water, the stagnant and cooked-down muck of a ten-thousand-year-long drought, yes she was bursting, would be fattened and distended by this undead sludge until her skin split from inside to out, splitting like her mind, that electric chasm of signs, now devoid of all but a single word: Julia, Julia, once the pure sign of all she was and would be, now losing meaning by the second, becoming pure sound, Julia, Julia, Julia, Julia—
“Julia!”
She bolted upright in her bunk.
“What’s going on?”
“Nothing. Bad dream.” But she was hyperventilating, as if she’d really been out of air.
Craig’s face was blue in the moonlight. He looked at her for a long time, then lay down.
The nightmare left her with a lingering, obsessive anxiety, not about drowning or even death in particular, but about the research project. She lay awake all night questioning whether there was any real value to it at all. Pupfishes live for about ten months in the wild. They had evolved due to freakish coincidences piling up across geologic time, their adaptations so precarious it was a wonder they’d adapted at all. In the 1960s, it was discovered that even modest extractions of groundwater from the Death Valley aquifer threatened to choke the pupfish out of existence, and the resulting conflicts over groundwater rights led to a protracted legal battle between pupfish conservationists and local ranchers. The industry representatives were so secure in their position, so certain that all this amounted to a tremendous waste of time and money, with no measurable impact on the lived experience of any human being, they adorned their pickups with KILL THE PUPFISH bumper stickers and openly threatened to dump pesticides into the springs. Maybe they’d been right. Maybe it was pure environmentalist hubris, and there was no logical reason to conserve anything in the hottest, most inhospitable place on the planet. Maybe she had made a terrible mistake about how to spend her life. These thoughts plagued her unmercifully until sunrise, and then Craig rose to make oatmeal, and the A/C kicked on.
IV.
Nine out of twenty-two eggs hatched successfully into C. sepultus larvae. Forty-one percent. This was nearly three times higher than the rate observed in Burial Spring, especially in October when the nights began to rebel against the torturous summer heat, producing day-to-day temperature swings of forty degrees or more and corresponding drops in algae cover. The sampling and insemination procedures had been successful. Now the task was to keep the juveniles alive until they could safely be moved into the refugium. She transferred each one to an individual tank (this was to prevent cannibalism). The temperature and pH were carefully balanced to match the upper layer of the Burial Spring.
She added algae to the tanks, not enough to alter the oxygen concentration, just something for her little guys to eat.
Over the following week her routine was the same every day: breakfast at 8 AM, monitoring the rearing tanks every half-hour, dinner at 5 PM. In the time she had in between measurements she outlined research reports and data analyses for various audiences, all according to Craig’s design.
Craig was hands-off about her day-to-day tasks, which she appreciated. But their conversations, held mostly at dinner, were increasingly difficult. He plainly had no interest in her background, her aspirations, or her thoughts on the project. She tried filling the air with her favorite quandaries, everything from “What do you think of the Bayesian approach to rare-event impact analysis?” to “Is monogamy the natural mode of human reproduction?” to “Shouldn’t the human race enact a program of voluntary self-extinction, if the goal is really to minimize suffering?” Craig was a little more receptive to these abstractions, but it was clear he thought he had better things to do than indulge her.
The result of his aloofness, which may have been intentional, was that she spent a great deal of her free time with the pupfish. When she was alone with the juveniles in the breeding tank she felt at ease, watching them nip at the fuzzy green algae, feeding and growing stronger. Sometimes, when Craig’s snoring or the fact of his presence kept her awake, she slipped out at night to watch them, moonlight glinting in their tiny black eyes as they flitted innocently around their tanks, uncritical of their fabricated world.
V.
Out on the salt pan, Julia lifted her chest to the star-polluted sky. It was very cold outside. She let out a wordless scream, scraping her voice over the dolomite horizon. At dinner she’d gotten in an argument with Craig over the relationship of ecological complexity to the thermodynamic entropy of the universe. It had gotten bad—she’d stormed out in dramatic fashion. Probably not necessary to make a scene like that. Until now, the two of them had operated within the guardrails of professionalism, with a certain mutual expectation about the mode and tenor with which they related to one another. Now there was no telling how things would be.
This was the problem with entropy.
She recognized—and in this they both agreed—that the general picture of things was a progression from order to disorder, from high energy to low, from a situation where much could be inferred from a small amount of information to one where even perfect knowledge tells you nothing. She knew this from the Second Law of Thermodynamics, but anyone could tell based on raw experience alone, it was the story of everyone’s life, perhaps the only story there was. But in the context of ecology, “high entropy” referred to the most diverse, lively ecosystems on Earth. The microstate represented by a given sample told you less about a complex ecosystem than it did about a simple one. Shannon’s entropy was highest in rainforests and tidepools, lower in the barren deserts, lower still in the frozen wastes of the permafrost. How could it be that in a universe of dissipation, homogenization, progressive dementia on a cosmic scale, the pockets where chaos and uncertainty were at their most extreme were the very places where life, which was necessary for anything to be known at all, flourished?
Craig’s answer was simple: life was a combustion engine. The complexification of organic matter was the process by which the Sun’s energy could be most efficiently used up, squeezed through the trophic layers and burned into random heat energy. Evolution by natural selection, though appearing to its subjects as a tenacious search for survival through experiential diversity, was really just a convenient way to cook off the energy gradient produced by solar bodies. Life, according to Craig, existed solely to accelerate death. But Julia could not accept this. She knew—knew it in her bones, knew it at the very core of whatever it was that made her a human being and allowed her to know anything at all—that something else had to be going on. That the level of complexity, the amount of information required to describe the biosphere, represented something orthogonal to the law of loss, and more formidable: a living power whose constant evolution stood in contravention to the universe’s frenzied dash towards equilibrium. Craig said this was nonsense, that it didn’t hold up philosophically, that she was conflating two distinct concepts that in reality had little to do with one another. But Craig was an asshole. He said these things because he knew they would terrify her, so she would stop asking for his thoughts. Anything to keep her in the dark.
But the desert glowed. She hiked up the side of a limestone pile and looked down over the playa. In the moonlight she could make out the wineglass-shaped stains where streams had once flowed down the sides of the mountains. Twenty-five thousand years ago this whole area was underwater, the site of an enormous endorheic lake. Fish from the Colorado River colonized what was now the dry, empty air that chilled her face. Only the pupfish, secluded in their private springs and flooded fissures, had survived the retreat of those ancient waters. Julia imagined geological time in fast-forward, the lake forming and evaporating in a transglacial pulse, each time spawning a great diversity of life fated only to fade away.
She followed a trail around to the sheer side of the butte, stepping over rocks stained with orange ochre. Suddenly she froze in her tracks. Down there, on the far side of the salt pan, something was wrong.
There were trees.
A whole forest of junipers, pinyons, and other conifers stretched from the butte to the edge of the border mountains. The moon lit their needles a deep silver-green, and in the canopies she saw the rustling of birds. She rushed down the slope toward the tree line for a better look. The smell of pine and a hint of salt filled the air. She ran a hand along the coarse, warping bark of a juniper and wondered how it was possible such flora could have been here. And how had she not noticed it before? There was vegetation scattered throughout Death Valley, but mainly high up in the mountains, and nothing like this level of density.
Passing into the trees, she heard the skittering of small animals on all sides. Blades of moonlight sliced through the canopy, leaving stripes on her arms as she walked. It was beautiful. She forgot all about what was and wasn’t plausible and wandered with abandon, crunching twigs underfoot, feeling a sense of comfort for the first time since she’d started the research project. Then she heard the growling.
It came from a darkened cluster of shrubs in the distance—a hungry snarl, wet with anticipation. She saw the eyes, green and narrow, and under them, barely visible, a pair of gigantic, knifelike teeth. Eyes and teeth, disembodied in the darkness, moving steadily towards her. She turned and ran, ripping through vines and whiplike twigs, and she was certainly being chased, could hear the creature padding after her, mere inches from wrapping its teeth around her spine. She burst out onto the salt pan and slipped immediately, crashing through the thin whitish crust and plunging into a pit of mud. She struggled to her feet and bounded for the rocky outskirts, which she followed in a mad, staggering sprint all the way back to the facility. She knelt in the shower until sunrise, watching dirt swirl down the drain. She was beginning to understand.
VI.
One of the pupfish died. They found it belly-up in its tank, swirling around the filter. The temperature and pH readings were perfect, but the fish had stopped eating. Perhaps it was disease, something microscopic. Or it could have been some environmental condition they’d failed to identify as significant.
“Where were you all night?” Craig asked as he scooped the dead fish unceremoniously into a freezer bag.
Julia carefully gathered each of the living pupfishes in a small transport tank. “Outside,” she said. She didn’t want to tell Craig about what she’d witnessed on the salt pans. She felt as if she’d seen a ghost—in fact, she was sure that’s what had happened. Her experience had terrified her, but it had also enthralled her. She would keep it to herself. Her secret.
“This next phase of the project is critical,” Craig said. “I need you in top form. Well rested. We can’t risk a repeat of whatever happened to this little guy.” He gave the dead pupfish a shake. Was he blaming her?
“I monitored them constantly,” she said. “You can check the spreadsheet. All their levels were exactly right.”
“I checked the spreadsheet. There are dozens of missing measurements, and some that can only be errors.”
“That’s weird. Maybe the file got corrupted. You should check the version history.”
“Right,” Craig sighed. “It probably wasn’t your fault. They’re finicky creatures, after all.”
Julia brought the transport tank into the refugium. The surface was a hundred square feet of algae-caked water, the interior a near-perfect reconstruction of the stony bathymetry of Burial Spring. They’d stocked it with plankton and seed shrimps, flatworms and mud snails, the natural ecological community reproduced ex situ, equal in species richness save for one all-important taxon, which Julia was providing now, as she slowly lowered the transport tank under the surface of the refugium and watched her eight remaining pupfish swim out. They looked excited to move into their new home. If the fish reproduced on their own in here, the experiment was a success. And her time in the facility would draw to a close, the day-to-day monitoring and management tasks turned over to National Park staff. She’d only have to drive in once a month to follow up on things, and she’d never sleep in the same room as Craig ever again. Two of the pupfish darted in circles over a cluster of algae that hung on an underwater ledge. They were already starting to eat.
VII.
She wasn’t going to leave.
She realized it the second time she found the Lake.
It appeared late at night, and only to her, when she snuck out of the facility to go wander the fringes of the salt pans. For several nights she returned to her spot on the far side of the butte, and finding only the hexagonal cracks of the playa she began to accept that it must have been a hallucination (or more appropriately, a mirage). But then she found it again, in a different part of the basin, spread across the fringes of a mudstone crag. This time, when the monster growled, she didn’t run. She turned and walked calmly towards the far side of the woods, followed by footpads and creeping things which did not disturb her. She came to a place where the trees gave way to ferns and tall grasses, and she learned that the forest surrounded the shore of a vast body of water, its gentle waves crashing at her feet, its surface throttling the moonbeams into brilliant electric shimmers. On the far shore she glimpsed a shadow, a great hulking thing that moved gently in the distance. Then she saw the tusks—it was a mammoth, approaching the water and lowering its trunk for a drink. She’d never seen anything so beautiful.
As far as she could tell, what was happening was a regression, or a reflection, of a time when the ecosystem was in a state of greater complexity. The exact method by which she was able to observe it was a mystery, but what interested her was the fact that its appearance represented a localized shift into a state of higher entropy, the Lake much more diverse, and with statistical qualities far harder to predict, than the desolate playa surrounding it. This was information which had never been known, at least not to any human being, yet it had been preserved and reproduced, somehow, just for her. And it was no mirage. In fact it was realer than anything she’d ever encountered in her life, this secret garden of the Pleistocene, this recreated oasis where time ceased its arrowlike flight and fanned out into uncertain vectors. She had discovered a way to see this place as it had once been, as it was before the great extinctions of the Anthropocene—as it was meant to be, she wanted to think, but then she remembered Craig’s theory—
Craig. The refugium. She couldn’t afford to stay here too long. There were things that had to be done.
VIII.
“What were you doing out there?”
Craig was sitting at the dining table in the dark, watching her as she slipped through the facility door.
“You scared me.”
“You are scaring me.” Craig kicked back his chair and stood. “You’ve been sneaking out every single night, you’re barely sleeping. You take the strangest tone with me whenever we talk. What’s going on, Julia?”
“I’m allowed to take walks.”
“Walks. You know I can see you out there, right? Tonight you stood in one spot for four and a half hours. Just gawking there with your flashlight pointed at nothing. And you’re hardly monitoring the refugium at all. I’ve had to correct the D.O. and pH myself a dozen times. Are you doing drugs? Is that it?”
“I’m not doing drugs.” She started for the hallway. “You wouldn’t understand. You don’t even understand what life is. I’m going to bed now. Goodnight.”
“I’m taking you off this project.”
Julia froze. There was a long silence.
“I don’t think you’re well,” Craig said. “Look, in the morning I’ll drive you into Vegas and get you a flight home. Once you’ve had a chance to clear your head we’ll discuss how to wrap up the data analysis and—”
“You’re joking. That’s a joke.”
“I’m very serious. This place is not good for you. You need rest, and better support than you're getting here.”
Julia laughed. The two of them stood in the midst of something incredible, a sign from the universe that defied physical laws and tested the limits of human comprehension, and here Craig was trying to. . . fire her? Because this place wasn’t good for her? It was so absurd she could only laugh. She laughed and laughed. She laughed her fucking ass off.
“You should come down to the Lake sometime,” she said.
“Julia, what are you talking about?”
“The views are just out of this world.”
IX.
Julia stood in a herd of wild horses. One of them bent over the lakeshore to drink, the ripples from its snout spooking a dragonfly off the surface of the water. Farther up the strand an enormous stork stalked the shallows, tracking down fish and amphibians and swallowing them whole. The sun was setting. The weather was perfect.
Only some of the Lake revealed itself at a given moment. She might doze off on the grassy shore and reawaken on barren salt, and have to climb one of the outlying mountains until she caught sight of some other region of conifers, marshes, and wandering animals. She had eyes on the past, but not all of them were open at once. That was fine—she enjoyed the little journeys, and was starting to map out the full picture by stitching together these disparate glimpses. Like a patient Camelops she followed the water from place to place, keeping crepuscular patterns of behavior, napping when she wanted, eating only what she needed. Mostly she was trying to grasp what it all meant. She wondered about the ultimate fate of the universe, and whether life really contained enough informational complexity to challenge the law of decay. She didn’t know anything for sure, but she was getting a clearer sense all the time, learning more with each passing hour. And now she could explore it at her leisure. She had all the time in the world.
Here is how she did it: after the standoff in the kitchen, she’d gone into the bathroom and taken a long shower. Actually, she left the shower running long after she dried off, left the water sprinkling until she heard the first of Craig’s snores from the bunkspace outside. She slipped into the kitchen, picked up the fire extinguisher from under the stove, returned to the bedroom, and slammed it into Craig’s face as hard as she could. She hit him many more times after that, kept hitting him even after his teeth were on the floor, even after he stopped making sounds. Then she dragged his body to the forest and left it there.
Later, she brought the pupfish to the Lake as well. It didn’t feel right leaving them in the artifice of the refugium, now that she had access to their natural habitat in all its glory. She waded out to a dropoff and set them free in the big water, to eat and grow and reproduce as they had for tens of thousands of years. These C. sepultus specimens, at least, would begin again, here in this atemporal steady state, this biome ghost. And there would come a day, though it may be some epochs in coming, when the glaciers once again would swell on the mountaintops, and the streams and aquifers of the Great Basin would swell to bursting, and the colossal pores of Death Valley would bloom into green cienegas teeming with life, imbued with that immanent power that creates, dissolves, and recreates, twisting into more configurations than could ever be recorded, or described in terms of numbers.
X.
In addition to measuring species diversity, Shannon’s entropy can be used to estimate how many species in a given ecosystem are yet to be identified. This is accomplished by reformulating the entropy measurement in terms of the rate of new species discovery. A sample where only a few different species appear suggests that the community is well-described, while a sample where many species appear only once is evidence of a deeper, unsampled diversity under the surface. Current estimates suggest that roughly 85% of all the species on Earth are still unknown to taxonomy. Many of these will go extinct before being described in any study.
-- Karter Mycroft is a writer, musician, and fisheries scientist from Los Angeles. He has never seen a ghost, but his dog has.
