ALWYN GENTRY WORKED at the Missouri Botanical Garden in St. Louis throughout the 1970s and 1980s. He specialized in identifying and classifying a group of tropical vines called the Bignoniaciae, or bignones for short. As a graduate student in the late 1960s, Gentry wanted to show that bignones were the most numerous and important tropical vines. For this he needed a way of measuring the forest’s plants as a whole. He went to a forest in Panama and laid out a line 50 meters long. Then he went along the line and, whenever he came to a plant that was less than a meter from the line and had a stem that was more than 2.5 centimeters across at chest height, he recorded its size, position, and species. Besides trees his survey included many vines, which can grow thick, woody stems. When he reached the end of the line, he had a long, thin rectangle of forest in which he knew the position, size, and identity of every large plant. He did nine other lines in the same plot, ending with an intimate portrait of 1,000 square meters of forest.

Looking at his data, Gentry realized that he could go beyond bignone advocacy. He had invented a technique for getting a handle on forest biodiversity that required only a few days’ work. Ecologists had done plenty of surveying in forests, but no two used the same method,

and they tended not to be experts at identifying plants, so there was no global picture of how the species, sizes, and spacing of forest plants varied from place to place. Over the next 25 years, Gentry, a scientist with much energy and enthusiasm, and less patience, put that right. He became an expert at getting hold of small amounts of money to fund short expeditions, and he toured the world collecting what came to be known as Gentry plots. He enlisted his colleagues and students in the project and employed locals and their children to measure, collect, and process samples. When he went somewhere to give a talk, he would make time to survey any nearby forest. In total he gathered data from 227 plots on six continents, from Germany to Chile and Madagascar to Australia, measuring and identifying 83,121 plants. He also carried on his work on plant taxonomy, collecting more than 80,000 specimens for the Missouri Botanical Garden.

Gentry’s database showed how forests varied with factors such as latitude, altitude, and rainfall. But the project was always more than an academic exercise. Gentry also worked for the environmental organization Conservation International, and invented his surveying technique partly as a quick and cheap way to get a snapshot of forest diversity, to record the loss of species, and to provide information to plan conservation policy. His surveys helped reveal the impact of people on the natural world. In 1975, for example, he visited the Centinela Ridge in the Ecuadorean cloud forest and discovered more than 100 species new to science. The next year the ridge was cleared for timber.

On August 3, 1993, Gentry was back working in the mountains of Ecuador. He missed his flight out of Quito and chartered a small plane to take him and his team on one more collecting trip. Flying through a cloud bank, the pilot misjudged his altitude, caught a treetop, and crashed. Gentry, the pilot, and one other researcher were killed. Before he died, Gentry broke the plane’s windows with the poles he used to collect tree samples, allowing another passenger to escape.

The day after visiting Santa Fe I fly south to San Jose in Costa Rica, swapping the New Mexican desert for tropical green. There I am to

meet Brian Enquist and his team, to join them as they do fieldwork and learn about forest ecology. I think that driving my rental car from the airport to the hotel where we are to meet will be a cinch: San Jose has a grid system of streets. What I don’t know is that hardly any of them bear signs. I inch my way across town a block at a time, driving until I know where I am, then reorienting and setting off on a new bearing. I feel rather self-conscious in my white, soccer mom’s SUV, which might as well have a flashing neon sign that says TOURIST on the roof. When I despair, I put things in perspective by reminding myself that there are journalists driving around Baghdad. After driving once in each direction down every road in town, not excluding one-way streets, I reach the hotel.

We rendezvous and leave town for the forest. After one stop to buy beer and two stops to look at plants, we arrive at our destination, an ecotourist lodge on the banks of the Rio Savegre, catering to bird watchers from North America and Europe. Several species of humming-birds zoom in and out from the hotel’s nectar dispenser. Their names paint their pictures: Scintillant, Purple-Throated Mountain Gem, Green-Crowned Brilliant. The day after our arrival we drive up into the cloud forest. As soon as we get out of the cars, we hear the whooping call of the bird everyone comes to see. Sitting on a branch above the track is a male Resplendent Quetzal. It looks like a bird invented by the Costa Rican tourist board: the size of a large pigeon, scarlet on its breast and green everywhere else. It is hard to imagine that more vivid shades of red or green exist anywhere else in the world. The quetzal flies away, it’s 2-foot-long tail undulating behind it, and we turn our attention to the trees.

This is my first time in a tropical forest. The first thing I notice are the big trees—40-meter monsters that burst through the canopy, with trunks more than a meter across, propped up by buttress roots that double this breadth. In this forest all such trees belong to various species of oak. Then I notice ways of being a tree you never see in the British woods I know—tree ferns, palms, and bamboo. After that I notice how each tree supports a city of other plants. Every branch and trunk is swathed in moss and studded with orchids and bromeliads. These plants-on-plants are called epiphytes. Even the leaves have a film

of other plants growing on them. Lianas, such as Gentry’s beloved bignones, snake up around trunks. Other dangling stems look like they belong to vines but in fact come from species that germinate on high branches, like epiphytes, and send their roots downward to make contact with the ground. Over decades or centuries, these can encase and kill their host tree: The strangler fig is the best-known example of such a strategy.

But to really appreciate the diversity of this forest, you need to be an expert botanist. Luckily, our party includes Brad Boyle, a grad student of Gentry’s when he was killed and now a postdoc in the Enquist lab. Brad knows a remarkable number of ways to identify a tree. He looks at the curve and shape of a leaf, whether it is hairy or smooth, and how the leaves are arranged on the stem. He looks at leaf stalks. He pulls out a small magnifying glass and looks for translucent spots in the leaf, which botanists call punctations, and the remnants of structures that protect the young leaf, called stipules. Sometimes, he is the only one who can interpret the presence, or absence, of these features. He crushes leaves and learns from their smell and texture. He examines the color and texture of bark, and slashes trunks with a blade to see the color and smell of the wood beneath and any sap that oozes out. This technique teaches me how to spot trees in the nutmeg family, because their wood smells like the spice; it also teaches me that the wood of the genus Croton smells like gari, the preserved ginger served in sushi restaurants. Sometimes Brad pops a leaf in his mouth and chews for a few moments before announcing the plant’s identity. Drimys leaves, I learn, taste bitter and make your mouth go numb. Within a few hundred meters of our parking spot, Brad tracks down more than 40 tree species.

Over the next three days we complete our own Gentry plot—the group calls it a gentraso—in the cloud forest alongside the Rio Savegre. We lay out 50-meter lines and move along them, measuring and recording. Not even Brad can identify every tree right then and there, so each species gets a temporary name, such as “saw leaf,” “donkey ears,” or “son of donkey ears,” and we collect a sample for later identification. Nate Svensson, a graduate student in Enquist’s lab, bores small

cylinders of wood out of tree trunks and slips each sample into a drinking straw for storage. Back in the lab, he will measure the density of the wood. I had expected the forest canopy to cover the sky, and it does, but I am surprised to find that every space between the treetops and the ground is filled with plant life. Moving through the forest is like swimming along the bed of a sea of vegetation—swimming uphill, that is, as the plot lies on a 45-degree slope.

Each day’s work yields half a dozen black plastic sacks filled with plant samples. In the evening, our room at the lodge becomes a temporary lab. Brad sits at the head of the table and pays out specimens for the rest of us to slip between sheets of newspaper. These will later be pressed properly, filed in a museum collection of plant specimens, called a herbarium, and eventually identified. On each sample is written Brad’s name and a number that marks the running count of specimens he has collected in his career. The first one made on this trip is 7,500; the last is 7,736. (Among plant collectors this count is a measure of status. The very few who get to 100,000 obtain a higher plane among their colleagues, a botanical nirvana.) Each sample taken from a plant is split into four smaller bits for pressing. Two copies will stay at institutions in Costa Rica and one will go back to Arizona. The fourth is for tricky cases that may need to be sent to a world expert in a particular plant group, perhaps at the Missouri Botanical Garden, the Kew Gardens in London, or New York’s Botanical Garden. It’s satisfying to think that the specimens I am making will be good for centuries, a permanent record of what was growing at a particular place and time, a brick added to the botanical edifice. Perhaps—who knows?—they will end up in a herbarium rubbing shoulders with plants collected by Darwin or Linnaeus.

Meanwhile, Drew Kerkhoff, another postdoc in the Enquist lab, is analyzing the thickness and chemical composition of leaves. He spends the evening with a hole puncher, perforating leaves to create uniform disks of tissue for later analysis. To record the area of unpunchable leaves, such as fern fronds, he uses a modified image scanner, a device that reminds me of the modified paint roller Samuel Brody used to measure the surface of cows. Jason Pither, another postdoc, completes the team. He is not a forest ecologist; at the moment he is working on

diatoms, microscopic water plants. But he can use a hole puncher as well as the next person, particularly when the next person is me.

The team is a blend of complementary expertises: Brad is a naturalist, Drew primarily a theoretician, and Brian somewhere between the two. Their personalities are similarly interlocking: Brad gives out a Zen-master air, and from his anecdotes seems to be omni-competent. (One that particularly sticks in my memory is best summed up as “The time the engine fell out of my VW camper van, but I fixed it with a chain and a plank of wood and drove on to Guatemala City.”) Drew is sardonic and makes most of the jokes, and Jason absorbs most of them. Jason also keeps things running smoothly. He is usually the first to plunge into the forest trailing a tape measure, and the first to pack up equipment and gather up rubbish, and to check that everyone else is OK. Brian is in charge, but I don’t remember seeing him, or anyone else, give a direct order on the whole trip. The dynamic is a bit like a jazz band. Everyone is simultaneously working for the group and doing his own thing, without an obvious leader. Sometimes we drink beer and gossip about science, scientists—whose ideas make sense, whose don’t, who’s collegiate, who’s paranoid—academic life, and which rock groups should be sent to the bottom of the sea in a submarine. Other nights we work heads down, in near-silence. It’s not exciting, but it requires just enough concentration to stop your mind from wandering. And there are plenty of opportunities to make dumb mistakes. My heart sinks when I realize I have been labeling specimens wrongly, but fortunately the error is correctable, and no academic careers are ruined. Over the course of an evening, the plastic bags of leaves and branches are transformed into piles of specimens flattened and wrapped in newspaper, like bundles of freshly ironed shirts.

After finishing the plot at Savegre, we go north to do another gentraso, in a forest just shy of the Nicaraguan border. We stop once to buy beer, once to drop specimens off at the Costa Rican National Biodiversity Institute in San Jose, where they will be dried and mounted, and once at a stationery store to buy an extra hole puncher, so Drew can get more help—the punchers are having trouble keeping up with the pressers. As I drive, I speculate about what sort of power law best describes the size of the potholes on the Pan-American

Highway. Our destination is the Volcan Cacao biological station, half an hour in a four-wheel-drive vehicle from the nearest road and half an hour on foot from that track. We arrive after dark and walk through a forest loud with cicadas and bright with fireflies. Unlike Savegre, Volcan Cacao doesn’t have a bar, buffet meals, or hot showers. It does have cold showers, in which a colony of several hundred wasps has set up home, and wooden bunkhouses with corrugated iron roofs. At night the noise of the rain makes me dream of applause. It also has a veranda from where you can watch the sun go down over the hills and into the Pacific. The morning after our arrival we hike from the station up into the forest, crossing paths with columns of marauding army ants. The trade winds blow continuously from east to west over Cacao, washing a river of cloud over the trees around the mountain’s summit. The clouds deposit a small pool of water into the center of each bromeliad and turn every clump of moss into a sponge; the forest is like an aerial bog.

Just about anyone could do a gentraso. Our most sophisticated pieces of equipment are long aluminum poles with clippers at the end, of the sort Gentry used, to snip leaves from high branches, and a forester’s tape measure that, when wrapped around a tree trunk’s circumference, gives a reading of its diameter. It’s not exactly the Hubble Space Telescope. Nor will our measurements have a microscopic precision. Vines and moss growing around the trunk can inflate the measure of its width. Chest height is set as 1.3 meters up the body but is then judged by eye, so the measurement varies between trees and between people. Measurements of tree trunk breadth are converted into a reading for the volume of the whole tree, because a tree’s height and width are correlated, but such calculations are approximate. It’s impossible to lay out the 50-meter lines perfectly parallel to one another or perfectly straight. At one point, while running out a line at Cacao, and already wet and muddy from pushing through the forest, I fall several feet into a gully. When I climb out, I change course to avoid this happening again. It’s said that Gentry would change course to take in any interesting tree that caught his eye. There is some subjectivity to where the 1-meter boundary falls for a tree being in or out of the plot. This expedition seems more like old-fashioned natural history than a route to a grand theory of biology.

And at first glance it looks a forlorn hope that anyone could understand the forest. It’s a green riot, a place of disorder and confusion, a jungle. The only possible statement seems to be that if a thing can grow, it will. But as the measurements build up, pattern begins to emerge. The number of stems we measure on each line is fairly constant. At Savegre each 50-meter run brings in about 30 plants—the range is from 25 to 37. Cacao shows a similar consistency, but the lines there have upward of 40 individuals in them. The most crowded have nearly 60. As Brad says, “It’s a busy forest.” But whereas the biggest trees at Savegre have trunks more than a meter wide, there are no such giants at Cacao. The biggest stem we encounter is less than 60 centimeters across. So the Savegre cloud forest has fewer, bigger trees, whereas the forest at Cacao has a greater number of smaller ones.

It would, of course, be rash to make any firm conclusions about the world’s forests from visiting two places in one Central American country. But while the techniques of measurement and collection have changed little in the past couple of centuries, computer power and methods of data analysis have. To do a statistical regression of 100 data points by hand, finding the equation that best describes the pattern in the data, requires a day or two of laborious calculations. A computer can do it before your finger comes off the return key. The Internet makes it much easier to find and share data from different sources. Through a combination of their own fieldwork and ferreting in the scientific literature, the Enquist lab has collected a set of gentrasos three times larger than that collected by Gentry himself. And the more measurements you collect the more strongly order emerges.

Think about the differences between Cacao and Savegre in the population densities and sizes of trees. It’s obvious that any area will support fewer big individuals than small ones, because big plants (and animals) need more space and more resources. This scenario is played out in time as well as between different places. In a forest after a fire or in a gap created by a fallen tree, many saplings will sprout—many more, in fact, than the number of full-grown trees that previously lived on the

spot. For a while there will be enough resources for them all to coexist. But as they get bigger, they will start to crowd and compete with one another, and most will die. Gardeners and foresters plant many more seeds than their plots can support and then thin out the seedlings as the plants grow, leaving room for some to become large. Something similar happens in natural communities. The same process is at work in any place where there is competition for space and resources, in any place where life is a struggle. In other words, everywhere.

Botanists, in a nod to horticulture, have called the way density changes with size self-thinning. Not surprisingly, the relationship between size and population density is best described by a power law. The questions are: What form does this power law take? As individuals grow, by how much must their density go down? In 1963 a group of Japanese ecologists, led by Kyoji Yoda, concluded that the slope relating the logarithm of the size of plants in a plot to the logarithm of their density was −3/2. Other studies, on species ranging in size from moss to trees seemed to confirm that both within and between species this power law reflected a precise relationship between plant size and population density. Self-thinning became a prominent part of ecology’s intellectual landscape and the exception to the rule that botanists don’t do theories. The pattern was seized on as a rare example of a precise mathematical expression of nature and described as “the only generalization worthy of the name of a law in plant ecology.”

Like Kleiber’s law, it wasn’t clear how the mathematical pattern could be explained. The most popular idea was based on a geometrical argument similar to Rubner’s surface law. The area of a plant’s canopy—the amount of ground it occupies, which will control the number of plants you can pack into an area—is proportional to the square of that canopy’s radius, in the same way that the area of a circle equals pi times its radius squared. The whole plant’s volume is proportional to that radius cubed, in the same way that body mass is proportional to the cube of body length. A quick algebraic rearrangement therefore shows that plant volume is proportional to the 3/2 power of canopy area. The inverse of this number—the −3/2 power of each plant’s volume—would describe the number of plants of a given size that an area can support and how that number would decrease as they

got bigger. But, like the surface law, self-thinning did not stand the tests of academic scrutiny. In the mid-1980s it was shown that Yoda’s team and those who followed had made mistakes in the way they compared plant size with population density. These mistakes made the relationship between the two properties look stronger than it really was. When the data were reanalyzed, no clear-cut pattern relating size to population density could be seen. By the mid-1990s most ecologists had given up on self-thinning.

In their metabolic model, West, Brown, and Enquist saw a new way to tackle the question. Instead of dividing up space, population density could be a consequence of the way that plants divide up energy. If there is a fundamental unity in the way individuals use energy—if everyone is playing the same game by the same rules—the path from the diversity of individuals and species to the patterns seen in living groups becomes clear. The fractal theory explains what happens to energy as it pours into an individual organism. It seems to apply to all organisms. So an ecosystem becomes a network of networks: Energy pours into it, and flows through all its component organisms depending on how large, competitive, or lucky they are. From this angle, ecology becomes a kind of meta-metabolism.

The network theory of metabolic rate predicts how tubes should be packed into a body to spread energy through it as efficiently as possible. Its ecological extension predicts the best way to pack trees into space. Sunlight is so valuable—and trees are so good at getting it—that by assuming trees use energy optimally, we can work out how a forest ought to spread out. Body size controls this spacing pattern. Just as elephants need more food than mice, an area will support fewer large plants than small ones. But just as an elephant’s cells burn energy more slowly than a mouse’s, so we must take the relatively slower metabolic rates of large plants into account when working out how many of them can fit into an area.

Metabolic theory predicts that the population density of trees should decline with their increasing size so that the total metabolic activity of the plants remains constant. In 1998, West, Brown, and Enquist published a paper showing that, for plants from herbs to trees a billion times larger, the number of individuals in an area declines

proportional to the −3/4 power of their body masses. That is, population density falls at the same rate as metabolic rate rises. A 100-fold increase in plant mass leads to a 30-fold decrease in population density; a square meter of ground can support 200 plants each weighing 10 grams, or seven plants if each weighs a kilogram. Data on plant population density support this prediction: At the extremes, a square meter supports about a million duckweed plants, each weighing one ten-thousandth of a gram, totaling 100 grams of plant matter, or 1 percent of a sequoia tree weighing 10,000 kilograms, totaling 100,000 grams.

As well as predicting how many trees of a certain size can fill an area, metabolic theory predicts the range of tree sizes in a forest and how those trees space out. Large trees are few and far between. In Savegre and Cacao no survey line in any gentraso had more than one truly hefty tree, with a trunk more than 40 centimeters across. But each line contained many trees that just make it over the 2.5-centimeter cut off point. Look at lots of trees and a scaling law emerges: The wider the trees, the greater the space between them. So if you are standing by a tree you can predict how far you will have to walk before you find atree of the same size. The bigger the tree, the longer the journey. The forest consists of a few giants, keeping their distance from one another, and many small, more gregarious trees filling the gaps between them. To see why this is so, imagine you had to fill a crate with balls of different sizes. There would be room for maybe only two or three basketballs. But the gaps between them would leave room for perhaps five or six volleyballs. Between these volleyballs you might be able to insert a dozen baseballs and still have room to cram 20 golf balls into any remaining gaps. The amount of energy in the forest—representing the size of the crate in this analogy—can accommodate only a few really big trees. But many more small trees can squeeze into the gaps between them.

The trees of different sizes are like a network for using the sun’s energy, and trees fill up space in the same way as transport networks. The same mathematics that predicts how to design a blood system also predicts the numbers of each size of tree, with the number of large, medium-sized, and small trees following the same pattern as an aorta that leads to several arteries and many capillaries. It’s another example

of how, by assuming that life is structured so as to grab as much energy as possible, you can predict what large-scale order will emerge.

In their efforts to relate body size to population density and metabolism, botanists were once again following in zoologists’ footsteps. In 1981, John Damuth looked at the data on body size and population density for 307 species of herbivorous mammals. He found that population density declines as the −0.75 power of body size. Because metabolic rate increases as the 0.75 power of body size, this means that all animal populations extract approximately the same amount of energy from an area, regardless of how big they are. This is just what West, Brown, and Enquist found for plants nearly 20 years later—that 1 hectare of grassland uses the same amount of energy as 1hectare of forest. The principle has become known as the energy equivalence rule. In a later study of more than 600 species, Damuth found that the same relationship held for animals ranging from a mite, Chamobates schützi, which weighs 0.0000083 grams, to the African elephant, which weighs 2,900 kilograms. A square kilometer’s worth of mites—about 4 billion animals, weighing about 33 kilograms—uses approximately the same amount of energy as the lone elephant that the same area could support. Similarly, the population density of parasites in animals declines with the −3/4 power of the host’s body size. One of the advantages of being large is that, pound for pound, bigger animals have fewer parasites than small ones because the parasites, just like their host’s cells, must make do with a slower supply of energy.

But although energy equivalence worked well for herbivores, plants, and parasites, it did not seem to apply to animals higher up the food chain. For them population density declined more steeply with size than metabolic rates would predict. Instead of energy use remaining constant, the brute mass of carnivores in an area seemed not to vary—a square kilometer could house the same mass of lion flesh as weasel flesh. This was puzzling because the smaller weasels, with faster metabolic rates, ought to require more energy, but the data seemed

robust, and by the late 1990s it looked as if energy equivalence had no claim to be a general biological principle.

But in 2002, two zoologists, Chris Carbone and John Gittleman, found a way to bring carnivores back into the metabolic fold. Their trick was to stop thinking about animal populations in terms of the land they needed, and instead to think about the amount of food they needed. For plants and herbivores, land and food are much the same thing. As much light falls on a hectare of grassland as on a hectare of forest; grazing rabbits and grazing wildebeest encounter grass in much the same way. But carnivores are more idiosyncratic. They live in lots of different places and hunt in lots of different ways, and they tend to specialize in hunting certain prey. In particular, small carnivores tend to focus on eating invertebrates—like a hedgehog snuffling for worms—which are much smaller than them, whereas large ones tackle vertebrates that are often nearly their own size, such as a cheetah in pursuit of a gazelle.

The switch between the two styles of hunting occurs around a dozen kilograms. For example, the European badger and the American coyote both weigh about 13 kilograms. But the badger feeds mainly on invertebrates such as worms and beetles, whereas the coyote prefers mice and rabbits. Anything larger than a coyote will likewise hunt relatively large prey. Worms are spread evenly, like plants, but mice and rabbits are spread much more thinly, so coyotes must spread out more thinly than badgers. This means that the population density of carnivores takes a sudden drop around the 12-kilogram mark, and so trails off more steeply with increasing body size than does the density of herbivores, which do not show the same switch.

When Carbone and Gittleman looked at carnivore populations in terms of the amount of prey available, rather than the amount of land, energy equivalence was restored. For species ranging from the least weasel, which weighs 140 grams and needs less than a square kilometer of land, to the polar bear, which weighs 310 kilograms and needs 50 square kilometers or more, the population density of carnivores falls at a rate proportional to the −3/4 power of prey density. This energy equivalence means that every kilogram of meat eater needs about 111 kilograms of meat to keep it going (the ratio remains constant

despite changing body size because, although a kilogram of weasel burns fuel more quickly than a kilogram of bear, and so you might expect it to need more meat, the species that weasels hunt are themselves small and so grow and reproduce more quickly than bears’ prey). Carbone and Gittleman’s finding also shows that discovering general patterns requires local knowledge. Without an understanding of the feeding behavior of different predators and the population densities of their prey, the rules describing carnivore numbers would have remained obscure.

The match between metabolic rate and population density also explains why any area can support a greater mass of reptiles than mammals, which in turn live in more dense populations than birds. As an animal’s body temperature, and so its metabolic rate, goes up, its population density must go down. This is why, as Carbone says, “we have fisheries but not birderies”—and there’s no point trawling for leopards. Many economically important fish, such as cod and salmon, are predators, but their relatively slow metabolisms allow them to live in numbers that would be impossible for a group of warm-blooded predators to sustain. The population density of predatory theropod dinosaurs, the group from which birds evolved, seems to have been much lower, relative to the density of their prey, than other predatory dinosaurs, hinting that the theropods might also have been warm-blooded.

As we have seen, conservationists use the links between body size and the pace of life to work out which species are most at risk of extinction. Likewise, they can use the links between energy and land to work out whether, and how, species could be saved. A nature reserve cannot protect an endangered rhino species unless it contains enough food to support a breeding population of rhinoceros (working out how many rhinos make a self-sustaining breeding population is a whole other issue). The patterns in population density give another rule of thumb. You can get a rough idea of how many animals of a given size could live in the area you are proposing to make into a reserve. This would be simple for herbivores and a bit more complicated for carnivores, as you would also have to measure the population density of the predator’s prey species. The rules also give a guide to how well conser-

vation measures are going. Carbone is working to conserve the Sumatran tiger, which hunts mainly wild pigs; an area of forest with much less than 1 kilogram of tiger for every 111 kilograms of pig flesh might be a sign that something else, such as the effects of inbreeding, is keeping tiger numbers down. Macroecological patterns are only a starting point: There is still a lot of variation in population density around the energy equivalence line. But even a crude prediction is better than having no idea of what to expect, and, while tiger conservationists might have the time and resources to do detailed studies, anyone aiming to monitor, say, all the carnivores in a large area of forest or savannah is going to have to take shortcuts.

There is another aspect to how animals use space beyond their population density. Unlike plants, animals move about. Each animal roams over an area of land called its home range. Not surprisingly, big animals have bigger home ranges: One elephant covers nearly 30 square kilometers of land; the same area could accommodate 10,000 mice. But home-range size is not proportional to body mass raised to the power of 3/4; instead, range size rises at the same rate as body size. For some reason, large animals use more land than would be expected based on their energy requirements.

Many animals secure energy by defending territories, as either individuals or a group. They patrol their ranges and repel intruders. The reason that large animals need proportionately larger territories, metabolically speaking, is because they have a harder time defending them. The distance traveled by an animal in a day is proportional to its body size raised to the power of 1/4. The amount of food it needs is proportional to the 3/4 power of its body mass. So the amount of food needed increases with body size more quickly than the area covered. A mouse travels 110 meters in a day, more than adequate to cross its entire territory. An elephant manages 2 kilometers. Large animals therefore find it harder to defend their borders, because they are less likely to bump into an intruder. They must put up with more incursions and share more of their territories and resources with their neighbors. These intruders eat, so each territory holder is forced to roam over a still larger area to find enough food—which is why home range size increases with body size more quickly than metabolic rate.

To express this relationship mathematically, Carbone, working with a team of other ecologists that included Jim Brown, borrowed the equations that physicists use to predict the frequency of collisions between the randomly wandering particles in a gas. Applying this model to animals, incorporating factors such as population density and mobility, they predicted that the relationship between an animal’s food requirements and the distance it must travel to get that food would be linearly related to body mass: a good agreement with real-world patterns. The problem that large animals have in defending their territory is probably one explanation of why large animals, such as zebra and bison, tend to live in groups but why, to quote William Calder again, one never sees a herd of mice. When defending a territory becomes unfeasible for one animal alone, it is a better to tolerate company than rush around trying to fight it off.

This is a static view of populations: a snapshot of numbers and density, frozen in time. But animals and plants aren’t like this, of course. In 1798, Thomas Malthus noticed that animals seemed capable of increasing their numbers at an exponential rate. A female rabbit produces a litter of six pups. If all six manage to avoid foxes and find enough food, this female’s three daughters will each produce six young, creating 18 more rabbits. These will then give birth to 54 rabbits, then 162, and so on. Each generation will contain three times more rabbits than the last. And yet in the long term, most populations, of rabbits and everything else, must maintain almost constant numbers; otherwise they would either go extinct or cover the earth. Malthus argued that the world is not covered in rabbits because famine, disease, winter, and such keep their numbers in check. Famously, he also argued that the same would happen to a growing human population. Charles Darwin realized that this overproduction provides the raw material for natural selection. Since then, life’s capacity for Malthusian geometric population growth has been recognized as one of nature’s few universals.

We saw in the previous chapter how metabolic rate controls the growth of individuals. For some species, such as bacteria, the link between individual and population growth is obvious: They are the same thing, because new cells are also new individuals. For others it is more complex: Mothers might invest resources in eggs, fetuses, and

parental care. Males might help care for their young, but most do not; instead they put all their reproductive efforts into finding mates. Nevertheless, these are all decisions about what to do with energy, and the rate at which an organism can turn resources into offspring depends on the rate at which it uses resources itself—in other words, on its metabolic rate.

It ought to come as no surprise that the maximum population growth rate—the number that defines each species’ Malthusian potential—depends on body size, and that populations of large animals grow more slowly. Like cellular metabolic rate, the maximum rate of population growth for each species is proportional to the −1/4 power of its body size. Temperature is also important. Fish populations in polar seas increase more slowly than those in tropical waters. Together, size and temperature can account for about 95 percent of the variation in population growth rates for organisms from plankton and algae up to large vertebrates. As well as controlling how numerous a population of plants and animals can get, metabolic rate controls how quickly it will get there.

I am no Brad Boyle, but if I was transported at random to some wooded part of the earth, even I could guess whether I was more likely to be in, say, Colombia or British Columbia. The types of trees in a place, and the number of species, vary hugely. The plots in Gentry’s data set contained between 2 and 275 species. Why this is so is a puzzle, of which more will be said later. But by analyzing Gentry’s original data set, Enquist and Karl Niklas were able to show that, in their large-scale structure, all forests are essentially the same. So maybe the gentrasos really are ecology’s equivalent of the Hubble telescope, because they give a view of nature that is of unprecedented scope and depth.

All forests, for example, follow the −3/4 relationship of individual size to body size. This is true of the trees in a single Gentry plot, an entire continent, or the whole world. And all forests contain approximately the same number of individuals and quantity of plant tissue, or

biomass. There are the same number of trees (about 400) and the same amount of wood (about 35,000 kilograms) in 0.1 hectares of forest in Amazonia or Alaska. Regardless of the species that live there, natural selection, limited by the constraints of energy and allometry, has pushed all forests up against the same physical limit of the size and number of individuals that a place can support.

The Gentry plots also revealed that no type of forest has a monopoly on tall trees. The Amazonian rain forest, Australian eucalyptus forests, and North American conifer forests all contain trees about 100 meters tall. But why stop there? From a ridge on Volcan Cacao I can look out across the treetops, undulating but level—the surface of the sea in which I have just been thrashing about. This evenness is commonplace but also strange. Each tree, after all, has a powerful incentive to get taller, as it could then grab a greater share of sunlight. Why do forests have a canopy? Why aren’t there some trees as tall as the Eiffel Tower?

Part of the answer will, like life span, be a question of life’s risks, with storms, or rot from within, bringing down any tree before it got fantastically large. Partly the answer will be biomechanical, to do with the problems of supporting large bodies. But none of these factors offer an obvious explanation of why, in all the world’s forests, there is no tree 200 meters tall. But the fractal theory can explain this by showing how the effect of size on transport networks puts an upper limit on tree height. This upper limit is set by the fact that trees rely on water evaporating from their leaves to draw water into their roots, and also by the tapering of the xylem vessels that carry this water.

The width of the narrowest xylem tubes—the leaf stalks that do not vary between species—is fixed. But like animal blood vessels, the tubes’ maximum width can vary. Tall trees need wider xylem tubes just as large animals need wider aortas. But evaporation is not as good as pumping at driving water down a pipe, and if xylem vessels got too wide the evaporation from a tree’s leaves would be too weak to draw water up from its roots. So the vessels’ maximum width is also fixed.

Perhaps if xylem vessels tapered infinitesimally slowly between these two limits trees could become massively tall. But this is not an option. The rate at which xylem vessels taper is set by the need to pro-

vide every leaf with an equal flow of water. The physics of fluid flow means that if xylem vessels tapered too slowly a tree’s lower leaves would get all the water and its upper branches would perish. So the maximum height of trees corresponds to the length of the xylem tube that bridges the thinnest tubes at the treetop and the fattest possible tubes at the root, while tapering at the right rate. This bridge can reach about 100 meters in length—corresponding to the tallest real trees—before it collapses. Looking down on the treetops and thinking of this concept, I imagine the canopy as a solid, immovable layer of invariant terminal units and the forest growing downward, like a carpet of strangler figs, with shoots and trunk becoming ever broader until they reach the limits of their capabilities and hit the ground.

The fractal theory can predict a maximum tree height, but it can’t predict why trees reach the height they do. The Cacao forest canopy, and that of most forests, isn’t 100 meters tall. What sets forest canopy heights is still a mystery. One danger of wide xylem vessels is that they are prone to develop air bubbles, cutting off the water supply to the leaves. This may cramp trees’ ability to get tall. The wetness of the environment is probably also a factor. Trees need the air around their leaves to be drier than the soil around their roots, otherwise water will not flow through them, and they will not be able to photosynthesize and grow. In very humid places, such as cloud forests, this flow will be slow, which might prevent trees from reaching their full potential.

The gentrasos are not the only large data set to reveal uniformities among the world’s plants. You can’t stick a plastic hood over a forest to measure the flow of oxygen and carbon dioxide through its trees, but you can catch its breath in other ways. In the mid-1990s, as global warming rose to the top of environmental scientists’ concerns, researchers began to wonder how to study the effects of climate change on ecosystems. Would warmer conditions and more carbon dioxide fertilize plant growth, for example, or would soils become drier and stunt growth? Researchers’ solution was to establish monitoring towers that would give an hour-by-hour picture of the conditions in an eco-

system, such as the temperature and the levels of carbon dioxide and water vapor. FLUXNET, as it is called, now numbers 140 sites in five continents, covering all sorts of forests, wetlands, grasslands, agricultural ecosystems, and tundra. Such projects mark the birth of Big Ecology, large international teams of researchers collecting stupendous amounts of information on a global scale (although the cost is still minuscule compared to space missions). And besides being a canary for the effects of climate change, FLUXNET was just what ecologists such as Enquist needed to measure ecosystem metabolism.

The results from FLUXNET confirm some basic truths about metabolism, showing, for example, that forests respire more quickly in warmer weather. FLUXNET data also match the metabolic theory’s predictions of energy equivalence. The amount of respiration does not depend on the amount of living plant matter in the ecosystem. It is the same for temperate and tropical forests, grasslands, and soybean plantations—corrected for temperature, every plant-covered hectare of land takes in the same amount of oxygen and produces the same amount of carbon dioxide. This makes sense considering how size affects metabolism. Adding biomass seems like it should increase the amount of respiration going on. But if you do this, you end up with fewer bigger individuals, which must respire at a relatively slower rate. Although the metabolism of individuals depends on their mass, the metabolism of ecosystems doesn’t. In every place, individuals, regardless of their size, have—as energy equivalence predicts—evolved to grab hold of as much energy as they can and use it as efficiently as possible.

But forests also do some things not predicted by the metabolic models. The pattern of respiration between forests does not reflect the average temperature—they all seem approximately similar. For any given temperature, temperate forests can process energy between three and six times more quickly. This is why Drew Kerkhoff has been punching holes in leaves.

Moving from the equator toward the poles, and so into colder environments, trees’ leaves become steadily richer in phosphorus. Leaves’ nitrogen content, on the other hand, remains constant, so the nitrogen-to-phosphorus ratio becomes biased toward phosphorus.

This change seems to allow temperate trees to compensate for their cold environment with relatively accelerated growth. The amount of new wood that each hectare of forest makes each year does not vary from place to place. Phosphorus is a critical component of the cell’s protein-making machinery; temperate trees might grow faster thanks to increased investment in such machinery. Presumably there is also a cost for this increased growth that prevents tropical trees, which do not need to cram all their growth into a short summer, from investing in leaves rich in phosphorus.

After leaving Volcan Cacao, we drive toward the coast and nearby Santa Rosa National Park. The park was established in 1971, before which most of its land was used for cattle ranching. By stopping grassland fires and allowing horses and cows to spread the seeds of trees that once relied on large, but now extinct, mammals such as ground sloths, to do the job, Costa Rican conservationists and their U.S. colleagues have helped the trees grow back. The result is a very different type of ecosystem than that of a cloud forest. We are only 20 kilometers from the Cacao plot, but none of the same tree species will be found here. It’s the dry season, the temperature is above 30°C, and most of the trees have shed most of their leaves in an effort to conserve water. There are few vines, and the space beneath the canopy is much more open, making it easier to move around the forest. If you squinted and tipped a bucket of cold water over your head, you could almost believe you were in an autumnal English woodland. Except that, instead of moisture-loving mosses, the most obvious branch dwellers are cacti. And the acacia bushes have fierce ants living inside their hollow thorns. And ctenosaur lizards several feet long scuttle out of the road as we approach.

Enquist has been coming to Costa Rica since 1992; in total he has spent more than two years in the country. Most of this time was passed at Santa Rosa, and most of the time at Santa Rosa was spent working on a plot in a part of the forest called San Emilio. The ranchers moved out of here more than a century ago, making this one of the oldest forests hereabouts, with many mature trees. In 1976 another U.S. ecolo-

gist, Steve Hubbell, set up a permanent plot for studying the forest here. A gentraso is a snapshot for comparing forests in different places—you can’t go back to the same forest and be sure you’re measuring the same trees. In San Emilio you can. A grid of stakes divide the forest, allowing every tree’s position to be mapped. The larger trunks have metal tags with identification numbers. Unlike a Gentry plot, this system allows the forest to be followed through time. As a graduate student, Enquist inherited the San Emilio plot and spent most of 1994 resurveying the 17-hectare site. With the help of his wife and the occasional visiting undergraduate, he recorded the position, size, and species of every tree with a trunk more than 3 centimeters wide. He measured about 3,000 plants of 45 species. Like a scientific Davy Crockett, he knows every tree in this forest and, giving us a tour of his favorites, is obviously excited to be back. “I’m getting misty-eyed,” he says, only half-jokingly.

Gentry plots reveal that a common structure unites forests in different places. The San Emilio surveys showed that the same is true in time. In the interval between the two surveys, the climate became drier, causing a change in the species living in the plot. But there was no change in the size or structure of the trees: The size of the biggest trees remained unchanged, as did the number of trees of each size, and the population density. And the progress of the 2,283 trees that did survive the two decades between the first and second surveys revealed that a unity underpins the biology of different tree species as well as of forests as a whole.

Plants have different life histories, just like animals. Some tree species shoot up quickly; others are slow growing. But in San Emilio, although the sizes of individuals changed at very different rates, their mass did not. All of the trees added biomass at the same rate. In the now-familiar pattern, growth rate was proportional to body mass raised to the power of 3/4, so small trees grew relatively more quickly than big ones. A tree’s growth rate depends on its size, not its species, and there are really no slow- or fast-growing trees.

What does differ between tree species is the density of their wood.As well as measuring tree diameter, Enquist took his own set of wood cores; Nate Svensson is extending this data set and might do a

third survey of the San Emilio plot. Some trees have wood like polystyrene; others are so dense they sink in water. Enquist broke several drill bits trying to bore into the toughest trunks. It’s another case of trade-offs, this time of wood quantity against quality. If a tree wants to gain height quickly, it can make less dense wood. This seems like a good idea—it can overshadow its neighbors, and win the race to grab a spot in the canopy. Such fast-expanding trees tend to be the first to fill the gaps left by fallen trees. But there is a price to be paid. Speedy growers sacrifice sturdiness in their race for height and have shorter lives than trees that make dense wood. The slow-and-steady growers, grinding out their existence in the shadier spots, are in it for the long haul—tougher, better able to withstand storms and disease, and longer lived.

What applies to wood also applies to leaves. Some evenings I wield the hole puncher. Handling leaves, I learn that some species have foliage like tissue paper; others are more like cards. The same costs and benefits apply: Flimsy leaves are quick and cheap to make but vulnerable to herbivores. Tough ones are expensive but last longer.

Wood density and leaf toughness aren’t the only decisions facing a growing tree. There’s also the question of how much of each tissue to invest in. There are three options: leaf, trunk, and roots. All have their advantages. Having lots of roots would provide a firm anchor in the soil and suck up lots of water and minerals; a long trunk and branches add precious height; and the more leaves you have, the more light you can gather and turn into food. So what’s the best way for a plant to divide up its resources?

Enquist and Niklas tackled this question theoretically. The key consideration is the way water flows through the plant, from root to stem to leaf. The laws of fluid dynamics rule that, to minimize the resistance in the plant’s tubes, the mass of roots and stems should be proportional, although not identical, to one another. As a tree’s trunk grows, its roots should also grow at a constant rate. The same theory predicts that the amount of leaves—which control metabolic rate—should vary with the tree’s total mass to the power of 3/4. This means that a 100-fold

increase in trunk mass brings only a 30-fold increase in leaf mass—small plants have proportionately lots of leaves, whereas big ones have lots of roots and trunk. The relative decline in leaf mass also means that bigger trees have proportionately more of their masses below ground. A plant weighing 100 grams has one-fifth of its mass in its roots; this proportion rises to one-quarter for a plant weighing 10 kilograms. Fortunately for them, Enquist and Niklas did not have to dig up and chop up thousands of plants to test their ideas, because other researchers already had. The ready-made data gave a good fit to the theoretical predictions. Across species from conifers to oaks to mahogany, trees of the same size are investing roughly equal proportions in root, shoot, and leaf.

Forests are still complicated places, and allometry cannot explain everything. Trees of a similar size can vary 100-fold in the mass of their leaves. Some of the trees at San Emilio have massive trunks in which they store water, and so are relatively less leafy than their cloud forest counterparts, for whom the problem is more likely to be how to lose water by pulling it through their bodies and out their leaves. There are also differences that reflect evolutionary history: On average, a conifer has more than twice the weight of leaves of a broad-leafed tree of the same size. Populations also vary, as Gentry found. The number of trees in the original gentrasos varies by a factor of 20, from 50 to 1,000. The rules of networks and energy set the limits of what is possible, but a harsh winter, strong gales, or explosion in the caterpillar population may prevent any one forest from approaching these limits. Like animals, plants have some ability to bend these rules, depending on where natural selection pushes them, and trees specialized to live in shady or sunny, or wet or dry, places will need different strategies. The chemical variation in leaves shows one way that plants can change their biology to compensate for their metabolic limits. But the regularities that emerge on a global scale show that, although their routes may differ, the world’s forests have arrived in the same place.

Leaving Santa Rosa, we head south again. Stops include one to buy beer and one for the police to flag me down for speeding. As I wait sheepishly to be given a ticket, the policeman waits for us to offer to “pay the fine here,” which as it happens would be rather cheaper. By

the time we realize the confusion, he has given up and cheerily sends us on our way, unfined. (I suspect that Brad, who is in the passenger’s seat, has used the Jedi mind trick.) The last forest on the trip is back in the clouds, high on the slopes of another volcano, Barva. We collect leaf and wood samples in the general area of a gentraso that Brad surveyed in the past. Hiking out of the woods with our final bags of specimens and our final crop of chigger bites, a male quetzal flies across our path, pursuing a female.

I think of Gentry, who would have marched through this forest putting a Latin name to every tree. Then I think of the message of the gentrasos: All that seems to differ between forests is the number of species that live there. Trees across the world are remarkably constant in the ways in which they use energy and grow, and this uniformity leads to a constancy of structure in the world’s forests through space and time. So why is life diverse? If all living things use energy in the same way, why do they come in so many different types? If life is a struggle for energy, why does the cloud forest around me contain scores of tree species, rather than just one that has managed to outdo all the others? If you’ve seen one tree, why haven’t you seen them all?