The Grandeur in this View of Life

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Of π Day, Plants, and Paleoclimates

Happy π Day! After not posting anything on Darwin Day, I decided that I could not let another geek holiday go by without a post. So let’s talk about the importance of π in the global biogeocoenosis.

Now you may say, “But π is just about geometry! That’s not biology!” Or maybe if you’ve blocked out 10th grade math, you may say, “But pie is just for dessert!” Allow me to retort:


Biology is all about structure and function and the mathematics of structure (and to some extent, function too, come to think of it….) is geometry. Much of evolutionary biology is concerned with the history, diversification, and development of biological form. On some level, most evolutionary biologists study changes in the geometry of organisms and why it matters. Also, pie makes an excellent breakfast.

So because π relates the diameter of a circle and its circumference, we need to think about the important circles of life. I like trees and the cross-section of a tree trunk is roughly circular, so that seems like a productive place to start! Imagine a beautiful sugar maple like the ones local farmers here in Knox County tap to make maple syrup early every spring. My checker at Wal-Mart told me that just last weekend her husband had really smoked up her house boiling down the last of their haul of sap for this season.


So where does that sap come from? The tree stores starch in its roots and early in the season, the roots start moving the starch into the sap to fuel the production of leaves way up in the canopy. The sap flows through little tiny tubes just under the bark of the tree, which is why we can tap into the sap. These tubes, collectively called the xylem system, stretch continuously through the body of the tree, from the tiniest tips of the roots to the veins of every leaf. But how does the sap flow? Are there little pumps down in the roots that push the fluid up? Does it simply “climb” up the little tubes by capillary action? For a long time, this was one of the major mysteries of botany: how do plants, which have nothing resembling a heart, get water from the soil to their leaves, fighting all the while against gravity?

The answer, which has only become fully established over the past few decades, turns out to be a little crazy. The water in the little tubes is not being pushed, but pulled up the tubes. The water molecules form long, continuous strands from the roots to the leaves, stuck together by the electrochemical force of cohesion. And all those tiny strands of water are under tension – they are being stretched like minuscule rubber bands. And the crazy part is that they are being stretched by the air! The underside of leaves are pocked by tiny pores called stomata, and as the water evaporates, it pulls just a bit on the strand of water behind it, all the way down to the roots. So simply because it is drier than the plant’s tissues, the air “sucks” water up from the soil, perfusing all of the plants cells along the way. Plant xylem is one of the wonders of engineering accomplished by evolution. In a single large tree, the xylem can move hundreds of gallons of water over large distances without any direct input of energy on the part of the organism. Talk about efficiency!

About now, you may be wondering, “What about the π?”

To find the importance of π here, we just need to consider the circles in the picture. Not just the big circle of the trunk, but all of the tiny circles that make up the tubes of the xylem. And how tiny they are matters, because the same forces that hold the water molecules together in strands also make it stick to the side of the tubes. In bigger tubes, less of the water is in contact with the wall, so it flows faster. Back in the mid 19th century, scientists figured out that the flow rate (Φ) through a pipe could be described by the following equation:

HP-LawSo there! There is my favorite pi in biology!

The πr4 term, where r is the radius, has to do with the cross sectional area of the pipe and how much fluid is in contact with the wall of the pipe. What is so important about it is not so much the π (sorry, but such is the life of a constant) but the fact that the radius is raised to the fourth power. That means that if you double the radius of a tube, all else equal, you actually increase the flow by a factor of 24 or 16-fold! So plants with bigger tubes can move more water, more quickly.

It turns out that this simple fact has terrific importance for both plant evolution and perhaps even for the history of Earth’s climate. Back in the Cretaceous, 65.5-145 million years ago, Earth’s vegetation was dominated by conifers and ferns. No Triceratops ever munched on a sugar maple. The lineage of flowering plants that are so common today were only just beginning to evolve, and evolutionary biologists have long marveled at their rather explosive (in geological/evolutionary terms, at least) diversification and rise to dominance. Darwin himself called it, “an abominable mystery.” What were the secrets to their success?

Almost certainly, some of them were physiological, and one of the most notable differences between flowering plants and their cousins was in the xylem. Flowering trees had not just discovered flowers and animal pollination (another of the secrets to their success), they had also found a way to make the tubes bigger than those of conifers. And not just a little bigger, a LOT bigger: up to fifty times wider! And because of the πr4 term, even though one of these humongous vessels takes up as much space as 2,500 smaller tubes, the flow rate increases more than 6 million fold! At the same time, the leaves of flowering plants were changing too. The density of leaf veins increased enormously during the Cretaceous, bringing more of the water and soil nutrients in the sap closer to the sites of photosynthesis, and releasing much more water vapor into the atmosphere. The evolutionary relationship between these innovations, their relative order and mutual influence, remain uncertain, but together they changed the world. In fact, they sped it up.

Provided with more water and nutrients, the photosynthetic machinery of the leaves went into overdrive. Vegetation became more productive, capturing more carbon from the atmosphere, though it released more through respiration as well. Those faster living leaves also died younger, speeding up the cycling of nutrients through decomposition. And after the cataclysmic transition from the Cretaceous to the Paleocene, whole forests of flowering trees became dominant over large swaths of the continents, and they even began to make their own rain. With their huge vessels and richly veined leaves, theses trees collectively accelerated the hydrological cycle, moving water into the atmosphere that eventually had to return to the ground as rain. Even erosion may have increased. Recent modeling studies suggest that if Amazon rainforests were constrained to more ancient conifer-style rates of water transport, the dry season would lengthen by up to 80 days, well beyond the tolerance of most rainforest species.

And in making their own world here on Earth, the flowering plants have made our world. No primate ever knew a world without them. Even our climate is a product of their evolution. And we could not understand it without understanding that the ratio of the circumference to the radius of a circle is a transcendental constant.

π for now.

Evolutionary research on the vascular innovations of flowering plants is incredibly exciting right now. Two recent interesting papers (which I drew on for this post) include:

C. Kevin Boyce and Maciej A. Zwieniecki. 2012. Leaf fossil record suggests limited influence of atmospheric CO2 on terrestrial productivity prior to angiosperm evolution. Proceedings of the National Academy of Sciences of the USA.

Taylor S. Feild, Timothy J. Brodribb, et al. 2011. Fossil evidence for Cretaceous escalation in angiosperm leaf vein evolution. Proceedings of the National Academy of Sciences of the USA.


Eye on Research: Cretaceous Extinction Cascades


We all know that an asteroid impact* ended the age of the dinosaurs roughly 65.5 million years ago. That event, known as the K-Pg extinction**, marks the cataclysmic demise not just of the non-avian dinosaurs (yes, that was a dinosaur you ate on Thanksgiving!), but of a large number of other living things, including the pterosaurs and pleisiosaurs, as well as many lineages of plants and marine and terrestrial invertebrates like insects, cephalopods, bivalves, and echinoderms. In terms of overall destruction***, the K-Pg extinction was one of the worst extinction episodes in the history of life, second only to the “Great Dying” at the Permian-Triassic boundary. The current consensus is that the asteroid impact threw so much debris and ash into the atmosphere that it greatly reduced the incoming sunlight, which in turn hindered photosynthesis and cooled global climate for years to decades. The resulting declines in plant productivity then cascaded through the food chain, leading to the extinction of herbivores and subsequently to the carnivores that depend on them. So long, T. rex!

But like any other event in life, even the outcome of an asteroid impact may depend in part on context. Did the impact, itself, doom the dinos to extinction, or did the particulars of the interactions among species play some role? Recently, Jonathan Mitchell and his colleagues addressed this question by comparing extensive fossil assemblages from the last few million years of the Cretaceous, just before the impact (the Maastrichtian age) to those of previous Campanian age, thirteen million years earlier. They used a mathematical model to investigate whether the structure of Maastrichtian food-webs made them particularly vulnerable to the kind of disturbance produced by the impact (i.e., declines in plant productivity).

As you can imagine, figuring out who-eats-who is a difficult proposition, even in extant communities, and while gut contents do occasionally occur in fossils, ancient food-webs are even more difficult to ascertain, especially when they involve up to 92 different animal species. But while we can rarely be certain that any extinct species ate any other particular species, we can have more confidence in assigning species to particular feeding guilds, based on their anatomy and their size. For example, while we don’t know exactly which plants it found tasty, Triceratops is definitely a Very Large Herbivore (let’s call it the VLH guild).

Once all of the species at a particular site were assigned to guilds, Mitchell and his colleagues used a computer simulation to assign the feeding connections among the species in the different guilds (see schematic above), based on the “connectedness” of existing food-webs. They dealt with uncertainty in the feeding relationships by repeatedly drawing random connections among the particular species in different guilds to make a large number of sample communities for each site. This approach, which is focused on general aspects of food-web structure rather than a detailed characterization of any particular community, allowed them to meaningfully compare the communities despite uncertainty about the particulars of who-eats-who.

For each randomly sampled food-web, they then simulated the asteroid impact by reducing the productivity of plants and algae and tracked the “cascade” of declines and extinction as they wound their way through the complex network of feeding connections. Their approach is particularly compelling because it is not limited overly simplistic linear chains of causation (e.g., plants decline -> herbivores decline -> carnivores decline) and permits a richer set of indirect interactions (e.g., plants decline -> herbivore A declines -> carnivore B eats more of herbivore C -> herbivore A recovers due to reduced competition from herbivore C.) By compiling sets of simulations from seven different Maastrichtian sites and ten different Campanian sites, they could then ask whether differences in food-web structure affected the robustness of a community in the face of a cataclysmic loss of plant productivity.

They found that the later Cretaceous communities were indeed more fragile, suffering greater degrees of simulated extinction at lower disturbance levels. This is certainly not to say that an asteroid impact earlier in the Campanian would not have resulted in a mass extinction – it certainly would have, but the degree of extinction, and the particular taxa that disappeared, may have been different. Interestingly, they also point out that increases in the average diversity of several guilds from the Campanian to the Maastrichtian, including the dinosaur-dominated VLH guild, was actually associated with a decrease in the robustness of the community. They hypothesize further that the importance of the VLH species was due to the fact that they fed many other guilds as they grew, from the small predators that cracked their eggs to the large carnivores unafraid to confront a fully-grown Triceratops.

This study shows that, even in an apocalypse of planetary proportions, context matters. The structure and diversity of ecological guilds, the numbers and functional types of species present, determines, in part, which species survive and which go extinct. This context-dependent complexity of ecological systems is what makes them so difficult to understand and so deeply fascinating. It also means that as we move forward with an extinction crisis of our own making, we are going to have to consider the interactions among species if we hope to mitigate our own impact.

*The evidence is drawn from the global iridium layer, characteristics of the boundary deposit, and the discovery of the Chicxulub crater in present day Mexico. Other accessory causes might include volcanic activity in the Deccan Traps of present day India.

**K-Pg marks the boundaries between two geological periods (or strata), the Cretaceous (K, C was already taken… not really, it is from the German name, Kreidezeit (chalk-time)) and the Paleogene (Pg). It is also known as the K-T extinction, with the T representing the Tertiary period. However, that nomenclature has been discarded by paleontologists and geologists. Bye, Tertiary! Thanks to the International Commission on Stratigraphy for changing the names of periods to make things extra confusing!

***In terms of the proportion of documented taxa going extinct

The research of Jonathan Mitchell and his colleagues, Peter Roopnarine and Kenneth Angielczyk, “Cretaceous restructuring of terrestrial communities facilitated the end-Cretaceous mass extinction in North America”was published November 13, 2012 in The Proceedings of the National Academy of Science of the United States (2012, vol. 109, pages 18857-18861.) A promotional blurb is also available over at Science Daily.

For an up-to-date review of the strong evidence for the role of the Chicxulub impact, see the paper “The Chicxulub asteroid impact and mass extinction at the Cretaceous-Paleogene Boundary” by Peter Schulte and his colleagues in the journal Science (2010, vol. 327, pages 1214-1218.)

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¿Cuántas Especies?


This roadside sign (“Many Species Live Here”)  is from the Rincon de la Vieja Rainforest Reserve*, in Guanacaste, Costa Rica, where I have been fortunate enough to do a bit of research on forest biodiversity. But it might just as well represent Earth in its entirety.

But how many species do live on Earth?

This is one of those big questions, perhaps the big question of biodiversity. And as with most big questions, it has many answers, the first of which is, quite simply, “We don’t know.”

However, this typical small answer to big questions is also terribly unsatisfying. So if we want to struggle on against uncertainty, how can we go about estimating the number of species on Earth? First, it is important to note that we can’t simply count up all of the names published by expert taxonomists. The named species total up to about 1.5 million, but while such lists are fairly complete for some groups of organisms, like mammals, for others, like fungi or nematode worms, they are woefully spotty. Scientists have simply not had the time and resources necessary to describe and name all of the organisms. In fact, even this year a new species of monkey was described from the central African rain forests, so we’re still getting to know even some of our closest relatives on Life’s family tree.

So where do we start? Sometimes in science, it pays to start with the obvious, and work from there. Back in 1988, a physicist turned ecologist named Robert May (now Lord May – perhaps the most ennobled ecologist) used a paper in the journal Nature to outline the kind of information that would be relevant to making such an estimate. He pointed out that most of the undescribed species tend to be small and/or rare, either in the sense of having low overall abundance or by being endemic to a very particular environment, because small, rare creatures are hard to find. Sounds obvious to me, but it highlights some of the factors we might want to consider.

Focusing on size, May pointed out that overall, there are generally many more small species than large species, but that the pattern shifts, declining for critters under about a centimeter long. If the decline observed among small species was only because of undersampling, May extrapolated that there could be anywhere from 10-50 million terrestrial animal species alone. While May admits the questionable nature of this estimate, the point remains that there may be many, many animal species out there waiting to be described, especially among the smallest critters. Indeed, several recently discovered vertebrates have been record-setting miniatures, including a fly-sized frog from New Guinea that could easily sit on your pinkie nail and four species of similarly sized chameleons from Madagascar.

Another option is to go to a place where many undescribed species are likely to dwell, sample them extensively, then extrapolate to other unsampled regions. This approach was pioneered by the entomologist Terry Erwin, who in the late 1970’s, went down to Panama to study rain forest beetles. (You’re probably starting to see the pattern that most of the undescribed terrestrial species are from the tropics; the reasons for that will be the subject of another post.) Since most of the beetles in a rainforest live high in the canopy, Erwin had to bring them down to the ground for study, so he constructed large tents around 19 trees belonging to a single, relatively common tree species, Luehea seemannii, then fogged the enclosed trees with an insecticide. Combing through the insects that rained down from the canopy, Erwin found about 1,200 different beetle species. But Erwin didn’t just want to know how many beetle species were on one tree species; he wanted to know how many insect species there were in the world’s tropical forests.

So once he’d killed them all and sorted them out, he did some extrapolating. First, he assumed that beetles were about 2/5 of all arthropods, the group that includes insects, spiders, etc.  This is a pretty well-supported number; nature does seem to love beetles. Having a fair amount of experience hunting for tropical beetles, he also estimated that about 2/3 of them lived in the canopy, while the rest lived low on the trunk (or inside it), inside the leaves, or down in the soil among the roots. Being an expert on beetles, he was able to estimate that about 13.5% of the species he found were specialists, living only in the canopy of Luehea seemannii.  Putting these numbers together, and assuming that other insect groups were similar in the diversity of their habitats and their degree of specialization, he estimated that their were about 611 specialist insects on a single tropical rainforest tree species. Taking the next, more daring step, given that there are an estimated 50,000 tree species in Earth’s tropical rain forests, Erwin ended up with a global estimate of about 30 million tropical insects.

Now given all of the attendant assumptions, Erwin’s number was not meant to be a hard-and-fast estimate. Nor, for that matter, was May’s. Instead, they are meant to put some bounds on our thinking, based on a set of rational, and of course debatable, assumptions. Compiling these sorts of estimates for different types of organisms and consulting taxonomic experts for their opinions has lead to a best guess of there being between 5 and 300 million species on Earth. The very broadness of this answer makes it almost as unsatisfying to me as “we don’t know.” In any case, it points to the fact that we still have a wealth of biodiversity for taxonomists to discover. Moreover, we could really use some better methods for narrowing down our estimates.

A recent (2011) paper by Camilo Mora and colleagues attempts to provide such a narrower estimate. Instead of just considering the number of species, Mora’s group took an historical approach and looked at the rates at which new species were described. This angle had been taken on biodiversity estimation before, but they expanded the approach by capitalizing on the fact that while scientists have certainly not described all of Earth’s species, we have a pretty good handle on the number of some “higher taxa,” meaning higher in the taxonomic hierarchy you probably learned in school: kingdom, phylum, class, order, family, genus, species. They examined data on the rates at which new groups were described for each taxonomic level, from 1750 to today. Early in the development of biodiversity classification, new groups were accumulating quickly in the scientific record, but eventually, the numbers of most of the higher taxonomic groups, like phyla and classes, level off. Using these estimates for the number of higher taxonomic groups in a mathematical model, they are able to estimate the number of species. Across all eukaryotes (anything that is not a bacterium, archaean, or virus), they estimate that the Earth harbors between 7.4 and 10 million species, at the lower end of the 5-300 million range, but still a pretty big number. In fact, if they are right, despite 250 years of intensive study, scientists have described less than 15% of the species that call Earth home.

Like May’s and Erwin’s numbers, Mora’s is not a definitive statement, but a step along the way to further scientific insight. In the grand and messy tradition of science, their approach has attracted both support and criticism, with taxonomic, evolutionary, and statistical experts weighing in. In any case, the tall order of describing and quantifying Earth’s existing biodiversity is given added urgency by the current extinction crisis, and scientists are engaged in developing a variety of field, laboratory, and computational methods to better answer the question. So while we don’t actually know how many species there are on Earth, by any estimate, it’s clear that we have a lot of work to do, and a lot of it needs to be done in the tropics.

*The Rincon Reserve is part of the larger Area Conservacion Guanacaste (ACG), which is a UNESCO World Heritage Site. The ACG encompasses about 2% of Costa Rica’s land area, including tropical dry forest, rain forest, and cloud forest, as well as a substantial marine reserve. It is managed by the government of Costa Rica for conservation and scientific research. It houses about 60% of the species that occur in Costa Rica and is one of the most well-surveyed, and beautiful tropical regions on Earth. Find out more about the ACG (in Spanish) or learn why you should donate to the Guanacaste Dry Forest Conservation Fund (which also protects rain forest and cloud forest (in English).