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SPEAKER 1: This is a production of Cornell University.
SPEAKER 2: Over 90% of all visible living matter is plant life. Plants clean the air, provide food, fuel, and fiber, and yield vital pharmaceuticals. In a Chats in the Stacks book talk at Mann Library in October 2012, Karl J. Niklas discusses his new book Plant Physics. Emerging from long-term collaboration between plant evolutionary biologist Niklas and physicist Hanns-Christof Spatz the book interweaves themes that emphasize biology and physics. It explains how plants cannot be fully understood without examining how physical forces and processes influence growth, development, reproduction evolution, and the environment.
KARL J. NIKLAS: Thank you all for taking the time and effort to come to this talk at all, because I have to say, if I was going to put two words together that might be the bigger snoozer, it's "physics" and "plants."
[LAUGHTER]
But my primary task today is to try and show you how physics can inform the study of plant biology, and how the study of plant biology can inform our understanding about physics, and physical laws and processes. The images that come about, when you think of the botanist, is this old fogey staring at little flowers and thinking about pollination biology. And then you think about the rigors, the mathematical, quantitative rigors, that define physics.
And physicists sometimes have a low regard for the biological scientists. I put in the little title there, "Botanists are so cute when they are trying to learn quantum mechanics." You see the little dog. It really said "dogs are so cute." But I thought botanists were appropriate.
But the collaboration that instilled this book is that-- this is my co-author, Hanns-Christof Spatz, who got his PhD in physics, and then went on later on to study neurobiology. He was interested in the electrophysiology of neurons in the fruit fly drosophila. So both of us came from a quantitative mathematical background, and we were attracted to the study of biology key to the zoological questions, and me to the botanical questions.
So the collaboration has been going on now for over 10 years. Plant Physics was the last product. We've published a number of papers together, and we will continue to do so.
So what's the connection between physics and botany? I'll just take this as a little cartoon. We all know the apocryphal story of Newton learning about gravity, and force equals mass times acceleration by the falling of an apple on his head.
But one doesn't have to be historian of science or physics, and I am certainly not, to realize how physics has contributed to the study of biology, and how biology contributes to the study of physics. One of the contributions of the great mathematician and physicist Galileo was something that we take for granted right now, and that is the scaling of surface area with regards to volume. Until his treatise on mathematics, it wasn't common knowledge, even to well-informed scientists, that surface area scales is the square of some reference dimension, and that volume scales is the cube. And therefore, surface area to volume should scale as the 2/3 power of that dimension.
Now, there's a few things that Galileo didn't mention-- the little caveats. And that is that that scaling to the 2/3 power only holds true if things differ in size, but they retain the same geometry and the same shape. If they violate either of those two constraints, the scaling of the linear dimension is not to 2/3. It can take on a number of numerical values. How many here think that geometry and shape are the same thing? I expect the physicists not to raise their hands.
OK, so you understand that they're not. Give you a simple example. Think of a cylinder. A cylinder is nothing more than a circle that's translated in the linear dimension.
But depending on the diameter of that circle, and how long I translate it, the ratio, or the quotient of length to diameter, can take on different numerical values. And that dimensional, [? this ?] number, is essentially the defining feature of shape for a cylinder. The only geometric object that can't change shape or geometry is the sphere. So this holds very nicely if you're dealing with spherical objects. But anything that can change shape and geometry, together or individually, will violate this rule.
And I'm going to show you later on how plants and animals violate this rule in a different, but very profoundly interesting, way. And it's right here. That scaling relationship was taken to heart by Max Kleiber, who was interested in the allometry, the scaling of metabolic rate. This is respiration as a function of mass.
And this is now called Kleiber's rule, or the mouse to elephant rule. And that is, if you plot on a log-log graph the relationship between metabolic rate and mass, it is a linear relationship. The y-intercepts, that is the height of those linear relationships, differ for cold-blooded and warm-blooded animals. But the slope of the line, nevertheless, is uniform throughout. This is for plants, this is dry body mass, and this is annual growth, which is an indirect measure of respiration and metabolic activity.
And just to show you that, we're talking about 20 orders of magnitude in body size. And we're talking about 16 orders of magnitude in annual growth rate, ranging from little unicellular algae, all the way to giant trees with intermediate plant species that are non-woody. And the slope here is log-log linear.
By the way, if you Google my name you will see this chap. I thought it would be appropriate to put his face. He's an actor living in London, and so that's why I put the question mark for both of us, optimistically. He's much younger than. I But I prefer the question mark as to when we demise.
So getting back to this scaling relationship, if you have a three-dimensional object, height, length, and width, then surface area is that dimension minus 1. Volume is that dimension. And so the scaling of surface area to volume is 2/3 when n equals a three-dimensional object. And that's what Max Kleiber and I thought we were going to find when we looked at certain scaling relationships.
But in fact, what we found was a very different relationship. The slope is 3/4. For those of you that know something about N dimensional space, surface area of any N dimensional object is that dimension minus 1, where the volume is that dimension. So if you have an object that has four dimensions, the scaling of surface area to volume isn't 2/3. It's 3/4.
Now, you can say to yourself, OK, what's the fourth dimension? Well, if you're Einstein, you say it's time. And that's actually not an unreasonable thing, because all sorts of metabolic processes are time-dependent, as well as temperature-dependent.
But there's something else that is universal, even of bacteria. And that is that they have an internal dimension. There are membranes that are throughout the cytoplasm, certainly amongst eukaryotic organisms, and even amongst prokaryotes organisms like bacteria, that are vesicular-like internal structures. And if you look at that as an addition to the external surface area, you very quickly come around to a scaling relationship of 3/4.
I won't bore you with all of the details. But I will tell you that the finding of 3/4, that goes back almost 50 years for animals. It goes back fairly recently in terms of the research that I published. But it is hotly debated right now as to what is the mechanistic explanation for this 3/4 scaling relationship that goes across 20 orders of magnitude of plants and animals, from unicellular organisms to some of the largest.
So this is a controversy, in some respects, that could be laid at the doorstep of Galileo. And you physicists are all to blame because of this. So we can say Galileo cheated in a way, because he didn't give us this more global perspective of surface area to volume. But boy, did he get the little spherical balls rolling, little cells.
Now, Galileo contributed a lot to understanding biology in his Mechanica. But he also learned a lot from plants. Apparently, as legend goes, he played around with the stems of grasses. Those of you that have ever done that, you know that most grass stems are hollow. They're tubular, and that's what is trying to be drawn right here.
And he noticed something very curiously. And that is that if you compress a hollow cylinder, it takes a lot more effort in some geometries-- in some shapes, I should say, a lot more effort, a lot more compressive force, than it does to compress a solid sphere. Some question of scaling, of course. And he played around, and his notes indicate that he began to speculate that there might be some component.
This is [INAUDIBLE] the second moment of area, and these are the equations for the second moment of area. But if you played with the ratio of the outer radius to the inner radius, you might get almost equivalent mechanical strength with the added benefit of something else. The missing mass wouldn't contribute to the compressive force.
So you're gaining considerable strength without investing a lot of material, and you're also gaining considerable mechanical stability. And this all relates to something that he intuited. And now we know, as a matter of fact, in actually much more quantitative rigor than he did, even though his studies are just brilliant.
And what you're seeing here is the cross-section through a cylinder, solid cylinder. And what you're looking at are the magnitudes of the bending stresses. So in other words, if my arm is a cantilevered beam and it is subjected to the acceleration of gravity-- so it's bending down, or I could have a weight at the very end, you can intuit that the outer elements on the upper surface are placed in tension, and the outermost elements on the bottom side are placed in compression. And it turns out that if you plot the magnitudes of those, they reach their maximum magnitudes right at the edge, right at the outside. And dead center, there's 0, or nearly so.
I see people shaking their head. These are bending stresses. This is certainly not true for torsion or shear stresses. But the bottom line is that this is a very elegant way of saying that I don't need all that material in the middle. I can eliminate it to a certain degree.
And for those of you that know about what happens when you over-eliminate the material, it's called Brazier buckling. You have a hollow tube, place it in bending, eventually it locally cramps, because there's is nothing on the inside to resist that kind of bending, that kind of bending force. But he figured this out.
And I have to say, to the credit of plants, they figured it out way ahead of Galileo. Because some of the oldest plants, going back about 350 million years ago in the form of equisetum, the horse tail ancestors, have hollow stems. And there are many plants whose leaves, the base of the leaves that acts as a cantilevered beam, is also hollow.
So it's conservative in terms of biomass. It's relatively strong and it's lightweight. It doesn't contribute a lot of material.
And if you begin to think about some of the Asian stratagems for building scaffolding, this is bamboo. Bamboo is one of the strongest things in the biological world that we can think of. And in fact, there are many edifices that are constructed entirely of bamboo. These columns are bamboo-- which by the way, for those of you that know this physics, that phenomenon that I called about Brazier buckling. If I take a hollow tube and I place it in bending, it can go through a local crimp, the straw collapses.
One way to get rid of that, or at least reduce the effects, is to put in little struts temporarily. And if you look at this bamboo, you will see-- for those of you that don't know the anatomy of bamboo or grass, there's nodes and internodes. And right here are these nodal diaphragms.
And plants have done remarkable experiments. They've had millions of years to fail. It's called extinction. But they've had millions of years not to fail, and that's called biophysical innovation. And even in extreme bending, bamboo can be a very strong, lightweight, incredible material.
So I bow before natural selection creating these magnificent monocots. They also have created the largest things that ever lived. The giant calamites, horse tails-- woody horse tails with hollow internodes and nodal septum at their nodes. This is a reconstruction [? of ?] the tallest axis.
The tallest stem of a calamite is 85 feet. The rhizomes, the underground stems, are about three feet in diameter. If we scale this up to how modern day little herbaceous equisetums grow, one of these plants could cover all of downtown Ithaca.
From above ground, it would look like a forest. But it really would be one individual. These were definitely the largest things that ever existed-- individual things that ever existed.
Leonardo da Vinci-- how can anybody talk about physics and not talk about an old friend, Leonardo? Leonardo was, according to his notes, looking at trees. And he made an observation. He noticed that if you look at the diameter of a basal subtending branch, it is roughly equal-- or I should say the cross-sectional area, roughly equal to the cross-sectional areas of the branches above. So in other words, if you took all the branches together, you get a solid cylinder.
Now, there's variation in that, of course, and it's not true for all species. But for many dicots, it is. And he began to think about hydraulics. He began to think about water coming up through the roots.
He wasn't dumb, obviously. And he knew that the water had to be distributed to all of these pipes, essentially. And it was from this that he deduced considerably the hydraulics of river systems. So he learned from plant hydraulics and took that lesson to hydraulics, sedimentology, and applied a lot of this to war.
He was a genius at doing things for war, one of which is the helicopter. Not the helicopter-- what am I saying? The parachute, which according to his notes was devised after the pappus, the modified calyx of composite flowers in most of Europe. They're these [? damn ?] yellow composites. And when the fruits mature, the calyx, the [INAUDIBLE], grow up into these parachute-like things.
And what he did very elegantly, he measured the terminal settling velocity-- the rate at which this thing falls, with or without the pappus. And he said, well, gee, I can decrease the rate of fall by putting something that produces drag. And he played around with little pieces of paper, and lo and behold, the parachute. Of course, there was no aeroplanes to fall out of. But parachutes, that's a really clever idea.
The other thing that's really clever is the helicopter. This is his sketch of the helicopter. And his notes indicate that it came from watching the fruits of maple trees descend.
If you watch these fall-- and they will be doing it now pretty soon, they're autogyroscopic. And so they will rotate rapidly. They break apart, and they rotate very rapidly. And that, of course, decreases the rate of fall.
And so what he did, of course, is there wasn't a wasn't a motor for him to create an autogyroscopic object. But by constructing a piece of paper that is a spiral, it behaves in the same way and it reduces the settling velocity. And of course, if you actuated that, it could actually get you off the ground, as well as reduce the rate at which you fell. Again, he dropped things from towers, but there were no planes much to his regret. I often wonder, if he got on one of our modern-day planes and didn't know what it did, and it started taking off and it suddenly left, what an amazing, awesome experience that he probably would have to share with the bathroom.
[LAUGHTER]
Here's one of the unsung heroes of mathematics and physics. This is Leonhard Euler. He was probably the greatest mathematician of the 18th century. I mean, he invented the calculus of variance just to solve one problem which I'll talk about in-- right now in fact.
He was shipped off to Russia during the reign of-- actually, before the reign of Catherine the Great. It was during Peter II. But during the reign of Catherine the Great, she was having a lot of trouble.
She had ships whose masts would break. They would just break. They would be sitting in dock without any scuff, sails. No drag, nothing. And then they would just suddenly break.
And what he figured out, using the calculus of variance, is that there a critical self load. In other words, I can get so tall, at such and such a way, that I actually begin to deflect under my own weight. And this is the critical buckling load, which is equal to numerical value here.
This is Young's modulus. It's a measure of material strength. I is that second moment of area, which is the contribution made by geometry.
A lot of people don't understand geometry is really important. Unless, of course, they take a class in geometry and fail. But let me show you, I hope will all agree that this piece of paper is made of a certain amount of material that gives it stiffness.
Now, you notice that this piece of paper is not capable of supporting its own weight. But what? All I did was change the geometry.
That's what the I does. That's the second moment of area. It's the consequence of size and geometry and shape that contributes to the ability of any material to resist externally applied mechanical forces. And that whips-- the length, I keep doing this. The length here is here height.
And he just found out by calculation that they were building their masts too big. I mean, duh. No wonder they didn't have a good navy.
[LAUGHTER]
So the critical buckling formula Euler was re-described by another brilliant mathematician, Alfred Greenhill. You can rearrange Euler's formula by putting the length over there and saying, well, that mass is equal to density times volume, blah, blah, blah. And you get a formula that looks like this. And this is the critical buckling length of not just mass, but trees.
This is that material property thing. That's the density. That's the acceleration of gravity. And this is the radius of the stem, the flag mast, whatever. This thing has incredible implications to ecosystems, to plant biology, and, well, to lots of things.
And out of that [? it ?] came out by one Frenchman and one German, the Barbre-Kick law. And I won't get into it, but it looks like this. Yes, and that's simple. That's very simple.
Thank you. I appreciate it. [INAUDIBLE] talks about the deflection of things that have difference is in cross-sectional geometry, shape, and size.
And guess who used that formula. Eiffel, to build the Eiffel Tower. The tapering of that tower, which is exquisitely aesthetic, but also mechanically robust and extremely well-informed. He was a sharp man.
So now, all of this is how physics informs biology, how biology can inform physics. Now let's talk about this in a little bit more detail, and I hope with equal amount of fun. All plants, regardless of when they exist, or whether they're aquatic or terrestrial, or whatever their size, shape, or geometry, have to perform these four essential tasks.
They have to intercept light because they're photoautotrophs. They have to conduct fluids [? either ?] internally or externally. They have to deal with externally applied forces.
And they have to reproduce. They don't have to reproduce, but if they don't reproduce, they can't evolve. Sexual reproduction, genetic recombination, you have to do that. Otherwise, you become a tenured faculty member and stagnate.
So my task is to tell you that, with the use of physics and chemistry and mathematics, we can quantify the performance of each of those tasks with considerable quantitative rigor. Consider light interception. Now, this is just a little diagram showing the arrangement of leaves that are arranged in a spiral on one vertical stem. There's a lot of notation there. Those are the mathematical parameters that you require to describe the geometry and the shape of that single stem with those leaves.
Then what you can do with the aid of computers is subject these hypothetical plants to the diurnal path of the sun from dawn to dusk. And you can quantify how much sunlight that geometry intercepts. That's really simple, brute force numerical calculation.
The trick is, can you create different geometries by manipulating the numerical values of these parameters, and say what are the best geometries-- what are the most efficient? Well we did that. Took a few weeks, chugging along with the computer.
And so we now have what's called the morphospace. We have a hypothetical N dimensional space filled with all the different geometries, sizes, and shapes that are possible. And we're going to take slices through the morphospace.
And what you're looking at now are four slices, and they're landscapes. They show peaks, and then in the back, plateaus. Wherever you see a peak, like up front and here, it's saying that the object that rests right here is better at intercepting light than an object here, here, here, or here. So this is telling us that there are some geometries that are extremely good, and others that are extremely bad.
But notice, if you go in this direction in some of these morphospaces, the landscape almost becomes flat. And what that means is that, by varying certain parameters, like the distance between leaves, the geometry of the leaf, the deflection angle of the leaf, I can compensate for the arrangement of the leaves, whether they're in spirals, whether they're in whirls, et cetera, et cetera. So we can quantify the effect of phyllotaxy, the arrangement of leaves-- leaf size, leaf shape, et cetera, et cetera.
You have to read the paper. Well, you don't have to read it. But if you want to see that this can be done, let me know. I'll give you a reprint.
How about mechanics? Well, that's the easy part. Solid mechanics is easy.
You have a formula for a bending moment, which is the force multiplied by the lever arm. You have the calculation for drag force. How much is that force? It's a function of projected area. It's a function of ambient wind speed.
If I know the display of something, I can calculate its projected area. I can say how much drag on that based on some kind of ambient wind speed. I can calculate the bending moment if I know how far up from the ground the leaf is, blah, blah, blah, blah, blah. Very simple. That's the easy part.
Hydraulics, now, this gets a little bit nastier. This is the formula for-- I love this. It's the Hagen-Poiseuille equation.
A German and a Frenchman, they described something at virtually the same time. And they said that the hydraulic conductivity of hollow tubes is a function of a pressure gradient times the radius of the tube raised to the fourth power. That's really neat.
By the way, that fourth power scaling is because the flow through a tube is really parabolic. It's high in the middle, and at the no slip condition is zero, right at the edge. And that describes a parabola, and blah, blah, blah.
But anyway, yes, if you know about this geometry, the number of cells, et cetera, et cetera, you can calculate how much water can get through it. And if you know how tall the object is, you know what the gravitational head pressure is. So there are all sorts of things you could do with hydraulics, which is lot fun. But if I told you, you'd fall asleep.
Reproduction is the most brute force. But yes, plants do reproduce, often by shedding things into the wind, the four corners-- pollen, spores, fruits, little fruits. Aerodynamics, what you're looking at here is the trajectory of pollen grains. Each little dot is that same pollen grain moving that's been photographed with a stroboscopic light.
If I take photographs simultaneously from the top and the bottom, I can look at the motion of that particle in three dimensions. Since I know the frequency at which the light is flashing, and I know the direction, I have a vector. I don't just have speed. I have direction and speed, so I now can do neat things. Yes, OK, blah blah, blah.
So let's put this in the context of evolution, with the quote of Charles Darwin, "Endless forms most beautiful and most wonderful have been are being evolved." That's not great grammar, but he was the Victorian.
And the other thing that I dislike the most is plants are right here at the bottom. They should be at the pinnacle, because they are the best. Plants really are better than animals. You have to believe me. Animals cannot create their own food.
AUDIENCE: [INAUDIBLE] .
KARL J. NIKLAS: Yeah, but we don't create that food. Yes we can. Yes, OK.
[LAUGHTER]
Thank you, Mr. [? Mortlock. ?] So when we think about applying biophysics to plant evolution, most ill-informed people think of angiosperms. Let's think about the biophysics of roots, stems, leaves, flowers.
Oh, they're so pretty. There's so many of them. [? I think ?] 280,000 species, blah, blah, blah, blah, blah.
But they're Johnny come lately lately. There are only about, what, 100 million years old, give or take 50 years? I don't know. But they're-- 3 million? OK, whatever.
There's always an expert. Which I appreciate. That's the nice thing about coming to Cornell. If you make a mistake, there's at least 20 people in the audience that will tell you you've made a mistake.
[LAUGHTER]
But I want to take this down a notch, and I want to talk about plants that look like this. These are reconstructions of some of the earliest known land plants. So these are the terranauts. Not cosmonauts, not astronauts-- terranauts. Not "terror," but "terra firma."
They're botanical tuning forks, the first vascular land plants. They didn't have leaves, they didn't have roots, and they technically didn't have stems. And most of them were nicely branched, and almost all of them had terminal spore-producing structures. Then they were really elegantly stupid, because all of the functions basically had to be performed by these little axes.
And look at the elegance here. [? This is ?] part of the anatomy of one of these plants, a central vascular strand through which water was conducting, stomata for gas exchange on the surface. And these spores, through meiosis, produced in these sporangia.
No roots. They just had little fibrous-like cellular outgrowths, rhizoids that absorb minerals and water. Really nice. Easy to study if you were a physiologist.
Think about how easy it would be if you had these plants today. Well, you do. You have psilotum, but nobody studies them.
Now, the point that I'm going to make is that mathematically, these things are easy to describe. You can construct these geometries very easily. They don't have leaves, so I don't have to worry about phyllotaxy.
What I need to know is the bifurcation angles. What's the degree to which these axes branch? Then I need to know the rotation angle. You'd look at the profile, my shadow of the finger, you can see the different rotation angles project different surface areas towards the sun or towards the wind.
And then what's the probability of these things branching? So in the simplest case, I can construct a three-dimensional universe, a Cartesian universe, a rotation angle, bifurcation angle, branching probability. Now, there's more dimensions here. I could say, OK, the branching angles aren't equal. So one angle is more, one angle is less.
The lengths are not equal. The diameters aren't equal. So you start plugging that in, and you have an N dimensional hyperspace of geometries. But we can take slices through it and look at what they look like.
And there you go. There's three slices through this N dimensional space. This is when the bifurcation angles are equal. This is when they're unequal. And this is when rotation angles are equal or unequal.
Then you look at these geometries, and some of these look darn familiar. Without stretching your credulity, these look like apple trees and things like that. These [INAUDIBLE] like things may be like conifers. These are like, witch's brooms or psilotum.
I used to give a lecture and say this is completely stupid. Nothing grows like that. Then I went to New Zealand.
[LAUGHTER]
And they showed me the divericating shrubs of New Zealand. These are juvenile forms of different species, where the branches will actually grow down at strange angles. And it's thought to be an adaptation to bird herbivory-- the moa, which were driven to extinction by the nature-loving native people who settled in New Zealand.
So there's something else that's important. We can't only describe them. We can quantify how they perform these functions. I just showed you that there's ways of doing that.
So I'm going to show you now our first experiment. This was done before some of you were even born. And that is, what happens if you say to the computer, quantify the ability of all those different geometries to maximize mechanical stability and maximize light interception at the same time.
Now, please understand, there is a conflict. There's a design antagonism here. If I want to maximize light intensity, I put things out like this. Unfortunately, this maximizes the bending moment at the same time.
Now, the options are-- you'll excuse this. You can either do this or you can do that, and that reconciles. But it gets a little bit more complicated as time goes on. So, OK, now we can quantify, and we've quantified all the geometries in that morphospace. And now we could say, what did the first land plant look like, the first vascular [INAUDIBLE].
This is a fossil of cooksonia. It branched equally, had terminal sporangia, itsy-bitsy small. The computer sees cooksonia that looks like this. That's cooksonia.
Now, a search algorithm, we just say to the computer, computer, search around this geometry and find a geometry that does the two tasks equally well or better. And keep doing that. Keep going through this morphospace. And stop when everything around that last shape is worse. So it's like a little island.
So this is what the computer found. Now, we've left the equal branching space, because now we have anisometric branching. Probably New Zealand.
That's where it stopped. There are geometries that look very much like that-- conifers and [INAUDIBLE] and these [INAUDIBLE] branching systems. And also, this adaptive walk that I just described for you is exactly what Walter Zimmermann predicted we would find in the fossil record for the evolution of leaves, the telom theory. So that's interesting.
But remember, we have four tasks. And I told you, plants have to do all four simultaneously. Don't worry. I'm almost there.
So what I'm going to do now is show you what happens if you have a walk through a one-task space, a two-task space, a three, and then a four. So this is what happens when they only have to perform one task. Light interception, these three are equally good. Mechanical stability, these three are equally good.
Hydraulics, those are equally good. And this is reproduction, only one. These don't look like very much, do they?
Now, two tasks. Reproduction and light, light and mechanics, mechanics and reproduction, reproduction and water, light and water, mechanics and-- yeah, OK. You get the idea. Now, three tasks. And finally, four.
So you might notice something that's happened. We've increased the number of tasks. There are more things that can do them equally well.
But what you can't see is that, as I increased those tasks, the global fitness of each of those things decreases. The height gives you a sense of how well they can perform their functions. More options, but less of a difference. This makes perfect sense, and the physicists will understand this, as all of you.
Imagine that this is an engineering class, and I give you as your week assignment go out to design toaster. Next week, you come in, and you've got nice designs for toasters. And they probably all work very nicely. Then that week, I say, I want you to design a machine that's a toaster and a hairdryer. Things get a little-- and then the following week, a vacuum cleaner, all those things.
Designs start getting probably very hairy. And probably, those things that work, they will work, because you want to grade. But I will tell you, they're not going to be great vacuum cleaners, hair dryers, or toasters. But probably, you'll toast your bread on the output of the vacuum cleaner. I don't know.
[LAUGHTER]
But this explains something that we see in the fossil record. This is the appearance of different morphological and anatomical innovations during the rapid period of land plant evolution of the Devonian. The hardest thing that these plants had to do is to get on land and stay dry, and not dry up.
Once that was solved-- that was the principal task, all those other tasks had to be performed simultaneously. The playing field was leveled and the innovations went in all directions-- massive extinctions and massive solutions. Evolution isn't always pretty.
I'm going to not talk much longer, because it's almost 45 minutes, now that I'm talking. But I just wanted to show you something else about physics, and now about trees. We're going to jump up in the [INAUDIBLE]. We're going to talk about these [? damn ?] angiosperms and conifers, and basically, light interception, mechanical support, absorption, and hydraulics-- those four tasks.
But now we've got a canopy of leaves, and the canopy is represented by this. And this is the root system. And this is an algorithm that my last graduate student developed, using the math, that I was happy to provide a computer program that allows us to simulate the interactions of plants in a community growing.
And the model is based on only two assumptions. And that is competition drives growth, and the competition is for only two things-- sunlight and space. No two objects occupy the same space, and objects that are shaded don't grow as quickly as the objects that aren't shaded. It's very simple. Very mathematical, but it's very simple.
And now I'm going to show you how one of these little puppies grows. And for graphical purposes, the canopies are these little umbrellas. Those little blebs that you see, those are the little seeds. They're dispersed. Its ballistic random dispersal, and the radius of dispersal is proportional to the height of the parent plant.
Now I want to show you a community based on these simple interactions. And what you're going to see here is as if you're a deer, [? hate ?] them, looking through the forest. And here, da Vinci and one of his parachutes looking down at the community.
Each iteration is one year's growth. You see the understory, and then the understory starts thinning. You will see light gaps. Whoops, I didn't mean to do that.
You will see light gaps. Where older trees die, the mortality is stochastic. And it's based on age. The older trees have a higher probability of stochastic death. And you see these little-- oh, every time I press on that, which is the light. Isn't that strange?
Ah, physics, optics, OK. So I'll point now. See the light gaps, and you see little things coming in?
Now, the neat thing about this simulation is that we could not get the paper published. Because the ecologists, who were anonymous who reviewed this, said this can't be right. It's too simple.
Have you ever heard of a spherical cow dealing with heat dissipation? No. I mean, if it works, it works. Let me show you how well it works, and this is really quick. These are graphs of [INAUDIBLE].
[LAUGHTER]
Plotting the little dots here are data that were observed for a forest of trees growing in France, Italy that were observed by the foresters for 95 years. And every five years, they collected data. And they published it.
So we parametrized a forest of that particular species of tree. We ran the models and predicted, tried to predict, these scaling relationships. And the model predicted the data that you see in big circles.
AUDIENCE: [INAUDIBLE].
KARL J. NIKLAS: I'm old. You're going to have to talk a lot louder.
AUDIENCE: [INAUDIBLE].
KARL J. NIKLAS: Yes, yeah. And even if we had looked at the data, the model doesn't take those data in consideration. So, whatever. So, in many cases, the data and the simulation points are so overlapping you can't-- this is too simple.
That's what the ecologists said. It can't be right. We got it published. In PNAS, I might add.
[LAUGHTER]
And it all goes back to Apollonian packaging. Physicists will know about this. How do you package? How do you maximize the space in the gaps that are created by, let's say, the canopy of two large trees? What's the distribution of things in there?
And then mortality. It's really that simple and it's that elegant. But it's too simple, and it can't be right.
So, in conclusion-- I love the one on the left. "After the discovery of 'antimatter' and 'dark matter,' we've just confirmed the existence of 'doesn't matter.'"
[LAUGHTER]
Which does not have any influence on the universe whatsoever. Well, if I've done anything, I've tried to make you see that physics, physical laws, really do provide us with a better appreciation, certainly of plant biology. And the physics allows the botanists and biologists to not do this.
I think you should be a lot more explicit in step two. Says, "Then a miracle occurred." So I want you to see that both of these things really are solved by a happy marriage between physics and plants, which are much better than those animals. Thank you very much.
[APPLAUSE]
SPEAKER 1: This has been a production of Cornell University, on the web at cornell.edu.
Over 90 percent of all visible living matter is plant life. Plants clean the air, provide food and fuel, fibers for clothing, and pharmaceuticals. Interweaving themes that emphasize biology and physics, the book explains how plants cannot be fully understood without examining how physical forces and processes influence growth, development, reproduction, evolution, and the environment.
In a "Chats in the Stacks" book talk, Karl J. Niklas, the Liberty Hyde Bailey Professor of Plant Biology in the College of Agriculture and Life Sciences at Cornell University, discusses his new book "Plant Physics" (University of Chicago Press, April 2012). The book, the result of a long-term collaboration between plant evolutionary biologist Niklas and physicist Hanns-Christof Spatz, is unique in the field of biomechanics and a valuable reference for researchers interested in how plants work from a physical perspective.
