# Liveblagging: Geoffrey West

I’m sitting in MIT’s lecture hall 34-101, where a Venerable Personage is introducing today’s physics colloquium speaker, Geoffrey West (Santa Fe Institute). Like most colloquium speakers (or so it seems to me) West has a string of academic honors to his name; perhaps more unusual is his membership in Time magazine’s “100 most influential people” list, for which he was profiled by Murray Gell-Mann. (At that, he had more luck than Richard Dawkins.) West’s talk will concern scaling laws in living systems, and its abstract is as follows:

Life is very likely the most complex phenomenon in the Universe manifesting an extraordinary diversity of form and function over an enormous range. Yet, many of its most fundamental and complex phenomena scale with size in a surprisingly simple fashion. For example, metabolic rate scales as the 3/4-power of mass over 27 orders of magnitude from complex molecules up to the largest multicellular organisms. Similarly, time-scales, such as lifespans and growth-rates, increase with exponents which are typically simple powers of 1/4. It will be shown how these “universal” 1/4 power scaling laws follow from fundamental properties of the networks that sustain life, leading to a general quantitative, predictive theory that captures the essential features of many diverse biological systems. Examples will include animal and plant vascular systems, growth, cancer, aging and mortality, sleep, DNA nucleotide substitution rates. These ideas will be extended to social organisations: to what extent are these an extension of biology? Is a city, for example, “just” a very large organism? Analogous scaling laws reflecting underlying social network structure point to general principles of organization common to all cities, but, counter to biological systems, the pace of social life systematically increases with size. This has dramatic implications for growth, development and sustainability: innovation and wealth creation that fuel social systems, if left unchecked, potentially sow the seeds for their inevitable collapse.

Now, let’s see if I can keep up!

SCALING BEHAVIOR

“I think it’s patently obvious that I’m not one of the hundred most influential people in the world,” West says, “which should be obvious after I’ve finished my talk.” There follows an amount of fumbling as West and the distinguished personage try to turn on the overhead projector — “We need an experimentalist!” — before the big red button is found, and the projector screen glows into life.

It’s difficult to imagine “Newton’s laws” for biology, unifying principles which allow quantitative predictions, because biological systems have many degrees of freedom, large amounts of historical contingencies and so forth. However, it’s conceivable that one could find general principles for coarse-grained descriptions of biological phenomena, roughly analogous to the kinetic theory of gases: we know these descriptions are incomplete, but they have proven themselves practically useful.

For example: when strolling through the forest, we could ask, how many branches would this tree have, given the circumstances in which it lives? Finding a shrub of a certain size, we’d like to know, how long would we have to walk before finding another of the same size? If we look at a typical physiological quantity — of which we can provide many, many examples — and compare it against organism size, we find a remarkable relationship: basal metabolic rate, for example, scales as the 3/4 power of body mass. The cross-sectional areas of both tree trunks and aortas also scale as organism size to the 3/4 power, as does (with a certain amount of scatter) genome size.

If the metabolic rate increases as $$M^{3/4}$$ than the metabolic rate per unit mass scales as $$M^{-1/4}$$. It’s an economy of scale: “You are more efficient than your dog, but your horse is more efficient than you.”

Where do these curious scaling laws come from?

NETWORK DYNAMICS

West and colleagues suggested that these “universal” scaling relationships stem from the universal properties of the networks which underlie and organize the biological phenomena. A useful idealization of a biological transport system — think circulatory or respiratory — is that it is a hierarchial, branching network whose terminal units (the tiniest capillaries, or the alveoli) are all the same size. Of all the networks satisfying these properites which could exist, the ones which do exist have been optimized by natural selection to maximize some measure of efficiency.

The flow in the aorta must equal the flow per capillary times the number of capillaries:

$$Q_0 = N_c Q_c.$$

From the properties of the network we listed earlier, it can be deduced that in $$d$$ dimensions, the basal metabolic rate $$B$$ scales with body mass as

$$\displaymode B \propto M^{\frac{d}{d+1}}.$$

Optimization enters the picture via impedance-matching at the branch points, which leads to area-preserving branching.

Scaling relationships for individual organisms can also be applied to collections of organisms: chop off all the branches of a tree and plant them in the ground, and you get what looks statistically like a forest. We can make an even bigger step and apply network dynamical properties to cities. (In 1800, 3% of the United States population lived in cities; in 2007, 80% did.) West and a transparency-full of collaborators looked at resources and products of cities, comparing them against population size, and found that those resources associated with distribution networks scale somewhat like those in biology. Again, there exists an economy of scale, with infrastructual quantities having a common exponent of about 0.8.

## 6 thoughts on “Liveblagging: Geoffrey West”

1. Interesting. The idea that there are ‘power laws’ for metabolism and body size is one that I was exposed to as an undergrad in a comparative physiology course (Thanks, Dr. Grubbs!). The idea that general principles can be deduced for complex adaptive systems (CAS) I first read about in a book by John Holland, one of West’s SFI colleagues.

I don’t have the math to do this kind of thing in my head, while typing on somebody else’s blog, but I do have a question for you guys and gals who do. Is it possible to write the expression ‘B is proportional to M ^ (d/d+1) as some sort of fractal? That would have some interesting connections and consequences if so.

2. West said in passing that the 1 in the $$d + 1$$ is due, in a qualitative sort of way, to the fractal nature of the branching network. When I’m not trying to juggle quite as many things (I have a review article on a different subject to read, digest and say intelligent things about by this evening) I’ll essay an exploration into the mathematical details.

3. This is pretty fascinating stuff, and it makes some logical sense. However, I do wonder where the power-law relationships come from. I’m sure they’re based on some kind of actual experimental analysis, but the way they just kind of pop out in the premises here triggers my suspicion. (Probably just an unfortunate result of reading too much creationist bullshit where you really have to question every single premise they use, because they all turn out to be questionable.)

4. We do have plots of metabolic rate (and other quantities) against organism size, gathered from empirical data, and they do follow straight lines on log-log plots. (Moreover, the data cover enough decades that we’re probably not being fooled by a log-normal distribution.) AFAIK, the data isn’t very good on the really tiny scales, like when you’re talking about the bits inside a mitochondrion, but from cells to trees, it’s a pretty well-established relationship.

5. Ok, I figured it would be something like that: i.e., well-established enough that it can be safely cited without reference.

6. The other problem is that I was writing this while the guy was talking, so I didn’t have time to find and hyperlink references. Here’s a paper which covers most of the same ground as the talk, except for the stuff at the end about cities, which is new and still in progress.