Theoretical biologist George Sugihara draws some parallels between complex biological systems and man-made systems:
A key phenomenon known for decades is so-called “critical slowing” as a threshold approaches. That is, a system’s dynamic response to external perturbations becomes more sluggish near tipping points. Mathematically, this property gives rise to increased inertia in the ups and downs of things like temperature or population numbers — we call this inertia “autocorrelation” — which in turn can result in larger swings, or more volatility. In some cases, it can even produce “flickering,” or rapid alternation from one stable state to another (picture a lake ricocheting back and forth between being clear and oxygenated versus algae-ridden and oxygen-starved). Another related early signaling behavior is an increase in “spatial resonance”: Pulses occurring in neighboring parts of the web become synchronized. Nearby brain cells fire in unison minutes to hours prior to an epileptic seizure, for example, and global financial markets pulse together. The autocorrelation that comes from critical slowing has been shown to be a particularly good indicator of certain geologic climate-change events, such as the greenhouse-icehouse transition that occurred 34 million years ago; the inertial effect of climate-system slowing built up gradually over millions of years, suddenly ending in a rapid shift that turned a fully lush, green planet into one with polar regions blanketed in ice.
The global financial meltdown illustrates the phenomenon of critical slowing and spatial resonance. Leading up to the crash, there was a marked increase in homogeneity among institutions, both in their revenue-generating strategies as well as in their risk-management strategies, thus increasing correlation among funds and across countries — an early warning. Indeed, with regard to risk management through diversification, it is ironic that diversification became so extreme that diversification was lost: Everyone owning part of everything creates complete homogeneity. Reducing risk by increasing portfolio diversity makes sense for each individual institution, but if everyone does it, it creates huge group or system-wide risk. Mathematically, such homogeneity leads to increased connectivity in the financial system, and the number and strength of these linkages grow as homogeneity increases. Thus, the consequence of increasing connectivity is to destabilize a generic complex system: Each institution becomes more affected by the balance sheets of neighboring institutions than by its own. The role of systemic risk monitoring, then, could simply be rapid detection and dissemination of potential imbalances, much as we allow frequent underbrush fires to burn in order to forestall catastrophic wildfires. Provided that these kinds of imbalances can be rapidly identified, maybe we will need no regulation beyond swift diffusion of information. Having frequent, small disruptions could even be the sign of a healthy, innovative financial system.
Further tactical lessons could be drawn from similarities in the structure of bank payment networks and cooperative, or “mutualistic,” networks in biology. These structures are thought to promote network growth and support more species. Consider the case of plants and their insect pollinators: Each group benefits the other, but there is competition within groups. If pollinators interact with promiscuous plants (generalists that benefit from many different insect species), the overall competition among insects and plants decreases and the system can grow very large.
Relationships of this kind are seen in financial systems too, where small specialist banks interact with large generalist banks. Interestingly, the same hierarchical structure that promotes biodiversity in plant-animal cooperative networks may increase the risk of large-scale systemic failures: Mutualism facilitates greater biodiversity, but it also creates the potential for many contingent species to go extinct, particularly if large, well-connected generalists — certain large banks, for instance — disappear. It becomes an argument for the “too big to fail” policy, in which the size of the company’s Facebook network matters more than the size of its balance sheet.
I would be interested in Sugihara’s references for his assertion that “there was a marked increase in homogeneity among institutions, both in their revenue-generating strategies as well as in their risk-management strategies.” I do not disagree, but it’s vague.
And I haven’t pored over the link, but these aren’t so much “parallels” between a core biology model and a metaphoric financial ecosystem as simply examples of a known behavior in all models. Critical slowing, autocorrelation, increased volatility, and the like are features of all systems near their critical points. Biological systems, financial systems, mechanical systems — even the Illuminati and our Reptile Overlords are subject to them.
To geek out for an instant, this just pertains to the behavior of eigenvalues near un/stable equilibria as the model moves through parameter regimes. In particular, the “slowing” in “critical slowing” refers to the increasing time required to return to an equilibrium point after a system change.
A very nice lay discussion (with helpful diagrams) of this for the biology set is found in the last chapters of “Critical Transitions in Nature and Society” by M. Scheffer.
I don’t think the author would disagree with your point that those are features of all systems near their critical points. I don’t think he’s wrong to point to the biological ecosystem models as primary and to consider the financial models as secondary though, because the application of these general models is more established in ecology and fairly new to finance. Or isn’t that the case?
Interesting point. I think you’re right.
While I have a personal prejudice (post-judice?) that it’s the mathematics that is primary and all else is secondary, you’re absolutely correct: if we focus on the models and applications, there is a long, unbroken and fascinating history of math finding it’s best application in biology. Especially ‘this kind’ of math (very roughly, topological dynamics.)
Starting in the modern era with D’Arcy Thompson (morphology), continuing with Rene Thom (catastrophe), Hodgkin-Huxley and Robert May (broad dynamics) and many hundreds of others, biology is a fruitful playground.
It’s funny, because one might think (I did) that we’d see dynamics and bifurcation theory in physics or chemistry before it appeared in biology. And in fact there are many such examples and applications in physics and chemistry.
But people are less like to see physics’s “doubly-connected pendulum” in the wild than predators and prey doing their Lotka-Volterra tango. And in chemistry I suppose that by the time the dynamics get “interesting” enough to apply bifurcation theory, and perturbed dynamics, you’re leaving things like “Na + Cl → NaCl” in the rear-view mirror, and starting with the periodic Belusov reactions, or Eigen/Schuster hypercycles, or metabolic dynamics of biochemistry…which is again at the doorstep of biology.
Probably biology is in that sweet spot of “just familiar enough” and “just complex enough” to fruitfully host this kind of mathematics.
By the same token, we’re not as likely to see logic or algebra in biology (but if Carl Woese and NIgel Goldenfeld have their way, we will see renormalization group theory soon….)
But, yeah, you’re right, finance is a relative newcomer. Mandelbrot used finance to ride his fractal surfboard to mathematical fame, but he’s rather the exception. Ralph Elliot and his “Elliot Wave” theory is really just riffing off Fibonacci series, which in turn is an 800 year old application of… rabbit population dynamics. Biology, again.
The only other big name coming to mind now who’s in the hard sciences and made it big in finance are the protagonists of The Eudaemonic Pie and the Prediction Company, particularly J. Doyne Farmer.