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.

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.