I can’t be dogmatic but after the endless time and effort trying to decipher the fake science in economic theory (neo-classical), I have ZERO confidence there is a mathematical biology corresponding to Darwin’s theory. The first question is, is the mathematician aware that naturals selection can’t explain evolution…
The formal Darwinism project
on June 15, 2015
charles-darwin.jpg_1396593169[From time to time the Editors at Scientia Salon select an interesting paper from the primary scientific or philosophical literature to highlight for a broader public. These posts simply include the abstract of the paper and a few choice quotations, occasionally accompanied by brief editorial comments. The idea is to develop an appreciation for what front line scholarship looks like, and hopefully why it matters.]
Our new pick for a “notable” paper is “The formal darwinism project in outline” by Alan Grafen, published in Biology and Philosophy on 25 January 2014. (Unfortunately, the full paper is behind a paywall, but you can request a copy from the author here.)
Here is the abstract:
The formal darwinism project aims to provide a mathematical frame- work within which important fundamental ideas in large parts of biology can be articulated, including Darwin’s central argument in The Origin (that mechanical processes of inheritance and reproduction can give rise to the appearance of design), modern extensions of evolutionary theory including ESS theory and inclusive fitness, and Dawkins’ synthesis of them into a single structure. A new kind of argument is required to link equations of motion on the one hand to optimisation programs on the other, and a major point is that the biologist’s concept of fitness maximisation is not represented by concepts from dynamical systems such as Lyapunov functions and gradient functions. The progress of the project so far is reviewed, though with only a brief glance at the rather complicated mathematics itself, and the centrality of fitness maximisation ideas to many areas of biology is emphasised.