Saturday, September 5, 2015

The branch of biology with the most mathematics is also widely known as the most soft! Why?

The field of population genetics and molecular evolution was largely founded by mathematicians/statisticians such as Fisher, Haldene, and Wright. Even pure mathematician like Hardy has contributed a key equation to the field. But contrary to naive expectations, this field of study is more like soft social science than to hard core physics. In the words of Jerry Coyne (an extremely enthusiastic propagator of the Darwinian evolution theory and a professor of evolutionary studies at the University of Chicago): "In science's pecking order, evolutionary biology lurks somewhere near the bottom, far closer to phrenology than to physics".

Why? The reason is simple. Math depends on assumptions or paradigms. The assumptions for hard core sciences are axioms or self evident intuitions. Euclid and Newtons axioms come to mind. They are all a priori true or self evidently true. In contrast, there is not a single assumption in the evolution field that is self evidently true or can qualify as axiom. Nearly all assumptions in that field are in fact self evidently false. Just a few examples, the infinite sites model, the neutral/junk DNA assumption, random mating, and the independent mutations assumptions.

Key figures in the field has also acknowledged this, as Ohta and Gillespie said in 1996: "all current theoretical models suffer either from assumptions that are not quite realistic or from an inability to account readily for all phenomena." (Theoretical Population Biology,1996, 49: 128-142) 

To show a flavor of the amount of math in the field, below are two pages of my notebook from an undergrad evolutionary genetics course taken 32 years ago at my Alma mater Fudan University.

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