Computational complexity of evolutionary equilibria

FoundersThe first half of the 20th century is famous for revolutionary changes — paradigm shifts as Kuhn would say — across the sciences and other systems of thought. Disheartened by the scars of the First World War, European thinkers sought refuge by shifting their worldviews away from those of their fathers. In fields like biology, this meant looking for guidance to your grandfathers, instead. The founders of the modern synthesis reconciled the fading ideas of Wallace’s natural selection with Mendelian genetics. In the process, they unified many branches of biology, that at the dawn of the 20th century had been diverging, into a single paradigm that persists today. A return to evolution by natural selection illuminated their field and ended the eclipse of Darwinism. At the same time, mathematicians questioned Hilbert’s formalism and Russell’s logicism as valid foundations for their own field. As a result, they formalized mechanistic calculation and logical thought as computation and founded theoretical computer science to study its power and limitations. Even though some pioneers — like Alan Turing — kept an eye on biology, the two streams of thought did not converge. The coming of the Second World War pushed both fields away from each other and deep foundational questions, entrenching them in applied and technological work.

For the rest of the 20th century, the fields remained largely independent. Computer science only looked to biology for vague inspiration of heuristics in the form of evolutionary computing (Holland, 1975), and biologists looked at computer science as an engineering or technical field that could only provide them with applied tools like bioinformatics. Neither field saw in the other a partner for addressing deep theoretical questions. As I mentioned previously, my goal is to remedy this by applying ideas from analysis of algorithms and computational complexity to fundamental questions in biology. Sometime in late October, I tweeted my joy at seeing evolution clearly through the algorithmic lens. On Friday the 23rd, after much delay, I turned this into an ArXiv preprint ambitiously titled “Complexity of evolutionary equilibria in static fitness landscapes“. The paper combines the discussion of evolution from my previous few blog posts with three simple technical results. Although it was written for theoretical computer scientists, I tried to make it accessible to mathematical biologists as well; the hope is to serve as a launching point for discussion between the two disciplines.
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