There's plenty of time for evolution

TL;DR

This paper demonstrates that natural selection significantly reduces the number of mutations needed for evolution, making Darwinian processes feasible within realistic timeframes by showing the required mutations are proportional to K log L instead of K^L.

Contribution

It introduces a new theoretical framework that accounts for natural selection, reducing mutation estimates from exponential to logarithmic scale, connecting evolutionary theory with computer science algorithms.

Findings

Natural selection lowers mutation requirements to about K log L.

The mutation estimate aligns with radix-exchange sorting theory.

Evolutionary time constraints are less severe than previously thought.

Abstract

Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and that the numbers of necessary mutations are thereby reduced to about $K\log{L}$, rather than $K^L$, where $L$ is the length of the genomic "word", and $K$ is the number of possible "letters" that can occupy any position in the word. The required theory makes contact with the theory of radix-exchange sorting in theoretical computer science, and the asymptotic analysis of certain sums that occur there.