Title: Using Numerical Simulation to Better Understand Fixation Rates, and Establishment of a New Principle - "Haldane's Ratchet"

Author: Christopher L. Rupe and John C. Sanford

Category: Life Sciences

Conference Year: 2013


In 1957, Haldane first described a fundamental problem with evolutionary theory. This problem eventually became widely known as "Haldane's Dilemma". The essence of this problem is that even given a steady supply of beneficial mutations plus deep time, the rate that such mutations reach fixation is too slow to achieve meaningful evolution. After more than 50 years, this fundamental problem remains unresolved. ReMine has gone far beyond Haldane's original mathematical analysis, and has developed "cost theory analysis" which strongly supports Haldane's thesis. Here we examine this long-standing problem using an entirely different approach. We employ advanced numerical simulation of the mutation/selection process to empirically measure the fixation rates of beneficial, neutral, and deleterious mutations. We do this employing both realistic and optimized population parameters. In our numerical simulations, each new mutation is tracked through time until it is either lost due to drift or becomes fixed in the population. We first confirm that our numerical simulations correctly tallying the fixation of neutral mutations. We show that neutral mutations go to fixation just as predicted by conventional theory (i.e., over deep time the fixation rate approached the gametic mutation rate). We also show that the reason the vast majority of neutral mutant alleles fail to go to fixation, is because they lost due to drift, and this rate of loss rapidly approached 100% as population size is increased. We then show that given realistic distributions of mutation fitness affects, the vast majority of all mutations (including deleterious and beneficial mutations), are similarly lost due to random drift. In terms of fixations, deleterious mutations went to fixation only slightly slower, while beneficial mutations went to fixation only slightly faster, than neutral mutations. We then perform large-scale experiments to examine the feasibility of the ape-to-man scenario over a six million year period. We analyze neutral and beneficial fixations separately (realistic rates of deleterious mutations could not be studied in deep time due to extinction). Using realistic parameter settings we only observe a few hundred selection-induced beneficial fixations after 300,000 generations (6 million years). Even when using highly optimal parameter settings (i.e., favorable for fixation of beneficials), we only see a few thousand selection-induced fixations. This is significant because the ape-to-man scenario requires tens of millions of selective nucleotide substitutions in the human lineage. Our empirically-determined rates of beneficial fixation are in general agreement with the fixation rate estimates derived by Haldane and ReMine using their mathematical analyses. We have therefore independently demonstrated that the findings of Haldane and ReMine are for the most part correct, and that the fundamental evolutionary problem historically known as "Haldane's Dilemma" is very real. Previous analyses have focused exclusively on beneficial mutations. When deleterious mutations were included in our simulations, using a realistic ratio of beneficial to deleterious mutation rate, deleterious fixations vastly outnumbered beneficial fixations. Because of this, the net effect of mutation fixation should clearly create a ratchet-type mechanism which should cause continuous loss of information and decline in the size of the functional genome. We name this phenomenon "Haldane's Ratchet".