Time and Information in Evolution

Wilf and Ewens argue in a recent paper that there is plenty of time for evolution to occur. They base this claim on a mathematical model in which beneficial mutations accumulate simultaneously and independently, thus allowing changes that require a large number of mutations to evolve over comparatively short time periods. Because changes evolve independently and in parallel rather than sequentially, their model scales logarithmically rather than exponentially. This approach does not accurately reflect biological evolution, however, for two main reasons. First, within their model are implicit information sources, including the equivalent of a highly informed oracle that prophesies when a mutation is “correct,” thus accelerating the search by the evolutionary process. Natural selection, in contrast, does not have access to information about future benefits of a particular mutation, or where in the global fitness landscape a particular mutation is relative to a particular target. It can only assess mutations based on their current effect on fitness in the local fitness landscape. Thus the presence of this oracle makes their model radically different from a real biological search through fitness space. Wilf and Ewens also make unrealistic biological assumptions that, in effect, simplify the search. They assume no epistasis between beneficial mutations, no linkage between loci, and an unrealistic population size and base mutation rate, thus increasing the pool of beneficial mutations to be searched. They neglect the effects of genetic drift on the probability of fixation and the negative effects of simultaneously accumulating deleterious mutations. Finally, in their model they represent each genetic locus as a single letter. By doing so, they ignore the enormous sequence complexity of actual genetic loci (typically hundreds or thousands of nucleotides long), and vastly oversimplify the search for functional variants. In similar fashion, they assume that each evolutionary “advance” requires a change to just one locus, despite the clear evidence that most biological functions are the product of multiple gene products working together. Ignoring these biological realities infuses considerable active information into their model and eases the model’s evolutionary process.