Fixation Probability Favors Increased Fecundity Over Reduced Generation Time

Abstract

The cornerstone of population genetics is a probabilistic understanding of the ultimate fate--survival or extinction--of rare mutations. If a mutation is beneficial, it enables its carrier to reproduce faster than native wild-type individuals. In classic derivations and in the considerable body of research that has followed, "faster" has been defined mathematically to mean "able to produce more surviving offspring per generation." Many organisms, however, may increase their reproductive rate by producing the same number of offspring in a shorter generation time: a mutant bacterium, for example, may complete the cell cycle and produce two offspring more quickly than the wild type. We find that the ultimate fixation probability of a mutation conferring a shorter generation time differs from that of a mutation conferring more offspring by a factor of 2 ln(2)-nearly 40%. This predicts a reduction in the overall substitution rate for any mutation that decreases the generation time: fixation probability is biased toward increased offspring number.