Fixation probability and fixation time in structured populations

Abstract: The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants. But these `amplifiers of natural selection' typically increase fixation time. Here we study population structures that achieve a trade-off between high fixation probability and short fixation time. First, we show that no amplifiers can have asymptotically lower absorption time than the well-mixed population. Then we design population structures that substantially augment the fixation probability with just a minor increase in fixation time. Finally, we show that those structures enable higher effective rate of evolution than the well-mixed population provided that the rate of generating advantageous mutants is relatively low. Our work sheds light on how population structure affects the rate of evolution. Moreover, our structures could be useful for lab-based, medical or industrial applications of evolutionary optimization.