Evolutionary predictability and complications with additivity

Adaptation is a central topic in theoretical biology, of practical importance for analyzing drug resistance mutations. Several authors have used arguments based on extreme value theory in their work on adaptation. There are complications with these approaches if fitness is additive (meaning that fitness effects of mutations sum), or whenever there is more additivity than what one would expect in an uncorrelated fitness landscapes. However, the approaches have been used in published work, even in situations with substantial amounts of additivity. In particular, extreme value theory has been used in discussions on evolutionary predictability. We say that evolution is predictable if the use of a particular drug at different locations tends lead to the same resistance mutations. Evolutionary predictability depends on the probabilities of mutational trajectories. Arguments about probabilities based on extreme value theory can be misleading. Additivity may cause errors in estimates of the probabilities of some mutational trajectories by a factor 20 even for rather small examples. We show that additivity gives systematic errors so as to exaggerate the differences between the most and the least likely trajectory. As a result of this bias,evolution may appear more predictable than it is. From a broader perspective, our results suggest that approaches which depend on the Orr-Gillespie theory are likely to give misleading results for realistic fitness landscapes whenever one considers adaptation in several steps.