  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 landscape. 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.
