Alphabet cardinality and adaptive evolution

One of the most fundamental characteristics of a fitness landscape is its dimensionality, which is defined by genotype length and alphabet cardinality-the number of alleles per locus. Prior work has shown that increasing landscape dimensionality can promote adaptation by forming new 'uphill' mutational paths to the global fitness peak, but can also frustrate adaptation by increasing landscape ruggedness. How these two topographical changes interact to influence adaptation is an open question. Here, we address this question in the context of alphabet cardinality, using theoretical fitness landscapes with tuneable fitness correlations, as well as three empirical fitness landscapes for proteins. We find that the primary effect of increasing alphabet cardinality is the introduction of a new global fitness peak. Controlling for this effect, we find that increasing alphabet cardinality promotes adaptation on uncorrelated fitness landscapes, but frustrates adaptation on correlated fitness landscapes. The primary explanation is that the increased ruggedness that accompanies alphabet expansion is characterized by an increase in mean peak height on uncorrelated fitness landscapes, but a decrease in mean peak height in correlated fitness landscapes. Moreover, in two of the empirical fitness landscapes we observe no effect of increasing alphabet cardinality on adaptation, despite an increase in the number of peaks and a decrease in mean peak height, calling into question the utility of these common measures of landscape ruggedness as indicators of evolutionary outcomes.