^{1}

^{2}

^{3}

The authors have declared that no competing interests exist.

In a comment [

The disagreement is based on two different interpretations of the meaning of pairwise epistasis, and the comment gives us an opportunity to discuss those.

We do not disagree that epistasis refers to mutational effects that are conditional on the states of other alleles. In our paper, we are in particular interested in pairwise epistasis—that is, how the fitness effects of mutations at two loci depend on each other. Of course, the dependence between those two loci could depend on the state of many other alleles in the genome. The different interpretations of epistasis hinge upon whether a quantitative assessment of the epistasis between two loci should be conditional on the state of other loci in the genome, or whether instead we should consider the state of these loci averaged over what their state would be in a population at mutation–selection balance. Crona’s example helps us illustrate that distinction.

A fitness landscape constructed in the supplementary information of [

The values are judiciously chosen such that

Crona defines the epistasis between loci B and C as either

Note that these values are conditional on the state of locus A, but for the case discussed here they happen to be equal and vanishing. Clearly, this is a special case. In general, the pairwise epistasis conditional on the state of another locus can depend on that state, and if there are ^{n} different values for the pairwise epistasis. Surely this is not satisfactory, as pairwise epistasis then would not be defined. Instead, pairwise epistasis should be unconditional on the state of other loci in the genome. How do you calculate this?

We assert that pairwise epistasis between two loci should depend on the fitness effect of mutations at those loci where the states of the other loci are determined by mutation–selection balance in a population. In other words, we assert that fitness effects should be measured by the effect on the growth rate of a population. For the three locus system, the fitness of the BC system depends on the frequency of the A = 0 allele and the A = 1 allele in the population. Let _{0} stand for the frequency of the A = 0 allele, with _{0} _{1} =

These four values can be used to calculate the epistasis between loci B and C unconditional on the state of A as

We plot this quantity in _{0} and see that it is everywhere positive except for _{0} = 0 or _{0} = 1, which are the conditional epistasis values of Crona (Eqs

Pairwise epistasis between loci B and C calculated using Eqs _{0}, with fitnesses as in

However, given the fitness landscape _{0} ≈ 0.998 in equilibrium, leading to _{BC} ≈ 0.191, which is nonvanishing. Thus, the positive shared entropy between those loci is indeed sufficient to determine nonvanishing pairwise epistasis between them. We also remark that at that frequency _{0}, the information between B and C is exceedingly small:

Needless to say, the example discussed here is a fairly contrived one, and we show in Fig 9 of [

In conclusion, the assertion in [