Although the simulation data as well as the conclusion on the proportionality between V
_{
ip
}(i) and V
_{
g
}(i) in the work
1
is correct, interpretation of some data therein should be corrected. As the sampling number (L = 200) to measure the average gene expression level is not large enough, there is a bias in the estimate in V
_{
g
}(i). Finiteness in the number of sampling L will generally cause a bias of the order of V
_{
ip
}(i)/L, in the estimate of the variance V
_{
g
}(i). The too good proportionality between V
_{
ip
}(i) and V
_{
g
}(i) for large σ, shown in Figure two (a)(b) of
1
(especially for small V
_{
g
}(i)), is due to this artifact. Accordingly, the sharp peak at ∼1/L = 1/200 in Figure three of
1
is due to this insufficiency by the sample number.
Still, the proportionality between the two variances V
_{
ip
}(i) and V
_{
g
}(i), albeit not so sharp, holds, as already observed in the region with larger V
_{
g
}(i) in
1
. We have simulated the model with a larger number of samples, i.e., N = L = 1000. As is shown in Figure
1, the proportionality is well discernible, where the proportion coefficient V
_{
g
}(i)/V
_{
ip
}(i) decreased with the increase in the noise level σ, which was already observed in the broad peak beyond 1/L in Figure three of
1
. This broad peak beyond 1/L in Figure three of
1
was found to be sharper as N was increased, from 200 to 1000. This peak indeed corresponds to the proportion coefficient extracted from Figure
1 in the present Correction. As the noise level σ was increased, the peak position ρ = V
_{
g
}(i)/V
_{
ip
}(i) decreased. Hence for larger σ, larger L is needed to get reliable estimate in the proportion coefficient. As for Figure five and Figure six of
1
, the sharp proportionality for V
_{
g
}(i) ≲ 0.001 is due to the above bias, while the discussion therein concerns with the approach of V
_{
g
}(i) to V
_{
ip
}(i) at larger V
_{
g
}(i), which is not affected by the bias here.
<p>Figure 1</p>Relationship between V_{g}(i) and V_{ip}(i)
Relationship between V_{g}(i) and V_{ip}(i). As described in the Method section of
1, V_{ip}(i) was computed as the variance of the distribution of Sign(x_{i}) over L runs for an identical genotype, while V_{g}(i) was computed as a variance of the distribution of
(
Sign
(
x
i
)
¯
)
over N individuals, where
Sign
(
x
i
)
¯
was the mean over L runs. Here we adopted N = L = 1000, instead of 200 in
1. σ = 0.09 (blue *) and 0.03 (red +). The plot of (V_{g}(i) and V_{ip}(i)) for all genes i over 5565th generations, where we have plotted only those genes with V_{g}(i) > .0002, as the those with smaller than that may have little accuracy in estimating V_{g}(i).
To sum up, the main claim of
1
, i.e., proportionality between V
_{
ip
}(i) and V
_{
g
}(i) is valid, but the value of the proportion coefficient ρ = V
_{
g
}(i)/V
_{
ip
}(i) should be corrected. It decreases with the noise level, in contrast to the discussion in
1
for large σ. Major factor on this proportionality is attributed to the correlation of each variance with the average value
Sign
(
x
(
i
)
)
¯
: In other words, a state with an intermediate expression level (i.e., smaller

Sign
(
x
(
i
)
)
¯

) can be more easily switched on or off, both by noise and also by mutation, and hence the variances generally increase as

Sign
(
x
(
i
)
)
¯

approaches 0. Still, some correlation between V
_{
ip
}(i) and V
_{
g
}(i) remains even after removing this correlation through
Sign
(
x
(
i
)
)
¯
.
I regret any inconvenience that misintepretation of the data with an insufficient sample size may have caused.