We thank the referee for the constructive comments on the manuscript, that
helped us to improve it. We have responded to all the comments (see below),
and have indicated the changes to the text in red fonts.

> - It is nice to be able to measure transport coefficients for dynamos
> directly, which make the TFM quite powerful. However in this paper it
> has come at the price of changing the equations. It is important for
> the reader/community to be able to clearly assess what this price
> is. With this in mind, it is important to provide a more detailed
> comparison with standard MHD (FMHD in the paper). First, although there
> is a lot of discussion about the structure of the butterfly diagram
> (and later transport coefficient fluctuations) for the FK cases,
> this is not shown. It is important for a reader to be able to see the
> difference, since a fair amount of weight is placed on this in comparing
> to magnetically forced ones. Second, although it is difficult to measure
> transport coefficients, it is important to see the difference with some
> magnetically forced FMHD runs, again in the butterfly diagrams (also
> the growth rates). This way we can assess the impact of SMHD and whether
> this is likely to significantly change the main conclusions of the paper
> (e.g., does the field wandering change), as well as better understanding
> the observed similarities/differences to Squire & Bhattacharjee 2015
> and Brandenburg et al. 2008. It would be nice to see both standard and
> decimated forcing here (given uncertainties around the latter as well).

We have now added two new panels to Fig 2, where we show our FMHD results from
the run FK1b and a new run FKM1a. We have extended our discussion on the 
similarities and differences to the works of Brandenburg et al. (2008) and Squire &
Bhattacharjee (2015). In our experiment with FMHD with magnetic 
forcing we encountered similar difficulties as in SMHD, with the rapid emergence
of the mean fields, that contaminate the measurement of the growth rates,
even with the decimated forcing function. What we can confirm is that
the patterns emerging in magnetically forced FMHD are very similar to 
the SMHD cases, showing no increased coherence of the field
structures, as was the claim of Squire and Bhattacharjee 2015, when going from kinetic
to magnetic forcing. We have now modified our earlier discussion, and added text about 
this to the manuscript. We also note that perfect agreement with Squire and 
Bhattacharjee (2015) cannot be expected in any case, as their simulations 
were incompressible.

Modified discussion now reads, in the beginning of Section 3.1 (p. 6):

"Our kinetically forced FMHD runs reproduce the earlier results 
of similar systems (compare the upper leftmost panel 
of our \Fig{fig:but} to Figure~7 of \cite{BRRK08})
with rather coherent patches in $\meanB_y$, while the SMHD counterpart
(lower left panel of \Fig{fig:but}) shows a somewhat more erratic pattern; here, 
however, we must note that the time series in the case of the SMHD run is much 
longer. These results are in disagreement with the purely kinetically forced,
incompressible, runs of \cite{SB15b} (their Figure~9(a)), which show a 
somewhat more erratic pattern than what we observe either in FMHD 
or SMHD."

We have added the following to the end of 3.1:

"We also performed a magnetically forced FMHD run,
where rapidly emergent mean fields are seen despite of the
usage of the decimated forcing (see Fig.~\ref{but} lowest panel,
showing run FKM1bd, with parameters corresponding roughly to FK1b and SKM1ad. 
The emerging patterns are very similar to 
the magnetically forced SMHD cases, the large--scale field
structures being less coherent than in the kinetically forced FMHD case.
Similar to the SMHD cases with standard forcing function, the growth rates
are difficult to estimate, but we do note that the dynamo is now easier
to excite as in the kinetically forced FMHD case, where the large--scale field 
structures emerged only after time scales corresponding to the 
whole integration length of FKM1bd.  
Hence, we cannot confirm the finding of \cite{SB15} that more
coherent structures emerge when one goes from kinetic to magnetic forcing,
as was the case in their incompressible study."

> 1. A similar point applies to the zeroing out of the mean U. While I
> appreciate that the authors do not want to extensively explore this,
> a basic comparison of a case with and without zeroing U is important
> for readers to understand if this also affects B (and thus the main
> conclusions) significantly.

Such a study has actually already been performed by Yousef et al., 2008,  
AN, 329, 737, who state the following in their Section 3.4 "Vorticity dynamo":

"Finally, we observe that the emergence of the large-amplitude, long-lived, 
large-scale fluctuations in the velocity field does not appear to be strongly 
correlated with the operation of the shear dynamo: compare, e.g., the time 
evolution of urms and Brms shown in Fig. 6. As we are about to see, the absence 
of these velocity fluctuations in the simulations with Keplerian rotation 
(see Fig. 7) does not change any of the basic properties of the shear dynamo, 
so we feel safe in ruling out the possibility that the large-scale velocity 
fluctuations are a required ingredient in the shear dynamo."

This is largely consistent with our own experiments, where we saw no difference
in the properties of the dynamo with/without the suppression of the mean flows.
Unfortunately, we have not performed any runs with parameters exactly matching 
those presented in this manuscript, hence were not able to include the requested
material. Instead, we have now added a reference to Yousef et al. (2008a), and 
added the following sentence to the manuscript:

"With respect to a possible effect on the magnetic field, we refer to
Yousef et al. (2008a)
who reported for a very similar simulation setup as is used here
that the presence of the mean flow did not significantly change the 
properties of the shear dynamo, see 
their Section 3.4."

> 2. The NLTFM is the important novelty of this work but I found its
> description quite confusing. A few points that would help:
> - Mention at the start of 2.3 the basic purpose of the NLTFM and explain
> that it is tested in more detail in appendix. Those (like myself) who
> are not familiar with RB10 will not understand just how complicated the
> NLTFM has to be, and it will help to give them a warning.

We have now rearranged the structure of Sec. 2 with a general subsection
2.3 "Test-field method" and 2.3.1 "Nonlinear TFM" at the beginning of
which we make its crucial extension compared to the QKTFM clearer.

> 3. Explain the removal of U earlier in the discussion. It is finally
> introduced in 2.8, but it's been mentioned twice previously without
> forward reference (e.g., below equation (8) and in 2.5). This is quite
> important (see previous point) so needs to be very clear. Currently it
> comes across as being related to the NLTFM, not the equations themselves.

Mean flow removal is now first mentioned in Sec. 2.5 (new) where we also
put the remark on Yousef et al. (2008a). The presentation prior to that
point is now fully general.

> 4. I think there is maybe a typo in (1)-(2), (6) and (7)-(8), since
> F_K is magnetic and F_M is kinetic forcing. It is also a bit confusing
> to define both lower and upper case F, when F=f.

We thank the referee for pointing out these typos. We have now corrected them.

> 5. Section 2.3, the discussion following "Normally taken to be a Reynolds
> average, in situations with shear..." is confusing and I didn't understand
> what it was saying. Please reword and make any definitions clearer.

We have now reformulated the beginning of the para to read
"The horizontal average is normally taken to obey the Reynolds rules.
In situations with linear overall shear though, the complication arises that
$\overline{\UU^S} \ne \UU^S$ (when $\UU^S$ is defined to be $\propto x$, 
the mean even vanishes), being hence not a pure mean,
while ${\partial_i U^S_j}$ is spatially constant, hence a pure mean.
So the Reynolds rule ``averaging commutes with deriving" is violated."
and added
"Thus $\UU^S$ can effectively be treated as a mean flow." at the end
of this paragraph.

> 6. The sentence below (16) "Here we chose to use in Eqs. (14)-(16)
> and the corresponding versions of the fluctuating terms the first
> one," I believe this means that all of the left hand sides are being
> used. Following RB10 and the appendix, it would be much clearer to write
> (14)-(16) by introducing the ju, jb... notation, and explaining in a
> bit more detail the different choices.

We have now explained the naming convention in a footnote.

> 7. Shouldn't section 2.7 go into 2.3 on the TFM? It's an important part
> of the method.

We have now a new overall section "Test-field method" of which 
"Resetting" is a subsection.

> 8. Lu didn't seem to be used. The dimensionless number Brms/urms might
> be easier to understand.

We have used the Lundquist number in Table 2, where we report on the shear 
dependence of the dynamo solutions and measured transport coefficients for
the kinetically and magnetically forced cases. We think that for these 
runs listing Lu is useful, as the numbers demonstrate that those 
runs, where magnetic forcing is used, are strongly magnetically dominated, 
because the Lundquist number is also a measure of Brms/urms, as we have 
now added after Equation (20). We have also added to 
the text in Section 3.2.2.:

"As can be seen from the listed $\Lu$, these runs are all strongly
dominated by the small-scale magnetic fields generated by the magnetic 
forcing."

> 9. It would be helpful to define \lambda in 2.6 so that readers can
> easily find the important symbols.

The definition is now provided in 2.6.

> 10. Given that they're key for the entire paper, it would be nice to
> introduce eta and alpha more than currently done in (11)-(12). A separate
> section explaining intuitively what each term (alpha_xx, eta_yx...) does
> would be helpful.

We have now added in para-length some explanation of the mean-field 
effects at the end of 2.3.1 (new).
 
> 11. In figures 1a and 1b, SMK1ad has different colors, which is confusing
> when one first looks at the figure.

We have now swapped the black and blue colors in Fig 1b, so that the decimated forcing
cases are plotted with the same color in both panels.

> 12. Just before 3.3, the authors discuss the results of Shi et al. (2016),
> and why they might be different, mentioning rotation. Much more important
> is probably that Shi et al. (2016)'s simulations were undriven (the MRI)
> which means the saturation amplitude is set self-consistently, perhaps
> in conjunction with other processes.

Yes, we agree with the referee, and have now changed the sentence
about the Shi et al. (2016) models as follows:

"The dependence of the growth rate on the aspect ratio could also 
be due to different dynamo modes being excited in boxes of different 
size, as was found by Shi et al. (2016) in a similar context, but 
including rotation,in which case the turbulence and dynamo action 
was self--sustained (i.e. not driven as in our study) due to the 
magnetorotational instability."

> 13. Figure 6 is interesting and useful at explaining the observed dynamo
> growth rates (with most cases well explained by the 0-D model). But it
> is not properly explained how it is computed. Please add more discussion
> of this, at least the equations solved and how they're used to construct
> the contour plots.

We have now added the mean-field induction equation on which the 0D-model is based. 

> 14. Also, f6's labels are too small to read clearly.

We have now remade the figure with larger labels throughout.

> 15. Which run in figure 8? And are the two snapshots just different times
> (if so when)?

We have now modified the captions of Figures 7, 8 and 9, to now mention
that these refer to the two shearless hydrodynamic runs discussed in
Appendix A. Times are also explicitly stated in the caption of Figure 8.
Also, we have suitably modified the text of Appendix A where we provide
more details of these two runs that were performed to explore the
possible anisotropies in the decimated forcing case.

In addition to replying to the referee's comments, we have made the following
changes in the manuscript:

1. Abstract has been shortened by 55 words to comply with the length required 
by ApJ.

2. A decimated forcing run with aspect ratio of 16 was added, to complete the set
of simulations with the decimated forcing function. This did not change any
results or conclusions of the study.

3. We have modified the discussion about the role of diagonal versus off-diagonal
alpha tensor components for the incoherent alpha shear effect:

"... They [B08] also reported that the diagonal and off--diagonal 
components of the $\alpha$ tensor were nearly equal. In the SMHD cases 
studied here, this is no longer the case, as is shown
in \Fig{fig:histo}, where the diagonal $xx$ component dominates."

4. To better address how the SMHD assumption might affect the 
results, we have now added an analytical derivation of the 
expected shear current effect in the ideal limit and in the 
presence of primary magnetic turbulence (Appendix C), but 
neglecting the pressure term. In summary, our analysis shows 
that a non-zero effect is to be expected even when the pressure 
term is dropped, but some uncertainties remain concerning 
the sign, the calculation of which requires even more drastic 
simplifying assumptions. Using these, however, the sign appears 
to be preferentially positive, that is unfavorable for dynamo 
action, which is also confirmed by our numerical experiments.

Due to the added analytical work, we have also added references to 
similar analytical work to the main part of the paper, and discussed
similarities and differences between the obtained results in the
Introduction and Conclusions.