% Response to reviewers % Bivariate spatial point patterns . . . by S. J. Eglen
Dear Christophe,
I thank you and the reviewers for the positive comments on the manuscript.
Please see below for my response to each reviewer. Comments from each reviewer are numbered and indented below. Changes made to the manuscript are highlighted in Olive Green and annotated in the manuscript with the corresponding number. e.g. R2.5 refers to point 5 of referee\ 2.
Yours faithfully,
Stephen
2015-09-29
\defr{R1.1} eq. 2: correct equation is $\sqrt{K_{12}/\pi}$
Corrected \lastref.
\defr{R1.2} Fig. 3: I wonder why there is no confidence interval. It will gives an estimate of d_\mbox{min}.
I have added confidence intervals to Figure 3, together with an explanation of how they were generated in the legend \rpref{R1.2b}. The confidence intervals are described further in the text \rpref{R1.2a}.
\defr{R1.3} Choice of d_\mbox{min} is questionnable. You mainly described an hard-core process (or Strauss process). You may find the set of d, the exclusion distance compatible with your data. Compatible means that the process does not go out the confidence interval (at 5% level for example).
The dmin algorithm has both a hard-core and soft-core acceptance region, similar in spirit to alternatives like Strauss processes. I use it here simply as it is most familiar within the field of retinal mosaics. I do note however that changing models might improve the fit slightly (page \arabic{lastr}).
\defr{R1.4} Fig 4 since we mostly print inblack and white, I personnaly prefer different symbols than different colors.
I have used colour consistently throughout the paper to refer to different cell types: the colours in figure 1 are used in figure 2, 4 and 7. Also, the colours in figure 8 naturally reflect the colour sensitivity of the cell types. So, if possible, I'd like to keep the colours.
\defr{R1.5} Why do you present the results for functional independence ?
I have expanded on the reasons for the three examples and explain functional independence is the "null hypothesis" for no interactions, to be compared against cases when interactions must exist \lastref.
\defr{R1.6} According to Fig. 6 you reject random for distances between 100 and 150. Please discuss.
I have added a note to this point in the text \lastref. However, the departure from the envelope is very small and could also be driven simply be small amounts of noise in the original data. In my experience, these deviations are relatively minor.
\defr{R1.7} In order to avoid confusion among readers, please precise difference between independence and random labelling.
I have clarified this \lastref.
\defr{R1.8} Fig. 7: By simulating CSR, you may construct confidence interval.
In Figure 7B, there is no model to simulate CSR, and hence to confidence intervals to generate from repeated runs. In the paper by Diggle (1986), confidence intervals were generated by comparing the observed $L_{12}$ function against 99 simulations, where one of the mosaics was toroidally shifted by some random amount in the x and y direction. Toroidal shifting is a poor approximation to generate synthetic data sets as neurons that were not neighbours in the real data can become neighbours in the simulated data.
\defr{R1.9} You may be interested to read paper like Illian, J., Benson, E., Crawford, J., & Staines, H. (2006). Principal component analysis for spatial point processes—assessing the appropriateness of the approach in an ecological context. In Case studies in spatial point process modeling (pp. 135-150). Springer New York.
Thank you.
\defr{R2.1} The introduction needs more background. As it is the text jumps from the fact that the retina does unique computations to (x,y,z) positions, and doesn’t explain why we should care about the latter.
I have added text to the first paragraph of the introduction to address this point \lastref.
\defr{R2.2} The title is a bit too general considering the paper’s contents. I’d replace “in the visual system” with “in the retina”, since no other structure is mentioned.
Corrected \lastref.
\defr{R2.3} Confidence bands are missing from fig 3 and fig 7B.
I have added them (see R1.3) for Figure 3. See my response to R1.8 for Fig 7B.
\defr{R2.4} I know very little about how the retina develops, but maybe the author could explain why complete spatial randomness would be a reasonable null model? Somas are to a good approximation 2D objects, but whole neurons aren’t. Dendrites and axons need to be packed in there as well, doesn’t that constrain where somas can be?
I have added a comment to this effect \lastref.
\defr{R2.5} I’m not sure to what extent this belongs in a review paper, but second-order statistics such as Ripley’s K function become much harder to use when you can’t assume a uniform intensity function. Does uniform density really holds in the retinal mosaics the author examines?
This is a good question, but indeed I think too specific for such a review. Our experience is that when examining cells within a spatial field of less than 1mm in each dimension, any gradients in cell density tend to be quite modest. We have occasionally examined kernel density estimates to check that the field is approximately homogeoneous. There is a tradeoff -- increasing the field of view increases the number of cells within the field of view, but then increases the chances of hitting density-dependent variations (as are expected: cells in the centre tend to be at higher density than the periphery).
\defr{R2.6} I appreciated that the author put an entire R package on github for easy distribution, and docker sounds extremely useful. My only worry is that we rely on private companies (github, docker) that might stop providing free services any time. Perhaps reproducibility would require public, durable infrastructure but that’s not a problem for this review to solve.
Again I agree with this comment but feel it may be too specific for this review. I have however added a small comment to note this point \lastref.
I have made one extra change to the manuscript:
\defr{R3.1} I have included a mention of the ENCODE consortium (2012) project which was a prominent early example of using a virtual machine to package code and data for reuse \lastref.
\rule{\textwidth}{1pt}
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