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  1. Evaluation Summary:

    This paper uses an impressively rich dataset (obtained and curated by the authors) to compare the structural brain connectomes of many animals spanning 6 taxonomic orders. The approach is innovative and relies on graph theoretical measures to describe the connectivity, which means it can be done without the need to spatially/functionally match the brains. The authors find that there is more variability between than within order. They attribute this effect to changes in local connectivity features, whereas global patterns are preserved. The approach can potentially be a useful way to study phylogeny and brain evolution.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 and Reviewer #3 agreed to share their name with the authors.)

  2. Joint Public Review:

    The present manuscript compares the connectomes of a large range of mammal species using diffusion MRI data. The manuscript reports two main findings: (1) connectomes of more related species are generally more similar, as assessed using Laplacian eigenspectra, than of unrelated species; (2) differences between species' connectomes are generally driven by local regional connectivity profiles, whereas global features are generally preserved.

    The first finding is comforting, but in a way not extremely surprising. It would be extremely surprising if more related species do not show more similarity in their connectome. Indeed, this is the reason many phylogenetic analyses use statistical techniques that take the relatedness of species explicitly into account. I find the statement that connectome organization recapitulates traditional taxonomies a bit over the top, as this suggests that a phylogenetic tree constructed based on connectomes would be similar to a tree based on other measures, such as morphology or genetics. This will probably be the case, but is not what the authors have tested here.

    The second result is in my opinion the key result of the paper. The main novelty of the paper is that -finally, for the field-bridges approaches taken by some researchers in searching for differences across species (these are usually researchers interested in anatomy) and researchers searching for conserved principles across species (usually researchers approaching connectivity from a network or graph theory perspective). By showing what aspects of a connectome are generally conserved and which are changed, this paper starts unifying the two views and this is an important contribution.

    It would, however, have been nice if the authors had explored this notion a bit further. Now, they just state that taking certain features into account means the connectomes look more different, but they do not zoom into the specific brains to see what this means at a biological level. Some of the authors have published, for instance, on the unique connectivity profiles of parts of the human brain and it would have been nice to show that these fall under the local regional connectivity profile aspects of the connectomes. This is a missed opportunity to even further unify the different research traditions.

    The manuscript suggests that white matter connectivity in mammals is more similar between species within one taxonomic group than across different groups, proposing that the brain's connectome reflects phylogenetic relationships. The manuscript further details which features of the network organisation are associated with larger differences across groups and hence may drive speciation; and which features seem to be a common principle across mammals.

    The authors present evidence based on the analysis of diffusion-weighted brain imaging data across 124 species, 111 of which were included in the comparison. The dataset is a great resource to address their research question.

    The paper is clear and the evidence compelling. The manuscript adds valuable insights into the connectome architecture across species, potentially opening a new perspective on the link between genetics and behaviour. I would like to point out the great open science practice of the authors - code is available with a great ReadMe to guide potential users, connectivity matrices are available, and all software packages used in the analyses have been cited.

    The figures are clear and complement the manuscript.

    Technical Comments:

    - Spectral approach / Interpretation
    It would be good to have more insight into the meaning of the spectral distance results. My understanding is this: the eigenvalues of the normalised Laplacian obviously have a mean of 1 (because their sum equals the trace of the Laplacian, which is equal to N [number of nodes]). Therefore, the distances between the spectra essentially amounts to comparing higher moments, and in particular the variance (as the histograms look quite Gaussian, I am guessing the distances are dominated by differences in the variance). But what does it mean that bats have a higher variance in these Eigenvalues than primates? I know that the authors try to give *some* insight, e.g. that when the distribution is peaky around 1, it means there are more stereotypical local patterns of connectivity. I understand that. But what are these patterns?

    - Effect Size / Null Distribution
    I like the idea and the ambition of this paper. My main concern is that the differences are very small. Pretty much all the measures (laplacian eigenspectra and network-theoretic measures) are very similar between animals. This can be interpreted in two ways. (1) it may mean that the brain organisation is preserved, which is the interpretation of the authors. But it could also mean that (2) the metrics are not very informative. How do we know if we are in situation (1) or (2)? There is no comparison to a good null model (except in Fig4 but I don't think a random network is a good null). One possible null is two random networks connected to each other with a few random connections (to mimic left-right brains)?

    * The authors use cosine similarity to compare the eigenspectra distributions. I think this does them a disservice. cosine similarity normalises the distributions quadratically instead of linearly. But the main thing that is changing is the variance. So normalising quadratically diminishes the dissimilarities between distributions. I have looked at their data (thanks for sharing!) and using multidimensional scaling with Euclidean looks much better than with cosine distance. I would suggest using euclidean.

    * The authors use a bootstrapping method to calculate an average distance which they claim is useful because they don't have the same number of animals in each category. I don't think this bootstrapping is useful at all. If anything, it just adds noise. Averaging 10,000 samples with replacement does not change the outcome compared to simply averaging the matrices without the sampling. To test this: vary n and it should converge to the average of the original non-sampled data. (I've tried it!)

    * The authors should clarify whether they are using the weighted or binarised connectivity matrices in the spectral approach (and also what threshold). I suspect that they are using binarised matrices, which probably explains why the spectral results fit better with the graph topology results when the latter uses binarised matrices.

    - Parcellation.
    One main issue is the way in which the connectomes are divided up into 200 regions each, independent of the brain size. This to me seems a confound. I know it's rather standard practise in the field, but I have yet to see a validation that this does not influence the results. Given the enormity of the dataset here I would ask the authors to run their analyses in a way that the number of regions is a function of the size of the brain-this is a much more realistic assumption, as we know that a shrew size brain has about 20 cortical areas, whereas the human has about 180 according to Glasser et al.