Reviewer #1 (Public Review):
Animal colour evolution is hard to study because colour variation is extremely complex. Colours can vary from dark to light, in their level of saturation, in their hue, and on top of that different parts of the body can have different colours as well, as can males and females. The consequence of this is that the colour phenotype of a species is highly dimensional, making statistical analyses challenging.
Herein the authors explore how colour complexity and island versus mainland dwelling affect the rates of colour evolution in a colourful clade of birds: the kingfishers. Island-dwelling has been shown before to lead to less complex colour patterns and darker coloration in birds across the world, and the authors hypothesise that lower plumage complexity should lead to lower evolutionary rates. In this paper, the authors explore a variety of different and novel statistical approaches in detail to establish the mechanism behind these associations.
There are three main findings: (1) rates of colour evolution are higher for species that have more complex colour phenotypes (e.g. multiple different colour patches), (2) rates of colour evolution are higher on island kingfishers, but (3) this is not because island kingfishers have a higher level of plumage complexity than their mainland counterparts.
I think that the application of these multivariate methods to the study of colour evolution and the results could pave the way for new studies on colour evolution.
I do, however, have a set of suggestions that should hopefully improve the robustness of results and clarity of the paper as detailed below:
1) The two main hypotheses tested linking plumage complexity and island-dwelling to rates of colour evolution seem rather disjointed in the introduction. This section should integrate these two aspects better justifying why you are testing them in the same paper. In my opinion, the main topic of the paper is colour evolution, not island-mainland comparisons. I would suggest starting with colours and the challenges associated with the study of colour evolution and then introducing other relevant aspects.
2) Title: the title refers to both complex plumage and island-dwelling, but the potential effects of complexity should apply regardless of being an island or mainland-dwelling species, am I right? Consider dropping the reference to islands in the title.
3) The results encompass a large variety of statistical results some closely related to the main hypothesis (eg island/mainland differences) tested and others that seem more tangential (differences between body parts, sexes). Moreover, quite a few different approaches are used. I think that it would be good to be a bit more selective and concentrate the paper on the main hypotheses, in particular, because many results are not mentioned or discussed again outside the Results section.
4) Related to the previous section, the variety of analytical approaches used is a bit bewildering and for the reader, it is unclear why different options were used in different sections. Again, streamlining would be highly desirable, and given the novel nature of the analytical approach (as far as I know, many analytical approaches are applied for the first time to study colour evolution) it would be good to properly explain them to the reader, highlighting their strengths and weaknesses.
5) The Results section contains quite a bit of discussion (and methods) despite there being a separate Discussion section. I suggest either separating them better or joining them completely.
6) The main analyses of colour evolutionary rates only include chromatic aspects of colour variation. Why was achromatic variation (i.e. light to dark variation) not included in the analyses? I think that such variation is an important part of the perceived colour (e.g. depending on their lightness the same spectral shape could be perceived as yellow or green, black or grey or white). I realize that this omission is not uncommon and I have done so myself in the past, but I think that in this case, it is highly relevant to include it in the analyses (also because previous work suggests that island birds are darker than their mainland counterparts). This should be possible, as achromatic variation may be estimated using double cone quantum catches (Siddiqi et al., 2004) and the appropriate noise-to-signal ratios (Olsson et al., 2018). Adding one extra dimension per plumage patch should not pose substantial computational difficulties, I think.
7) The methods need to be much better explained. Currently, some methods are explained in the main text and some in the methods section. All methods should be explained in detail in the methods section and I suggest that it would be better to use a more traditional manuscript structure with Methods before Results (IMRaD), to avoid repetition (provided this is allowed by the journal). Whenever relevant the authors need to explain the choice of alternative approaches. Many functions used have different arguments that affect the outcome of the analyses, these need to be properly explained and justified. In general, most readers will not check the R script, and the methods should be understandable to readers that are not familiar with R. This is particularly important because I think that the methodological approach used will be one of the main attractions of the manuscript, and other researchers should be able to implement it on their own data with ease. Judging from the R script, there are quite a few analyses that were not reported in the manuscript (e.g. multivariate evolutionary rates being higher in forest species). This should be fixed/clarified.