This manuscript addresses a very interesting area of research that has great potential. Being able to clearly differentiate assembly processes based on the characteristics of trait distributions will inform theory about the drivers of community structure and help identify these forces in real community data. I believe the authors have done a good job addressing the editor’s criticism about differentiating this manuscript from Gross et al. 2017. However, I have some other concerns about design and interpretation of results that I feel must be addressed before this manuscript can be considered for publication.

Most importantly, I’m concerned about the use of overlap as a test to distinguish alternative filtering processes in trait distributions. The authors use overlap among ALL filtering scenarios as their metric, but overlap between pairwise scenarios is much more appropriate. In fact, overlap among all scenarios is effectively useless if you want to identify differences among scenarios or differences between any one scenario and the null expectation (neutral scenario). Furthermore, there is no threshold or statistic to provide confidence that lack of overlap actually significant. As a result, it is not possible to determine whether the authors’ conclusion that SKR parameters, but not trait moments or other functional diversity indices, are actually supported by the results.

Additionally, we need more detailed explanations about 1) which aspects of diversity all the SKR parameters and individual trait moments reflect and 2) how each of these relates to particular assembly processes. Otherwise, it’s difficult to understand why these metrics are appropriate for analyzing diversity to begin with or how they compare with previously used diversity metrics.

Some details about the methods regarding simulations and assumptions must also be clarified.

Specific comments:

• L49-55: Way too vague—please be more specific about the results. What exactly are these “signatures of contrasting deterministic processes”? Which “assembly rules” are you able to discern? What are the “key implications”? This abstract basically says you did some things and found some things, but never really says what the results actually are.

L119-121: An important part of the argument is that variance and other indices are insufficient descriptors of diversity, but you should state explicitly what you mean by “high trait diversity” here, specifically what aspects of diversity skewness and kurtosis represent.
L133: Again, it would be much easier to follow what you’re doing if you just said what these “trait-based scenarios” actually are here. It would also help the reader digest the results later if you explain what we might expect in terms SKR parameters and the individual moments under these different scenarios up front. In fact, it might even be sensible to have a third, conceptual panel in Figure 1 or even just a Table that clearly and simply explains which aspects of trait diversity each of the SKR parameters, moments, and other diversity indices represent. This would really help tie all of your analyses together into a coherent picture of trait diversity and how to measure it.
L216-220: This is really important information, although the grammar is a little bit confusing in these sentences. Something like this is needed for the rest of the diversity metrics (SKR parameters and individual moments).

L137 & Methods: Perhaps you should say “trait pool size”. Isn’t the idea of trait-based ecology to shift the focus from species to traits per se? What is the relationship between species and traits in your model—is it just 1:1? Can species have more than one trait value? Can multiple species have the same trait value?
L194-196: Ah, this should be made clear earlier, especially if you plan to stick with “species pool” in the intro. Another question, is the abundance of each species = 1 in your simulations, or are we dealing with abundance-weighted distributions?
L186: Wait, individuals or species? How many individuals per species?

L153: Maybe make it clear that “trait-based filtering” intentionally includes/differentiates between both abiotic (environmental filtering) and biotic (niche differentiation) processes.

L174: What increments were used for trait values? And was redundancy of trait values allowed? Both of these assumptions can have serious consequences for the initial trait distributions.

L176: Is “m” a direct rate? If so, then these are very extreme values and perhaps an intermediate migration treatment is warranted. Or, explain what’s going on here and why intermediate dispersal is not worth exploring. You also call this “no dispersal” and “dispersal” in the figures, but here in the methods it’s “low” and “high” dispersal—please be consistent.

L180: But the environment is still static (i.e., not fluctuating), right? “Changing” sounds like a single environment changing over time. And if it’s true that this is static environmental variation, then how do you generate the “directional” filtering scenario?

L206: What software is this package from?

L220-225: Is there a threshold that differentiates non-significant versus significant overlap? This is critical if we want to identify the signatures of different assembly process with any confidence. Also, shouldn’t overlap be calculated in pairwise fashion in order to differentiate each scenario from each of other scenarios? Otherwise, how can you tell which one stands out? Overlap among ALL scenarios seems meaningless.
L230-232, L243-245 & elsewhere: I think this is because you’re not calculating pairwise overlap. Some of these scenarios appear to stand out quite distinctly, e.g., mean values for directional filtering are very different from the rest of the scenarios and variance under disruptive filtering seems very different from that under stabilizing and directional filtering, but you can’t pick this up if you just calculate overlap among all scenarios.

L237-239: The correct test would be pairwise comparisons of overlap between the neutral scenario each deterministic filtering scenario.

Discussion: You make some really nice points here. I particularly like the discussions about 1) multiple sources of signal and noise and how they can be differentiated (L327-350), 2) the risk of considering either skewness or kurtosis individually (L360-373) and 3) the importance, but absence in this model, of different types of direct interactions (L389-397). Although, I don’t really follow the argument about scaling and how it’s represented in this paper (L351-359).

• Figures 2-5: Differentiating the 4 filtering scenarios would be more effective if they were listed in a legend instead of being in the middle of the figure. It makes me think that each ROW is a filtering scenario (as is actually true in Figs 4a & 5a), rather than a moment. Also, the colors used here could be mistaken for the common distributions shown in Figure 1b.

Figure 2: I can understand why you did it, but showing distributions of the moments of distributions is pretty confusing. Is there some feasible way you could also show the raw distributions, too, so people don’t think they are looking at them in the current panels?

I believe the authors have successfully addressed all of the concerns in my initial review. The revised manuscript has greatly improved in clarity—particularly regarding 1) clarification of relationships between trait distribution metrics and functional diversity and 2) statistical differentiation between alternative assembly scenarios. The new figures are also way more intuitive than the old versions.

I have two final thoughts that I believe deserve attention.

1) Figures 4a & 5a show the distribution of communities in skewness-kurtosis space across a variety of assembly scenarios given variation in the regional species pool (Fig 4a) and the environment (Fig 5a). I’m interested in the patterns demonstrated by dark vs. light blue dots. Dispersal limitation not only controls the overall spread of communities in S-K space (as mentioned at L2080-282), but Fig. 4a also shows that richer communities tend toward more normal distributions under low dispersal limitation, but this trend is weakened with high dispersal limitation. I think this makes sense because we would expect dispersal limitation to reduce the strength of underlying assembly processes and thus increase the chance that communities with fewer trait values (lower richness) exhibit more extreme S-K values. The patterns in Fig. 5a are also interesting because, while dispersal limitation controls scattering (as in Fig. 4a), individual communities are also organized within S-K space based on whether assembly is stabilizing or disruptive. These are neat results that deserve at least a few sentences in the results and perhaps discussion sections, but right now none of this is mentioned in the manuscript anywhere.

2) Less important, but why not use “low dispersal” and “high dispersal” instead of “high dispersal limitation” and “low dispersal limitation”? The latter two seem unnecessarily complicated.

I appreciate the authors attention to my final comments. I believe this manuscript is now ready for publication.