[x] Abstract: Should there be a distinction in the wording of local network vs metaweb? For instance, would it make more sense for it to be a local-web vs a meta-web, or a local-network and a meta-network? Just a thought. I say this since a network can also be something like a metacommunity.
[x] Lines 2-8: I'm not sure this is relevant, since taking a probabilistic view of networks doesn't change the fact that they are hard to characterize effectively.
O, I see the probabilistic networks can capture the uncertainties (as you later write). It may be better to bring up that idea earlier?
[x] Lines 7-8: Great. Should it be mentioned that you are referring to trophic interactions (e.g., not competition).
[x] Lines 10-19: Even then, they may not interact. As you put it earlier, a third species could alter direct interactions between two species.
[x] Lines 23-26: And so you would get a binary network after t -> infinity (i.e., the probability that an interaction 100% occurs or 100% does not occur over the course of infinite time/infinite area)? Or would it always be a probability (i.e., \mathbb{R}), in terms of if your asking about what the network is like at any smaller time or area?
[x] Line 26: Why respectively?
[x] Lines 26-27: Ooo, I see. I think this is a very important point - Maybe bring it up in the first paragraph as to why probabilistic interaction networks are useful. Side note: could you specify that you are 100% certain that a species and their interactions occur 50% of the time?
[x] Lines 27-29: May be useful to indicate that you still refer to binary networks, not as probabilistic networks, throughout the manuscript.
[x] Lines 29-31: as well as forbidden species presences.
[x] Line 33: Might have to define metaweb here (although you do it later). Or remove "metaweb" reference here.
[x] Lines 35-36: I think probabilistic networks "may" provide a more realistic portrait of species interactions. I.e., I think you would have to have evidence to show this.
[x] Lines 36-37: Species interactions or network structure are major drivers of ecosystems worldwide?
[x] Lines 59-60: I'm not sure I say this.
[x] Lines 65-66: What do you mean by "realized interactions" here? To me it sounds like binary/weighted local networks (i.e., networks where interactions or evidence of interaction has occurred). And does this mean you cannot have a local probabilistic network?
[x] Line 80: These are both bipartite networks. Maybe consider something different, e.g., multilayer? I don't know, just spitballing.
[x] Lines 92-94: Are there empirical examples of these in the literature? For example, I don't think I've come across probabilistic networks in any repositories.
[x] Lines 105-106: Could also cite this food web paper for this: https://doi.org/10.1002/ecy.3256, which I think you already have.
[x] Line 109: Would the number of trials be the number of times someone goes out and tries to observe the interaction (success) between two species?
[x] Line 109: I think A_{i,j} is the adjacency matrix? Maybe best to define.
[x] Lines 109-110: Wouldn't this just give a probability, and not (necessarily) a 1 or a 0.
[x] Line 111: I'm getting a bit confused: on LN 65 it says that local networks are realized and metawebs are probabilistic.
[x] Lines 114-115: Which probabilistic network representations? Binary networks?
[x] Line 138: Might be a bit confusing to represent the Adjacency as an "A" since you are also using it to represent area later.
[x] Lines 145-146: Is this true? What about Ecopath type networks (i.e., those that you can obtain via EcoBase)? Would this be weighted? Although I (as a matter of opinion) also do not think these are necessarily better than binary networks .
[x] Line 146: What's a Bernoulli interaction?
[x] Lines 155-157: I'm getting a bit mixed up here, are you saying the binary networks are probabilistic networks? Or are you saying that because Kopelke et al. (2017) have many different networks consisting of similar species, it gives the probability of observing interactions between these species across space and time.
[x] Line 161: Why three coordinates?
[x] Eq1: I think you need to define why "N". O, I think you define it later (on LN 195). It should probably be moved earlier. Also, should the subscript now include the location (i.e., x,y,z)?
[x] Lines 185-187: This is the same as the previous paragraph right?
[x] Line 190: What's a shelter?
[x] Lines 195-196: You've got me thinking: what is the difference between "co-occurrence", "environmental and biological conditions", and "area"? I understand them independently, as you have done well, but putting them together seems a bit difficult for me to understand: after all the amount of area/environment is trying to capture a measure of species' co-occurrence (as written on Ln 177), right?
[x] Table1: Should the probabilities be with the "A". I.e., for the second row: A{i,j} ~ P{N}(i \to j)?
[x] Table1: Is "realization" what you want here? I.e., realization is defined as it actually occurring. So is it more like potential realization?
[x] Lines 212-213: Cool - so local networks cannot really become metawebs.
[x] Line 226: But you also have P_{N}(i \to j) in the table which is also not conditional on anything.
[x] Lines 258-259: Of course, these networks are not perfect. E.g., how much area did they sample, how often did they go out, etc.
[x] Lines 260-263: You bight have to define these Betas (in an equation).
[x] Lines 271-273: How do you know, for example, what a false negative is? Or are you just acknowledging that you included false positive/negatives in the metawebs?
[x] Line 281: Big "P"? Or do you mean later on you use little "p"?
[x] Line 289: Wouldn't S^2 include cannibalization? Also, aren't these tripartite webs, so not all species can interact?
[x] Eq5: The equation is like this because you want to include the probability of (i) both networks obtaining the interaction, (ii) network_1 obtaining the interaction while network_2 doesn't, and (iii) the same as (ii) but network_2 has the interaction while network_1 doesn't. Might be helpful to state this, especially since it is also used in the next section.
[x] Lines 328-329: I'm unsure of the term "trophic species".
[x] Line 344: Might be helpful to remove acronyms - I don't think you use it to often anyway. Same goes for IACs.
[x] Line 354: or duration of the sampling period used to construct the network.
[x] Lines 355-357: While this is true, doesn't binary or weighted networks do this as well? I.e., does this statement make probabilistic networks better than traditional networks for evaluating spatiotemporal
variability of interaction?
[x] Lines 360-361: Of course, as you have already written, a more complete metaweb will have different interaction probabilities. Perhaps a distinction between the "true" metaweb and a anthropogenically derive metaweb (which obviously has errors) should be stated? Just a thought.
[x] Line 364: Subsampling in terms of species and obtaining ALL their interactions with subsampled species.
[x] Lines 366-368: Shouldn't it always be the case that the metaweb is larger or equal to the subsampled web in terms of number of interactions?
[x] Line 384: Not sure what goes here.
[x] Line 384: Should this be a new subsection?
[x] Lines 386-387: Might need a citation for this.
[x] Lines 389-391: I'm not sure what is being said here: isn't probabilities of interactions precisely in the wheel house of predictive applications?
[x] Line 400: may be determined?
[x] Line 426: Sampling for binary networks?
[x] Line 427: (Bernoulli trials)
[x] Lines 429-430: So you perform a Bernoulli trial and get a probability. When do you know the interaction is occurring in the network? And this is sampling the metaweb?
[x] Lines 435-438: Of course, you would need the temporal network before you could create these null models.
Can also cite (for difficulty of cataloging interactions): https://www.jstor.org/stable/2462536
https://books.google.ca/books?hl=en&lr=&id=bF3JoZgoo24C&oi=fnd&pg=PA27&dq=The+structure+of+food+webs&ots=0Rff_GUACh&sig=S1m_Iv15rmYRCM-9KzfbwWe3I5c#v=onepage&q=The%20structure%20of%20food%20webs&f=false
O, I see the probabilistic networks can capture the uncertainties (as you later write). It may be better to bring up that idea earlier?