Review History
Numerical ability and improvement through interindividual cooperation varied between two cyprinid fish species, qingbo and crucian carp

Thank you for attending to these last final important edits. Please ensure proper spacing between words during the proofing stage as I noticed some words missing spaces between them in the tracked sections.

# PeerJ Staff Note - this decision was reviewed and approved by Nigel Andrew, a PeerJ Section Editor covering this Section #

I have reviewed your tracked manuscript and rebuttal letter and I would still like you to improve the clarity of your writing in the following places.
“Increase” is just as problematic as “Improvement” for the same reasons. Please change to “better” on line 24 of the tracked change version. On line 213, also change “increased” and “numerical ability.” See also line 259.

On line 61, use “be facilitated by” rather than “facilitate.”

Again, given that you are assessing a preference, not testing an ability, please strike reference to “numerical ability test” and refer to as “numerical preference assessment” or something along those lines. Please check carefully throughout.

You do not need to thank me for suggestions, as this is the role of editor and expected.

Thank you for addressing the reviewers’ comments in your revision. I still have some issues I would like to see addressed before I can render a final decision on the MS.

On line 24, I would strike the word “profound.” I would also not use the term, “improvement” given that you did not test singletons first and then test the same fish in dyads. Throughout, you could change “improve” to “benefit from” or “facilitate”, such as on lines 58, 160, 204, 205.
Why is there a – on line 43?

Delete “the” on line 58.

On line 61, change “stumulus” to “stimulus” and insert a space after shoals.

I still think you should avoid talking about “ability” to choose (e.g., line 74) as if there is a correct/incorrect response when really it’s just a preference.

I still find the description of the procedure confusing. It is not clear what the shoals were made up of for each test fish condition (e.g., always mixed species or sometimes only conspecifics)? If this was a variable, why is it not accounted for in results? It seems to be a variable in Figure 2 but this is not described clearly in the text.

Why use only large quantities (8 or more) without assessing possible preferences for smaller numbers given the extensive literature on different systems for quantifying small versus large numbers? If group-living is preferable to living alone, perhaps the difference between 1 and 4 is more relevant than the difference between 8 and 12? You do address this briefly in the Discussion, but I think this consideration should temper some of your conclusions about the lack of preference of carp.

I received two expert reviews of your MS. One of the reviews was quite positive with the reviewer suggesting a number of points of clarification and minor corrections. The other reviewer was more critical and has several amendments and corrections to your literature review. Both raise possible issues of pseudoreplication, and ask for clarification regarding your statistical approach. You mention that each fish was tested only once, so I think you might just expand on how fish were identified and eliminated from multiple tests. However, both reviewers also find merit in your work and thus, I would like to invite you to submit a revision addressing their concerns. I agree that the study is of interest and will make a contribution to the literature but I have a few comments of my own:

In the abstract, strictly speaking, you didn’t “conduct a… choice..” You may have conducted a test in which the fish made a choice. Please reword.

Is it accurate to say that they could not discriminate because they did not show a preference? These are two different things. If there was no benefit to discriminate, you cannot conclude that a lack of preference reflects an inability to discriminate quantities. You address this is in the discussion, but be careful then how you word this in the abstract.
What do you mean, “showed poor cooperation on numerical ability.” This doesn’t make sense as written. I don’t think the construct of cooperation is well defined here. It isn’t clear what the rationale is behind the manipulation of presenting singletons and dyads. Please expand in the introduction. In general, the introduction is very lean. It would be helpful to expand more on the species differences and expectations, and the background for the methodology used here. Is it really that fish “cooperate” to perform better, or is it just that their preferences differ when alone or not alone? Could you please say more about what it means for quantity discrimination to be “improved by cooperation” (line 48)?
Lines 53-54, I think an “if” is missing between “test” and “the abovementioned…” manifests should be plural.
Please be sure to call out your Figures within the text.
On line 154, Agrillo is missing an o. Please check spelling carefully throughout.
Replace “since” with “because” when using in a non temporal context.

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