This is the second time I am reading this manuscript.
Overall, I think the manuscript has improved a lot. However, the results are over-interpreted in the discussion, and that is reflected in the whole manuscript. I am wary even of the title implying causation. So I would suggest a semantic overhaul there, as you do not run any manipulative experiments.
Furthermore, I have a few more comments on the analysis - mainly:
- inconsistency in how you treat your variables - log-transform them for one analysis, but not the other (or at least that's how I read it) - this needs either rewording or making consistent or justifying properly
- non-repeatable traits can't be used in assortative mating analysis as means
- non-statistically significant results do not differ from zero, so they are not "trends" in any direction - this needs to be reworded in results and appropriately changed in the discussion - you can't discuss them as they are significant. You can say that maybe with more statistical power they might go there but even then to discuss this potential result is a stretch.
- shorten discussion to main points
- move main analyses results into main text. We're not constraint by page limits, we should put the important bits (even if not significant!) into the main text for transparency - the supplement is officially not for review!

Comments:
Title implies causality - is that ok or not? Influence of personality on formation of breeding strategy

Abstract: is it "influence mating patterns" or are associated with mating patterns

"had the not significant tendency - no there was no effect - this can't stand like This

another instance of "influenced" - reword

Introduction:
better linked with fitness, better understandable. Well done.
Line 47 - consequences maybe better correlates

Line 80 - "affects mating patterns" - is associated with

106 make clear that the other studies have not shown this in Dunnocks (it reads as such), and also, please watch causation/correlation language - it sounds now as if there's been causal evidence - there isn't. change "influence" to something less causal e.g. "is associated with"

Line 133 "of these two behavioural traits" here it's unclear which two traits you refer to (I think because you've added to much text the link is now gone) - best restate this. From the previous sentences it would be FID and provisioning but from what you write next it's boldness so it's not clear.

Line 156 define ASR

Line 229: add to the end of the sentence: "and can thus be considered less vigilant than those that peck less often" This way the logical argument is complete.

You say you measured behaviours in random order but it seems to me that the bird left after you measured FID - can you please add a half-sentence explaining that? Did you measure FID last or did you wait until the bird came back after escaping?

259 - "more comparable to other log-transformed variables"
260 space
260: justify in text why not provisioning

Assortative mating: You need to justify why you treat a variable once in a way that it needs to be transformed, and in the next analysis you do not transform it. That is illogical. I can live with it if you provide a reasonable justification in text, but if you do not do that it looks like somewhat fishy.

line 307: Effect of FID on mating system - reword - association
line 326 - see above - association or are correlated with

line 327 - the annual number of fledglings
line 327 - can you give here mean ±SE of annual number of fledglings, please
line 331 - 338 - this is still odd. When you fit both focal and partners trait then you practically fit the same model for males and females twice. If your intention is to look at differences between sexes then this is still formally impossible because you fit two different models for the sexes. I think we need a better justification for these models. I am also not sure what the interaction means biologically - you must explain that. Finally, the explanation of what you did with two male partners - adding up their provisioning rate - also requires a justification, and also an explanation of what that parameter would then mean biologically. It also highlights the problem with pseudoreplication that comes in from selecting only first broods, but also second broods in case of repairing (line 167) - the female shows up twice in the data, has a higher chance for higher reproductive success, so I am not convinced this is a good idea.

Results:

Repeatability: please remind the reader it's repeatability of log-transformed traits

If repeatability of vigilance and activity were low does this not mean it's non-sensical to use annual means in the assortative mating analyses - you can drop them from these analyses because they can't really be meaningful.

Line 376-385: if something is not statistically significant, that means it is not different from zero, so please reword "trend" to there was no effect. Zero is neither positive nor negative. Reword all instances of this.

Please put Table S5 into the main text. We're not constrained and you refer to the table twice, and cite single estimates - a reader should be able to see all estimates without the need to download several supplements. Results from your main analyses mentioned in methods should be in the main text. Same for S6 - maybe you can put both into one table similarly to how you combined models in table 3.

In discussion there are multiple instances of using "effect on" or "influence" reproductive success - please reword these to make sure you do not imply causality. Furthermore, revise language to make sure you do not over-interpret non-significant results. For example, there is no assortative mating on activity and vigilance as opposed to low levels. This goes on throughout the discussion.

The manuscript improved significantly, however, I have a few minor issues, the main one being that the problem of confounding correlations with causality still remains.

Title: you do not know whether personality influences alternative breeding strategies and reproductive success, or whether it's the other way around. You need to do an experiment for that. Change the wording. It is unclear what drives what.

In line 5-6 it's true - because it's really difficult to do such sort of experiments.

Line 15: change "affect" (implying causality) to "associated with"
Line 25: change "affected"

Line 194-195, and following: please either write (mean, SD) or (mean±SE) and if you give the latter make sure you do present the standard error, and not the standard deviation.
This may seem odd and I would like to apologetically explain why I have come to feel somewhat strongly about this. SD is a property of all of the data indicating its spread, while SE is a measure of precision of the mean, and as such both indicate differnt things. In particular, SE is associated with the mean (hence the link through the ±), while SD is not per se associated with the mean (although some authors make it look like it is). It's confusing and I think we should strive to be more precise in this, if only for readers less versed in statistics than us to not be confused - many students do not understand the difference well.

Table 1 legend should be stand-alone - please add information so a reader knows what they are looking at by just reading the legend (e.g. add species ect.). Same for most tables

Line 309: change effects to associations or similar

Line 374: You changed that estimate from non significant to significant - how come? (that's not meant accusatory - just curious and making sure it's all sound)

Line 416: "influence" change wording - it's not what you tested as you didn't do a cross-foster experiment - could just well be individual quality

Line 446 - "influenced" change wording

Line 448 - change "had an effect"

Line 516 - "influence" change wording

Line 556 - "influence" change wording - could be individual quality instead. I realise in particular when it comes to provisioning that it is easy to make an intuitive assumption that it is causal but there's papers that show it's not necessarily the case.

Line 573 - plays -> play