The present paper provides a useful overview over the mechanisms that may lead to assortative mating (within species), and it suggests a statistical framework for distinguishing the different sources of trait covariance between partners.
The bulk part of the manuscript (up to line 210) is very thoughtful and also written in a way that it is relatively easy to understand (despite the complicated topic), so I only have a few minor suggestions on how the clarity could be increased in a few places (details under ‘specific comments’ below).
The second part (lines 211-307) deals with questions regarding the adaptive value of assortative mating and with other evolutionary consequences of assortative mating, such as the increase in additive genetic variance and the issue of speciation. This part, I have to admit, I felt was less helpful to me in providing a well-structured overview, and at some places I felt it was a little confusing. Regarding the latter, I provide detailed comments below on what might need to be clarified (see ‘specific comments’), yet before that, I try to describe two general aspects that I was somewhat missing in this text. This may be a personal point of view, so I merely want to offer this as a suggestion.
The current text tries to contrast adaptive (lines 212-229) versus non-adaptive (lines 229-236) explanations of assortative mating. In my opinion, (1) there is too much emphasis on adaptation, (2) adaptation should be distinguished from exaptation [if I may use this term in this context], (3) the evolution of mechanisms of species recognition should be considered, (4) the consequence of inbreeding should be considered. Re (1), I think that assortative mating primarily arises as a byproduct of mechanisms that exist anyway or have evolved for other reasons. The only case where I see scope for adaptation, is the behavioral convergence of partners, which may help to reduce conflicts and facilitate cooperation in the couple. Re (2), even in cases where assortative pairs are doing better than disassortative pairs, assortative mating need not have evolved as an adaptation per se, since the mechanisms may have evolved for other purposes (e.g. species recognition). So, even where assortment is currently beneficial, I would be hesitant to call this an adaptation. Re (3 & 4), the most essential first step in mate choice is usually the correct identification of opposite-sex conspecifics. Hence, mechanisms of species and sex recognition have evolved primarily for the purpose of ensuring conspecific mating, and these mechanisms may then result in assortative mating also to occur within species as a byproduct. This byproduct may then be beneficial (hence an exaptation), neutral, or maladaptive. For instance, learnt species recognition via sexual imprinting on parents, is likely an adaptation for ensuring conspecific mating, and it is conceivable that imprinting on parents will also lead to assortative mating preferences within species as a byproduct (yet the evidence is surprisingly sparse, see Rantala & Marcinkowska 2011 Behav Ecol Sociobiol; Schielzeth et al. 2008 J Evol Biol; Grant & Grant 2018 PNAS). The resulting assortment within populations need not be beneficial at all, since it tends to promote incestuous mating with the consequence of inbreeding depression. Besides imprinting, also other mechanisms of species recognition (including recognition alleles and self-referent phenotype matching) might show a similar tendency to promote mating among close kin.

My second point regards the discussion on speciation (lines 269-293), where I was missing to find the general conclusion that, in the vast majority of cases, assortment and local adaptation are usually not strong enough to counter gene flow. Hence, in most cases, speciation will not take place despite of some (mostly minor) differentiation and moderate levels of assortative mating. Even though we can imagine numerous dimensions along which a population can differentiate, the separation and finally speciation along one of these remains the rare exception rather than being the rule.

Specific comments:
(1) Line 39: I can imagine 3 mechanisms here: (1) mate choice for similarity, (2) mutual choice for quality, (3) unidirectional choice for quality (e.g. by females) combined with competition (e.g. in males) may also lead to assortment by some quality-related trait.
(2) Line 42: Do you agree that this could also arise as a byproduct of variation in habitat choice (e.g. due to imprinting on natal habitat)?
(3) Line 66: “myriad” and “5” appears like a contradiction to me, as I equate myriad with uncountable
(4) Line 76: Maybe also consider that the phenotype could be affected by the environment in a passive way (e.g. dust on feathers changing the plumage color).
(5) Line 101: “(or relatedness)”: please explain this a bit, otherwise it might confuse readers (or omit if not needed).
(6) Line 104: the concept of the ‘individual merit’ should be explained. Is that the repeatable part of the phenotype? The concept of the breeding value is more widely known, but maybe also should be explained for some of the readership.
(7) Line 129: estimated
(8) Line 133: “identity as a random effect”: maybe worth explaining that this captures the individual repeatability
(9) Line 136: fitted
(10) Line 138: Such a model
(11) Line 145: do you mean “(e.g. territory identity as a random effect)”? Maybe it is worth mentioning that territoryID and pairID should not be fully aliased if one wants to distinguish between them.
(12) Line 150: investigate the presence of
(13) Lines 152, 153: “assortative mating”: do you mean assortative preferences?
(14) Lines 204, 206: “strongly imply that… might be overestimated”: how about just “imply” or “indicate” (without “strongly”)?
(15) Line 211: “Line 212: “Assortative mating can evolve due to adaptive or non-adaptive mechanisms”. Do you really mean “evolve” or “arise from”? Such a binary distinction between adaptive and non-adaptive is confusing me. I think it would be more useful to start from the assumption that assortative mating arises primarily as a byproduct of mechanisms that exist anyway or that have evolved for other purposes. For instance, the mechanism of sexual imprinting is adaptive, but it may result in inbreeding as an undesirable byproduct and hence appear maladaptive in the context of mate choice WITHIN species (while adaptive for preventing heterospecific mating).
(16) Line 213: With the current wording, I think that most readers will not be able to understand why, under the adaptive scenario, traits need to be heritable (and also line 218: “as long as it is caused by heritable traits”). Maybe this would be easier to understand, if you explain that assortative pairs might have higher fitness than disassortative pairs, but nevertheless this might not lead to the evolution of higher levels of assortative mating, because the tendency of an individual to pair assortatively might not be heritable. For instance, a population might be genetically uniform regarding its mechanisms of species recognition, and assortative mating might arise as a byproduct of these mechanisms. Variation in the degree of assortment may primarily have environmental, yes, even stochastic, causes such as changes in mate availability.
(17) Line 219: “which already benefit from widespread empirical evidence”: rephrase
(18) Lines 219-224: I can see the point of declaring some mechanisms as being the default, while others requiring explicit evidence, but I do not think that self-referent phenotype matching would be a far-fetched explanation of e.g. assortative mating by plumage in carrion vs hooded crows. Line 223: why do the true merits have to be assessed? A noisy assessment would simply lead to a weaker correlation.
Further, I can also imagine very simple mechanisms leading to ‘like attracts like’ that do not require any complicated assessment of self and potential partner. Moving through space at similar speed bring similar phenotypes together. There may be a preference for a partner with similar tendencies to stay or leave and similar speed of movement (this creates less conflicts about “should we stay or should we go?”), but even such preferences might not be needed since one automatically tends to get exposed to similar types as oneself (‘like meets like’).
(19) Line 229: “Bebbington and Hatchwell, 2016”: I understand that the idea of coordination is intriguing, but, if I followed the debate correctly, we might be talking only about statistical artefacts here (see Schlicht et al. 2016 in Behav Ecol 27:e2-e5; Ihle et al. 2019 in Front Ecol Evol 7: doi.org/10.3389/fevo.2019.00142)
(20) Lines 241-249: “For assortative mating to impact adaptation…” I find this a difficult start into the topic, and I am not sure whether I have understood the message. Do you mean to say something like this? If a trait is heritable and under current selection, then assortative mating for that trait can speed up selection. Traits that are selected against will be removed more quickly, and traits that are favored will evolve more rapidly (e.g. Godineau et al. 2021).
(21) Line 243: The “For example” can be cut.
(22) Line 269: A number of studies focuses on
(23) Line 273: I think the “preference/trait rule” is explained incorrectly. In this scenario the trait and the preference are independent, meaning that they are not physically linked. Linkage disequilibrium (LD) between preference and trait can arise from assortative mating, but LD is not the same as “in linkage” (which probably means physically linked).
(24) Line 276: mentioned is that (not “mentioned that is”)
(25) Line 279: do you mean “and cause non-random mating”?
(26) Line 282: do you mean “signaling the degree of local adaptation”?
(27) Line 284: Here would be the place to mention that gene flow will typically prevent speciation.
(28) Line 284: “Even after species have differentiated, assortative mating remains of high importance”. I find this use of the term “assortative mating” here confusing. Up to line 284, assortative mating refers to mating within species, yet here, all of a sudden, it means conspecific mating (rather than hybridization). Such a jump in meaning, if it cannot be avoided, would need more careful explanation. In line 287, “absence of assortative mating” means hybridization.
(29) Line 289: Maybe mention the Latin names of the two species.
(30) Lines 295-307: I find this not so convincing. At least in line 299, I would say “might allow us to” and in line 306, I would replace the “certainly” with “might”.

Review signed
Wolfgang Forstmeier