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  • The initial submission of this article was received on August 29th, 2013 and was peer-reviewed by 2 reviewers and the Academic Editor.
  • The Academic Editor made their initial decision on September 14th, 2013.
  • The first revision was submitted on November 13th, 2013 and was reviewed by 1 reviewer and the Academic Editor.
  • A further revision was submitted on November 20th, 2013 and was reviewed by 1 reviewer and the Academic Editor.
  • The article was Accepted by the Academic Editor on November 26th, 2013.

Version 0.3 (accepted)

· Nov 26, 2013 · Academic Editor


The reviewer is satisfied with the revised manuscrpt. The paper is now suitable for the publication in PeerJ.


Basic reporting

No Comments.

Experimental design

No Comments.

Validity of the findings

No Comments.

Additional comments

I am now happy with the manuscript and think it should be published. I commend the author on his patience, candour, and keenness to take suggestions on board.

Version 0.2

· Nov 17, 2013 · Academic Editor

Minor Revisions

Please make the revised version together with a list of your replies to the comments. The manuscript will be checked by the reviewer again.


Basic reporting

The paper is much improved, and I now only have a few relatively minor suggestions.

Chief among these suggestions is that I would like to see acknowledgement of the paper "The Dynamics of Honesty: Modelling the Growth of Costly, Sexually-Selected Ornaments" by Rands et al. from PLoS One in 2011, as well as discussion of how your findings differ from theirs. They also seem to find (in line with the Kokko, and Proulx et al. papers you cite) that at younger ages, high-quality males are likely to have smaller ornaments, while at older ages the reverse is true. They use a stochastic dynamic programming approach rather than your major gene model, so it would be interesting if you would compare the results and approaches, either in the Introduction or the Discussion (or both, as you currently do with the other papers mentioned).

Other points:

Abstract: "Evolution of age-independent traits depends on trait size, whereas evolution of age-dependent traits depends on strength of selection and growth rate (i.e. size)"
This reads like you're saying "Evolution of age-independent traits depends on size, whereas evolution of age-independent traits depends on size". Seems a bit strange. So maybe stress that the former depends ONLY on trait size, while the latter depends on two parameters.

p6, line 110: "mean males of a particular genotype"
Consider amending this to "mean that males..." since the juxtaposition of "mean" and "males" after the parentheses might make the insufficiently careful reader think you are referring to a specific kind of average male, rather than what larger values of b mean.

p7, equation (2): I'm afraid I still don't follow your logic for tbar. Firstly I don't understand the sentence "I calculated tbar at each iteration such that males carrying F2 contributed to the population mean as if their traits were age-dependent". I apologise if I have confused matters further with my comments last time around. I thought that F2 males (in this instance) are simply defined regardless of their age as having an ornament size equal to the mean ornament size for age-dependent males of their condition? But you now seem to be saying that F2 males all have ornament size equal to the mean ornament size of F1 males, regardless of condition. Or maybe not?

Further, I still don't see why there is the denominator of ymax+1. If f(t) is the frequency of males with trait size t, and the sum in the numerator is over all possible discrete trait sizes t, then isn't the numerator already the mean trait size in the population?

p8, line 158: "represents the traits size"
typo, should be "trait size"? Unless you want to adopt "the trait's size" throughout, which I would personally advise against.

p11, line 206: maybe add "initial" before the word "size" in your parenthetical explanation of parameter b?

p13, line 252: "The left-hand column of Figure 5"
Right-hand, surely?

p15, line 300: Maybe point the reader to Figure 1?

p16, line 341-2: "avoid viability selection, by contrast, avoid selection..."
Probably should remove the redundant repetition here.

p17, lines 357-360: I'm afraid I still don't quite get the comparison between Proulx et al and Kokko. Is the conclusion in both papers that poor condition young males should signal more than good condition young males?

p18, line 389: Put the Evans citation in parentheses?

Experimental design

No Comments

Validity of the findings

No Comments

Additional comments

No Comments

Version 0.1 (original submission)

· Sep 14, 2013 · Academic Editor

Major Revisions

Please make a revised version considering all the comments by the reviewers and resubmit it to PeerJ. Looking forward to receiving a revised version that will be reviewed again by the same referees.

Reviewer 1 ·

Basic reporting

Please see comments below.

Experimental design

Please see comments below.

Validity of the findings

Please see comments below.

Additional comments

This theoretical study addresses an interesting and important question –the mode of development of a secondary sexual trait in relation to its evolution. Unfortunately, it’s not clear to me that this study succeeds in capturing some biologically-important aspects of the problem being modeled, so I’m not sure what to make of the results.

Specific comments:

(1) The relative advantages of age-dependent and age-independent secondary sexual trait expression are likely to depend very much on the relative costs and benefits of “large” trait expression in early life versus the costs and benefits of gradual and continual growth in the trait through the reproductive lifespan. It’s not clear to me that this model captures these costs and benefits. For example, is there a disproportionate viability cost of large trait expression early in the reproductive lifespan (when males are smaller)? The finding that age-independent trait expression tends to evolve at larger trait sizes suggests that this cost is not captured by the simulations. Some other aspects of the simulation and results are also difficult to understand (see below).

(2) The procedure of assigning males with age-independent traits the population-mean trait value at each iteration (L103-114) needs more explanation. I suppose this was done in order to avoid having the competition between the F1 and F2 alleles influenced by differences in mean trait size under these different strategies? My concern is that this peculiar procedure is likely to affect the behaviour of the simulation in ways that make the results difficult to interpret. Moreover, I wonder whether this procedure actually removes some of the biologically meaningful variation. An age-independent allele (as defined in this paper) may be favoured by selection because it allows males to take advantage of mating opportunities in early life, when an age-dependent trait would not yet be developed enough to make the male competitive. By setting the expression of age-independent traits equal to the population mean, do you not lose this effect? I think this procedure needs to be justified in terms of the biological questions of interest in this study, and the consequences of this approach for the behaviour of the simulations should be considered and discussed.

(3) It’s odd that trait and preference were invariably lost when there was any cost to choice. Does this mean that the “good genes” modeled here were of almost no consequence for fitness, or that a genetic correlation between trait and preference couldn’t be established? This result needs more discussion, and perhaps suggests that the simulation parameters need to be adjusted to make the model behave in a more reasonable way. Would it make more sense to start with a model where costly preference can be supported with an age-independent trait, and then ask whether an age-dependent trait allele can invade?

(4) I’m also confused by the conclusion that the evolutionary fate of age-independent traits depends only on their size. What does this mean, biologically? Presumably, a trait with age-independent expression can arise and spread at a small size, but eventually evolve a larger size (i.e., become exaggerated). I think this is how the evolution of such traits is generally envisioned. In the simulations conducted here, trait size cannot evolve, so it’s not clear to me whether the conclusion that trait evolution depends on trait size has biological meaning.

(5) L244-254: Again, I’m confused by some of these statements. Classic LH theory predicts that selection will favour greater investment in reproduction at a young age when mortality rate is high. I’m also not sure what’s meant by “frivolous” traits. I’m also confused by the statement that female mate choice is favoured because it allows them to produce offspring that survive well to old age. Surely, the important parameter here is offspring fitness, not their longevity per se. Subsequent parts of the discussion contain similarly confusing statements (e.g. that males benefit by expressing large traits in old age because selection strength declines with age).


Basic reporting

The article is generally well written, aside from the few specific points I make below. It sets out its arguments in a clear and reasonably well-structured manner. There are a few points I would like to make, however, as follows:

P2, line 19-20 it would be nice to have a few references here of examples of some of the “most” sexual selection models to which you refer.

P3, line 47-48: I don’t follow you that males growing age-dependent traits will necessarily rarely encounter choosy females during early reproduction. Do you mean that in species in which age-dependent reproduction occurs, we might expect to observe that males rarely encounter females during early reproduction, since under these circumstances males can afford to “throw away” the few early reproduction opportunities that they get (thrown away since they are unlikely to get a mating with a small ornament)?

P3, line 48-49: Again, is it necessarily the case that most males will have similar trait values at young ages regardless of condition? It could be the case that condition-dependence is strongly reflected throughout the life span, even with age-dependent growth. This could still weaken the reliability of the signal of a large ornament, though, so your point is fundamentally still sound.

P3, line 53: It would be good if you could cite some of the voluminous literature.

P4, line 66: strongly age-dependent traits can increase in frequency in the population – as it stands I initially thought you meant that they could increase in size, either throughout an individual’s lifetime, or on average.

P4, line 79-p5, line 80: I don’t really understand what you mean by “age-0 males supply female allele frequencies”. Surely the female allele frequencies are supplied by the combined efforts of all males, through mating? Do you mean that female allele frequencies are the same as age-0 male allele frequencies?

P5, equation (1): You assume exponential trait growth for the age-dependent trait. I wonder whether you have considered other functions of trait growth? Perhaps a note about why exponential growth is appropriate (i.e. is it actually seen in the wild? Does it simplify the simulation? etc) and what effect other possibilities could have. The note could be here or in the discussion, or both.

P6, line 106: I find it difficult to follow you when it comes to the population mean trait value. First maybe consider changing notation, and using t_bar, or some such symbol, to denote the population mean trait size, and not just t, since as it stands Equation (2) has the index t in the sum, which is potentially confusing. Second, is the population mean trait value averaged over all males, or only F_2-bearing males? Third, I don’t quite follow you as to why the denominator of equation (2) is y¬_max + 1. Finally, does this all mean that age-independent male trait size can in fact change with time from one generation to the next as the population mean value changes? This seems on the face of it somewhat strange, and warrants explanation (though I may have misunderstood).

P7, equation (5): A very small point. I may have missed it, but t_j(y) appears to be undefined – am I correct in thinking that it’s the same as t(j,y), i.e. equation (1) evaluated at C = j? I can see that the rewritten notation makes things much easier here, but I think you should define it.

P7, line 130: “after selection P_i^i” should be “P’_i”?

P7, line 135-136: What is the rationale for the recombination regime you have assumed? Why should condition loci recombine freely, and the other loci be less likely to recombine freely? A word on this would be helpful.

P8, line 141-144: I confess I don’t follow your specification of initial age structure. Is equation (11) the “arbitrary Gaussian survivorship function centred at 0” mentioned on line 142? If so, then you could consider defining it as such in the text. At the moment you start by defining lambda, and then you don’t mention it except in equation (12). Also, why is the left-hand side of equation (12) phi(y)? I thought phi was the female’s mating propensity? Should it be pi(y) here?

P8, line 148: typo, “alelel” should be “allele”.

P9, line 167: perhaps stress fixation versus loss of trait, since the first time I read it through I thought this was fixation versus loss of age-dependence.

P10, lines 169-184: The description here could be simplified if you simply note that strength of selection nu does not seem to affect results in the case of age-independence.

P10, lines 186-192: I think the explanation of Figure 5 could be much clearer. At present it doesn’t address any of the features seen in the figure. I don’t really follow how the trajectories in Figure 5 show the trait declining until condition reaches mutation-selection balance, for example. Is this because there is negative linkage disequilibrium between trait and condition initially in the trajectories, and you know that there must be positive selection on condition? If so then perhaps you could explain this. On a related note, Figure 5 is a bit messy and unclear at present. It’s very hard to tell the difference between many of the six types of point represented on it. Perhaps you should use all squares for “AI” types, and all circles for “AD” types? Though even then, I am at a loss to work out which trajectory belongs to AI Age 1 and AI Age 2, for example. Also it took me a while to work out what “AD” and “AI” are as you haven’t used these abbreviations elsewhere in the document. I think this figure could be a great feature of this work – it’s fantastic to actually see the linkage disequilibrium evolving. At the moment the lack of clarity means the impact of the figure is rather lost, which I think is a shame.

P11, line 195-6: “Fixation of F_2 depended on the associated level of trait expression with initial polymorphism variance at the F locus”. I found this confusing, I’m afraid, because I thought you meant the fixation depending on how much initial polymorphism there was, and then I saw that you had fixed p_F. So maybe you should say that in the case where there was an initial polymorphism, fixated depended on the level of expression, or something like that?

P11, line 200: this relates to my earlier confusion about the mean level of trait expression in the population, but in the case where t(C,y) = t (the mean trait expression), how can the F_2 allele cause males to have smaller average traits than male with age-dependent traits? Surely if t(C,y) = t, the F_2 allele in fact causes males to have the same average trait size as males with age-dependent traits (by definition, in fact)? Maybe I’m missing something?

P11, line 205 Perhaps add “in this region” to the sentence that starts “In other words”, to make it doubly clear that you are only talking about the light grey area of the Figures in question. It’s dead cool that you get polymorphism, by the way!

P11, lines 209-212: “Net selection seems to favor…” I’m not 100% sure I follow this. The ratio of age-independent male trait to young-age age-dependent male trait is b exp{C*y_max} / b exp{C*0} = b exp{C*y_max} / b = exp{C*y_max}, which is independent of the parameters b and nu which affect fixation in Figure 6. Again, maybe I’ve missed something?

P11, line 213: typo, “threwshold”.

P13, lines 262-265: Forgive me, I don’t know the source material, but you say that Proulx et al (2002) find that young males should “downplay their signaling”, and Kokko (1997) finds that young males (of lower condition, admittedly) “should signal more”, and you say these two conclusions are “similar”. Are these findings similar? They seem to me (again, I’m sorry I don’t know the original papers) to be opposed.

P15, lines 302-303: I don’t understand what you mean by “…which could produce strong linkage disequilibrium between condition loci and preference loci under selection against the trait”. Are the preference loci under selection against the trait (if so I don’t understand at all)? Do you mean that, under conditions in which there is selection against the trait, and in which female choice depends on female condition, strong linkage disequilibrium between preference loci and condition loci could be produced? If the latter, is this expected to be positive or negative linkage disequilibrium?

Finally, I wonder whether you could comment in the Discussion about the fact that in your simulation there is a maximum age of 2? What effect, if any, do you think increasing the age limit would have? Why did you choose 2?

Experimental design

No Comments (no experiment).

Validity of the findings

As far as I can tell (see caveats above for the elements of the model and simulation that I don’t follow), the findings are robust and valid. I also think they are very interesting.

I particularly think that a lot of very good (and probably boring to do!) work has gone into sweeping the parameter space, and I commend the author on this.

Additional comments

I think this is a cool piece of work, and deserves to be published, and soon. There are a few small things that I would like cleared up (most of them probably due to my own lack of comprehension rather than any fault with the work), but in general this is a nice study.

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