The study of sexual selection goes as far as Darwin himself. Since then, elaborate theories concerning both intra- and inter-sexual sexual have been developed, and elegant experiments have been designed to test this body of theory. It may thus come as a surprise that the community is still debating on the correct way to measure simple components of sexual selection, such as the Bateman gradient (i.e., the covariance between the number of matings and the number of offspring)[1,2], or to quantify complex behaviours such as mate choice (the non-random choice of individuals with particular characters as mates)[3,4] and their consequences.
One difficulty in the study of sexual selection is evaluating the consequences of non-random mating. Indeed, when non-random mating is observed in a population, it is often difficult to establish whether such mating pattern leads to i) sexual selection per se (selection pressures favouring certain phenotypes), and/or ii) the non-random association of parental genes in their offspring or not. These two processes differ. In particular, assortative (and disassortative) mating can shape genetic covariances without leading to changes in gene frequencies in the population. Their distinction matters because these two processes lead to different evolutionary outcomes, which can have large ripple effects in the evolution of sexual behaviours, sexual ornamentation, and speciation.
In his paper, entitled “Multi-model inference of non-random mating from an information theoretic approach” , Carvajal-Rodríguez tackled this issue. The author generated a simple model in which the consequences of non-random mating can be inferred from information on the population frequencies before and after mating. The procedure is as follows: from the initial population frequencies of phenotypes (or genotypes) of both sexes, the model generates predictions on the frequencies after mating, assuming that particular mating patterns have occurred. This leads to different predictions for the phenotypic (or genotypic) frequencies after mating. The particular mating pattern leading to the best fit with the real frequencies is then identified via a model selection procedure (performing model averaging to combine different mating patterns is also possible).
This study builds on a framework introduced by Carvajal-Rodríguez’s colleagues  and encompasses later methodological developments involving the author himself . Compared to early work, the new method proposed by the author builds on the relationship between mating pattern and information  to distinguish among scenarios that would lead to non-random mating due to different underlying processes, using simple model selection criterion such as the AICc.
The great asset of the proposed method is that it can be applied to the study of natural populations in which the study of mate choice and sexual selection is notoriously difficult. In the manuscript, the procedure is tested on a population of marine gastropods (Littorina saxatilis). This allows the reader to grasp how the method can be applied to a real system. In fact, anyone can try out the method thanks to the freely available software InfoMating programmed by the author. One important assumption underlying the current method is that the frequencies of unmated individuals do not change during the mating season. If this is not the case, the reader may refer to another publication of the same author which relaxes this assumption . These papers are both instrumental for empiricists interested in testing sexual selection theory.
 Bateman, A. J. (1948). Intra-sexual selection in Drosophila. Heredity, 2(3), 349-368. doi: 10.1038/hdy.1948.21
 Jones, A. G. (2009). On the opportunity for sexual selection, the Bateman gradient and the maximum intensity of sexual selection. Evolution: International Journal of Organic Evolution, 63(7), 1673-1684. doi: 10.1111/j.1558-5646.2009.00664.x
 Andersson, M., & Simmons, L. W. (2006). Sexual selection and mate choice. Trends in ecology & evolution, 21(6), 296-302. doi: 10.1016/j.tree.2006.03.015
 Kuijper, B., Pen, I., & Weissing, F. J. (2012). A guide to sexual selection theory. Annual Review of Ecology, Evolution, and Systematics, 43, 287-311. doi: 10.1146/annurev-ecolsys-110411-160245
 Carvajal-Rodríguez, A. (2019). Multi-model inference of non-random mating from an information theoretic approach. bioRxiv, 305730, ver. 5 peer-reviewed and recommended by PCI Evolutionary Biology. doi: 10.1101/305730
 Rolán‐Alvarez, E., & Caballero, A. (2000). Estimating sexual selection and sexual isolation effects from mating frequencies. Evolution, 54(1), 30-36. doi: 10.1111/j.0014-3820.2000.tb00004.x
 Carvajal-Rodríguez, A., & Rolan-Alvarez, E. (2006). JMATING: a software for the analysis of sexual selection and sexual isolation effects from mating frequency data. BMC Evolutionary Biology, 6(1), 40. doi: 10.1186/1471-2148-6-40
 Carvajal-Rodríguez, A. (2018). Non-random mating and information theory. Theoretical population biology, 120, 103-113. doi: 10.1016/j.tpb.2018.01.003
 Carvajal-Rodríguez, A. (2019). A generalization of the informational view of non-random mating: Models with variable population frequencies. Theoretical population biology, 125, 67-74. doi: 10.1016/j.tpb.2018.12.004
DOI or URL of the preprint: 10.1101/305730
Version of the preprint: 3
We have received the revised version of your manuscript, which represents a great improvement relative to the first version, especially concerning the clarity of the message. In line with this, I will not send it our to the reviewers again, but I’d like to ask you to consider still doing a few changes, which I think will make the article even clearer. While you do these changes, I will prepare a recommendation.
Here it goes:
- Line 38: there is still disagreement on its actual definition.
- Line 39: has been challenged.
- Lines 43-44: which ‘various aspects’ are you talking about?
- -Line 44: I would replace “to make things worse” by “Moreover”.
- I would remove all the text that goes from lines 45 to 55. Lines 45-49 repeat a bit what was written before and the paragraph on patterns and processes I think is not needed.
- I would also remove the paragraph from lines 70 to 77, it does not provide much new information.
- Line 82: remove “same”.
- Line 98: the comma should come after “frequencies”, not after “that”.
- Line 101: remove “when measured with matings”.
- I would also remove the paragraph from lines 103-108, as it is quite clear what mating at random is, we don’t need this to be explained.
- Lines 120-123: isn’t it more the opposite: formulating random mating as the zero information model allows expressing the patterns obtained in the other models, right?
- Line 170: remove “the” before “model”.
- Line 210: you haven’t explained what an “information index” is. Please do this before you use the term.
- Line 349: kinds.
- Line 355: remove “as” before “caused”.
- Line 373: replace “be produced” by “occur”, then end the sentence, and state “In fact, in this case…”.
- Line 374: replace “as” by “it is”.
- Line 375: I would put “see also….” Inside the brackets.
- Line 438: another, not other.
- Line 459: replace “at” by “in”.
- Line 466: to apply information criteria to select.
- Line 539: replace “that” by “as”.
- Line 568: to generate.
- Line 627: replace “were” by “was”.
- Line 655: to estimate.
- Lines 659-661: I still think there is insufficient detail in the description of data collection. Do you sample all individuals present? What is a ‘copulation pair’? With which criteria do you distinguish between species? Are these criteria also what you think is involved in sexual selection?
- Lines 715-722: I miss a summary of what happened in the absence of replacement and in the empirical example.
- Lines 723-724: mating tables are not a set-up, please rephrase.
- Line 741: population sizes.
Additional requirements of the managing board:
As indicated in the 'How does it work?’ section and in the code of conduct, please make sure that:
-Data are available to readers, either in the text or through an open data repository such as Zenodo (free), Dryad (to pay) or some other institutional repository. Data must be reusable, thus metadata or accompanying text must carefully describe the data.
-Details on quantitative analyses (e.g., data treatment and statistical scripts in R, bioinformatic pipeline scripts, etc.) and details concerning simulations (scripts, codes) are available to readers in the text, as appendices, or through an open data repository, such as Zenodo, Dryad or some other institutional repository. The scripts or codes must be carefully described so that they can be reused.
-Details on experimental procedures are available to readers in the text or as appendices.
-Authors have no financial conflict of interest relating to the article. The article must contain a "Conflict of interest disclosure" paragraph before the reference section containing this sentence: "The authors of this preprint declare that they have no financial conflict of interest with the content of this article." If appropriate, this disclosure may be completed by a sentence indicating that some of the authors are PCI recommenders: “XXX is one of the PCI XXX recommenders.”
DOI or URL of the preprint: https://doi.org/10.1101/305730
Version of the preprint: 2
Dear Author, We have now received three reviews of your manuscript entitled “Multi-model inference of non-random mating from an information theoretic approach”. All reviewers found merit in the approach you’re proposing, but they also raised several issues. I concur with their appreciation and comments. I think this model could be useful to people working on sexual selection. However, I think that the clarity of the manuscript could be improved. In addition to the referees comments, I have a few of my own. I hope that addressing all of them will significantly improve the clearness of your manuscript.
- Line 11: “to perform”;
- Line 13: please state “in the marine gastropod” before the species name.
- Line 22: explain what you mean by “both kind of patterns”.
- Line 22: remove “models”.
- Line 51: “a posteriori” from what?
- Lines 102-103: replace by “Let a sample have n’ matings”.
- Line 123: replace by “are either known or they need to be estimated”.
- Line 131: “it is convenient”.
- Line 135: remove “Let”.
- Lines 157-158: either you explain which conditions you are referring to or remove this and state it later.
- Line 160: Replace “Following” by “Next”.
- Line 165: “within all others (it is…”.
- Line 177: remove the first “model”.
- Line 186: “if some males have a different value than the other matings”.
- Line 191: “relaxing the first”.
- Line 193: “produce an assortative mating pattern”.
- Line 194: “involves mate choice, which”.
- Line 202: “models”.
- Line 205: “there should be no”.
- Line 215: “all mate types mate at an equal rate”.
- Line 228: “there can be as much”.
- Line 246: “all femate types mate at an equal rate”.
- Line 267-270: I found this section pretty unclear, can you reformulate?
- Line 286: remove “Let”.
- Line 312: “produces”.
- Line 377: “to distinguish”.
- Line 423-424: It would be nice to add a few sentences to explain what you’ll be doing in this section.
- Line 424: “applied to describe”.
- Line 425: “to perform”.
- Line 461: “this indicates”.
- Line 489: the average of what?
- Line 510: “because of”.
- Line 566: please explain “likewise size-assortative mating…”.
- Line 581: “possibly”.
- Line 619: “from these models”.
- Line 623: “SU males do not discriminate between female ecotypes”.
- Line 783: “consists in building”.