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Modeling the Evolution of Visual Sexual Signaling, Receptivity, and Sexual Signal Reliability Among Female Primates

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Modeling the Evolution of Visual Sexual Signaling, Receptivity, and Sexual Signal Reliability Among Female Primates University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 8-2017 Modeling the evolution of visual sexual signaling, receptivity, and sexual signal reliability among female primates Kelly Anne Rooker University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Recommended Citation Rooker, Kelly Anne, "Modeling the evolution of visual sexual signaling, receptivity, and sexual signal reliability among female primates. " PhD diss., University of Tennessee, 2017. https://trace.tennessee.edu/utk_graddiss/4710 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Kelly Anne Rooker entitled "Modeling the evolution of visual sexual signaling, receptivity, and sexual signal reliability among female primates." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Mathematics. Sergey Gavrilets, Major Professor We have read this dissertation and recommend its acceptance: Judy Day, Timothy Schulze, Yu-Ting Chen, Lowell Gaertner Accepted for the Council: Dixie L. Thompson Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Modeling the evolution of visual sexual signaling, receptivity, and sexual signal reliability among female primates A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Kelly Anne Rooker August 2017 c by Kelly Rooker, 2017 All Rights Reserved. ii To Terry, my future husband and forever life partner iii Acknowledgments First and foremost, this dissertation would not have been possible without the help and guidance of my doctoral advisor Sergey Gavrilets. Ever the hardened mathematician, I learned more from him than I ever thought possible. My research would not be as impactful in the scientific community were it not for his keen mathematical eye, and I will always be the first to admit that. One enters his lab a student and leaves a researcher; I was no different. Despite always having challenging and demanding expectations for me, I would not be the mathematician I am today without him. I also wish to thank my other committee members: Yu-Ting Chen, Judy Day, Lowell Gaertner, and Timothy Schulze for helping me make this dissertation into what it is. In addition, I wish to recognize all the faculty members I have known at UTK who each helped me in their own way. In particular, I thank Lou Gross, for always being a cheery face in the hall and always caring about my professional development. I also thank NIMBioS and all its many visitors, for providing me an enriching mathematical biology environment during my entire time at UTK. I wish to thank my colleagues in the UTK Math Department for helping to keep me sane: namely Joe Daws, Khoa Dinh, Betsy Heines, Josh Lipsmeyer, Nate Pollesch, and Eddie Tu, among many others. My multiple labmates over the years not only kept me sane and were my friends, but they also helped to shape my research. These include Jeremy Beaulieu, Caroline Farrior, Sarah Flanagan, Mauricio Gonzalez-Forero, Liz Hobson, Ivan Juric, Mahendra Shrestha, Sergei Tarasov, and - most notably - Jeremy Auerbach, Vicken Hillis, and Matt Zefferman. I also wish to thank RAND Corporation and the U.S. Department of Defense for allowing me to intern with each and learn what industry mathematicians do. In particular, I thank my two mentors at each, Isaac Porche and Bill Hensley, for showing me both true leadership and how to be technically gifted while still having great people skills. Finally, I was supported throughout graduate school by research fellowships, first SCALE-IT (an NSF IGERT program) and then an NSF Graduate Research Fellowship. My Ph.D. would not have been possible without these, and I am forever grateful for having received them. All numerical simulations presented here were run on the Volos computer cluster in the Gavrilets lab (NIH grant GM56693); my work would have taken some years longer without the help of this cluster. iv Abstract Communication between individuals of a species happens in myriad ways, especially among pri- mates. Not only are verbal cues important, visual and behavioral cues can be just as important as well. Two non-verbal characteristics of the estrous period in many primate species are visual signs of ovulation and sexual receptivity. Visual signs of ovulation take the form of bright colorations and/or sexual swellings around the female's genital region on/around her time of ovulation. Dif- ferent primate species also have varying lengths of receptivity, that is, willingness of a female to accept a male and permit copulation. In some species, this length of receptivity is equal to the length of time the female has visual ovulation signs present, while in other species such lengths can be much shorter or longer. Species will also vary in the amount of reliability in such signals, i.e. how closely do a female's visible ovulation signs and period of receptivity line up with her period of fertility? In this dissertation, I use mathematical modeling techniques to help answer each of these research questions relating to the evolution of primate non-verbal sexual communication. In Chapter 1, I show how certain ecological factors, such as increased group size and/or the presence of infanticide, can increase visual ovulation signaling among female primates. In Chapter 2, I show female continuous receptivity and concealed ovulation to be correlated, and how only in groups with visible ovulation signs present would one expect to find a relatively short length of time when the female will be receptive to mating. In Chapter 3, I investigate the evolution of sexual signal reliability, evaluating under what conditions will a female's visual sexual signaling line up perfectly (or not) with her peak time of fertility. Finally, in Chapter 4, I outline a future, related biological problem (the evolution of long-term pair-bonding) which could be addressed with many of the same mathematical methods/models used in the earlier chapters. Together, the results presented in this dissertation use mathematics to give new insight into primate evolution and help to resolve old mysteries surrounding primate non-verbal sexual communication. v Table of Contents Introduction 1 0.1 Background . .1 0.2 The Estrous Cycle . .1 0.3 Phylogeny . .2 0.4 Hypotheses for the Evolution of Concealed Ovulation . .5 0.4.1 To Support Food-for-Sex . .7 0.4.2 Protection against Infanticide . .8 0.4.3 To Reduce Crude Female Contraception . .9 0.4.4 To Escape Mate-Guarding . 10 0.4.5 To Cement the Pair-Bond . 11 0.4.6 To Reduce Male-Male Competition . 12 0.5 Concealed Ovulation in Human Females . 13 0.6 Methods . 14 0.6.1 Evolutionary Game Theory . 14 0.6.2 Adaptive Dynamics . 15 0.6.3 Agent-Based Modeling . 18 0.6.4 Overview of the Genetic Algorithm Used . 19 0.6.5 Overview of all Parameters Used . 21 0.7 Female Sexual Signals, Receptivity, and Signal Reliability . 23 0.8 Paternity Concentration vs. Paternity Confusion . 24 0.9 Dissertation Outline . 26 Chapter I: On the evolution of visual female sexual signaling 28 0 Abstract 30 vi 1 Introduction 31 1.1 Background . 31 1.2 Costs and Benefits of Visual Ovulation Signs . 31 1.3 Infanticide . 33 1.4 Reliable Indicator and Graded Signal Hypotheses . 33 1.5 Research Questions . 35 2 Introduction to the Model 36 2.1 Model Set-Up . 36 2.2 The Female Cycle . 37 2.3 Male-Female Mating . 38 2.4 Infanticide . 38 3 Methods 39 3.1 General Model . 39 3.2 Modeling Infanticide . 41 3.3 Simulations . 41 4 Results 42 4.1 Without Infanticide . 42 4.2 With Infanticide . 44 4.3 Effects of Reproductive Stochasticity . 44 5 Discussion 46 5.1 Overview . 46 5.2 Comparison to Empirical Data . 46 5.3 Conclusion . 48 6 Acknowledgments 51 vii 7 Supplementary Information: Analytical Results 51 7.1 The Two-Male Infanticide Model . 51 7.1.1 Analytical Model Set-Up . 51 7.1.2 Invasion Female Fitness . 52 7.1.3 Invasion Fitness Gradient . 52 7.1.4 Considering the Case τ =1............................ 53 7.1.5 Considering the Case τ =2............................ 54 8 Supplementary Information: Numerical Results 56 8.1 Further Details of the Model . 56 8.1.1 The Female Cycle . 56 8.1.2 Determining Male-Female Mate Pairs . 57 8.1.3 Calculating Probabilities of Paternity . 57 8.1.4 Infanticide . 57 8.1.5 Female Fitness Functions . 59 8.2 List of All Parameters . 59 8.3 Effects of All Parameters . 61 8.4 Empirical Data . 67 8.4.1 Statistical Tests . 67 8.4.2 Raw Data . 67 Chapter II: On the evolution of female sexual receptivity 73 0 Abstract 75 1 Introduction 76 1.1 Definitions . 76 1.2 Receptivity in Non-Primate Mammals . 77 1.3 Variation in Receptivity among Primates . 78 1.4 Other Aspects of Receptivity . 78 viii 1.5 Female Competition for Preferred Mates . 79 1.6 Infanticide . 79 1.7 Research Questions . 81 2 Introduction to the Model 81 2.1 Model Set-Up . 81 2.2 The Female Cycle . 82 2.3 Male-Female Mating . 83 2.4 Infanticide . 84 3 Methods 85 3.1 General Model .
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