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Modelling the Evolution and Consequences of Mate Choice Modelling the Evolution and Consequences of Mate Choice Samuel John Tazzyman October 2010 A thesis submitted to University College London for the Degree of Doctor of Philosophy CoMPLEX UCL Physics Building Gower Street London, WC1E 6BT I, Samuel John Tazzyman, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. 1 for Katie, with my love 2 Acknowledgements Thanks to my supervisors, Andrew Pomiankowski and Rob Seymour, for their guidance, ideas, and inspi- ration. Thanks also to Yoh Iwasa for supervising me during my time in Fukuoka, and to Duncan Greig and Tom Pizzari for help with chapters 2 and 6 respectively. Thanks to all the people in CoMPLEX who have provided assistance, enlightenment, and entertainment, especially Trevor, Alex, Lisa, Mike, Tom, Ben, Ed, James, Dot, Charles, and Lorette, who have had to put up with me more than many. Also thanks to my real non-science friends for keeping me sane. Finally thanks to Mum, Dad and Joe, for their love and support. 3 Abstract This thesis considers the evolution and the consequences of mate choice across a variety of taxa, using game theoretic, population genetic, and quantitative genetic modelling techniques. Part I is about the evolution of mate choice. In chapter 2, a population genetic model shows that mate choice is even beneficial in self-fertilising species such as Saccharomyces yeast. In chapter 3, a game theoretic model shows that female choice will be strongly dependent upon whether the benefits are fixed, so that females receive the same fitness boost from a mating with a given male regardless of how many matings that male has, or dilutable, where the more females a male mates with, the lower the expected benefit to each. This leads to the prediction that mating skew should be higher in species in which the benefits of mate choice are hypothesised to be due to good genes. Part II is about the consequences of mate choice. The theoretical prediction from chapter 3 is borne out by a literature review of studies of wild populations of birds in chapter 4. In chapter 5, a quantitative genetic model about poison-dart frogs suggests that sexual selection can speed up the effect of random genetic drift. This may be of more general importance, further widening the evolutionary impact of sexual selection. Fi- nally, in chapter 6, a game theoretic model of sperm competition shows that pre-copulatory mate choice can also have evolutionary effects upon post-copulatory behaviour, affecting the optimal ejaculate expenditure of males. Overall, mate choice is shown to be an important evolutionary force, with wide-ranging ramifications across diverse taxa, and effects so varied as to include the evolution of sex, the genetic variation in species, speciation, and post-copulatory behaviour, amongst others. These effects can be effectively explored using mathematical modelling. 4 Contents 1 Introduction 12 1.1 Sex .............................................. 12 1.2 Sexes . 13 1.2.1 What is a sex? . 13 1.2.2 The number of sexes . 14 1.2.3 Differences between males and females . 15 1.2.4 The sex ratio . 18 1.3 Sexual selection . 19 1.3.1 Competition . 19 1.3.2 Choice . 21 1.3.3 Sexual conflict . 23 1.4 The reasons for mate choice . 24 1.4.1 Direct benefits . 24 1.4.2 Indirect benefits . 28 1.4.3 Sensory bias . 34 1.4.4 Which kind of reason? . 35 1.5 Evolutionary effects of mate choice . 40 1.5.1 Speciation . 40 1.5.2 Extinction . 41 1.6 Modelling mate choice . 43 1.6.1 Population genetics . 43 1.6.2 Quantitative genetics . 48 1.6.3 Evolutionary game theory models . 56 1.7 Thesis outline . 66 5 CONTENTS I The evolution of mate choice 68 2 Suppression of mutational load in Saccharomyces yeast 70 2.1 Background . 71 2.2 Model . 73 2.2.1 The yeast life cycle . 73 2.2.2 One locus . 75 2.2.3 Multiple loci . 77 2.3 Results . 78 2.3.1 One locus . 78 2.3.2 Multiple loci . 81 2.4 Discussion . 81 2.5 Appendix . 86 2.5.1 Calculation of number of timesteps before selective intratetrad mating strategy be- comes the best . 86 2.5.2 The mutational load of a colony decreases as p increases . 87 2.5.3 Details of numerical modelling . 87 3 Fixed and dilutable benefits of mate choice 88 3.1 Background . 88 3.2 Model . 90 3.2.1 Fixed benefits . 90 3.2.2 Dilutable benefits . 91 3.3 Results . 92 3.3.1 Fixed benefits . 92 3.3.2 Dilutable benefits . 94 3.4 Discussion . 96 3.5 Appendix . 99 3.5.1 Justification of dilutable benefit function formulation . 99 3.5.2 Proof of results for dilutable case . 100 II The consequences of mate choice 105 4 Comparative study of mating skew in bird populations 107 6 CONTENTS 4.1 Background . 107 4.2 Methods . 108 4.2.1 Data retrieval . 108 4.2.2 Mating skew measurement . 112 4.3 Results . 114 4.3.1 Comparison of λ-values . 114 4.3.2 Comparison of Iδ-values . 115 4.4 Discussion . 116 4.5 Appendix . 118 5 Colour polymorphism in Oophaga pumilio 121 5.1 Background . 121 5.2 Model . 124 5.2.1 O. pumilio model . 124 5.2.2 Control species model . 131 5.3 Results . 132 5.3.1 Comparison of variances . 132 5.3.2 Coupled Drift . 132 5.4 Discussion . 135 5.5 Appendix . 140 5.5.1 Approximation of B ................................. 140 5.5.2 Derivations of var [∆d x¯], var ∆dy¯ , cov ∆d x¯; ∆dy¯ . 141 5.5.3 Use of ΩA[t] and ΩB[t]................................ 142 5.5.4 Recursion solution forx ¯t ............................... 143 5.5.5 Calculation of var[x ¯t]................................. 144 6 Differential ejaculate expenditure 145 6.1 Background . 145 6.2 Model . 147 6.2.1 Variation in Resources and Costs . 148 6.2.2 Risk and Intensity of Competition . 149 6.3 Results . 149 6.3.1 Analysis . 149 7 CONTENTS 6.3.2 Numerical Simulations . 151 6.4 Discussion . 155 6.5 Appendix . ..
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