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Computational Models for the Study of Sexual Selection Dynamics

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Computational Models for the Study of Sexual Selection Dynamics UNIVERSIDADE FEDERAL DO RIO GRANDE DO SUL INSTITUTO DE INFORMÁTICA CURSO DE BACHARELADO EM CIÊNCIA DA COMPUTAÇÃO MARCELO DE OLIVEIRA ROSA PRATES Computational models for the study of sexual selection dynamics Monograph presented in partial fulfillment of the requirements for the degree of Bachelor of Computer Science Prof. Dr. Luis Lamb Advisor Porto Alegre, July 28th, 2014 CIP – CATALOGING-IN-PUBLICATION Marcelo de Oliveira Rosa Prates, Computational models for the study of sexual selection dy- namics / Marcelo de Oliveira Rosa Prates. – Porto Alegre: Graduação em Ciência da Computação da UFRGS, 2014. 87 f.: il. Monograph – Universidade Federal do Rio Grande do Sul. Curso de Bacharelado em Ciência da Computação, Porto Alegre, BR–RS, 2014. Advisor: Luis Lamb. 1. Keyword 1. 2. Keyword 2. 3. Keyword 3. 4. Keyword 4. 5. Keyword 5. I. Lamb, Luis. II. Título. UNIVERSIDADE FEDERAL DO RIO GRANDE DO SUL Reitor: Prof. Carlos Alexandre Netto Vice-Reitor: Prof. Rui Vicente Oppermann Pró-Reitor de Graduação: Prof. Sérgio Roberto Kieling Franco Diretor do Instituto de Informática: Prof. Luís da Cunha Lamb Coordenador do CIC: Prof. Raul Fernando Weber Bibliotecário-chefe do Instituto de Informática: Beatriz Regina Bastos Haro Draft 1.0 June 19, 2015 morprates @inf.ufrgs.br http://inf.ufrgs.br/∼morprates “Because the history of evolution is that life escapes all barriers. Life breaks free. Life expands to new territories. Painfully, perhaps even dangerously. But life finds a way.” - Michael Crichton, Jurassic Park ACKNOWLEDGMENTS I owe a great deal to my teacher and supervisor, Luís Lamb, who not only provided help and made it possible for this monograph to take its actual form, but also persuaded me to venture into research and gave me freedom to work on projects of my own interest in all these years as a scientific initiation scholarship holder. Suffice it to say that my professional and academic lives would have taken strikingly different paths if untouched by the teachings of my high school mathematics teacher, Marcelo Cóser. I value deeply his power of embedding profound and varied academic interests in a student that had none, and thank him for enabling me, through them, to study Computer Science. The structure of this work is partially due to Thiago Becker and Jonata Pastro, who accompanied me developing a research project on computational models for evolutionary dynamics on the INF-UFRGS course of Topics in Theoretical Informatics. Their experi- ence, intellect and motivation were responsible for a lot of ideas about how to organize the research I will detail in the following chapters. I would like to thank Eduardo Ferreira, Guilherme Leon and Lucas Tabajara for ac- companying me since my first day on my graduation in Computer Science. Their interests and companionship were certainly fundamental to the shaping of my academic profile. I would like to thank specifically Lucas Tabajara for accompanying me since 2012 as a fellow researcher, scientific initiation scholarship holder and for being the confidant of a substantial portion of my mathematical and scientific ideas. I would like to thank Marina Chaves and Wolnei Prates for our shared interests about evolution, Darwinism and particularly the work I developed in this monograph. I value sorely their role in persuading me, in my most doubtful moments, that my research is not only valid, but interesting. CONTENTS CONTENTS . 7 LIST OF FIGURES . 11 LIST OF TABLES . 13 ABSTRACT . 13 RESUMO . 15 1 INTRODUCTION . 19 1.1 Motivation .................................. 19 1.2 Goals ...................................... 20 1.2.1 Kin selection, Homosexuality and the gay uncle hypothesis . 21 1.2.2 Sexual selection, Fisherian runaway and the Sexy son hypothesis . 22 1.3 Contribution ................................. 23 1.4 Structure of this work ............................ 23 2 CONCEPTUAL BASIS . 25 2.1 Evolutionary theory ............................. 25 2.1.1 Natural selection . 25 2.1.2 Sexual selection . 25 2.1.3 Fisherian runaway . 26 2.2 Game theory ................................. 27 2.2.1 Normal-form games . 28 2.2.2 Types of games . 29 2.2.3 Solution concepts for game theory . 30 2.3 Evolutionary game theory .......................... 31 2.3.1 Replicator equation . 32 2.3.2 Evolutionarily stable strategy . 32 2.3.3 Inclusive fitness . 33 2.3.4 Hamilton’s rule . 34 2.3.5 The handicap principle . 34 2.4 Evolutionary computation .......................... 35 2.4.1 Evolutionary algorithms . 35 2.4.2 Genetic algorithms . 35 2.4.3 Selection in genetic algorithms . 36 2.4.4 Crossover in genetic algorithms . 39 2.4.5 Mutation in genetic algorithms . 41 2.4.6 Terminating condition in genetic algorithms . 43 3 METHODOLOGY . 45 3.1 Homosexuality and the gay uncle hypothesis ................ 45 3.1.1 Genotype structure . 46 3.1.2 Selection . 46 3.1.3 Reproduction . 46 3.1.4 Mutation . 47 3.1.5 Sexual orientation determination . 47 3.1.6 Nurture dynamics . 47 3.1.7 Kin selection dynamics . 47 3.2 Sexual selection, Fisherian runaway and the Sexy son hypothesis .... 47 3.2.1 Genotype structure . 48 3.2.2 Selection . 48 3.2.3 Mutation . 48 3.2.4 Definition of the sexual selection function . 48 4 EXPERIMENTAL EVALUATION . 51 4.1 Kin selection, Homosexuality and the Gay uncle hypothesis ....... 51 4.1.1 No kin selection . 51 4.1.2 Kin selection . 54 4.2 Unalike selection ............................... 58 4.3 Sexual selection, Fisherian runaway and the Sexy son hypothesis .... 63 4.3.1 Fitness landscapes . 64 4.3.2 Plain natural selection . 66 4.3.3 Gaussian sexual selection with fixed standard deviation . 68 4.3.4 Gaussian sexual selection with variable standard deviation . 71 4.3.5 Polynomial sexual selection . 74 4.4 Final remarks ................................. 77 4.4.1 Kin selection, Homosexuality and the Gay uncle hypothesis . 77 4.4.2 Unalike selection . 77 4.4.3 Sexual selection, Fisherian runaway and the Sexy son hypothesis . 77 5 CONCLUSIONS AND FUTURE WORK . 79 5.1 Future Work ................................. 80 REFERENCES . 81 APPENDICES . 85 .1 Fractals, multifractals and fractal dimensions ............... 85 LIST OF FIGURES 4.1 Pop. size: 1000; Mate pool size: 100; K = 0:0 ............ 52 4.2 Pop. size: 1000; Mate pool size: 100; K = 0:0 ............ 53 4.3 Pop. size: 1000; Mate pool size: 100; K = 0:1 ............ 55 4.4 All curves start at x = 0; y = 250. Pop. size: 1000; Mate pool size: x 100; K 2 [ 10 j x 2 N; 1 ≤ x ≤ 10] .................. 56 4.5 Fitting of the data points of the curve n(K) as n(K) ≈ −0:085 + 0:583 log K................................ 57 4.6 Evolution of natural selection (orange) vs homosexuality (blue): the average genotypes for both natural selection and homosexuality are plotted in a bi-dimensional grid. Pop. size: 1000; Mate pool size: 100; K = 0:01 ............................. 59 4.7 Measurement of the evolutionary path length N with respect to the 1 ruler size r . Pop. size: 1000; Mate pool size: 100; K = 0:01 ..... 60 4.8 Evolution of the measurement of the homosexuality evolutionary path length N for varying scales r. Pop. size: 1000; Mate pool size: 100; K = 0:01 ................................ 61 4.9 Pop. size: 1000; Mate pool size: 100; K = 0:01 ........... 63 4.10 Bi-dimensional Gaussian function seen from different angles . 64 4.11 Bi-dimensional Ackley’s function seen from different angles . 65 4.12 Bi-dimensional, modified Ackley’s function seen from different angles 66 4.13 Fitness evolution of natural selection (red) vs sexual selection (green). Pop. size: 1000; Mate pool size: 100; Without sexual selection. 67 4.14 Evolution of natural selection (orange) vs sexual selection (blue): the average genotypes for both natural selection and sexual selection are plotted in a bi-dimensional grid. Pop. size: 1000; Mate pool size: 100; Gaussian landscape; Without sexual selection. 68 4.15 Fitness evolution of natural selection (red) vs sexual selection (green). Pop. size: 1000; Mate pool size: 100; Gaussian landscape; Gaussian sexual selection with fixed standard deviation. 70 4.16 Fitness evolution of natural selection (red) vs sexual selection (green). Pop. size: 1000; Mate pool size: 100; modified Ackley landscape; Gaussian sexual selection with fixed standard deviation. 71 4.17 Fitness evolution of natural selection (red) vs sexual selection (green). Pop. size: 1000; Mate pool size: 100; Gaussian landscape; Gaussian sexual selection with variable standard deviation. 73 4.18 Evolution of natural selection (orange) vs sexual selection (blue): the average genotypes for both natural selection and sexual selection are plotted in a bi-dimensional grid. Pop. size: 1000; Mate pool size: 100; Gaussian landscape; Gaussian sexual selection with variable standard deviation. 74 4.19 Fitness evolution of natural selection (red) vs sexual selection (green). Pop. size: 1000; Mate pool size: 100; Gaussian landscape; Polyno- mial sexual selection with varying degrees. 75 4.20 Fitness evolution of natural selection (red) vs sexual selection (green). Pop. size: 1000; Mate pool size: 100; Modified Ackley’s landscape; Polynomial sexual selection with varying degrees. 76 1 Measurement of the natural selection evolutionary path length N with 1 respect to the ruler size r . Pop. size: 1000; Mate pool size: 100; K = 0:01 ................................ 86 LIST OF TABLES 2.1 The prisoner’s dilemma in normal form . 28 2.2 An example of an asymmetric game . 29 2.3 The prisoner’s dilemma is an example of a non-zero-sum game. In this table we have in each cell the added payoffs of the combination of strategies associated to it, always different from 0. 30 2.4 The driving game: an example of a game with multiple Nash equilibria 31 2.5 An example of game in which not all Nash equilibria are evolution- arily stable strategies . 33 4.1 Fitting of the curves for natural selection (See Figure 4.4) with hy- pothesis D(t) ≈ Ctn where t is the number of iterations and D(t) the distance to the origin on iteration t..................
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