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Thesis Rests with Its Author University of Bath PHD Mathematical models for the coexistence of sexual and asexual conspecifics Carrillo Medrano, Claudia del Carmen Award date: 2002 Awarding institution: University of Bath Link to publication Alternative formats If you require this document in an alternative format, please contact: [email protected] General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 09. Oct. 2021 Mathematical Models for the Coexistence of Sexual and Asexual Conspecifics Submitted by Claudia del Carmen Carrillo Medrano for the degree of Doctor of Philosophy of the University of Bath COPYRIGHT Attention is drawn to the fact that copyright of this thesis rests with its author. This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and no information derived from it may be published without the prior written consent of the author. This thesis may be made available for consultation within the University library and may be photocopied or lent to other libraries for the purposes of consultation. Signature of Author UMI Number: U601427 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI U601427 Published by ProQuest LLC 2013. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 paMBEeamvwm. •« - a f' <» J *.v-'" f. a 0*'**'. Y.n r I 'i * • * M 2 8 MAY 2 Abstract Eukaryotic sexual reproduction involves meiosis and outcrossing, processes by which haploid, genetically non-uniform nuclei fuse to produce the nucleus of a zygote. Thus, sexually reproducing organisms pass only half of their genes to their offspring. Asexual reproduction, on the other hand, may imply the full replication of the maternal genotype. There is an obvious two-fold cost of sex in the face of asexual reproduction. In the event that asexual reproduction evolved from sexual reproduction — after a mutation, for example — it would be expected to quickly displace its predecessor. However, sex remains the most common re­ productive strategy. Moreover, sexual and asexual forms of the same species coexist, even in those cases where the latter are clearly descended from their sex­ ual counterparts. These observations constitute what has been called the queen of evolutionary questions: why the evolution and maintenance of sex. This problem has attracted the attention of biologists and mathematicians alike. Traditional mathematical models have repeatedly shown that in a population where both forms of reproduction are present only one can prevail. Yet, the coexistence of sexual and asexual relatives is common in nature. Thus, mathematical models have failed to reflect the real world in this case (the exception being those where external agents, such as parasites, are invoked). In this thesis, a revision of the ways in which this problem has been modelled is advocated for. Namely, the introduction of some spatial aspects of the ecology of mixed populations will be given vast consideration. This work is a collection of mainly spatial models, within the context of populations of hermaphrodite flowering plants, that explore the coexistence of sexual and asexual conspecifics. Acknowledgements I cordially thank my supervisors, Dr. Nicholas F. Britton and Dr. Michael Mogie for presenting me with a very interesting problem in evolutionary biology, the coexistence of sexual and asexual forms within a species, and their guidance throughout the development of this project. Helpful advice was given by my examiners, Prof. Mark Chaplain and Dr. Jane White, during the defence of this thesis. All their observations greatly improved this work and I hope I did incorporate them correctly in this final version. I am grateful to Ignacio Barradas, Kirill Cherednichenko, Andreas Deutsch, Paul Fife, Pierre-Henri Gouyon, Laurence Hurst, Yoh Iwasa, Matthew Keeling, Philip Maini, Faustino Sanchez, Minus van Baalen and Franz Weissing for several helpful discussions at different stages of my studies. Thanks also to Jorg Berns-Miiller, Kirill Cherednichenko (again), David Es­ parza, Adam Mawby, Rob Scheichl and Fas Yousaf for their help with l^jXnicalities and to the computing support team: Mark Willis, Darrell Johnson and Adam Prowse. To Ruth Fuentes and Ramses Mena for helpful discussions on random numbers and their generators. I would also like to give my thanks to the people who helped me organise my academic life at Bath: Jill Parker, Mary Baines, Dawn Beckett and Sarah Lewis. The Council for Science and Technology in Mexico, CONACYT, has been the main source of financial support during the years I have studied and lived in the United Kingdom, providing money for overseas-student tuition fees and living expenses. Another source of important financial support for attendance to academic meetings, interlibrary loans, photocopies and stationery was the De­ partment of Mathematical Sciences at the University of Bath. I would also like to acknowledge the partial financial support of the Mexican Mathematical Society, the Society for Mathematical Biology, the European Society for Theoretical and Mathematical Biology, the group of Theoretical Biology in Groningen (NL) and the Isaac Newton Institute in Cambridge (UK) for attendance to conferences, seminars and workshops, which were a good opportunity to present this research as it progressed and make academic contacts. Ala UNAM Contents Introduction 1 1 The Biological Context 5 1.1 A common language ......................................................................... 5 1.2 Of sex and queens ................................................................................ 7 1.3 What this work is a b o u t................................................................... 19 1.4 Modelling assum ptions ...................................................................... 24 1.4.1 Simultaneous hermaphroditism ............................................ 24 1.4.2 Mating regime ........................................................................... 25 1.4.3 Dispersal.................................................................................... 26 1.4.4 Only one locus and two alleles ............................................... 26 1.4.5 Population s i z e ........................................................................ 28 1.4.6 Dealing with tim e ..................................................................... 28 1.4.7 The viability of sexuals and a sex u a ls ................................... 29 1.4.8 Male function in asexuals ...................................................... 30 2 Temporal Dynamics of Populations Mixed for Reproductive Mode: Sexuality vs. Asexuality 32 2.1 Assumptions of the model and notation ............................................ 33 2.2 Equations of the temporal dynamics model ...................................... 34 2.3 Intuitive approach to the analysis of the m odel ............................... 38 2.4 Conclusions ......................................................................................... 46 Appendix: A rigorous justification of the dynamics argum ent ............... 47 3 Sexuality vs. Asexuality: Implicit Introduction of Space with a Patch-occupancy Model 52 3.1 The patch-occupancy m odel ............................................................. 55 3.1.1 Assumptions of the model and notation ................................ 55 3.1.2 Mathematical framework......................................................... 56 3.1.3 Mathematical analysis of the model with a first-order ap­ proximation to the Poisson colonisation p ro c e ss ............... 57 3.1.4 Mathematical analysis of the original model with Poisson colonisation process ................................................................. 64 3.1.5 Study of the parameter s p a c e .............................................. 75 3.2 Inclusion of male function in asexuals .............................................. 79 3.3 Discussion ............................................................................................ 84 A p p en d ix ...................................................................................................... 87 4 Local Ecological Interactions in a Cellular Automaton Model 89 4.1 The model ...........................................................................................
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