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Modeling the Genetic Consequences of Mutualism on Communities University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 5-2013 Modeling the Genetic Consequences of Mutualism on Communities Carrie E. Eaton University of Tennessee - Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Ordinary Differential Equations and Applied Dynamics Commons Recommended Citation Eaton, Carrie E., "Modeling the Genetic Consequences of Mutualism on Communities. " PhD diss., University of Tennessee, 2013. https://trace.tennessee.edu/utk_graddiss/1714 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 Carrie E. Eaton entitled "Modeling the Genetic Consequences of Mutualism on Communities." 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 requirements 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: Suzanne M. Lenhart, Xia Chen, James A. Fordyce Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) University of Tennessee, Knoxville Trace: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 5-2013 Modeling the Genetic Consequences of Mutualism on Communities Carrie E. Eaton University of Tennessee - Knoxville, [email protected] 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 Carrie E. Eaton entitled "Modeling the Genetic Consequences of Mutualism on Communities." 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 requirements 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: Suzanne M. Lenhart, Xia Chen, James A. Fordyce Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official student records.) Modeling the Genetic Consequences of Mutualism on Communities A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Carrie E. Eaton May 2013 c by Carrie E. Eaton, 2013 All Rights Reserved. ii Dedication To my family iii Acknowledgments Thank you to my entire committee, Dr. Gavrilets, Dr. Lenhart, Dr. Fordyce and Dr. Chen for their support. I also thank all past and present members of the Gavrilets lab and Evolutionary Theory group for helpful feedback, and Aysegul Birand and Dr. Fordyce for giving comments on early manuscript versions. This work was supposed by NIH and NIH supplemental grants and an SREB Doctoral Scholars Award. iv Abstract Three models of coevolutionary dynamics between mutualistically interacting species are developed. The first is a three loci, haploid model describing a general plant- pollinator system, such as Greya moth and its host plant. In this case, the system will always collapse to a single plant type and pollinator type. In a community with an mutant plant type, it is possible for a host-switch to occur, governed by the initial relative abundance plant type and the pollinator choosiness. In addition, genetic diversity can be maintained if the pollinator has no differential host preference, only adaptation to a host. Next, this model is extended to the case of the fig-fig wasp system, implementing a more complex life cycle of overlapping generations due to asynchronous flowering populations. In the fig system, extensive hybridization due to asynchronous flowering can maintain genetic diversity for thousands of generations, when pollinator choosiness is high. Therefore, mutualism can lead to low confidence trees in phylogenetic reconstructions affecting discordance among plant and pollinator phylogenetic trees. Lastly, the consequences of host-switching and other speciation events on coevolving phylogenies are explored through stochastic numerical simulations. The goal is to determine to what extent cophylogeny should be expected between mutualistic partners and what features of mutualistic webs can be explained by mutualistic coevolution alone. v Contents 1 Introduction1 1.1 Mutualism and Coevolution.......................1 1.2 Mechanisms of Evolution.........................2 1.2.1 Mutation.............................2 1.2.2 Genetic drift............................3 1.2.3 Natural selection.........................3 1.2.4 Recombination and segregation.................4 1.2.5 Non-random mating.......................5 1.3 Consequences of Evolution........................5 1.3.1 Speciation.............................6 1.3.2 Coevolution............................6 1.4 Plant-Pollinator Coevolutionary Theory................8 2 Modeling a simple mutualistic system: Greya moth and its host 13 2.1 Greya Moth and its Host (H-GM) Model................ 13 2.1.1 Dynamics of insects........................ 14 2.1.2 Dynamics of plants........................ 16 2.1.3 Plant resource dependent model................. 17 2.1.4 Model without re-assortment................... 18 2.2 H-GM Model Analytic and Numerical Results............. 18 2.2.1 Assumptions............................ 18 vi 2.2.2 Analytical Methods........................ 20 2.2.3 H-GM model results....................... 20 2.2.4 Effect of parameters on H-GM model.............. 23 2.2.5 Approximation of H-GM model................. 29 2.3 H-GM Model Variations......................... 34 2.3.1 H-GM plant resource dependent model............. 34 2.3.2 H-GM plant resource dependent model without re-assortment 36 2.4 Discussion................................. 37 2.4.1 Discussion of the H-GM model................. 37 2.4.2 Discussion of the H-GM model variations............ 38 2.4.3 Conclusion............................. 38 3 Modeling the Fig-Fig Wasp Mutualism 40 3.1 Fig-fig Wasp Model............................ 41 3.1.1 Dynamics of insects........................ 41 3.1.2 Dynamics of fig trees....................... 43 3.2 Fig-Fig Wasp Model Results....................... 44 3.2.1 The effect of parameters in the F-FW model.......... 45 3.3 Discussion of Fig-Fig Wasp Model Results............... 53 3.4 Conclusion................................. 54 4 Effect of Mutualisms on Coevolving Phylogenies 55 4.1 Introduction................................ 55 4.2 Ecological Network Theory........................ 56 4.2.1 Properties of Mutualistic Networks............... 56 4.2.2 Mathematical Modeling of Mutualistic Networks........ 63 4.2.3 Cophylogeny: Coevolution and Phylogeny........... 66 4.3 Model Description............................ 68 4.3.1 Coevolution of mutualism trait................. 68 4.3.2 KLS Model............................ 68 vii 4.3.3 Kiester, Lande and Schemske Extension and Symmetric Fitness Modification............................ 71 4.4 Analysis.................................. 75 4.4.1 KLS Extension.......................... 76 4.4.2 SFC Model............................ 76 4.4.3 Equilibria............................. 77 4.5 Stochastic Simulation Models...................... 84 4.5.1 Connections Between Species.................. 84 4.5.2 Species Birth-death........................ 86 4.5.3 KLS Extension and Symmetric Fitness Model......... 87 4.5.4 Stochastic Asymmetric Coevolving Network Model...... 87 4.6 Numerical Results............................. 89 4.6.1 KLS Extension.......................... 89 4.6.2 SFC Model............................ 92 4.6.3 Stochastic Asymmetric Coevolving Network Model...... 94 4.6.4 Node Asymmetry......................... 100 4.6.5 Dependence asymmetry, nestedness and modularity...... 108 4.7 Discussion................................. 110 5 Summary and Future Directions 115 Bibliography 120 A 132 A.1 Analysis of Equilibria for H-GM Model................. 132 A.1.1 z = [1; 1; 1; 1], AB and C fixed, stable ........... 133 A.1.2 z = [−1; 1; −1; 1], Ab and C fixed, unstable ........ 134 A.1.3 z = [1; −1; −1; 1], aB and C fixed, unstable ........ 134 A.1.4 z = [−1; −1; −1; 1], ab and C fixed, unstable ....... 135 3+2 3+2 A.1.5 z = [− 4 ; 1; − 4 ; 1], biologically unrealistic ....... 135 viii 3+2 3+2 A.1.6 z = [− 4 ; −1; 4 ; 1], biologically unrealistic ....... 135 A.1.7 z = [1; 1; 1; 0], AB and c fixed, unstable .......... 136 A.1.8 z = [−1; 1; −1; 0], Ab and c fixed, unstable ........ 136 A.1.9 z = [1; −1; −1; 0], aB and c fixed, unstable ......... 137 A.1.10 z = [−1; −1; −1; 0], ab and c fixed, stable ......... 137 3+2 3+2 A.1.11 z = [ 4 ; 1; 4 ; 0], biologically unrealistic ......... 138 3+2 3+2 A.1.12 z = [ 4 ; −1; − 4 ; 0], biologically unrealistic ....... 138 A.1.13 z = [0; 1; 0; 1=2], half Ab, half AB, half
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