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Ecological and Evolutionary Implications of Shape During Population Expansion

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Ecological and Evolutionary Implications of Shape During Population Expansion ECOLOGICAL AND EVOLUTIONARY IMPLICATIONS OF SHAPE DURING POPULATION EXPANSION Submitted by Christopher Lee Coles to the University of Exeter as a thesis for the degree of Doctor of Philosophy in Biological Sciences January 2015 This thesis is available for library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. I certify that all material in this thesis which is not my own work has been identified and that no material has previously been submitted and approved for the award of a degree by this or any other University. Signature: ................................... ~ 1 ~ In loving memory of Laura Joan Coles ~ 2 ~ Abstract The spatial spread of populations is one of the most visible and fundamental processes in population and community ecology. Due to the potential negative impacts of spatial spread of invasive populations, there has been intensive research into understanding the drivers of ecological spread, predicting spatial dynamics, and finding management strategies that best constrain or control population expansion. However, understanding the spread of populations has proved to be a formidable task and our ability to accurately predict the spread of these populations has to date been limited. Microbial populations, during their spread across agar plate environments, can exhibit a wide array of spatial patterns, ranging from relatively circular patterns to highly irregular, fractal-like patterns. Work analysing these patterns of spread has mainly focused on the underlying mechanistic processes responsible for these patterns, with relatively little investigation into the ecological and evolutionary drivers of these patterns. With the increased recognition of the links between microbial and macrobial species, it is possible that many of the ecological/evolutionary mechanisms responsible for these patterns of spread at a microbial level extrapolate to the spatial spread of populations in general. Through an interdisciplinary approach, combining empirical, computational and analytical methods, the principal aim of this thesis was to investigate the ecological and evolutionary basis of microbial spatial dynamics. The first section of this thesis utilises the Pseudomonas microbial model system to show that the rate of microbial spatial spread across agar plate surfaces is affected by both intrinsic and extrinsic factors, thereby causing the exhibited rates of spread to deviate from the predictions made by the classical models in spatial ecology. We then show the spatial dynamics of microbial spread depends on important environmental factors, specifically environmental viscosity and food availability and that these spatial dynamics (particularly the shape of spread) has conflicting impacts on individual- and group-level fitness. From this, we used a geometric framework representing the frontier of a population, combined with an individual based model, to illustrate how individual-level competition along the leading edge of the population, driven by geometric factors and combined with simple life-history rules, can lead to patterns of population spread reminiscent of those produced by natural biofilms. The thesis finishes by establishing that the ~ 3 ~ spatial pattern of spread is not seemingly amenable to artificial selection, although based on other results in this thesis, we believe it remains likely that the patterns of spatial spread and the strategies responsible for them have evolved over time and will continue to evolve. Combined, the results of this thesis show that the array of evolutionary factors not accounted for by the simple ecological models used to help manage invasive species will often cause these models to fail when attempting to accurately predict spatial spread. ~ 4 ~ Acknowledgements First, I would like to thank my supervisors Dave and Stuart for their unwavering support and guidance throughout the course of my PhD. Stuart first introduced me to mathematical ecology in my undergraduate degree and had enough confidence in me to recommend me for the PhD. Dave took me on and helped mould me from a mathematician into a hybrid mathematician/ecologist. Their support has managed to keep my spirits up, especially when I was my lowest. Without their enthusiasm, this thesis would surely have faltered and for that, I am deeply indebted. I have made many friends during my time in Falmouth. In particular, I would like to thank Dom and Lou, who were great housemates and helped fuel a MasterChef addiction; Jenni and Neil, for their invitations to the pub and Barry Pepper/Rock films. I would also like to mention Katy and Sally for their support during the years. Further thanks must go to my friends from further afield. To Rich and Francesca, thanks for the tea, biscuits and general good company. Donna and Keith, thanks for letting me be your ‘adopted son’, you’ve helped so much over these past few years and your invitations to spends Christmases at yours have been a treat. It has been great to meet the Vinecombe clan! May there be many more nights of Trivial Pursuit and Uno! From my Undergrad days, Jason you have been great over the years, distracting me from my thesis when I have almost certainly needed it. Mark and Sam, our NFL talk should be on the radio! Of course, my thanks also go to my Dad and Theresa, both of whom have been influential on this thesis. I am happy that our bond has been repaired over the past few years and I hope it will continue to remain strong. Last of all, I would like to thank my Mum, to whom this thesis is dedicated. To lose you has hurt more than words can say, but I am so fortunate you were my mum. Your constant love and support carried me through to heights I do not think anyone ever expected. I am so sorry you could not be here to see it! ~ 5 ~ Contents Chapter 1 General Introduction and Literature Review: The 14 spread of species – Why is the rate of spread not always constant? Chapter 2 The spatial dynamics of biological invasions: when and 61 why do model systems defy model predictions? Chapter 3 How does food and environmental viscosity affect the 95 pattern of invasive microbial spread Chapter 4 How does the geometry of the microbial colony affect 11 2 the multi-level selection of social behaviour? Chapter 5 Games with frontiers – Part 1: Competition intensifies 13 9 as invasion waves expand Chapter 6 Games with frontiers – Part 2: Dispersal games along 15 1 an invasion front Chapter 7 Games with frontiers – Part 3: An Individual Based 17 8 Modelling Approach Chapter 8 Getting into shape: Can the shape of spatial spread be 21 9 selected for? Chapter 9 General discussion 24 1 Appendix A Image analysis protocol used in Chapter 2 26 4 Appendix B Sensitivity analysis of numerical model used in Chapter 26 6 4 Appendix C Calculating the overlap between two circles 271 Appendix D Calculating the overlap between three circles 27 6 Appendix E Calculate the asymptotic fitness of individuals along 281 edge of a circular population Appendix F Proof of values in table 6.2 28 7 Appendix G Collision detection algorithm used in IBM in Chapter 7 292 Appendix H Sensitivity analysis of IBM model used in Chapter 7 294 Appendix I Classification algorithm/criteria used in Chapter 7 301 References 305 ~ 6 ~ List of tables and figures Chapter 1 Figure 1.1 The three phases during the spatial spread of a population 19 Figure 1. 2 The three classifications for the rate of spread of a species 20 Figure 1. 3 An illustration of stratified diffusion 23 Figure 1. 4 The predicted propagation of a substance through a one- 31 dimensional environment according to Fisher’s equation Figure 1. 5 Gaussian and fat-tailed dispersal kernels 34 Figure 1.6 Pseudomonas aeruginosa grown on three different agar 51 plates containing KB agar Figure 1.7 The urban spread of London between the 17 th and 20 th 53 century Figure 1.8 The growth of the bacterium Escherichia coli and the 55 predictive results of reaction-diffusion models Figure 1.9 The growth of the bacterium Paenibacillus dendritiformis 56 and the predictive results of reaction-diffusion models -------------------------------------------------------------------------------- Table 1.1 The four types of social behaviour defined by Hamilton 45 -------------------------------------------------------------------------------- Chapter 2 Figure 2.1 The radial range of muskrat spread increases linearly with 63 time during its invasion of central Europe Figure 2.2 The areas of the static microcosm from which samples 68 were taken in order to isolate WS and SM mutants Figure 2.3 An overview of the experimental design 69 Figure 2.4 A Pseudomonas fluorescens WS biofilm exhibiting a non- 70 circular pattern of spread and it’s resultant binary image after the process of image analysis Figure 2.5 The three categories used to measure the rate of spread of 72 each colony Figure 2.6 The change of radial area against time for each colony 75 categorised according to morphology and the agar concentration of the environment. Figu re 2.7 The average rate of dispersal for each combination of agar 76 concentration and morphology Figure 2.8 Reaction norm graph showing the extrinsic effect of agar 77 concentration on the average rate of dispersal for each genotype Figure 2.9 The probability of a significantly accelerating spread for the 78 WS and SM morphologies in 0.5%, 0.75% and 1% agar concentrations (± 1 SE). Figure 2.10 The aggregated circularity of each genotype through time 79 on the three different agar environments. Figure 2.11 The change in circularity between the start point and end 80 point of each time series. Figure 2.12 A WS morphology on 50% agar at hours 12, 18 and 30 84 ------------------------------------------------------------------------------- Table 2.1 The overall proportion of the colonies exhibiting a constant, 74 ~ 7 ~ significantly accelerating or significantly decelerating rates of spread ------------------------------------------------------------------------------- Chapter 3 Figure 3.1 The average area of spread across all ten Pseudomonas 10 2 aeruginosa replicates for each of the environments tested.
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