RESSALVA Atendendo solicitação do autor, o texto completo desta tese será disponibilizado a partir de 17/10/2024 Doctorate Thesis IFT.T 06/2023 Mathematical models for ecological and evolutionary processes in biological invasions Silas Poloni Supervisor Prof. Dr. Roberto André Kraenkel Co-supervisor Prof. Dr. Renato Mendes Coutinho October 2, 2023 Lyra, Silas Poloni L992m Mathematical models for ecological and evolutionary processes in biological invasions / Silas Poloni. – São Paulo, 2023 123 f.: il. Tese (doutorado) – Universidade Estadual Paulista (Unesp), Instituto de Física Teórica (IFT), São Paulo Orientador: Roberto André Kraenkel Coorientador: Renato Mendes Coutinho 1. Equações de reação-difusão. 2. Biologia - Populações. 3. Matemática aplicada. I. Título Sistema de geração automática de fichas catalográficas da Unesp. Biblioteca do Instituto de Física Teórica (IFT), São Paulo. Dados fornecidos pelo autor(a). Dedico esta tese à minha esposa Fernanda i Agradecimentos Eu agradeço à minha esposa, Fernanda Moura, por todo o apoio e carinho durante toda a jornada acadêmica. Agradeço à minha mãe, por também me apoiar durante toda a jornada, não só acadêmica, mas da minha vida. Aos meus melhores amigos, Ricardo, Bruno, Maycon e Neto, que durante a pandemia foram essenciais para que eu permanecesse alegre, mesmo em um momento tão difícil e solitário. Eu agradeço aos meus amigos e colaboradores do Observatório Covid-19, que durante a pandemia desempenharam papel fundamental na divulgação científica, análise de dados da epidêmia e no esforço de modelagem para compreender o espalhamento da doença no Brasil durante os momentos mais críticos. Sou imensamente grato por ter tido a oportunidade de colaborar com todos. Agradeço aos meus colabores mais próximos nominalmente: Ao meu orientador, Roberto Kraenkel, agradeço por sempre confiar em meu trabalho e me dar total liberdade e apoio em minhas ideias e investigações, e ao Renato Coutinho, por sempre me auxiliar, e a ambos por sempre estarem abertos para discutir o meu trabalho. Sem eles, o capítulo 2 dessa tese seria bem menos interessante. Gostaria de agradecer a FAPESP pelo financiamento do doutorado e da BEPE, através dos processos 2018/24037-4 e 2020/15320-4. A partir daqui, eu mudo o idioma para agradecer alguns amigos e colabores que conheci durante a BEPE. I thank Prince, Jane, Cameron and Alice, for all the hospitality they offered me. Prince helped me find a place to live, and explained Canada 101 to me, Jane did all her best so I could meet new people, and Cameron and Alice where excellent new people I met. Thanks everyone for everything. I also thank Frithjof Lutscher, who supervised me in my period abroad, for several discussions regarding the content of chapter 3, and a little bit of chapter 2 as well. Also, I’d like to thank him for trusting in my ideas and giving me all the support I needed in order to develop them. Finally, several people helped me with chapter 3, by suggesting analyses and help with writing. Tom Hillen suggested looking at the perturbations of the multiplication operator, which led me to study C0 semi-group theory in detail, and this is now the 3rd theorem in chapter 3. Sebastian Schreiber gave significant feedback on the text. Finally, I thank Fields Institute for funding and organizing the “Workshop on New Mathematical Theory to Understand the Effects of Evolution on Range Expansion”, and people that participated in it, a lot of chapter 3 was benefited from the event and discussions therein. ii “Science, my lad, is made up of mistakes, but they are mistakes which it is useful to make, because they lead little by little to the truth.” Jules Verne, A Journey to the Centre of the Earth iii Resumo Invasões biológicas são onipresentes no antropoceno. Diversos fatores influ- enciam como uma espécie invasora se espalha pelo novo território e as escalas espaço-temporais usuais dificultam a realização de experimentos. Assim, aborda- gens teóricas e quantitativas auxiliam a entender os principais fatores e estimar velocidades de invasão e mudanças de regime causadas pela espécie não nativa. Nessa tese, nós revisamos modelos matemáticos clássicos para invasões biológicas, focando em modelos de equações de reação e difusão e integrais a diferenças. Construindo sobre a teoria de equações de reação e difusão, nós analisamos um modelo de invasão de espécies consumidoras em habitats homogêneos e heterogê- neos, formando redes de predação intraguilda com espécies locais. Determinamos velocidades de invasão desses consumidores em habitats homogêneos e condições para reversões competitivas em habitats heterogêneos, levando a regimes de co- existência e exclusão inesperados. Também construímos e analisamos modelos para populações estruturadas por fenótipos em termos de equações a integrais a diferenças. Mostramos que essas equações admitem soluções do tipo onda via- jante e velocidades assimptóticas linearmente determinadas, e também estudamos distribuições fenotípicas na frente de invasão e como elas mudam com diferentes trade-offs entre fertilidade e dispersão e taxas de mutação. Por último, apontamos algumas perspectivas e conclusões do trabalho. Palavras Chaves: Equações de reação e difusão, equações integrais a diferenças, biologia de populações, Áreas do conhecimento: Física, Matemática, Ecologia; Sistemas dinâmicos, Matemática Aplicada, Ecologia Espacial; iv Abstract Biological invasions are ubiquitous in the Anthropocene. With many factors in- fluencing how alien species spread into novel territory and large spatio-temporal scales often make experiments much more complicated. This way, theoretical quantitative approaches become a useful tool into understanding such factors and estimating spreading speeds and regime shifts caused by invading populations. In this thesis we review classical mathematical models for biological invasions in the form of reaction diffusion equations and integro-difference equations. Then, build- ing upon reaction diffusion equations theory, we formulate models for consumer population invasions leading to intraguild predation interaction networks with resident species in both homogeneous and heterogeneous landscapes. We show speeds are linearly determinate, and that competitive reversals among intraguild prey and predator might occur in heterogenous landscapes, leading to unnex- pected coexistence and exclusion regimes. Moving on, we also develop models for evolutionary processes in biological invasions, that have been show to take place in ecological timescale and significantly change spread phenomena. We show that discrete time recursions for trait structured populations can also exhibit traveling wave solutions and linearly determinate speeds, and determine the leading edge trait distributions for different growth-dispersal trade-offs and mutation rates. Finally, we outline some perspectives and conclusions of our work. Keywords: Reaction-diffusion equations, Integro-difference equations, population biology Knowledge fields: Physics, Mathematics, Ecology; Dynamical Systems, Applied Mathematics, Spatial Ecology v Contents 1 An Introduction to Mathematical Models for Biological Invasions 1 1.1 Single Species Models . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Framework Presentation . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Point release . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.3 Traveling exponential fronts . . . . . . . . . . . . . . . . . . . 7 1.1.4 Traveling waves . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.5 Further Readings in Single Species problems . . . . . . . . . 17 1.2 Interacting Species Models . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2.1 Framework Presentation . . . . . . . . . . . . . . . . . . . . . 20 1.2.2 Linear Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.2.4 Further Readings in Multiple Species problems . . . . . . . 35 2 Intraduilg Predation in Homogeneous and Heterogeneous Landscapes 37 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2 Intraguild Predation in Homogeneous Landscapes . . . . . . . . . . 41 2.2.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2.2 Invasion Regimes and Community formation . . . . . . . . 42 2.2.3 Asymptotic Invasion Speeds . . . . . . . . . . . . . . . . . . 47 2.3 Intraguild Predation in Heterogeneous Landscapes . . . . . . . . . 49 2.3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.2 Homogenization Technique . . . . . . . . . . . . . . . . . . . 51 2.3.3 Mutual Invasibility Conditions . . . . . . . . . . . . . . . . . 53 2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3 Integro-difference Models for Evolutionary Processes in Biological Inva- sions 65 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.2.1 Continuous Trait Space . . . . . . . . . . . . . . . . . . . . . 68 3.2.2 Discrete Trait Space . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2.3 Modelling Examples . . . . . . . . . . . . . . . . . . . . . . . 71 vi 3.3 Spreading Speeds and Trait Distributions . . . . . . . . . . . . . . . 75 3.3.1 Continuous Trait Space . . . . . . . . . . . . . . . . . . . . . 75 3.3.2 Discrete Trait Space . . . . . . . . . . . . . . . . . . . . . . . . 78 3.4 A Reduction Principle for Asymptotic Spreading Speeds . . . . . . 80 3.4.1 Continuous Trait Space . . . . . . . . . . . . . . . . . . . . . 80 3.4.2 Discrete Trait Space . . . . . . . . . . . . . . . . . . . . . . . . 82 3.5 Results and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.5.1 No Trade-offs . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.5.2 Weak Trade-offs . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.5.3 Strong Trade-offs . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.5.4 Effects of Deleterious Mutations . . . . . . . . . . . . . . . . 92 3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4 Perspectives and Conclusions 101 4.1 Theory for multiple species interactions . . . . . . . . . . . . . . . . 101 4.2 Sexually structured populations . . . . . . . . . . . . . . . . . . . . . 102 4.3 Fragmented Landscapes and the evolution of habitat selection . . . 103 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Bibliography 107 vii Chapter 4. Perspectives and Conclusions 105 explore how different landscapes lead to different selection processes and drive invading populations to different evolutionary outcomes and spreading speeds. For example, if patch preference in populations at the leading edge differs sig- nificantly to those at the core, we would expect different distributions between patches at the front and core of range. With that, control strategies drawn with core population behavior might not be as effective at newly colonized regions. 4.4 Conclusions In this thesis, we revisited classical mathematical formulations of biological invasions and their results. We have focused only on RDE and IDE frameworks, as those are the most present in current literature. Such formulations are focused on determining the speed of spreed of an invading population and the concept of linear determinacy of such speeds. We also showed some classically observed spatial profiles that invading populations form alongside resident communities, e.g., traveling wave solutions that shift local communities into novel equilibria as time passes, joint invasions of competitor species leading into multiple spatial transitions and predators inducing oscillatory regimes through space. We also obtained novel results and insights for intraguild predation communi- ties through an RDE framework. We numerically verified that speeds of invasion are linearly determinate for a large range of parameters and that the system exhibit traveling wave solutions as well as dynamical stability. Using recent advances and techniques in modeling population in fragmented landscapes, we showed how coexistence regimes can be modulated by each species movement behavior and patch preference, including resource population. Finally, we developed novel theory for evolutionary processes in biological invasions in IDE framework. We showed that monotone recursions to model trait structured populations present traveling wave solutions and asymptotic spreading speeds, and that these spreading speeds are non-increasing with mutation. We also explored leading edge trait distributions and highlight mechanisms that govern such distributions, such as traded-off shapes and mutation. All in all, many aspects of biological invasions gets simplified in mathematical formulations. Although slowly, we often need to get past these simplifications to account for more processes that are revealed, through novel empirical observations, to be important in range expansion, such as landscape fragmentation, species interactions and evolution in ecological timescales. By describing these biological Chapter 4. Perspectives and Conclusions 106 processes in greater detail, mathematical challenges arise, which require advances in different fields, such as function analysis and dynamical systems. In turn, by overcoming such challenges, our results can provide significant insight into ecology again, revealing important aspects of the phenomena that were overlooked and what directions novel experiments and observations could be performed. Bibliography [1] Anthony Ricciardi. Are Modern Biological Invasions an Unprecedented Form of Global Change? Conservation Biology, 21(2):329–336, 2007. ISSN 1523-1739. doi: 10.1111/ j.1523-1739.2006.00615.x. URL https://onlinelibrary. wiley.com/doi/abs/10.1111/j.1523-1739.2006.00615.x. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1523- 1739.2006.00615.x. [2] Petr Pyšek, Vojtěch Jarošík, Philip E. Hulme, Ingolf Kühn, Jan Wild, Mar- garita Arianoutsou, Sven Bacher, Francois Chiron, Viktoras Didžiulis, Franz Essl, Piero Genovesi, Francesca Gherardi, Martin Hejda, Salit Kark, Philip W. Lambdon, Marie-Laure Desprez-Loustau, Wolfgang Nentwig, Jan Pergl, Katja Poboljšaj, Wolfgang Rabitsch, Alain Roques, David B. Roy, Susan Shirley, Wojciech Solarz, Montserrat Vilà, and Marten Winter. Disentan- gling the role of environmental and human pressures on biological inva- sions across Europe. Proceedings of the National Academy of Sciences, 107 (27):12157–12162, July 2010. doi: 10.1073/pnas.1002314107. URL https: //www.pnas.org/doi/full/10.1073/pnas.1002314107. Publisher: Proceedings of the National Academy of Sciences. [3] Philip E. Hulme. Climate change and biological invasions: evidence, ex- pectations, and response options. Biological Reviews of the Cambridge Philosophical Society, 92(3):1297–1313, August 2017. ISSN 1469-185X. doi: 10.1111/brv.12282. [4] John J. Stachowicz, Jeffrey R. Terwin, Robert B. Whitlatch, and Richard W. Osman. Linking climate change and biological invasions: Ocean warming facilitates nonindigenous species invasions. Proceedings of the National Academy of Sciences, 99(24):15497–15500, November 2002. doi: 10.1073/ pnas.242437499. URL https://www.pnas.org/doi/10.1073/pnas. 242437499. Publisher: Proceedings of the National Academy of Sciences. [5] Anna Occhipinti-Ambrogi. Global change and marine communities: alien 107 https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1523-1739.2006.00615.x https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1523-1739.2006.00615.x https://www.pnas.org/doi/full/10.1073/pnas.1002314107 https://www.pnas.org/doi/full/10.1073/pnas.1002314107 https://www.pnas.org/doi/10.1073/pnas.242437499 https://www.pnas.org/doi/10.1073/pnas.242437499 BIBLIOGRAPHY 108 species and climate change. Marine Pollution Bulletin, 55(7-9):342–352, 2007. ISSN 0025-326X. doi: 10.1016/j.marpolbul.2006.11.014. [6] Gerardo Ceballos, Paul R. Ehrlich, Anthony D. Barnosky, Andrés Gar- cía, Robert M. Pringle, and Todd M. Palmer. Accelerated modern hu- man–induced species losses: Entering the sixth mass extinction. Science Advances, 1(5):e1400253, June 2015. doi: 10.1126/sciadv.1400253. URL https://www.science.org/doi/10.1126/sciadv.1400253. Pub- lisher: American Association for the Advancement of Science. [7] Edward Lowry, Emily J Rollinson, Adam J Laybourn, Tracy E Scott, Matthew E Aiello-Lammens, Sarah M Gray, James Mickley, and Jessica Gurevitch. Biological invasions: a field synopsis, systematic review, and database of the literature. Ecology and evolution, 3(1):182–196, 2013. [8] Carlos Castillo-Chavez, Bingtuan Li, and Haiyan Wang. Some recent devel- opments on linear determinacy. Mathematical Biosciences & Engineering, 10(5&6):1419–1436, 2013. [9] Mark A Lewis, Sergei V Petrovskii, and Jonathan R Potts. The mathematics behind biological invasions, volume 44. Springer, 2016. [10] Gregory P Brown, Cathy Shilton, Benjamin L Phillips, and Richard Shine. In- vasion, stress, and spinal arthritis in cane toads. Proceedings of the National Academy of Sciences, 104(45):17698–17700, 2007. [11] Katriona Shea and Peter Chesson. Community ecology theory as a framework for biological invasions. Trends in Ecology & Evolution, 17(4):170–176, April 2002. ISSN 0169-5347. doi: 10. 1016/S0169-5347(02)02495-3. URL https://www.sciencedirect.com/ science/article/pii/S0169534702024953. [12] Nicolas Schtickzelle and Michel Baguette. Behavioural responses to habitat patch boundaries restrict dispersal and generate emigra- tion–patch area relationships in fragmented landscapes. Journal of Animal Ecology, 72(4):533–545, 2003. ISSN 1365-2656. doi: 10.1046/j.1365-2656.2003.00723.x. URL https://onlinelibrary. wiley.com/doi/abs/10.1046/j.1365-2656.2003.00723.x. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1046/j.1365- 2656.2003.00723.x. https://www.science.org/doi/10.1126/sciadv.1400253 https://www.sciencedirect.com/science/article/pii/S0169534702024953 https://www.sciencedirect.com/science/article/pii/S0169534702024953 https://onlinelibrary.wiley.com/doi/abs/10.1046/j.1365-2656.2003.00723.x https://onlinelibrary.wiley.com/doi/abs/10.1046/j.1365-2656.2003.00723.x BIBLIOGRAPHY 109 [13] Tom EX Miller, Amy L Angert, Carissa D Brown, Julie A Lee-Yaw, Mark Lewis, Frithjof Lutscher, Nathan G Marculis, Brett A Melbourne, Allison K Shaw, Marianna Sz\textbackslashHucs, and others. Eco-evolutionary dy- namics of range expansion. Ecology, 101(10):e03139, 2020. [14] Ronald Aylmer Fisher. The wave of advance of advantageous genes. Annals of eugenics, 7(4):355–369, 1937. [15] Kolmogorov A, N, Piscounoff, and I, Petrovsky. Etude de l’equation de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique. Moscow Univ. Bull. Math., 1:1–25, 1937. URL https://cir.nii.ac.jp/crid/1571980074053692672. [16] J. G. Skellam. Random Dispersal in Theoretical Populations. Biometrika, 38 (1-2):196–218, June 1951. ISSN 0006-3444. doi: 10.1093/biomet/38.1-2.196. URL https://doi.org/10.1093/biomet/38.1-2.196. [17] Mark Kot, Mark A. Lewis, and P. van den Driessche. Dispersal Data and the Spread of Invading Organisms. Ecology, 77(7):2027–2042, 1996. ISSN 1939-9170. doi: 10.2307/2265698. URL https://onlinelibrary.wiley. com/doi/abs/10.2307/2265698. [18] Raymond J. H. Beverton and Sidney J. Holt. On the Dynamics of Exploited Fish Populations. Springer Science & Business Media, 1957. ISBN 978-94- 011-2106-4. [19] Hal Caswell. Matrix Population Models. Sinauer, 2001. ISBN 978-0-87893- 121-7. [20] W. C. Allee. Animal aggregations, a study in general sociology. The Uni- versity of Chicago Press„ 1931. URL https://doi.org/10.5962/bhl. title.7313. [21] Frithjof Lutscher. Integrodifference Equations in Spatial Ecology, volume 49 of Interdisciplinary Applied Mathematics. Springer International Publish- ing, Cham, 2019. ISBN 978-3-030-29293-5 978-3-030-29294-2. doi: 10. 1007/978-3-030-29294-2. URL http://link.springer.com/10.1007/ 978-3-030-29294-2. [22] H. F. Weinberger. Asymptotic behavior of a model in population genet- ics. In J.M. Chadam, editor, Nonlinear Partial Differential Equations and https://cir.nii.ac.jp/crid/1571980074053692672 https://doi.org/10.1093/biomet/38.1-2.196 https://onlinelibrary.wiley.com/doi/abs/10.2307/2265698 https://onlinelibrary.wiley.com/doi/abs/10.2307/2265698 https://doi.org/10.5962/bhl.title.7313 https://doi.org/10.5962/bhl.title.7313 http://link.springer.com/10.1007/978-3-030-29294-2 http://link.springer.com/10.1007/978-3-030-29294-2 BIBLIOGRAPHY 110 Applications, Lecture Notes in Mathematics, pages 47–96, Berlin, Heidel- berg, 1978. Springer. ISBN 978-3-540-35868-8. doi: 10.1007/BFb0066406. [23] D. G. Aronson and H. F. Weinberger. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. In Jerome A. Goldstein, editor, Partial Differential Equations and Related Topics, Lecture Notes in Mathematics, pages 5–49, Berlin, Heidelberg, 1975. Springer. ISBN 978-3- 540-37440-4. doi: 10.1007/BFb0070595. [24] Hans F Weinberger. Long-time behavior of a class of biological models. SIAM journal on Mathematical Analysis, 13(3):353–396, 1982. [25] Robert Stephen Cantrell and Chris Cosner. Spatial ecology via reaction-diffusion equations. John Wiley & Sons, 2004. [26] Adèle Bourgeois, Victor LeBlanc, and Frithjof Lutscher. Spreading phenom- ena in integrodifference equations with nonmonotone growth functions. SIAM Journal on Applied Mathematics, 78(6):2950–2972, 2018. [27] J. Nagumo, S. Arimoto, and S. Yoshizawa. An Active Pulse Transmission Line Simulating Nerve Axon. Proceedings of the IRE, 50(10):2061–2070, Oc- tober 1962. ISSN 2162-6634. doi: 10.1109/JRPROC.1962.288235. Conference Name: Proceedings of the IRE. [28] K. P. Hadeler and F. Rothe. Travelling fronts in nonlinear diffusion equa- tions. Journal of Mathematical Biology, 2(3):251–263, September 1975. ISSN 1432-1416. doi: 10.1007/BF00277154. URL https://doi.org/10.1007/ BF00277154. [29] Roger Lui. Existence and stability of travelling wave solutions of a nonlinear integral operator. Journal of Mathematical Biology, 16(3):199–220, February 1983. ISSN 1432-1416. doi: 10.1007/BF00276502. URL https://doi.org/ 10.1007/BF00276502. [30] Nanako Shigesada, Kohkichi Kawasaki, and Ei Teramoto. Traveling periodic waves in heterogeneous environments. Theoretical Population Biology, 30 (1):143–160, 1986. [31] Otso Ovaskainen and Stephen J Cornell. Biased movement at a boundary and conditional occupancy times for diffusion processes. Journal of Applied Probability, 40(3):557–580, 2003. https://doi.org/10.1007/BF00277154 https://doi.org/10.1007/BF00277154 https://doi.org/10.1007/BF00276502 https://doi.org/10.1007/BF00276502 BIBLIOGRAPHY 111 [32] Gabriel Andreguetto Maciel and Frithjof Lutscher. How individual move- ment response to habitat edges affects population persistence and spatial spread. The American Naturalist, 182(1):42–52, 2013. [33] Gabriel Andreguetto Maciel and Frithjof Lutscher. Allee effects and pop- ulation spread in patchy landscapes. Journal of biological dynamics, 9(1): 109–123, 2015. Publisher: Taylor & Francis. [34] Brian P Yurk and Christina A Cobbold. Homogenization techniques for population dynamics in strongly heterogeneous landscapes. Journal of biological dynamics, 12(1):171–193, 2018. [35] François Hamel, Frithjof Lutscher, and Mingmin Zhang. Propagation phe- nomena in periodic patchy landscapes with interface conditions. Journal of Dynamics and Differential Equations, pages 1–52, 2022. [36] Jeffrey Musgrave and Frithjof Lutscher. Integrodifference equations in patchy landscapes: II: Population level consequences. Journal of mathematical biology, 69, August 2013. doi: 10.1007/s00285-013-0715-1. [37] Jeffrey Musgrave and Frithjof Lutscher. Integrodifference equations in patchy landscapes : I. Dispersal Kernels. Journal of Mathematical Biology, 69(3):583–615, September 2014. ISSN 1432-1416. doi: 10.1007/ s00285-013-0714-2. [38] Tom EX Miller, Allison K Shaw, Brian D Inouye, and Michael G Neubert. Sex-biased dispersal and the speed of two-sex invasions. The American Naturalist, 177(5):549–561, 2011. [39] Roger Lui. Biological growth and spread modeled by systems of recursions. I. Mathematical theory. Mathematical Biosciences, 93(2):269–295, 1989. [40] Michael G Neubert and Hal Caswell. Demography and dispersal: calcula- tion and sensitivity analysis of invasion speed for structured populations. Ecology, 81(6):1613–1628, 2000. [41] Hans F Weinberger, Mark A Lewis, and Bingtuan Li. Analysis of linear determinacy for spread in cooperative models. Journal of Mathematical Biology, 45(3):183–218, 2002. BIBLIOGRAPHY 112 [42] Mark A. Lewis, Bingtuan Li, and Hans F. Weinberger. Spreading speed and linear determinacy for two-species competition models. Journal of Mathematical Biology, 45(3):219–233, September 2002. ISSN 1432- 1416. doi: 10.1007/s002850200144. URL https://doi.org/10.1007/ s002850200144. [43] Yuzo Hosono. The Minimal Speed of Traveling Fronts for a Diffusive Lotka–Volterra Competition Model. Bulletin of Mathematical Biology, 60(3):435–448, May 1998. ISSN 0092-8240. doi: 10.1006/bulm.1997. 0008. URL https://www.sciencedirect.com/science/article/ pii/S0092824097900082. [44] Michael G. Neubert and Mark Kot. The subcritical collapse of preda- tor populations in discrete-time predator-prey models. Mathematical Biosciences, 110(1):45–66, June 1992. ISSN 00255564. doi: 10.1016/ 0025-5564(92)90014-N. URL https://linkinghub.elsevier.com/ retrieve/pii/002555649290014N. [45] C. S. Holling. Some Characteristics of Simple Types of Predation and Parasitism. The Canadian Entomologist, 91 (7):385–398, July 1959. ISSN 1918-3240, 0008-347X. doi: 10.4039/Ent91385-7. URL https://www.cambridge.org/ core/journals/canadian-entomologist/article/abs/ some-characteristics-of-simple-types-of-predation-and-parasitism1/ 9E1E7D2CCC314766A424680444F4EA9F. Publisher: Cambridge Univer- sity Press. [46] C. S. Holling. The Functional Response of Invertebrate Predators to Prey Density. The Memoirs of the Entomological Society of Canada, 98(S48):5–86, January 1966. ISSN 0071-075X. doi: 10.4039/ entm9848fv. URL https://www.cambridge.org/core/journals/ memoirs-of-the-entomological-society-of-canada/ article/abs/functional-response-of-invertebrate-predators-to-prey-density/ 93597109DEB509626DD201D20207D287. Publisher: Cambridge Univer- sity Press. [47] J. D. Murray, editor. Mathematical Biology: II: Spatial Models and Biomedical Applications, volume 18 of Interdisciplinary Applied https://doi.org/10.1007/s002850200144 https://doi.org/10.1007/s002850200144 https://www.sciencedirect.com/science/article/pii/S0092824097900082 https://www.sciencedirect.com/science/article/pii/S0092824097900082 https://linkinghub.elsevier.com/retrieve/pii/002555649290014N https://linkinghub.elsevier.com/retrieve/pii/002555649290014N https://www.cambridge.org/core/journals/canadian-entomologist/article/abs/some-characteristics-of-simple-types-of-predation-and-parasitism1/9E1E7D2CCC314766A424680444F4EA9F https://www.cambridge.org/core/journals/canadian-entomologist/article/abs/some-characteristics-of-simple-types-of-predation-and-parasitism1/9E1E7D2CCC314766A424680444F4EA9F https://www.cambridge.org/core/journals/canadian-entomologist/article/abs/some-characteristics-of-simple-types-of-predation-and-parasitism1/9E1E7D2CCC314766A424680444F4EA9F https://www.cambridge.org/core/journals/canadian-entomologist/article/abs/some-characteristics-of-simple-types-of-predation-and-parasitism1/9E1E7D2CCC314766A424680444F4EA9F https://www.cambridge.org/core/journals/memoirs-of-the-entomological-society-of-canada/article/abs/functional-response-of-invertebrate-predators-to-prey-density/93597109DEB509626DD201D20207D287 https://www.cambridge.org/core/journals/memoirs-of-the-entomological-society-of-canada/article/abs/functional-response-of-invertebrate-predators-to-prey-density/93597109DEB509626DD201D20207D287 https://www.cambridge.org/core/journals/memoirs-of-the-entomological-society-of-canada/article/abs/functional-response-of-invertebrate-predators-to-prey-density/93597109DEB509626DD201D20207D287 https://www.cambridge.org/core/journals/memoirs-of-the-entomological-society-of-canada/article/abs/functional-response-of-invertebrate-predators-to-prey-density/93597109DEB509626DD201D20207D287 BIBLIOGRAPHY 113 Mathematics. Springer, New York, NY, 2003. ISBN 978-0-387-95228-4 978-0- 387-22438-1. doi: 10.1007/b98869. URL http://link.springer.com/ 10.1007/b98869. [48] H. Malchow and S. V. Petrovskii. Dynamical stabilization of an unsta- ble equilibrium in chemical and biological systems. Mathematical and Computer Modelling, 36(3):307–319, August 2002. ISSN 0895-7177. doi: 10.1016/S0895-7177(02)00127-9. URL https://www.sciencedirect. com/science/article/pii/S0895717702001279. [49] Sergei V Petrovskii and Horst Malchow. Critical phenomena in plank- ton communities: KISS model revisited. Nonlinear Analysis: Real World Applications, 1(1):37–51, March 2000. ISSN 1468-1218. doi: 10.1016/S0362-546X(99)00392-2. URL https://www.sciencedirect. com/science/article/pii/S0362546X99003922. [50] MR Owen and MA Lewis. How predation can slow, stop or reverse a prey invasion. Bulletin of mathematical biology, 63(4):655–684, 2001. [51] Steven R. Dunbar. Traveling Wave Solutions of Diffusive Lotka-Volterra Equations: A Heteroclinic Connection in R4. Transactions of the American Mathematical Society, 286(2):557–594, 1984. ISSN 0002-9947. doi: 10.2307/ 1999810. URL https://www.jstor.org/stable/1999810. Publisher: American Mathematical Society. [52] Wenzhang Huang. Traveling Wave Solutions for a Class of Predator–Prey Systems. Journal of Dynamics and Differential Equations, 24(3):633–644, September 2012. ISSN 1572-9222. doi: 10.1007/s10884-012-9255-4. URL https://doi.org/10.1007/s10884-012-9255-4. [53] Sergei V. Petrovskii and Horst Malchow. Wave of Chaos: New Mechanism of Pattern Formation in Spatio-temporal Population Dynamics. Theoretical Population Biology, 59(2):157–174, March 2001. ISSN 00405809. doi: 10.1006/tpbi.2000.1509. URL https://linkinghub.elsevier.com/ retrieve/pii/S0040580900915090. [54] M. G. Roberts. A pocket guide to host-parasite models. Parasitology Today (Personal Ed.), 11(5):172–177, May 1995. ISSN 0169-4758. doi: 10.1016/ 0169-4758(95)80150-2. http://link.springer.com/10.1007/b98869 http://link.springer.com/10.1007/b98869 https://www.sciencedirect.com/science/article/pii/S0895717702001279 https://www.sciencedirect.com/science/article/pii/S0895717702001279 https://www.sciencedirect.com/science/article/pii/S0362546X99003922 https://www.sciencedirect.com/science/article/pii/S0362546X99003922 https://www.jstor.org/stable/1999810 https://doi.org/10.1007/s10884-012-9255-4 https://linkinghub.elsevier.com/retrieve/pii/S0040580900915090 https://linkinghub.elsevier.com/retrieve/pii/S0040580900915090 BIBLIOGRAPHY 114 [55] A. J. Nicholson and V. A. Bailey. The Balance of Animal Popula- tions.—Part I. Proceedings of the Zoological Society of London, 105(3): 551–598, September 1935. ISSN 0370-2774. doi: 10.1111/j.1096-3642. 1935.tb01680.x. URL https://onlinelibrary.wiley.com/doi/10. 1111/j.1096-3642.1935.tb01680.x. [56] R. W. Wright and Alan Hastings. Spontaneous Patchiness in a Host- Parasitoid Integrodifference Model. Bulletin of Mathematical Biology, 69(8): 2693–2709, November 2007. ISSN 1522-9602. doi: 10.1007/s11538-007-9236-7. URL https://doi.org/10.1007/s11538-007-9236-7. [57] Frithjof Lutscher and Tzvia Iljon. Competition, facilitation and the Allee effect. Oikos, 122(4):621–631, 2013. ISSN 1600-0706. doi: 10.1111/j.1600-0706.2012.20222.x. URL https://onlinelibrary. wiley.com/doi/abs/10.1111/j.1600-0706.2012.20222.x. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600- 0706.2012.20222.x. [58] Kayla R. S. Hale and Fernanda S. Valdovinos. Ecological theory of mutualism: Robust patterns of stability and thresholds in two- species population models. Ecology and Evolution, 11(24):17651– 17671, 2021. ISSN 2045-7758. doi: 10.1002/ece3.8453. URL https: //onlinelibrary.wiley.com/doi/abs/10.1002/ece3.8453. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/ece3.8453. [59] Daniel R. Amor, Raúl Montañez, Salva Duran-Nebreda, and Ricard Solé. Spatial dynamics of synthetic microbial mutualists and their parasites. PLoS Computational Biology, 13(8):e1005689, August 2017. ISSN 1553-734X. doi: 10.1371/journal.pcbi.1005689. URL https://www.ncbi.nlm.nih.gov/ pmc/articles/PMC5584972/. [60] David Tilman and others. Mechanisms of plant competition for nutri- ents: the elements of a predictive theory of competition. Mechanisms of plant competition for nutrients: the elements of a predictive theory of competition., pages 117–141, 1990. [61] RD Holt and ME Hochberg. Indirect interactions, community modules and biological control: a theoretical perspective. Evaluating indirect ecological effects of biological control, pages 13–37, 2001. https://onlinelibrary.wiley.com/doi/10.1111/j.1096-3642.1935.tb01680.x https://onlinelibrary.wiley.com/doi/10.1111/j.1096-3642.1935.tb01680.x https://doi.org/10.1007/s11538-007-9236-7 https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1600-0706.2012.20222.x https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1600-0706.2012.20222.x https://onlinelibrary.wiley.com/doi/abs/10.1002/ece3.8453 https://onlinelibrary.wiley.com/doi/abs/10.1002/ece3.8453 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5584972/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5584972/ BIBLIOGRAPHY 115 [62] G A Polis, C A Myers, and R D Holt. The Ecology and Evo- lution of Intraguild Predation: Potential Competitors That Eat Each Other. Annual Review of Ecology and Systematics, 20(1):297–330, 1989. doi: 10.1146/annurev.es.20.110189.001501. URL https: //doi.org/10.1146/annurev.es.20.110189.001501. _eprint: https://doi.org/10.1146/annurev.es.20.110189.001501. [63] Robert D Holt and Gary A Polis. A theoretical framework for intraguild predation. The American Naturalist, 149(4):745–764, 1997. [64] Christina A Cobbold, Frithjof Lutscher, and Brian Yurk. Bridging the scale gap: Predicting large-scale population dynamics from small-scale variation in strongly heterogeneous landscapes. Methods in Ecology and Evolution, 13(4):866–879, 2022. [65] Renato Andrade and Christina A. Cobbold. Heterogeneity in Behaviour and Movement can Influence the Stability of Predator–Prey Periodic Travelling Waves. Bulletin of Mathematical Biology, 85(1):1, November 2022. ISSN 1522-9602. doi: 10.1007/s11538-022-01101-8. URL https://doi.org/10. 1007/s11538-022-01101-8. [66] Gabriel Andreguetto Maciel and Frithjof Lutscher. Movement behaviour determines competitive outcome and spread rates in strongly heterogeneous landscapes. Theoretical Ecology, 11:351–365, 2018. [67] Gary A. Polis and Robert D. Holt. Intraguild predation: The dynamics of complex trophic interactions. Trends in Ecology & Evolution, 7(5):151–154, May 1992. ISSN 0169-5347. doi: 10. 1016/0169-5347(92)90208-S. URL https://www.sciencedirect.com/ science/article/pii/016953479290208S. [68] Quenton M. Tuckett, Amy E. Deacon, Douglas Fraser, Timothy J. Lyons, Katelyn M. Lawson, and Jeffrey E. Hill. Unstable intraguild predation causes establishment failure of a globally invasive species. Ecology, 102 (8):e03411, 2021. ISSN 1939-9170. doi: 10.1002/ecy.3411. URL https:// onlinelibrary.wiley.com/doi/abs/10.1002/ecy.3411. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/ecy.3411. [69] M. Montserrat, S. Magalhães, M. W. Sabelis, A. M. de Roos, and A. Janssen. Invasion success in communities with reciprocal in- https://doi.org/10.1146/annurev.es.20.110189.001501 https://doi.org/10.1146/annurev.es.20.110189.001501 https://doi.org/10.1007/s11538-022-01101-8 https://doi.org/10.1007/s11538-022-01101-8 https://www.sciencedirect.com/science/article/pii/016953479290208S https://www.sciencedirect.com/science/article/pii/016953479290208S https://onlinelibrary.wiley.com/doi/abs/10.1002/ecy.3411 https://onlinelibrary.wiley.com/doi/abs/10.1002/ecy.3411 BIBLIOGRAPHY 116 traguild predation depends on the stage structure of the resident population. Oikos, 121(1):67–76, 2012. ISSN 1600-0706. doi: 10.1111/j.1600-0706.2011.19369.x. URL https://onlinelibrary. wiley.com/doi/abs/10.1111/j.1600-0706.2011.19369.x. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600- 0706.2011.19369.x. [70] Thomas H. Fritts and Gordon H. Rodda. THE ROLE OF INTRODUCED SPECIES IN THE DEGRADATION OF ISLAND ECOSYSTEMS: A Case History of Guam. Annual Review of Ecology and Systematics, 29(1):113– 140, November 1998. ISSN 0066-4162. doi: 10.1146/annurev.ecolsys. 29.1.113. URL https://www.annualreviews.org/doi/10.1146/ annurev.ecolsys.29.1.113. [71] E. D. Grosholz and G. M. Ruiz. Spread and potential impact of the recently introduced European green crab, Carcinus maenas, in central California. Marine Biology, 122(2):239–247, April 1995. ISSN 1432-1793. doi: 10.1007/ BF00348936. URL https://doi.org/10.1007/BF00348936. [72] Gary A. Polis, Wendy B. Anderson, and Robert D. Holt. Toward an In- tegration of Landscape and Food Web Ecology: The Dynamics of Spa- tially Subsidized Food Webs. Annual Review of Ecology and Systematics, 28(1):289–316, 1997. doi: 10.1146/annurev.ecolsys.28.1.289. URL https://doi.org/10.1146/annurev.ecolsys.28.1.289. _eprint: https://doi.org/10.1146/annurev.ecolsys.28.1.289. [73] Peter A Abrams. Habitat choice in predator-prey systems: spatial instability due to interacting adaptive movements. The American Naturalist, 169(5): 581–594, 2007. [74] C. A. Klausmeier and D. Tilman. Spatial Models of Competition. In Ulrich Sommer and Boris Worm, editors, Competition and Coexistence, Ecological Studies, pages 43–78. Springer, Berlin, Heidelberg, 2002. ISBN 978-3-642- 56166-5. doi: 10.1007/978-3-642-56166-5_3. URL https://doi.org/10. 1007/978-3-642-56166-5_3. [75] Min Ming Tang and Paul C. Fife. Propagating fronts for competing species equations with diffusion. Archive for Rational Mechanics and Analysis, 73 https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1600-0706.2011.19369.x https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1600-0706.2011.19369.x https://www.annualreviews.org/doi/10.1146/annurev.ecolsys.29.1.113 https://www.annualreviews.org/doi/10.1146/annurev.ecolsys.29.1.113 https://doi.org/10.1007/BF00348936 https://doi.org/10.1146/annurev.ecolsys.28.1.289 https://doi.org/10.1007/978-3-642-56166-5_3 https://doi.org/10.1007/978-3-642-56166-5_3 BIBLIOGRAPHY 117 (1):69–77, March 1980. ISSN 1432-0673. doi: 10.1007/BF00283257. URL https://doi.org/10.1007/BF00283257. [76] Horst Malchow. Spatio-temporal pattern formation in nonlinear non- equilibrium plankton dynamics. Proceedings of the Royal Society of London. Series B: Biological Sciences, 251(1331):103–109, January 1997. doi: 10.1098/rspb.1993.0015. URL https://royalsocietypublishing. org/doi/10.1098/rspb.1993.0015. Publisher: Royal Society. [77] CJ Bampfylde and MA Lewis. Biological control through intraguild pre- dation: case studies in pest control, invasive species and range expansion. Bulletin of Mathematical biology, 69:1031–1066, 2007. [78] Robert Stephen Cantrell, Chris Cosner, and William F. Fagan. Com- petitive reversals inside ecological reserves: the role of external habitat degradation. Journal of Mathematical Biology, 37(6):491–533, December 1998. ISSN 0303-6812, 1432-1416. doi: 10.1007/s002850050139. URL http://link.springer.com/10.1007/s002850050139. [79] Priyanga Amarasekare. Spatial dynamics of communities with intraguild predation: the role of dispersal strategies. The American Naturalist, 170(6): 819–831, 2007. [80] S. V. Petrovskii and H. Malchow. A minimal model of pattern formation in a prey-predator system. Mathematical and Computer Modelling, 29(8):49–63, April 1999. ISSN 0895-7177. doi: 10.1016/ S0895-7177(99)00070-9. URL https://www.sciencedirect.com/ science/article/pii/S0895717799000709. [81] Robert A. Armstrong and Richard McGehee. Competitive Exclusion. The American Naturalist, 115(2):151–170, 1980. ISSN 0003-0147. URL https: //www.jstor.org/stable/2460592. Publisher: [University of Chicago Press, American Society of Naturalists]. [82] Gabriel Maciel, Chris Cosner, Robert Stephen Cantrell, and Frithjof Lutscher. Evolutionarily stable movement strategies in reaction–diffusion models with edge behavior. Journal of mathematical biology, pages 1–32, 2018. [83] Robert D. Holt and Michael B. Bonsall. Apparent Competition. Annual Review of Ecology, Evolution, and Systematics, 48(1):447– https://doi.org/10.1007/BF00283257 https://royalsocietypublishing.org/doi/10.1098/rspb.1993.0015 https://royalsocietypublishing.org/doi/10.1098/rspb.1993.0015 http://link.springer.com/10.1007/s002850050139 https://www.sciencedirect.com/science/article/pii/S0895717799000709 https://www.sciencedirect.com/science/article/pii/S0895717799000709 https://www.jstor.org/stable/2460592 https://www.jstor.org/stable/2460592 BIBLIOGRAPHY 118 471, November 2017. ISSN 1543-592X, 1545-2069. doi: 10.1146/ annurev-ecolsys-110316-022628. URL https://www.annualreviews. org/doi/10.1146/annurev-ecolsys-110316-022628. [84] Benjamin L Phillips, Gregory P Brown, Justin MJ Travis, and Richard Shine. Reid’s paradox revisited: the evolution of dispersal kernels during range expansion. the american naturalist, 172(S1):S34–S48, 2008. [85] Richard Shine, Gregory P Brown, and Benjamin L Phillips. An evolutionary process that assembles phenotypes through space rather than through time. Proceedings of the National Academy of Sciences, 108(14):5708–5711, 2011. [86] Ben L Phillips and T Alex Perkins. Spatial sorting as the spatial analogue of natural selection. Theoretical Ecology, 12(2):155–163, 2019. [87] Emeric Bouin, Vincent Calvez, Nicolas Meunier, Sepideh Mirrahimi, Benoît Perthame, Gaël Raoul, and Raphaël Voituriez. Invasion fronts with variable motility: Phenotype selection, spatial sorting and wave acceleration. Comptes Rendus Mathematique, 350(15):761–766, 2012. ISSN 1631-073X. doi: https://doi.org/10.1016/j.crma.2012.09. 010. URL https://www.sciencedirect.com/science/article/ pii/S1631073X12002543. [88] Emeric Bouin, Matthew H Chan, Christopher Henderson, and Peter S Kim. Influence of a mortality trade-off on the spreading rate of cane toads fronts. Communications in Partial Differential Equations, 43(11):1627–1671, 2018. [89] Vincent A Keenan and Stephen J Cornell. Anomalous invasion dynam- ics due to dispersal polymorphism and dispersal–reproduction trade-offs. Proceedings of the Royal Society B, 288(1942):20202825, 2021. [90] Aled Morris, Luca Börger, and Elaine Crooks. Individual Variability in Dispersal and Invasion Speed. Mathematics, 7(9), 2019. ISSN 2227-7390. doi: 10.3390/math7090795. URL https://www.mdpi.com/2227-7390/ 7/9/795. [91] Sebastian J Schreiber and Noelle G Beckman. Individual variation in dis- persal and fecundity increases rates of spatial spread. AoB Plants, 12(3): plaa001, 2020. https://www.annualreviews.org/doi/10.1146/annurev-ecolsys-110316-022628 https://www.annualreviews.org/doi/10.1146/annurev-ecolsys-110316-022628 https://www.sciencedirect.com/science/article/pii/S1631073X12002543 https://www.sciencedirect.com/science/article/pii/S1631073X12002543 https://www.mdpi.com/2227-7390/7/9/795 https://www.mdpi.com/2227-7390/7/9/795 BIBLIOGRAPHY 119 [92] Frithjof Lutscher, Lea Popovic, and Allison K Shaw. How mutation shapes the rate of population spread in the presence of a mate-finding Allee effect. Theoretical Ecology, pages 1–15, 2022. [93] Gregory S Clarke, Richard Shine, and Benjamin L Phillips. May the (selective) force be with you: spatial sorting and natural selection exert opposing forces on limb length in an invasive amphibian. Journal of evolutionary biology, 32(9):994–1001, 2019. [94] Matthieu Alfaro, Jérôme Coville, and Gaël Raoul. Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypic trait. Communications in Partial Differential Equations, 38(12):2126–2154, 2013. [95] Matthieu Alfaro, Henri Berestycki, and Gaël Raoul. The effect of climate shift on a species submitted to dispersion, evolution, growth, and nonlocal competition. SIAM Journal on Mathematical Analysis, 49(1):562–596, 2017. [96] Matthieu Alfaro, Léo Girardin, Francois Hamel, and Lionel Roques. When the Allee threshold is an evolutionary trait: persistence vs. extinction. Journal de Mathématiques Pures et Appliquées, 155:155–191, 2021. [97] Elizabeth C Elliott and Stephen J Cornell. Dispersal polymorphism and the speed of biological invasions. PloS one, 7(7):e40496, 2012. [98] Nathan G Marculis, Maya L Evenden, and Mark A Lewis. Modeling the dispersal–reproduction trade-off in an expanding population. Theoretical population biology, 134:147–159, 2020. [99] James M Bullock and Ralph T Clarke. Long distance seed dispersal by wind: measuring and modelling the tail of the curve. Oecologia, 124(4):506–521, 2000. [100] Joseph P Stover, Bruce E Kendall, and Roger M Nisbet. Consequences of dispersal heterogeneity for population spread and persistence. Bulletin of Mathematical Biology, 76(11):2681–2710, 2014. [101] John FC Kingman. A simple model for the balance between selection and mutation. Journal of Applied Probability, 15(1):1–12, 1978. BIBLIOGRAPHY 120 [102] Quentin Griette. Singular measure traveling waves in an epidemiolog- ical model with continuous phenotypes. Transactions of the American Mathematical Society, 371(6):4411–4458, 2019. [103] Michael Doebeli. A quantitative genetic competition model for sympatric speciation. Journal of evolutionary biology, 9(6):893–909, 1996. [104] Robert M May. Stability and complexity in model ecosystems. In Stability and Complexity in Model Ecosystems. Princeton University Press, 2019. [105] Xing Liang and Xiao-Qiang Zhao. Asymptotic speeds of spread and travel- ing waves for monotone semiflows with applications. Communications on Pure and Applied Mathematics, 60(1):1–40, January 2007. ISSN 00103640, 10970312. doi: 10.1002/cpa.20154. URL https://onlinelibrary. wiley.com/doi/10.1002/cpa.20154. [106] Mark Grigor’evich Krein and Mark A Rutman. Linear operators leaving invariant a cone in a Banach space. Uspekhi mat. nauk, 3(1):3–95, 1948. [107] Lee Altenberg. Resolvent positive linear operators exhibit the reduction phenomenon. Proceedings of the National Academy of Sciences, 109(10): 3705–3710, 2012. [108] Horst R Thieme. Spectral bound and reproduction number for infinite- dimensional population structure and time heterogeneity. SIAM Journal on Applied Mathematics, 70(1):188–211, 2009. [109] Samuel Karlin. Classifications of selection-migration structures and condi- tions for a protected polymorphism. Evol. Biol, 14(61):204, 1982. [110] Joel E Cohen. Convexity of the dominant eigenvalue of an essentially nonnegative matrix. Proceedings of the American Mathematical Society, 81 (4):657–658, 1981. [111] Hans F Weinberger, Mark A Lewis, and Bingtuan Li. Anomalous spreading speeds of cooperative recursion systems. Journal of mathematical biology, 55:207–222, 2007. [112] Samuel Karlin and James McGregor. Towards a theory of the evolution of modifier genes. Theoretical population biology, 5(1):59–103, 1974. https://onlinelibrary.wiley.com/doi/10.1002/cpa.20154 https://onlinelibrary.wiley.com/doi/10.1002/cpa.20154 BIBLIOGRAPHY 121 [113] Alan Hastings. Can spatial variation alone lead to selection for dispersal? Theoretical Population Biology, 24(3):244–251, 1983. [114] Chris Cosner. Reaction-diffusion-advection models for the effects and evo- lution of dispersal. Discrete & Continuous Dynamical Systems, 34(5):1701, 2014. [115] Nicholas F Britton. Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model. SIAM Journal on Applied Mathematics, 50(6):1663–1688, 1990. [116] MA Fuentes, MN Kuperman, and VM Kenkre. Nonlocal interaction effects on pattern formation in population dynamics. Physical review letters, 91 (15):158104, 2003. [117] Olivia J Burton, Ben L Phillips, and Justin MJ Travis. Trade-offs and the evolution of life-histories during range expansion. Ecology letters, 13(10): 1210–1220, 2010. [118] Stephen P Ellner, Dylan Z Childs, Mark Rees, and others. Data-driven mod- elling of structured populations. A practical guide to the Integral Projection Model. Cham: Springer, 2016. [119] Horst R Thieme. Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread. Journal of Mathematical Biology, 8(2):173–187, 1979. [120] Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, and Chin-Chin Wu. Traveling wave solutions for a predator–prey system with two predators and one prey. Nonlinear Analysis: Real World Applications, 54:103111, August 2020. ISSN 1468-1218. doi: 10.1016/j.nonrwa. 2020.103111. URL https://www.sciencedirect.com/science/ article/pii/S1468121820300298. [121] Yan-Li Huang and Guo Lin. Traveling wave solutions in a diffusive system with two preys and one predator. Journal of Mathematical Analysis and Applications, 418(1):163–184, October 2014. ISSN 0022-247X. doi: 10.1016/j. jmaa.2014.03.085. URL https://www.sciencedirect.com/science/ article/pii/S0022247X14003345. https://www.sciencedirect.com/science/article/pii/S1468121820300298 https://www.sciencedirect.com/science/article/pii/S1468121820300298 https://www.sciencedirect.com/science/article/pii/S0022247X14003345 https://www.sciencedirect.com/science/article/pii/S0022247X14003345 BIBLIOGRAPHY 122 [122] Jian-Jhong Lin and Ting-Hui Yang. Traveling wave solutions for a dif- fusive three-species intraguild predation model. International Journal of Biomathematics, 11(02):1850022, February 2018. ISSN 1793-5245. doi: 10.1142/S1793524518500225. URL https://www.worldscientific. com/doi/10.1142/S1793524518500225. Publisher: World Scientific Publishing Co. [123] Lauren G. Shoemaker, Jonathan A. Walter, Laureano A. Gherardi, Melissa H. DeSiervo, and Nathan I. Wisnoski. Writing mathemat- ical ecology: A guide for authors and readers. Ecosphere, 12(8): e03701, 2021. ISSN 2150-8925. doi: 10.1002/ecs2.3701. URL https: //onlinelibrary.wiley.com/doi/abs/10.1002/ecs2.3701. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/ecs2.3701. [124] Allison K. Shaw and Hanna Kokko. Mate finding, Allee effects and selection for sex-biased dispersal. The Journal of Animal Ecology, 83(6):1256–1267, November 2014. ISSN 1365-2656. doi: 10.1111/1365-2656.12232. [125] Cameron M. Hudson, Gregory P. Brown, and Richard Shine. It is lonely at the front: contrasting evolutionary trajectories in male and female in- vaders. Royal Society Open Science, 3(12):160687, December 2016. doi: 10.1098/rsos.160687. URL https://royalsocietypublishing.org/ doi/full/10.1098/rsos.160687. Publisher: Royal Society. [126] Crystal Kelehear and Richard Shine. Non-reproductive male cane toads (Rhinella marina) withhold sex-identifying information from their rivals. Biology Letters, 15(8):20190462, August 2019. doi: 10.1098/rsbl.2019. 0462. URL https://royalsocietypublishing.org/doi/10.1098/ rsbl.2019.0462. Publisher: Royal Society. [127] Luděk Berec, Andrew M. Kramer, Veronika Bernhauerová, and John M. Drake. Density-dependent selection on mate search and evolution of Allee effects. The Journal of Animal Ecology, 87(1):24–35, January 2018. ISSN 1365-2656. doi: 10.1111/1365-2656.12662. [128] Brad M. Ochocki, Julia B. Saltz, and Tom E. X. Miller. Demography-Dispersal Trait Correlations Modify the Eco-Evolutionary Dynamics of Range Expan- sion. The American Naturalist, 195(2):231–246, February 2020. ISSN 0003- 0147. doi: 10.1086/706904. URL https://www.journals.uchicago. https://www.worldscientific.com/doi/10.1142/S1793524518500225 https://www.worldscientific.com/doi/10.1142/S1793524518500225 https://onlinelibrary.wiley.com/doi/abs/10.1002/ecs2.3701 https://onlinelibrary.wiley.com/doi/abs/10.1002/ecs2.3701 https://royalsocietypublishing.org/doi/full/10.1098/rsos.160687 https://royalsocietypublishing.org/doi/full/10.1098/rsos.160687 https://royalsocietypublishing.org/doi/10.1098/rsbl.2019.0462 https://royalsocietypublishing.org/doi/10.1098/rsbl.2019.0462 https://www.journals.uchicago.edu/doi/abs/10.1086/706904 https://www.journals.uchicago.edu/doi/abs/10.1086/706904 https://www.journals.uchicago.edu/doi/abs/10.1086/706904 BIBLIOGRAPHY 123 edu/doi/abs/10.1086/706904. Publisher: The University of Chicago Press. [129] Stephen Dewitt Fretwell. On territorial behavior and other factors influ- encing habitat distribution in birds. Technical report, North Carolina State University. Dept. of Statistics, 1969. [130] Silas Poloni and Frithjof Lutscher. Integrodifference models for evolutionary processes in biological invasions. Journal of Mathematical Biology, 87(1): 10, June 2023. ISSN 1432-1416. doi: 10.1007/s00285-023-01947-z. URL https://doi.org/10.1007/s00285-023-01947-z. https://www.journals.uchicago.edu/doi/abs/10.1086/706904 https://www.journals.uchicago.edu/doi/abs/10.1086/706904 https://www.journals.uchicago.edu/doi/abs/10.1086/706904 https://doi.org/10.1007/s00285-023-01947-z