Tentative Title: The theory of coevolution The genetic theory of coevolution Author: Scott L. Nuismer Coevolution between species drives diversification, promotes rapid and sustained evolutionary change, and facilitates major evolutionary transitions. When combined with its clear relevance to applied problems such as virulence evolution and the spread of invasive species, the recent explosion of studies exploring the coevolutionary process is unsurprising. To a large extent, empirical research on coevolution has been regularly and comprehensively synthesized by John N. Thompson in his wonderful books, Interaction and coevolution (1982), The coevolutionary process (1994), and The geographic mosaic of coevolution (2004). Although Thompson’s books include results of theoretical studies, the sheer scope of his books precludes detailed treatment of coevolutionary theory. Consequently, the mathematical models and key assumptions upon which our understanding of the coevolutionary process rests remain scattered throughout the primary literature. The central goal of this book is to present the key mathematical underpinnings of coevolution in a way that makes them accessible to a broad range of biologists. Although this book will synthesize coevolutionary theory, it is not intended to be an exhaustive review. Instead, each chapter will develop mathematical models of specific coevolutionary processes from first principles. These models will then be used to illustrate key assumptions, mathematical techniques, and coevolutionary results that define and inform broad areas of coevolutionary research. Early chapters will develop and analyze the most basic coevolutionary models upon which more advanced treatments are based. Later chapters will build on these basic models to tackle more challenging questions using sophisticated mathematical approaches that define modern coevolutionary research. By developing the mathematical formalism from the ground up, I hope to make coevolutionary theory accessible to a wide range of biologists. Furthermore, this structure will maximize the utility of the book as a template for graduate seminars and courses focused on species interactions and coevolution. The availability of online Mathematica notebooks developed to accompany each chapter will enable individual investigation and provide a scaffold from which individuals can build more complex models tailored to their specific interests and study systems. Tentative Outline Chapter 1. A brief history of coevolution Chapter 2. Why the time has come to re-define coevolution. Its really about reciprocal selection. This is what all the models study. The theory of coevolution is actually a theory of reciprocal selection. Section I. The origins of coevolutionary theory What was the empirical motivation? Section II. Fundamentals of coevolution Chapter 1. Janzen and reciprocal evolutionary change i. Reciprocal natural selection ii. Evolutionary fundamentals iii. Pre-requisites for coevolution Section II. Coevolution in simple genetic systems Chapter 2. Coevolution of major genes i. ii. iii. A brief introduction to infection genetics A generic single locus framework Infection genetics and coevolutionary dynamics Chapter 3. Coevolution of polygenic traits i. ii. iii. iv. The phenotypic interface of coevolution A general framework for the analysis of coevolving quantitative traits The coevolutionary dynamics of matching The coevolutionary dynamics of escalation Section III. Coevolution and Demography Chapter 4. Coevolution in Lotka-Volterra systems i. ii. iii. Merging coevolution and demography Separation of time scales approximations and adaptive dynamics Coevolution of predator and prey Chapter 5. Coevolutionary epidemiology i. ii. Integrating coevolution into epidemiological models The coevolution of virulence INDIRECT COEVOLUTION? Zh->Np->zp->Nh Section IV. Coevolutionary genetics Chapter 6. Dominance and segregation i. ii. Diploid infection genetics and dominance Coevolutionary dynamics, segregation, and deviations from Hardy-Weinberg Chapter 7. Multiple loci, epistasis, and recombination i. ii. Multi-locus infection genetics and epistasis Coevolutionary dynamics, recombination, and linkage disequilibrium Chapter 8. Modifier models and the coevolution of genome structure i. ii. iii. iv. What are modifier models and why are they useful? QLE approximations The coevolution of ploidy levels The red queen and coevolutionary models for the evolution of sex Section V. Spatial structure and local adaptation Chapter 9. Local adaptation, trait matching, and the geographic mosaic i. ii. Overview of empirical patterns The geographic mosaic theory Chapter 10. The coevolutionary dynamics of local adaptation i. ii. Quantifying local adaptation Local adaptation in coevolving metapopulations Chapter 11. The coevolutionary dynamics of trait matching i. ii. Quantifying trait matching Trait matching in coevolving metapopulations Section VI. Multi-species interactions and community structure Chapter 12. Coevolution in three species interactions i. ii. iii. Genetic correlations and interaction epistasis Diffuse vs. pairwise coevolution The dynamics of diffuse vs. pairwise coevolution Chapter 13. Coevolution within complex communities Chapter 1. A brief history of coevolutionary theory Although Ehrlich and Raven popularized coevolution, the modern idea of coevolution — and the term — was first formalized by Mode in 1950. Chapter 2. Fundamentals of coevolution In 1980, Janzen defined coevolution as reciprocal evolutionary change in interacting species, launching the modern era of coevolutionary research. Specifically, Janzen defined coevolution as Janzen 1980: “an evolutionary change in a trait of the individuals in one population in response to a trait of the individuals of the second population, followed by an evolutionary response by the second population to the change in the first” In more precise mathematical terms, Janzen’s definition requires that evolutionary change in the phenotype distribution of a focal trait within Species 1 be a function of the phenotype distribution of a trait in Species 2: ∆𝜑𝑧1 = 𝑓(𝜑𝑧2 ) (1a) ∆𝜑𝑧2 = 𝑓(𝜑𝑧1 ) (1b) and vice versa These two equations, which predict the evolutionary change in the phenotype distributions of the two species that occurs over a single generation, Where 𝜑𝑧1 is the phenotypic distribution of a trait within species 1, 𝜑𝑧2 is a phenotypic distribution of a trait within species 2 and Janzen’s definition provided a simple yet precise definition of coevolution and DISTINCTLY EVOLUTIONARY. VERY DIFFERENT FROM EARLIER MODELS WHICH USED THE TERM IN A DISTINCTLY ECOLOGICAL FASHION. MORE IN LINE WITH MODE, AND JAYAKAR WHO DEVELOPED TRUE COEVOLUTIONARY MODELS PRECEEDING JANZEN. Perhaps the clearest mathematical formalization of Although intuitive, a mathematical formalization of Janzen’s definition clarifies essential pre-requisites for coevolution. Perhaps the easiest way to understand Janzen’s definition Janzen’s verbal definition leads to a straightforward and very general criterion for coevolution: ̅ 1 𝜕𝑊 ̅ 𝜕𝑧̅ 𝑊