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 Introduction Chapter 1. A brief history of coevolutionary theory - 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. Chapter 3. The structure of coevolutionary models Infection matrices. What are they? Pattern vs process. How could we identify them? Evolutionary and experimental sampling effects Interaction functions. What are they? How could we identoify the,m? 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 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 OF NETWORKS Section VII. MacroCoevolution Chapter 13. Coevolution and phylogeny Section VIII. Three Myths of Coevolution 1. Local adaptation = winning 2. GFG genetics exists 3. Coevolution is a special case Introduction Coevolution: moving beyond the special case scenario upon which pop gen and q gen is built. Here I am going to argue for a twfold revolution: 1) rethink Janzenian definition and focus instead on Thompsonian selection mosaics which are, after all, what all coevolutionary models are made of 2) thrust coevolution into the general center of P-Gen and Q-gen. For too long coevolution has been relegated to “ecology” and PQ-gen has marched merrily along in ignorant bliss. AS RICHARD GOMULKIEWICZ ONCE TOLD ME: IT IS THE POPULATION GENETICISTS WHO ARE THE CONCIENSCE OF BIOLOGY. It is my hope that this book serves as a counter-point and acts in this way: as the conscience of coevolutionary biology. WE SHOULD MAINTAIN JANZEN’S DEFINITION TO COMBAT THE FORCES OF SLOVENLY SLOPPY THINKING. AS MIKE LYNCH WROTE “THE DETAILS MATTER AND THEY MATTER A LOT” . JANZEN BROUGHT RIGOUR TO COEVOLUTION; A RIZGOUR THAT HAS FADED. COEVOLUTION HAS BECOME ISOLATED DUE TO THE SRINGENCY OF THE DEFINITION. HOWEVER, A MORE ACCURATE VIEW OF MOST COEVOLUTIONARY THEORY IS AS A ***GENERALIZATION OF STANDARD Q and P GEN*** which relaxes key assumptions. IT IS TIME FOR COEVOLUTION TO ZGO MAINSTREAM AND NO LONGER DEFINED BY SOMEWHAT QUIRKY AND PARTICULAR METHODOLOGIES AND QUESTION. THIS SHIT IS FUNDAMENTAL. ALTHOUGH COEVOLUITON IS OFEN VIEW AS RARE OR AS A SPECIAL CASE, FROM A MATHEMATICAL STANDPOINT, IT IS IRREFUTABLE THAT COEVOLUTIONARY THEORY IS ACTUALLY A GENERALIZATION OF SINGLE SPECIES PGEN AND QGEN. IN ADDITION TO NOT REFLECTING WHAT WE ATUALLY MODEL, JANZEN’s DEFINITION IS FAR TOO DIFFICULT TO DOCUMENT IN THE NATURAL WORLD. WE ALMOST NEVER DOCUMENT EVOLUTION LET ALONE COEVOLUITON. AN AUXILARY PURPOSE OF THIS BOOK IS THAT THE TIME HAS COME TO MOVE COEVOLUTION INTO THE PURVIEW OF ORDINARY EVOLUTIONARY TECHNIQUES. THUS, AS WITH MUCH OF EVOLUTIONARY BIOLOGY, WE SHOULD FOCUS ON THE PRE-REQUISITES. IS THERE COEVOOLUTIONARY SELECTION FOR TRAITS WITH ADDITIVE GENETIC VARIANCE… I HAVE A LOVE HATE RELATIONSHIP WITH JANZEN’S DEFINITION. ON THE PLUS SIDE, IT MADE COEVOLUTION CONCRETE AND ALLOWED US TO FOCUS ON ONE SPECIFIC PHENOMENON IN A RIGOROUS WAY AND BROUGHT THE FOCUS IN ON PAIRS OF INTERACTING TRAITS. AT THE SAME TIME, HOWEVER, JANZEN’S DEFINITION IS SO IMPRACTICAL IT HAS ALIENATED MANY RESEARCHERS AND PUSHED COEVOLUTION INTO THE FRINGE. WORSE YET, I WILL DEMONSTRATE AND ARGUE THROUGHOUT THIS BOOK, THAT THE VAST BULK OF COEVOLUTIONARY MODELS INCLUDE THE PREREQUISOITES FOR JANZENIAN COEVOLUTION BUT DO NOT per se STUDY JANZENIAN COEVOLUTION. Chapter 1. A brief history of coevolutionary theory (COMBINE WITH INTRODUCTION?) Although Ehrlich and Raven popularized coevolution, the modern idea of coevolution — and the term — was first formalized by Mode in 1950. Not really clear why Ehrlich and Raven is considered so important when, at least to a theoretician, it was mode who nailed it. Thompson has provided an exhaustive history of coevolution in his books. My goal here is somewhat different. Specifically, I hope to provide a view of the historical development of coevolutionary modeling; one informed by the sequence of influential models related to the topic developing from Mode’s first published model to now… Empirical/Conceptual Motivation 1. Flor, Flax, and plant disease Mode and Jayakar 2. Epidemiology Anderson and May Frank 3. Evolution of sex Frank, Parker, Lively, Hamilton, NEE 4. Community ecology and assembly and stability Roughgarden, Abrams, Dieckman 5. Spatial structure and local adaptation (or call this modern era where we know coevolution matters for everything? Here we see coevolution being brought into the general fold of population genetics and quantitative genetics. No more freaky special case modeling, just a relaxation of normal pop gen and q gen assumptions) GMTC papers, Morand, Gandon, Gavrilets 6. Population genetic and quantitative genetic approaches with analytical results Seger 1988 Gavrilets Mode (1958). “A mathematical model for the co-evolution of obligate parasites and their hosts” EHRLICH AND RAVEN (1964) Jayakar (1970) Roughgarden and ecological coevolution leading the field astray… Down the path of any reciprocal influence = coevolution… Jaenike (1978)???? Slatkin and Maynard Smith (1979). Hamilton (1980) (696 Cites) LAWLOR, LR; SMITH, JM (1976). CO-EVOLUTION AND STABILITY OF COMPETING SPECIES. (210 Cites). JANZEN (1980) May and Anderson (1983). EPIDEMIOLOGY AND GENETICS IN THE COEVOLUTION OF PARASITES AND HOSTS (507 Cites) Kiester, Lande, and Schemske (1984) MODELS OF COEVOLUTION AND SPECIATION IN PLANTS AND THEIR POLLINATORS (92 Cites) TAPER, ML; CASE, TJ (1985) QUANTITATIVE GENETIC MODELS FOR THE COEVOLUTION OF CHARACTER DISPLACEMENT (139 Cites) Seger (1988) Nee, S (1989). ANTAGONISTIC CO-EVOLUTION AND THE EVOLUTION OF GENOTYPIC RANDOMIZATION (55 Cites) HOWARD, RS; LIVELY, CM (1994). PARASITISM, MUTATION ACCUMULATION AND THE MAINTENANCE OF SEX. (198 Cites). Morand (1996) (115 cites) Ebert, Dieter; Hamilton, William D. (1996). TREE. Sex against virulence: The coevolution of parasitic diseases (164 Cites). DIECKMANN, U; MARROW, P; LAW, R (1995). EVOLUTIONARY CYCLING IN PREDATOR-PREY INTERACTIONS - POPULATION-DYNAMICS AND THE RED QUEEN. (120 cites) Dieckmann, U; Law, R (1996). The dynamical theory of coevolution: A derivation from stochastic ecological processes. (329 Cites) Gandon et al (1996) (284 Cites) Abrams (1997) Caldarelli, G; Higgs, PG; McKane, AJ. (1998). Modelling coevolution in multispecies communities (110 cites) Gavrilets (1997 and 1998) FRANK, SA (1993). COEVOLUTIONARY GENETICS OF PLANTS AND PATHOGENS (120 cites) Frank (1993, 1994) and Frank Parker debates Pathogens and sex in plants Article Author: Parker, Matthew (1994) Modern times, the GMTC and the emergence of coevolutionary genetics, community ecology Chapter 2. Fundamentals of Coevolution: Pre-requisites for Reciprocal Evolutionary Change 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” Janzen’s definition provided a simple yet precise definition of coevolution DISTINCTLY EVOLUTIONARY. VERY DIFFERENT FROM Roughgarden types of MODELS WHICH USED THE TERM IN A DISTINCTLY ECOLOGICAL FASHION. MORE IN LINE WITH MODE, AND JAYAKAR WHO DEVELOPED TRUE COEVOLUTIONARY MODELS PRECEEDING JANZEN. Formalizing Janzen’s verbal definition mathematically is straightforward and provides valuable insights into the pre-requisites required for coevolution to occur. To take a concrete example, imagine the interaction between the plant species XX and its long tongued pollinating fly XX. In this system, the relative lengths of the flies tongue, x, and the plants corolla, y, are of central importance (REFS). If we disregard the possibility of coevolution, evolutionary change in the length of these quantitative traits can be predicted using the classical breeder’s equation: βπ₯Μ = βπ₯2 ππ₯ (1a) βπ¦Μ = βπ¦2 ππ¦ (1b) where βπ₯2 and βπ¦2 are the heritabilities of fly tongue and plant corolla respectively, and Sx and Sy are the selection differentials acting on these traits. Obviously, as written in (1), coevolution does not occur and the traits of the interacting species evolve independently in response to a constant and predictable strength of selection. This is a classical simplifying assumption common to the majority of population genetic and quantitative genetic theory (Figure 1a). If, however, we relax the assumption that selection acting on the length of plant corolla is independent of fly tongue length and vice versa (Figure 1b), we can easily extend the classical breeders equation in (1) to allow for coevolution as defined by Janzen: βπ₯Μ = βπ₯2 ππ₯ (ππ¦ ) (2a) βπ¦Μ = βπ¦2 ππ¦ (ππ₯ ) (2b) where the selection differentials Sx and Sy are now explicitly recognized to be functions of the distribution of phenotypes φx and φy within the interacting species. Equations (2) demonstrate two important pre-requisites for coevolution Sensu Janzen: 1. There must be additive genetic variation for the traits mediating an interspecific interaction 2. Selection acting on the traits mediating the interaction must depend upon the distribution of phenotypes within the trait of the interacting species The basic structure of coevolutionary models The pre-requisites for coevolution imposed by Janzen’s definition suggest that all coevolutionary models must have two fundamental ingredients: 1) a mechanism of inheritance and 2) a mechanism of reciprocal selection. As a crude generalization, most models accomplish this using either quantitative or population genetic approaches. Models based within the framework of quantitative genetics assume that a trait (or suite of traits) within one species interact functionally with a trait (or suite of traits) within another species. Reciprocal selection is then produced because the outcome of an interaction between two individuals is a function of their phenotypes. This interaction function must include a phenotype x phenotype interaction for the model to be truly coevolutionary. Figure X illustrates several examples of interaction functions which do, and do not, meet this criterion. In general, inheritance within such quantitative genetic models of coevolution is implicit, with additive genetic variance or heritability assumed to be a fixed model parameter (see Chapter 4 for details) Models based within the framework of population genetics assume that a gene (or collection of genes) within one species interact with a gene (or collection of genes) within the interacting species. In such cases, reciprocal selection is generated because the outcome of encounters between individuals depends on the interaction between their genotypes (e.g., infect/resist). Because genotypes are discrete, the outcome of encounters is defined by an interaction matrix which must include genotype x genotype interactions for the model to be truly coevolutionary. Figure X shows several interaction matrices which do, and do not, meet this criterion. In contrast to the quantitative genetic framework, population genetic models of coevolution explicitly model inheritance and thus allow the influence of genetic details such as segregation and recombination to be studied (See chapters 4 and 5 for details). In summary, all coevolutionary models include mechanisms of inheritance and reciprocal selection. Although the details and subtleties of inheritance and the mechanistic basis of interaction differ widely among models, all are united by a single essential feature: an interspecific interaction between the phenotypes or genotypes of individuals which determines the fitness of the interacting organisms. Evaluating the pre-requisites for coevolution in natural populations An obvious question facing anyone studying an interspecific interaction is whether or not the species are coevolving. Although superficially simple, answering this question in the wild has proven to be spectacularly challenging, with only a handful of compelling examples of coevolution (REFS). Although the absence of compelling examples may at first seem to suggest coevolution is rare and unimportant, the reality is that demonstrating coevolution in the strict sense outlined by Janzen is a virtually insurmountable task. Imagine trying to document XXX over the course of a single dissertation. The true difficulty of documenting coevolution is driven home by taking a sober look at the list of natural systems in which even garden variety evolution has been demonstrated. Set aside, Darwin’s finches, XXX, and XXX, and the list of natural systems where evolutionary change has been demonstrated in the wild over any substantial period of time becomes small indeed. As a consequence, much research has instead focused on the much more approachable task of evaluating the strength of selection and quantifying additive genetic variance. In other words, much evolutionary research on natural populations focuses on establishing that the pre-requisites for evolutionary met (additive genetic variance and selection), rather than documenting evolutionary change per se. I argue that this is exactly the shift we must make within coevolutionary biology in order to finally come to grips with the question of how important coevolution is within natural populations. The fundamental pre-requisites for coevolution are heritable variation for the relevant traits in the interacting species and reciprocal selection. If we are willing to accept the fact that heritable variation exists for virtually every quantitative trait studied to date (REFS), it becomes clear that the great unknown is the prevalence and strength of reciprocal selection. If reciprocal selection is common, it is likely that coevolution is a fundamentally important force; if it is rare, coevolution is nothing more than an evolutionary side show. It is imperative that over the next ten years, reciprocal selection be estimated in a sufficient number of systems for key generalizations to emerge about the strength of reciprocal selection in the wild. Although significantly more challenging than estimating the strength of selection in single species systems, appropriate statistical and methodological approaches are available for estimating the strength of reciprocal selection. Irrespective of approach, any empirical estimation of reciprocal selection requires two key pieces of information: 1) Phenotypes/Genotypes of interacting individuals and 2) Fitness of interacting individuals. ο¨ Quantifying the strength of reciprocal selection in natural systems is the single most pressing challenge within coevolutionary biology. Although Janzen’s definition focuses explicitly on traits and thus lends itself to a quantitative genetics formalization, it can be extended to a simpler population genetic framework without any loss of precision. Specifically, if we now imagine that some subset of genes βπ₯Μ = πΊπ₯ Μ π₯ 1 ππ Μ π₯ ππ₯Μ π βπ ≈ π (ππ¦ )ππ₯ ππ₯ Although written in quantitative genetics terms, (2) apply equally to population genetics where “gene” can more or less be subsititued for trait… equations (2) are too general to provide any real mathematical insight into coevolutionary dynamics, they are invaluable for what they teach us about empirical investigation of coevolution and as a starting point for the development of predictive models. Chapter 3. Coevolution of major genes One of the simplest possible models of coevolution arises when the outcome of encounters between interacting species is mediated by a single haploid gene in each of the interacting species. Although clearly an oversimplification, such single locus haploid models have provided valuable insights into the process of coevolution and are perhaps not such terribly poor approximations to reality in some systems. Take, for instance, the interaction between … L Biological Motivation Begin with an introduction about interactions between genes… Perhaps NOD? Vir? Or, a cartoon example with cute little cartoon molecules? EXPLAIN HOW THE INTERACTION WOULD WORK, THEN SAY, BUT HOW COULD WE MODEL THIS? HAPLOID Translating Biology into Equations We will take as our mathematical starting point the classical expression for evolutionary change in a haploid diallelic locus originally derived by Wright (REF): βπ = Μ ππ ππ€ Μ ππ π€ (1) Clearly, what we need to know is the mean fitness of the two species as a function of the genotype frequencies within the population. With this information in hand, coevolutionary dynamics can be predicted using (1). Equation (1) suggests our goal should be to calculate the mean fitness for each of the interacting species. Since a population mean fitness is nothing but the average fitness of the population, our road forward involves specification of the fitnesses of each of the possible genotypes. How can we derive this? Let’s use the information we gathered from our cartoon example… Assuming that individuals of the two species encounter one another at random, the fitness of each genotype is simply the sum of the fitness consequences of possible encounters weighted by the probability of each type of encounter: ππ΄ = 1 + π π₯ [π(π΄, π΅)ππ¦ + π(π΄, π)ππ¦ ] (2a) ππ = 1 + π π₯ [π(π, π΅)ππ¦ + π(π, π)ππ¦ ] (2b) ππ΅ = 1 + π π¦ [π(π΄, π΅)ππ₯ + π(π, π΅)ππ₯ ] (2c) ππ = 1 + π π¦ [π(π΄, π)ππ₯ + π(π, π)ππ₯ ] (2d) Can I just push this through in a completely general way? I don’t see why not… Using (2), it is straightforward to calculate the population mean fitness for each species. Specifically, the population mean fitness for species x is simply the expected fitness of genotypes segregating within the population: Μ π₯ = ππ΄ ππ₯ + ππ ππ₯ = π π₯ ππ₯ [π(π΄, π΅)ππ¦ + π(π΄, π)ππ¦ ] + π π₯ ππ₯ [π(π, π΅)ππ¦ + π(π, π)ππ¦ ] π (3a) Μ π¦ = ππ΅ ππ¦ + ππ ππ¦ = π π¦ ππ¦ [π(π΄, π΅)ππ₯ + π(π΄, π)ππ₯ ] + π π₯ ππ₯ [π(π, π΅)ππ₯ + π(π, π)ππ₯ ] π (3b) Plugging (3) into (1) yields expressions for evolutionary change in our two interacting species: A weak coevolution Approximation INCLUDE A BOX ON APPROXIMATION Application: Infection genetics and the GFG vs. MA debate Table 1. Interaction matrix for a single haploid diallelic locus. Each possible interaction between genotypes is specified by a probability of interaction π(π, π) Species x genotype A a Species y genotype B π(π΄, π΅) π(π, π΅) b π(π΄, π) π(π, π) Chapter 4. Coevolution of polygenic traits Biological Motivation Begin with an introduction about interactions between quantitative traits… Give a colorful example… Translating Biology into Equations KEEP IT GENERAL HERE A quantitative genetic approximation We will take as our mathematical starting point the equation: βπ§Μ = πΊ Μ 1 ππ Μ ππ§Μ π Rather than derive this well-worn equation from first principles, it is sufficient here to simply realize that its key assumptions are that selection is relatively weak and additive genetic variance is fixed. Mathematical Technique: DESCRIBING FREQUENCY DISTRIBUTIONS USING STATISTICAL MOMENTS (IN A BOX) Application: TRAIT MATCHING? NOTE THAT TAYLOR EXPANDING ASSUMING WEAK COEVOLUTION LEADS TO STRAIGHT UP EVOLUTIOn: SUGGESTS THAT IF COEVOLUTION IS GENERALLY WEAK, WE WON’T BE ABLE TO DETECT IT AND IT WILL LOOK JUST LIKE ORDINARY OLD EVOLUTION (AND BEHAVE LIKE IT)