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.
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
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.
Quantifying trait matching
ii.
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
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.
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. Not really clear why Ehrlich and Raven is considered so important
when, at least to a theoretician, it was mode who nailed it.
Mode
Jayakar
Roughgarden and ecological coevolution
Hamilton
Frank
Modern times, the GMTC and the emergence of coevolutionary genetics
Chapter 2. Fundamentals of Coevolution: Moving beyond 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 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.
In the most general mathematical terms, Janzen’s definition requires that evolutionary change in the
distribution of a phenotype within Species 1 be a function of the distribution of a phenotype within
Species 2:
∆𝜑𝑧1 = 𝑓(𝜑𝑧2 )
(1a)
∆𝜑𝑧2 = 𝑓(𝜑𝑧1 )
(1b)
and vice versa
Where 𝜑𝑧1 is the phenotype frequency distribution within species 1, 𝜑𝑧2 is the phenotype frequency
distribution within species 2, and ∆ indicates the change which occurs over a single generation. Although
equations (1) are quite general and clearly capture Janzen’s intent,
Putting Janzen’s definition into the mathematical formalism of quantitative genetics requires that
evolutionary change in the distribution of a phenotype within Species 1 be a function of the distribution
of a phenotype within Species 2:
∆𝑧̅1 = 𝐺1 𝛽1 (𝑧2 )
(2a)
∆𝑧̅2 = 𝐺2 𝛽2 (𝑧1 )
(2b)
and vice versa
Where 𝜑𝑧1 is the phenotype frequency distribution within species 1, 𝜑𝑧2 is the phenotype frequency
distribution within species 2, and ∆ indicates the change which occurs over a single generation. Although
equations (1) are quite general and clearly capture Janzen’s intent,
Putting Janzen’s definition into the mathematical formalism of quantitative genetics requires that
evolutionary change in the distribution of a phenotype within Species 1 be a function of the distribution
of a phenotype within Species 2:
∆𝑧̅1 = ℎ12 𝑆1 (𝑧2 )
(2a)
and vice versa
∆𝑧̅2 = 𝐺2 𝛽2 (𝑧1 )
(2b)
Where 𝜑𝑧1 is the phenotype frequency distribution within species 1, 𝜑𝑧2 is the phenotype frequency
distribution within species 2, and ∆ indicates the change which occurs over a single generation. Although
equations (1) are quite general and clearly capture Janzen’s intent,
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
Chapter 3. Coevolution of major genes
Begin with an introduction about interactions between quantitative traits… Give a colorful example…
We will take as our mathematical starting point the equation:
∆𝑧̅ = 𝐺
̅
1 𝜕𝑊
̅ 𝜕𝑧̅
𝑊
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.
Chapter 4. Coevolution of polygenic traits
Begin with an introduction about interactions between quantitative traits… Give a colorful example…
We will take as our mathematical starting point the equation:
∆𝑧̅ = 𝐺
̅
1 𝜕𝑊
̅ 𝜕𝑧̅
𝑊
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.