Chapter 2. Fundamentals of Coevolution
As with almost any major theme in evolutionary biology, the roots of coevolution can be traced
back to Darwin. Although he did not formalize the idea of coevolution, Darwin clearly believed species
interactions were prevalent, likely to impose significant natural selection, and important in driving coadaptation (REFERENCE). Unlike many of the other themes Darwin discussed, however, coevolution was
largely excluded from the rich mathematical and conceptual development of the Modern Synthesis.
Instead, our understanding of species interactions and coevolution developed largely within the field of
ecology, following a somewhat diffuse and wandering path (REFERENCE TO JOHN). Thus, despite its
promising beginnings within the Origin of Species, a unified conceptual framework for coevolution
remained elusive until Dan Janzen developed and popularized a rigorous definition of the process in
1980. In this seminal article, Janzen argued that the term coevolution should be restricted to cases
where
“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 short, Janzen argued that coevolution requires reciprocal evolutionary change in the traits of
interacting species (Figure 1).
Although Janzen’s definition provided an invaluable service by clearly linking a specific
evolutionary process to the term “coevolution”, it did little to drive coevolution into the mainstream of
evolutionary biology. There are two reasons for this, both of which stem primarily from an overzealous
interpretation of Janzen’s definition. First, coevolution is often dismissed as a special case of evolution
relevant only to tightly interacting pairs of species because of the naïve expectation that it requires
reciprocal evolutionary change in all places and times. Second, empirical evidence for coevolution has
been slow to accumulate because too much focus has been placed on reciprocal evolutionary change,
per se, rather than its more approachable building blocks -- reciprocal selection and genetic variation. In
the rest of this chapter we will develop formal mathematical expressions that capture the key elements
of Janzen’s definition. We will then use this mathematical formalism to: 1) identify the pre-requisites for
coevolution, 2) show how these pre-requisites are commonly integrated into mathematical models, and
3) illustrate how empirical studies can be used to evaluate whether the pre-requisites are satisfied
within natural populations.
Key Questions:



What are the pre-requisites for coevolution?
How are these pre-requisites integrated into mathematical models?
Are these pre-requisites satisfied within natural populations?
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Identifying the Pre-requisites for Coevolution
Janzen defined coevolution as reciprocal evolutionary change in the traits of interacting species.
Our goal in this section is to translate this verbal definition into mathematical expressions and use these
expressions to identify the pre-requisites for coevolution. Because Janzen’s verbal definition invokes the
notion of traits, a logical starting point is classical quantitative genetics. Almost without doubt you have
encountered the classical breeder’s equation of quantitative genetics before, whether in the classroom
as part of a course in evolutionary biology or quantitative genetics, or perhaps more unexpectedly and
unpleasantly as part of your prelims:
∆𝑧̅ = ℎ2 𝑆.
(1)
The terms in equation (1) all have familiar and intuitive meanings: ∆𝑧̅ is the change in the population
mean value of phenotype z that occurs over a single generation, ℎ2 is the narrow sense heritability, and
S is the selection differential. Thus, equation (1) emphasizes that for natural selection to cause
evolution, there must be additive genetic variation (ℎ2 > 0) and an association between phenotypes
and fitness (𝑆 ≠ 0).
In order to accommodate Janzen’s definition, we will obviously need to extend the simple
breeder’s equation (1) to a scenario with two interacting species, say species X and species Y, with traits
x and y:
∆𝑥̅ = ℎ𝑥2 𝑆𝑥
(2a)
∆𝑦̅ = ℎ𝑦2 𝑆𝑦
(2b)
where each species is now characterized by its own heritability and selection differential. With
equations (2) we have managed to capture a significant chunk of Janzen’s definition. Specifically, we
now have mathematical expressions for evolutionary change in the traits of interacting species. What
our equations miss, however, is the most critical word in Janzen’s definition: reciprocal. The clearest and
most biologically relevant way in which reciprocal evolution can be integrated into (2) is by assuming
that the selection differential acting on each species depends on the frequency distribution of traits
within the interacting species:
∆𝑥̅ = ℎ𝑥2 𝑆𝑥 (𝜑𝑦 )
(3a)
∆𝑦̅ = ℎ𝑦2 𝑆𝑦 (𝜑𝑥 )
(3b)
where 𝜑𝑥 is the frequency distribution of trait x and 𝜑𝑦 is the frequency distribution of trait y (FIGURE
2). With equations (3) in hand, we have a very general mathematical formulation for reciprocal
evolutionary change in interacting species driven by reciprocal selection. In addition to formalizing
Janzen’s seminal definition, equations (3) illuminate two pre-requisites for coevolution:
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Pre-requisite 1 — There must be additive genetic variation for the traits mediating an
interspecific interaction
Pre-requisite 2 — Selection acting on the traits mediating the interaction must depend
upon the distribution of phenotypes within the interacting species
In the following sections, we will explore how these pre-requisites are integrated into coevolutionary
models and evaluate the extent to which these pre-requisites are satisfied in natural populations.
Integrating the Pre-requisites for Coevolution into Mathematical Models
The pre-requisites for coevolution imposed by Janzen’s definition suggest that all coevolutionary
models must include two fundamental ingredients: 1) a mechanism of inheritance and 2) a mechanism
of reciprocal selection based on individual phenotypes. Although this can be accomplished in many
ways, it is important to recognize that substantial confusion remains within the literature over what,
exactly, a model must include to be truly coevolutionary. Perhaps the single most common alternative
arises within models employing an adaptive dynamics approach. Often such models integrate reciprocal
evolutionary change only indirectly, through feedbacks driven by changes in population densities rather
than the traits of individuals (REFS). Although interesting and biologically relevant, such models do not
qualify as coevolutionary using Janzen’s definition which requires direct feedback between traits of the
interacting species. Because of its historical importance and precedent, as well as its clarity, we will
adhere to Janzen’s definition throughout this book and study only models that include the two prerequisites identified above. The bulk of coevolutionary theory which meets these criteria can be rather
crudely lumped into studies which employ either a quantitative genetic or population genetic approach.
In the sections below, we will explore how the pre-requisites for coevolution are generally integrated
into these two different modeling frameworks.
Quantitative Genetics
Models developed within the framework of quantitative genetics assume that a continuously
variable trait (or suite of traits) within one species interacts functionally with a continuously variable
trait (or suite of traits) within another species. Reciprocal selection is often integrated into such models
using an interaction function which predicts the outcome of encounters between individuals as a
function of their phenotypes. For instance, whether a Cheetah captures and consumes an Impala
(outcome) could depend on running speed in both Cheetah and Impala (Traits). It is important to realize
that for reciprocal selection to be possible, the outcome of an encounter between individuals must
depend on both their phenotypes in a rather particular way. Mathematically, the outcome, P, of an
encounter between individuals with phenotypes z1 and z2 must depend on both individual’s phenotypes
such that:
𝜕𝑃
𝜕𝑧1
= 𝑓(𝑧1 , 𝑧2 )
(1a)
and
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𝜕𝑃
𝜕𝑧2
= 𝑓(𝑧1 , 𝑧2 )
(1b)
If condition (1) is not satisfied, selection in at least one of the species will be independent of the
phenotype distribution in the other, and selection will fail to be reciprocal. 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).
XXXXX
Population Genetics
Models based within the framework of population genetics assume that a discrete trait (or
group of traits) within one species interacts functionally with a discrete trait (or group of traits) within
another species. Often, the traits in such models are implicit with the focus instead on the direct
interaction between a gene (or collection of genes) within one species and a gene (or collection of
genes) within another. Reciprocal selection is often integrated into such models using an interaction
matrix which predicts the outcome of encounters between individual genotypes. For instance, whether
a rust fungus successfully infects a potential host plant (outcome) could depend on the particular variant
of a surface protein on the rust (genotype) and the particular variant of a recognition molecule in the
plant (genotype). It is important to realize that for reciprocal selection to be possible, the outcome of an
encounter between individuals must depend on both their genotypes in a rather particular way.
Mathematically, the outcome, P, of an encounter between individuals with genotypes U1 and U2 must
depend on both individual’s genotypes such that:
𝑉[𝑃|𝑈1 ] > 0
for at least one genotype in U1
(2a)
𝑉[𝑃|𝑈2 ] > 0
for at least one genotype in U2
(2b)
and
where 𝑉[𝑃|𝑈𝑖 ] is the variance in outcome conditioned on genotype Ui. If condition (2) is not satisfied,
selection in at least one of the species will be independent of the genotype frequencies in the other, and
selection will fail to be reciprocal. Figure X illustrates several examples of interaction matrices which do,
and do not, meet this criterion.
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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
STATISTICAL EMPIRICAL STUDIES OF GXG VS. PRE_REQS IN MATHEMATICAL MMODELS. THE
GREAT DISCONNECT. WHAT DOES IT MEAN FOR EMPIRICAL STUDY? Illustrate why we must focus on prereqs and not coevo per se. Why models of coevolution… AREN’T! Show a nice figure with cycles showing
how GxG varies over time… And SHOW HOW AT EQUILIBRIUM, COEVOLUTION IS ZERO, BUT RECPROCAL
SELECTION AND GENETIC VARIATION ARE ABUNDANT. Mirror this to a study of evolution. WOULD WE
SAY EVOLUTION IS NOT OCCURING AT EQUILIBRIUM UNDER A STABILIZING SELECTION MODEL?
THIS IS WHERE I LEAVE JANZEN BEHIND AND SWITCH TO THE THOMPSONIAN VIEW OF THE
UNIVERSE…
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.
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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.
 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
∆𝑥̅ = 𝐺𝑥
̅𝑥
1 𝜕𝑊
̅𝑥 𝜕𝑥̅
𝑊
∆𝑝 ≈ 𝑠(𝑝𝑦 )𝑝𝑥 𝑞𝑥
Although written in quantitative genetics terms, (2) apply equally to population genetics where “gene”
can more or less be subsititued for trait…
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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.
Answers to Key Questions:
What are the pre-requisites for coevolution?
Genetic variation and reciprocal selection. If these two things are present coevolution is inevitable.
How are these pre-requisites integrated into mathematical models?
Generally, some form of additive genetic variation is included, whether the fixed G matrix for
quantitative genetics or the more dynamic genotype frequencies of population genetics. More
importantly, all coevolutionary models include some form of reciprocal selection where the fitness of
each species depends on the frequencies of various phenotypes or genotypes within the interacting
species. A key observation we can make is that there is a disconnect between what coevolutionary
models refer to as the strength of coevolutionary selection and the actual strength of coevolutionary
selection that would be observed.
Are these pre-requisites satisfied within natural populations?
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