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 potentially lead to 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 our goal will be to develop formal mathematical expressions that capture the key
elements of Janzen’s definition. We will then use this mathematical formalism to identify the prerequisites for coevolution, show how these pre-requisites are commonly integrated into mathematical
models, and 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?
1
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, and that which really sets
coevolution apart: 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 such that:
∆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. With
equations (3) in hand, we have a very general mathematical formulation for reciprocal evolutionary
change in interacting species. In addition to formalizing Janzen’s seminal definition, equations (3)
illuminate two pre-requisites for coevolution:
2
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
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 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).
∆𝑥̅ = 𝐺𝑋 𝑆𝑋 (𝜑𝑌 )
(2a)
∆𝑦̅ = 𝐺𝑌 𝑆𝑌 (𝜑𝑋 )
(2b)
∆𝑥̅ = ℎ𝑥2 𝜉𝑥 (𝑥̅ − 𝑦̅)
(3a)
∆𝑦̅ = ℎ𝑦2 𝜉𝑥 (𝑥̅ − 𝑦̅)
(3b)
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:
∆𝑥̅ = ℎ𝑥2 𝑆𝑥
(1a)
∆𝑦̅ = ℎ𝑦2 𝑆𝑦
(1b)
3
where ℎ𝑥2 and ℎ𝑦2 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:
∆𝑥̅ = ℎ𝑥2 𝑆𝑥 (𝜑𝑦 )
(2a)
∆𝑦̅ = ℎ𝑦2 𝑆𝑦 (𝜑𝑥 )
(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.
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).
∆𝑝 ≈ 𝑠(𝑝𝑦 )𝑝𝑥 𝑞𝑥
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
4
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.
 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
5
∆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…
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?
6