Chapter 2. Fundamentals of Coevolution
INSERT INTRODUCTORY PARAGRAPH WHICH LEADS IN TO DEFINING COEVOLUTION.
Defining 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). THIS IS THE DEFINITION WE WILL USE. EXPLAIN WHY. EXPLAIN CURRENT
STATUS OF DEFINITION
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 prerequisites for coevolution, 2) show how these pre-requisites are commonly integrated into
mathematical models, and 3) illustrate why coevolution is likely to be sporadic.
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
1
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
1). 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:
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 generally integrated into
coevolutionary models of different types and evaluate the extent to which these pre-requisites are
satisfied in natural populations.
2
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, substantial confusion persists within the literature over what, exactly, a model must include to be
truly coevolutionary. Perhaps the single most common break from Janzen’s definition arises within
models employing INDIRECT COEVOLUTION MEDIATED BY POPULATION DENSITIES. 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 because they lack a
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 pre-requisites 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 could
depend on running speed in both Cheetah and Impala such that the probability of capture, P, could be
described by the function:
1
𝑃 = 1+𝐸𝑥𝑝[𝑥−𝑦]
(4)
where x is the maximum running speed of the Cheetah and y the maximum running speed of the Impala
(Figure X). Since we can safely assume being captured by a cheetah is detrimental to Impala fitness but
beneficial to cheetah fitness, we can easily incorporate the interaction function P into expressions
describing the fitness consequences of an encounter between Cheetah and Impala:
𝑊𝑋 = 1 + 𝑆𝑋 𝑃(𝑥, 𝑦)
(5a)
𝑊𝑌 = 1 − 𝑆𝑌 𝑃(𝑥, 𝑦)
(5b)
where the coefficients 𝑆𝑋 and 𝑆𝑌 measure how much capturing an Impala improves Cheetah fitness and
how much being captured by a Cheetah reduces Impala fitness, respectively. Biologically, fitness
equations (5) capture the idea that an encounter between a slow Impala and a fast Cheetah is likely to
improve Cheetah fitness at the expense of Impala fitness whereas encounters between a slow Cheetah
3
and a speedy Impala is unlikely to improve Cheetah fitness or reduce Impala fitness. With equations (5)
in hand, classical quantitative genetics tools can be used to calculate the strength of selection acting on
each of the interacting species (see Chapter 4 for details). As long as selection on each of the species
depends on the phenotype distribution within the interacting species, selection is reciprocal.
In contrast to the detailed mechanistic integration of reciprocal selection, inheritance is included
within quantitative genetic models of coevolution only implicitly, and represented only by a fixed
parameter summarizing the amount of additive genetic variance available to fuel a response to
reciprocal selection (see Chapter 4 for details). Consequently, the second pre-requisite for coevolution
— additive genetic variation for the traits mediating the interaction — is automatically satisfied within
such models. Assuming additive genetic variance is fixed can be justified over relatively short
evolutionary timescales by assuming traits are controlled by a very large number of genes such that the
strength of selection acting on any single gene is quite weak. Under such conditions, mutation can — in
principle — replenish additive genetic variation at a rate equivalent to the rate at which it is depleted by
natural selection (REFS). Of course, we know that additive genetic variance is not always constant, but
can instead evolve quite rapidly under some circumstances (REFS). In such cases, more complex models
which allow additive genetic variance to evolve become more appropriate (REFS). In these more
complex models, the potential for coevolution can wax and wane as the amount of additive genetic
variation for the traits mediating the interaction fluctuates over time (REFS).
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 elicitor on the rust (genotype) and the particular variant of a recognition molecule in
the plant (genotype) such that the probability of infection, α, is described by a matrix:
Plant
recognition genotype
bb
Bb
BB
AA 0.85 0.82 0.84
Rust
Aa 0.82 0.25 0.27
elicitor genotype
aa 0.79 0.22 0.26
where each entry represents the probability that an encounter between a plant genotype and rust
genotype leads to infection of the host. When an encounter between a rust (X) and plant (Y) leads to
infection, it seems reasonable to assume the fitness of the rust is increased by some amount 𝑆𝑋 while
the fitness of the plant is decreased by some amount 𝑆𝑌 . Generally, these assumptions lead to the
4
formulation of expressions for the fitness of individuals of the two species when an encounter occurs
between a rust of genotype i and plant of genotype j:
𝑊𝑋,𝑖 = 1 + 𝑆𝑋 𝛼𝑖,𝑗
(8a)
𝑊𝑌,𝑗 = 1 − 𝑆𝑌 𝛼𝑖,𝑗
(8b)
where the value of 𝛼𝑖,𝑗 is given by the matrix entry for the appropriate combination of plant and rust
genotypes. Biologically, fitness equations (8) capture the idea that an encounter between a rust and
host which eludes detection by the host immune system is likely to improve rust fitness at the expense
of plant fitness whereas an encounter between a rust and host which elicits a host immune defense is
unlikely to improve rust fitness or reduce host fitness. From this point, standard expressions drawn from
population genetics can be used to evaluate the strength of selection acting on each species (See
Chapter 3 for details).
In contrast to quantitative genetics, models employing a population genetic approach explicitly
model inheritance and thus allow the influence of genetic details, such as rates of segregation and
recombination to be studied (See chapters 5 and 6 for details). Of course, all of this genetic richness
comes at a high mathematical price. For even a single pair of coevolving diploid species whose
interaction is mediated by just two diallelic loci, a full mathematical description of the coevolutionary
process requires NINE equations for each species! Largely for this reason, we have a wealth of single
locus models and strong bias toward haploid organisms. Fortunately, coevolutionary models are now
beginning to move beyond these very simple genetic scenarios by employing moment based approaches
and separation of time scales approximations which allow more complex multi-locus models to be
studied (REFS). These approaches will be introduced in Chapters X and X and used to study how and
when coevolution can drive the evolution of sexual reproduction.
In summary, all coevolutionary models include mechanisms of reciprocal selection and
inheritance. 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 heritable phenotypes of individuals capable of generating reciprocal selection on the
interacting organisms.
The sporadic nature of reciprocal selection and coevolutionary change
Before we move on to discuss empirical support for the key pre-requisites of coevolution —
reciprocal selection and additive genetic variation — it is crucial to address one very common
misconception: the frequency with which coevolutionary models actually generate reciprocal selection
and reciprocal evolutionary change. As we saw in the previous section, all coevolutionary models include
mechanisms that can generate reciprocal selection and can allow for the inheritance of traits mediating
the interaction. What we did not see, however, is that these models do not actually generate reciprocal
selection and reciprocal evolutionary change —coevolution using Janzen’s strict definition — at all
points in time. Instead, your average, garden variety coevolutionary model might generate empirically
detectable reciprocal selection or reciprocal evolutionary change only sporadically, in perhaps 25-75% of
5
generations or “field seasons”, or might produce little or no reciprocal evolutionary change for
thousands of generations before unleashing a torrent of extremely rapid coevolutionary change in a
single burst (Figure XX). Although it is premature to delve into the nuanced reasons coevolutionary
change can be so sporadic (since we have yet to analyze even a single coevolutionary model!) the basic
reasons are that: 1) the strength of reciprocal selection waxes and wanes as the phenotype distributions
of the interacting species continually adjust and readjust to one another over evolutionary time, and 2)
additive genetic variance underlying traits mediating interactions can fluctuate significantly over time in
response to reciprocal selection. Thus, as Thompson has long argued (REFS), it is naïve to expect
coevolution to be ongoing and strong enough to be detectable in all populations and all times.
This fundamental result, which emerges over and over again from all types of coevolutionary
models, has important consequences for the design and interpretation of studies investigating
coevolution within natural populations.
6