Chapter 1. Fundamentals of Coevolution
Coevolution is the study of how species interactions evolve in response to the reciprocal
selection pressures they exert on one another. It is this dynamic interplay between evolutionary change
and selection which distinguishes coevolution from much of the rest of evolution. When selection is
driven by an interacting species that is also evolving, the potential arises for the adaptive landscape to
continuously change in a way that thwarts or facilitates adaptation (Figure 1). Although this unique
feature of coevolution is what makes it exciting and fun, it is also what makes modeling coevolution so
damn hard! As a general rule, any coevolutionary problem requires twice the number of parameters,
variables, and equations as an equivalent single species model. Worse, coevolutionary models often
generate strong non-linearities and produce complicated dynamics which can confound standard
analytical approaches.
So why even bother trying to model coevolution? The simple answer is that many fundamental
problems in evolutionary biology and ecology cannot be understood without grappling with how
interacting species evolve in response to one another. For instance, how can we even begin to
understand the assembly of biological communities without understanding the reciprocal evolution that
occurs between each new species and those species already present? How can biological invasions be
predicted or managed without first understanding the reciprocal evolution which occurs between
invaders and residents? How can the spread of a vector borne pathogen be predicted without
understanding how vector and pathogen coevolve? Although these and many other problems are
intrinsically coevolutionary, we have generally approached them using entirely non-coevolutionary
frameworks and theories. Perhaps it should come as no surprise, then, that we so often fail to accurately
predict the outcome of ecological and evolutionary processes where species interactions play an
important role.
The overarching goal of this book is to demonstrate the importance of a coevolutionary
approach to ecology and evolutionary biology. Where this book will differ from other books on
coevolution with similar goals is by focusing on how mathematical models can be used as a powerful
tool for improving our understanding of the coevolutionary process.
“The potential importance of a coevolutionary model does not follow from the addition of one more
type of interaction or constraint, but from the extent to which it can reveal some essential feature of
the interactions being modelled” Slatkin and JMS 1979,
Although we are making strides and much powerful coevolutionary theory has been developed, we still
lag so very far behind other fields of evolutionary biology where models are used on a daily basis and to
sch wonderful effect. For instance, the use of MLE and Bayesian approaches to select the best
underlying evolutionary model are standard practice within population genetics and phylogenetics but
1
are almost never used within coevolutionary biology. To begin catching up, we need to make
coevolutionary models accessible to a broader audience.
It is my hope that providing a straightforward introduction to the theory will allow more biologists
interested in species interactions, or intrinsically coevolutionary problems, to better appreciate what
coevolutionary models actually predict and why. Understanding coevolutionary models at this basic nuts
and bolts level will facilitate the development of more precise, robust, and powerful empirical tests of
coevolutionary hypotheses and theories. I also hope that by demystifying coevolutionary models, and
mathematical models in general, this book will encourage biologists to embark on the development and
analysis of coevolutionary models of their own.
ROADMAP TO THE CHAPTER In the rest of this chapter, we will first explore the history of
coevolutionary theory and use this historical context to identify and formalize the pre-requisites for
coevolutionary change. Next, we will learn how these pre-requisites are generally integrated into
mathematical models of coevolution. Here I will argue for a restricted view of coevolution as laid out by
Keister… Finally, we will explore why coevolutionary models suggest that empirically detectable
coevolutionary change should often be rare, even in cases where it is the most important force driving
the evolution of interacting species. The chapter will conclude with a brief overview of the remainder of
the book.
The development of coevolutionary theory
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 (Darwin 1859). Unlike many of the other themes Darwin discussed, however, coevolution
was largely excluded from the rich mathematical and conceptual development of the Modern Synthesis,
lying dormant until Flor’s discovery and description of gene-for-gene interactions between Flax and FlaxRust in the 1950’s (REFS). The discovery of relatively simple genetic interactions between host and
pathogen genes stimulated coevolutionary research and led to the development and analysis of the first
coevolutionary model (Mode 1958). In this model, Mode explored the process of coevolution using a
population genetic model integrating the specific genetic basis of resistance identified by Flor’s studies
of resistance in Linum marginale. Although Ehrlich and Raven (1964) popularized coevolution, the term
and its definition were first formalized by Mode in this vastly underappreciated paper.
Following Mode’s pioneering work, coevolutionary models of gene-for-gene interactions
continued to appear (Mode 1961; Person 1966; Jayakar 1970). However, it was not until the 1970’s that
the next major developments in coevolutionary occurred, spurred by increasing interest in
understanding the conditions that allowed competing species to coexist (Macarthur and Levins 1967).
During this time, several influential models appeared which took a new approach to coevolutionary
theory. Rather than using the framework of population genetics, these models explored how
coevolution of the parameters within Lotka-Volterra models of competition influenced coexistence
(Lawlor and Smith 1976; Roughgarden 1976). Although these models increased ecological realism by
2
explicitly integrating demography and ecological interaction, they did so at the expense of evolutionary
and genetic realism. Specifically, these models relied on analyses of evolutionary stable strategies (ESS)
or similar types of analyses which allow only equilibrium states to be explored, and not the actual short
term dynamics of coevolution (IS THIS TRUE)?
The next big innovations in coevolutionary theory occurred in the 1980’s with the publication of
three papers that moved coevolutionary theory into the mainstream of ecology and evolutionary
biology. First, Hamilton’s (1980) paper exploring how coevolution between hosts and parasites could
potentially drive the evolution of sexual reproduction launched a major them in coevolutionary biology
which has, perhaps, generated more coevolutionary models than any other single idea. This paper
studied a genetically explicit, multi-locus model, and showed that sexual reproduction could be favored
by shuffling and randomizing the host genome. USHERED IN THE IDEA THAT WE COULD STUDY HOW
COEVOLUTION INFLUENCES OTHER FEATURES OF BIOLOGY. Second, May and Anderson (1983)
introduced genetic variation into epidemiological models to show that coevolution between hosts and
parasites need not ultimately favor reduced virulence. As with the coevolutionary models of competitive
interactions introduced in the 1970’s this model integrated coevolution by allowing it to change the
parameters of an epidemiological model. Third, Kiester, Lande, and Schemske (1984) introduced a
model of coevolution between plants and pollinators which utilized a classical quantitative genetic
formulation. This model represented a new approach which, although not genetically explicit as were
the classical population genetic models of Mode, allowed for more evolutionary robust analyses than
the ecology focused coevolutionary models of the 1970’s.
Thus, by the end of the 1980’s three different approaches were commonly used to model
coevolution: 1) Population genetics, 2) ESS analyses of ecological models, and 3) Quantitative genetics.
As a broad generalization, these three approaches remain the basic engines of coevolutionary theory
although work in 1990’s and 2000’s developed powerful extensions and modifications. For instance,
population genetics models now commonly allow for multiple loci and make use of powerful new
analytical techniques involving moments based approaches and separation of timescales
approximations (Otto and Nuismer 2004; Agrawal 2006; Nuismer et al. 2008; Agrawal 2009). ESS
analyses have been largely replaced by adaptive dynamics approaches as the go to method for analyzing
models with rich ecological detail (Dieckmann and Law 1996; Doebeli and Dieckmann 2000; Jones et al.
2009), and quantitative genetics models can now be analyzed by studying allele frequency changes at
many underlying loci of small effect, blurring the distinction between quantitative and population
genetics (Nuismer et al. 2005; Kopp and Gavrilets 2006; Nuismer et al. 2007).
In addition to the technical improvements to the basic core approaches to coevolutionary
models discussed above, the 1990’s and 2000’s saw a huge increase in the scope of coevolutionary
models. For instance, coevolutionary models no longer focused on single isolated populations, but
began to integrate multiple populations and the complexities of spatial structure (Gandon et al. 1996;
Morand et al. 1996; Frank 1997; Gandon 1998; Gomulkiewicz et al. 2000; Sasaki et al. 2002; Thrall and
Burdon 2002; Nuismer 2006). Much of this development was driven by the identification of strong
patterns of local adaptation within host parasite interactions (Ebert 1994; Lively and Jokela 1996; Kaltz
and Shykoff 1998) and also by John N. Thompson’s development and promotion of the Geographic
3
Mosaic Theory (Thompson 1994; Thompson 1997; Thompson 1999; Thompson 2005). Similarly, models
began to explore the impact of coevolution on major evolutionary transitions beyond just sexual
reproduction, including ploidy, mate choice, dispersal, and mutation rates (Nuismer and Otto 2004,
2005; M'Gonigle et al. 2009; M'Gonigle and Otto 2011). Even more recently, models have been
developed that explore how coevolution influences the network structure of communities (Guimarães
et al. 2011; Nuismer et al. 2013), the likelihood of biological invasions (Jones and Gomulkiewicz 2012),
and the response of species to climate change (Northfield and Ives 2013). In short, coevolutionary
theory is exploding. With this explosion has come an increasing realization that many major problems in
evolution and ecology cannot adequately be addressed without considering the impact of coevolution.
All of these technical innovations make this a particularly exciting time to be developing and
analyzing coevolutionary models. Never before have such powerful analytical tools been so readily
available to tackle such a diverse array of compelling problems. At the same time, however, the
increased sophistication of coevolutionary models has made jumping into the field much more
intimidating than when I first started developing coevolutionary models in the mid 1990’s. Long gone
are the days when a single locus haploid model with two populations will get you a decent paper! Part of
my motivation for writing this book is to make using these modern analytical tools less intimidating. For
this reason, the structure of the book is hierarchical, with each chapter building on the material
presented in the preceding chapter. The first chapters are quite basic and should be approachable with
only a modest background in mathematics and evolutionary biology. Subsequent chapters introduce
more sophisticated models and analytical techniques, but should be manageable once the material in
preceding chapters has been mastered. In the remainder of this chapter, the core elements of
coevolutionary models will be introduced, beginning with the basic pre-requisites that must be included
within a model for it to be truly coevolutionary.
Identifying the Pre-requisites for Coevolution
Before we can begin building and analyzing coevolutionary models, we need to agree on what,
exactly, coevolution is. Throughout this book, I will stick with the current consensus definition
developed and popularized by Janzen (1980). In this seminal paper, 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 provides a great starting point, it doesn’t tell
us much about what we would need to include in a model to make it truly coevolutionary. All it really
tells is that our model must somehow produce reciprocal evolutionary change. In the rest of this section,
we will work backward from the observation of reciprocal evolutionary change to the underlying prerequisites that make it possible.
4
To make things concrete, let’s imagine we are studying an interaction between an insect and the
plant it pollinates. Perhaps we have reason to believe the outcome of this interaction is largely explained
by the length of the pollinator’s proboscis, x, relative to the length of the plant’s corolla, y. Let’s now
imagine that we measure the proboscis lengths of multiple insect individuals and the corolla depths of
multiple plant individuals in generation t and again in generation t+1. With this information in hand, we
can calculate the change in population mean proboscis length and corolla depth that occurs over a
single generation:
∆𝑥̅ = 𝑥̅𝑡+1 − 𝑥̅𝑡
(1a)
∆𝑦̅ = 𝑦̅𝑡+1 − 𝑦̅𝑡
(1b)
where 𝑥̅ and 𝑦̅ are the population mean proboscis lengths and corolla depths. If equations (1) are both
significantly different from zero, and we can rule out other evolutionary forces (e.g., gene flow, random
genetic drift), we can be relatively confident that selection has produced the observed changes in the
mean phenotypes. In this case, an appropriate model for the changes in the mean phenotypes might be
the classical breeder’s equation of quantitative genetics:
∆𝑥̅ = ℎ𝑥2 𝑆𝑥
(2a)
∆𝑦̅ = ℎ𝑦2 𝑆𝑦
(2b)
where each species is now characterized by a heritability, ℎ2 , and selection differential, S. Put
differently, the fact that the mean phenotype of each species has been changed by selection implies
that the traits of both interacting species must be heritable (ℎ2 > 0) and under selection (𝑆 ≠ 0).
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:
5
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.
Integrating the Pre-requisites for Coevolution into Mathematical Models
Earlier in the chapter we discussed an overview of coevolutionary models in a historical
perspective. Our goal in this section is to get down to the nitty gritty of coevolutionary models and show
how the pre-requisites for coevolution identified in the previous section provide a basic recipe for
creating a coevolutionary model. Specifically, 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, there are currently two basic
approaches which I will call the “ecological school” and the “evolutionary school”. The ecological school
builds on the historical work of Roughgarden, etc., etc. and explores how the parameters of ecological
or epidemiological models evolve in response to reciprocal selection. This school is currently dominated
by the ”adaptive dynamics approach” where…
THE ECOLOGICAL SCHOOL OF COEVOLUTION. Adds evolution to ecological models of species
interaction (roughgarden, adaptive dynamcis, slatkin, abrams, etc.). Focuses on ecological questions.
Interactions between traits are often indirect. Separation of timescales. This approach was developed by
XX and XX and now blends into the school of adaptive dynamics with little substantive change.
vs.
THE EVOLUTIONARY SCHOOL OF COEVOLUTION. Adds species interactions to evolutionary
models (Mode, Jayakar, Hamilton, Seger, kiester). Focuses on evolutionary questions. Interactions
between traits or genes are direct.
This book will focus on the latter but will broaden its scope by addressing truly ecological
questions such as the structure and function of communities…
6
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 2). 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
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
7
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. 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 (Nuismer et al. 2005; Kopp and Gavrilets 2006).
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
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
8
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 (Otto and Nuismer 2004; Agrawal 2006). 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 begin to develop formal mathematical models of coevolution, it is crucial to address
one very common misconception: the frequency with which coevolution generates sustained,
empirically detectable, 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
generate sustained reciprocal evolutionary change —coevolution using Janzen’s strict definition — in
only a subset of populations and at particular periods of 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 populations or “field seasons”, or might
produce little or no reciprocal evolutionary change for hundreds of generations before unleashing a
torrent of extremely rapid coevolutionary change (Figure 3). 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/genotype 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 (Thompson 1994; Thompson 2005, 2013), it is naïve to expect coevolution to
be ongoing and strong enough to be detectable in all populations and all times.
9
This fundamental result has important consequences for the design and interpretation of
studies investigating coevolution within natural populations, and will emerge time and time again
throughout the models we study in this book. OK, NOW, INSTEAD, DISCUSS THE STRUCTURE OF THE
BOOK. In chapters 1-3 we will explore the basic structure of coevolutionary models… Here we will see
that reciprocal selection and coevolution fluctuate. In chapters 3-6 we will build on these models to
explore how coevolution proceeds when we have multiple loci and dominance. Here, the central results
will appear by showing that coevolutionary models only sometims generates selection for major life
history shifts. In 6-9 we will explore spatial structure and local adaptation. Here again, it will become
apparent that coevolution only crops up occasionally. Finally in chapters 7-9 we will explore
communities and macroevolution. Here too, we will see that even when the potential for coevolution
always exists, it may be rapid, sustained, and empirically detectable for only some species within the
community, at some points in time, or for some types of communities…
Although the focus of each chapter will be placed more on the conclusions and predictions unique to
each model, it is important to keep this general theme in mind and repeatedly ask yourself: what do the
predictions of this model mean for our ability to detect sustained coevolutionary change within natural
populations?
Outline… Where am I going? What will happen in this book.
10
References:
Figure Legends:
Figure 1. A schematic representation of reciprocal evolutionary change (coevolution) between a
parasitic cuckoo and its host. The left hand column of graphs shows the frequency distribution of egg
coloration within the host population over time and the right hand column the frequency distribution of
egg coloration within the cuckoo population over time. Initially, most individuals within host and cuckoo
populations lay dark colored eggs. Under these circumstances, the eggs of most cuckoos are wellmatched to those of their host bird allowing the cuckoo eggs to avoid ejection by most host birds. Only
those host birds which lay lighter colored eggs are able to recognize the differently colored eggs of the
cuckoo and eject them. This generates selection within the host population (dashed line) for lighter
colored eggs. In response, egg coloration within the host population begins to lighten, and hosts become
better able to recognize and eject cuckoo eggs. In turn, this favors those few cuckoos that lay light
colored eggs, generating selection within the cuckoo population for lighter colored eggs. In response,
lighter colored eggs evolve within the cuckoo population. But alas, this evolutionary change within the
cuckoo population generates selection within the host population for darker egg coloration and the
cycle begins again.
Figure 2. An interaction function, P, which predicts the probability that a cheetah with sprint speed x can
capture an Impala with sprint speed y.
Figure 3. Temporal change in genotype frequencies (left hand panels) and selection (right hand panels)
for a coevolutionary interaction between a host (solid lines) and parasite (dashed lines). The top two
panels show genotype frequencies and selection over a period of 1000 years. The bottom two panels
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