Cytoplasmic incompatibility and host population structure

Abstract

Many arthropod species are infected by maternally inherited bacteria that induce cytoplasmic incompatibility (CI). CI causes embryonic mortality in offspring when infected males mate with either uninfected females or with females that are infected with a different strain of bacteria. Here, we review theoretical and empirical studies concerning the infection dynamics of CI-inducing bacteria, focusing in particular on the impact of the host population structure on the spread of CI. As different theoretical models have often produced divergent predictions with regard to issues such as the speed of CI spread and the stability of infection polymorphisms, we specifically aim to clarify how the various assumptions concerning population structure that underlie these models affect these predictions. We also discuss several implications of population structure, including the impact of CI on host gene flow reduction and speciation, the evolutionary dynamics of CI and strategies to control insect pest populations by means of CI-inducing microbes.

Full text

REVIEW
Cytoplasmic incompatibility and host population
structure
J Engelsta
¨dter
1
and A Telschow
2
1
Department of Integrative Biology, Swiss Federal Institute of Technology, Zurich, Switzerland and
2
Institute for Evolution and
Biodiversity, Westfalian University, Munster, Germany
Many arthropod species are infected by maternally inherited
bacteria that induce cytoplasmic incompatibility (CI). CI
causes embryonic mortality in offspring when infected males
mate with either uninfected females or with females that are
infected with a different strain of bacteria. Here, we review
theoretical and empirical studies concerning the infection
dynamics of CI-inducing bacteria, focusing in particular on
the impact of the host population structure on the spread of
CI. As different theoretical models have often produced
divergent predictions with regard to issues such as the
speed of CI spread and the stability of infection polymorph-
isms, we specifically aim to clarify how the various assump-
tions concerning population structure that underlie these
models affect these predictions. We also discuss several
implications of population structure, including the impact of
CI on host gene flow reduction and speciation, the evolu-
tionary dynamics of CI and strategies to control insect pest
populations by means of CI-inducing microbes.
Heredity (2009) 103, 196–207; doi:10.1038/hdy.2009.53;
published online 13 May 2009
Keywords: Cardinium; evolutionary dynamics; infection dynamics; insects; model; Wolbachia
Introduction
Marshall (1938) was apparently the first to note that
crosses between certain strains of the mosquito Culex
pipiens were incompatible in one direction (that is, males
from strain Aand females from strain B), whereas the
other direction (Bmales Afemales) produced viable
progeny. This phenomenon was further investigated in
the 1940s and 1950s by Roubaud (1941), Ghelelovitch
(1952) and, in particular, Laven (1951, 1956, 1957, 1959).
These early investigations showed that the incompat-
ibility trait was inherited maternally (Laven, 1956),
suggesting an extranuclear causative agent and giving
rise to the term ‘cytoplasmic incompatibility’ (CI). In
addition to unidirectional CI, bidirectional CI was also
observed between strains of C. pipiens (Laven, 1951, 1959;
Ghelelovitch, 1952). In the early 1970s, a connection was
drawn by Yen and Barr (1971, 1973) between CI and the
intracellular a-proteobacterium Wolbachia that had long
been known to infect C. pipiens (Hertig and Wolbach,
1924): unidirectional CI usually occurs when infected
males mate with uninfected females, but can also be
found in crosses between individuals infected with
different strains of bacteria (for example, Duron et al.,
2006). In bidirectional CI, both directions of a cross are
incompatible because of infection with different strains
of CI-inducing microorganisms (Figure 1). In both cases,
offspring from incompatible crosses suffer mortality at
early stages of their development.
Today, CI has been recorded in all major insect orders
as well as in mites and woodlice (Table 1). CI is induced
not only by Wolbachia but also by the unrelated
bacterium Cardinium hertigii (Hunter et al., 2003; Gotoh
et al., 2007a). Both bacteria are transmitted predomi-
nantly maternally through the egg cytoplasm, although
paternal or horizontal transmission may also occur at a
low rate (Turelli et al., 1992). In terms of evolutionary
theory, CI can be understood in the light of intragenomic
conflicts that arise from the maternal transmission of the
bacteria (Cosmides and Tooby, 1981). As males are
reproductive dead ends for cytoplasmic elements, it is
advantageous to ‘exploit’ them to increase transmission
through female hosts. CI is one of four strategies of such
‘reproductive parasitism’: males are exploited by the
bacteria to kill the offspring of uninfected females so that
infected females have a selective advantage (Werren,
1997). The other three phenotypes of reproductive
parasitism (male killing, feminization and parthenogen-
esis induction) all involve sex-ratio distortion and are not
discussed in this review.
CI is usually understood within a modification-rescue
(or poison-antidote) framework (Werren, 1997): sperm is
modified by the bacteria in males, and the same or a
similar strain must be present in the eggs to ‘rescue’ the
modification, enabling the progeny to develop normally.
The precise nature of this modification-rescue mechan-
ism is currently not understood. Cytological studies have
shown that in incompatible crosses, the paternal chro-
mosomes do not condense, are damaged and eventually
lost during the first mitotic divisions (Breeuwer and
Werren, 1990; Callaini et al., 1997; Tram and Sullivan,
2002). In diplodiploid and most haplodiploid species, the
loss of paternal chromosomes leads to disrupted devel-
Received 23 December 2008; revised 27 March 2009; accepted 30
March 2009; published online 13 May 2009
Correspondence: Dr J Engelsta
¨dter, Institute of Integrative Biology, ETH
Zurich, Universita
¨tsstr.16, ETH Zentrum, CHN K12.1, CH-8092 Zurich,
Switzerland.
E-mail: jan.engelstaedter@env.ethz.ch
We dedicate this article to Peter Hammerstein whose enthusiasm for
Wolbachia proved infectious for both of us and who is celebrating his
60th birthday this year.
Heredity (2009) 103,196–207
&
2009 Macmillan Publishers Limited All rights reserved 0018-067X/09 $32.00
www.nature.com/hdy

opment and death of the embryos (Breeuwer, 1997;
Callaini et al., 1997; Vavre et al., 2000). By contrast, in the
haplodiploid wasp Nasonia vitripennis the haploid em-
bryos survive and develop into males instead of females
(Breeuwer and Werren, 1990). For excellent reviews on
the mechanistic basis of CI, we refer to Poinsot et al.
(2003) and Tram et al. (2003).
It is well known in the fields of evolutionary biology
and epidemiology that the host population structure
strongly affects the infection dynamics of diseases or
symbionts as well as their evolutionary trajectories
(for example, Herre, 1993; Keeling, 1999), and some
sort of population structure certainly is a pervasive
feature of most natural populations. However,
models with population structure are often neglected.
This is partly because of the mathematical difficulties
that are involved in the corresponding models
(that is, partial differential equations (PDEs) are usually
more difficult to analyse than ordinary differential
equations), owing in part to the lack of empirical data
that would justify a model with a particular population
structure.
In the case of CI-inducing microbes, there is an
increasing number of field studies examining their spatial
distribution. Maybe most impressively, the rapid spread
of CI-inducing Wolbachia was observed in Californian
populations of Drosophila simulans (Turelli and Hoffmann,
1991), and other studies also clearly show such spatial
spread of CI-inducing microbes (Riegler and Stauffer,
2002; Hiroki et al., 2005). However, some surveys also
suggest rather stable infection polymorphisms, with some
populations being infected and others being uninfected or
infected with a different bacterial strain (Merc¸ot et al.,
1995; Clancy and Hoffmann, 1996; Riegler and Stauffer,
2002; Baudry et al., 2003; Keller et al., 2004; Jaenike et al.,
2006). Table 1 gives examples of species infected with CI-
inducing microbes, indicating results concerning infection
polymorphisms and population structure.
Figure 1 Illustration of uni- and bidirectional cytoplasmic incom-
patibility (CI). The two tables show success (green tick marks) or
failure (red crosses) of offspring production of crosses between
parents with different infection states. Empty symbols in the parent
generation denote that these parents are uninfected, whereas the
two shades of blue denote infection with two different strains of
bacteria. With unidirectional CI, only crosses between infected
males and uninfected females are incompatible. With bidirectional
CI, crosses between males and females infected with different
strains of CI-inducing bacteria are incompatible. Note that some-
times, unidirectional CI is also observed between hosts infected
with different strains of bacteria.
Table 1 Some species infected with CI-inducing bacteria, with remarks relating to infection polymorphism and host population structure
Species Remarks References
Insecta: Diptera
Culex pipiens Large number of CI-inducing Wolbachia strains in different
populations, resulting in complex incompatibility patterns
Laven (1951); Yen and Barr (1971);
Duron et al. (2006)
Drosophila simulans Infected with at least five strains of Wolbachia, some of which
induce CI; rapid spread of one strain (wRi) through CI
recorded in California
Reviewed in Merc¸ot and Charlat (2004)
Rhagoletis cerasi Singly and doubly infected populations; apparently recent spread
of double infection due to CI
Riegler and Stauffer (2002)
Insecta: Hymenoptera
Leptopilina heterotoma All populations appear to be completely infected with three strains
of Wolbachia, inducing different types of CI
Vavre et al. (2000, 2001);
Mouton et al. (2005)
Nasonia vitripennis Infected with two Wolbachia strains, bidirectional CI to sister species
N. longicornis and N. giraulti
Breeuwer and Werren (1990);
Perrot-Minnot et al. (1996);
Bordenstein and Werren (1998)
Encarsia pergandiella 92% prevalence of CI-inducing Cardinium in the field Hunter et al. (2003);
Perlman et al. (2008)
Insecta: Lepidoptera
Eurema hecabe Two Wolbachia strains, one causing feminization, the other CI;
double infected populations in Okinawa; spread of single
infection causing CI from southern to northern Honshu (Japan)
Hiroki et al. (2004, 2005)
Hypolimnas bolina Infection polymorphism across Southeast Asia and South Pacific
islands, two strains of CI-inducing Wolbachia, of which one
induces male killing in addition to CI
Charlat et al. (2005b, 2006);
Hornett et al. (2008)
Chelicerata: Acari
Tetranychus spp. Some populations uninfected, some infected with CI- and some with
non-CI-inducing strains of Wolbachia
Breeuwer (1997); Gotoh et al. (2007b)
The list of species given in this table is not exhaustive but represents a sample of species that have been studied intensively or are of
relevant for questions concerning population structure. CI is induced by Wolbachia in all cases except Encarsia pergandialla, where the
causative agent is Cardinium.
CI and host population structure
J Engelsta¨dter and A Telschow
197
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Here, we review the infection dynamics and evolution
of CI-inducing microbes with a focus on host population
structure. The various empirical observations have
motivated several theoretical studies, and the main aim
of this review is to clarify the assumptions that underlie
these models and explain how they may sometimes lead
to conflicting predictions. We start out by explaining
some basic features of CI infection dynamics that emerge
in simple models assuming single, panmictic popula-
tions of infinite size. This ‘null model’ of CI then forms
the basis for a detailed discussion of more elaborate
models that incorporate various forms of host population
structure. In addition to infection dynamics, population
structure also has an impact on evolutionary aspects of
CI. We discuss recent theoretical advances concerning
both the evolutionary consequences of CI-inducing
microbes on their hosts (including gene-flow modifica-
tion and potential facilitation of speciation) as well as the
evolutionary dynamics of the microbes themselves.
Finally, we review several CI-based strategies for insect
pest control and evaluate their applicability in the light
of the effects of host population structure.
The dynamics of CI in unstructured
host populations
The null model of CI
Induction of CI can enable maternally inherited bacteria
to spread in a host population. This is because if there are
infected males in a population, infected females (which
are compatible with all males) may on the average
produce more daughters than uninfected females (which
are compatible only with uninfected males). Thus, by
decreasing the number of daughters that uninfected
females produce, CI-inducing bacteria increase the
relative daughter production of infected females and
boost their own spread. This reasoning also shows a
fundamental property of CI dynamics, the positively
frequency-dependent selection for CI: the higher the
infection frequency of the bacteria in the population, the
stronger the selection for the bacteria. In what follows,
we will describe a basic ‘null model’ for the infection
dynamics of CI-inducing bacteria that serves as a starting
point for models incorporating more complicated fea-
tures of host biology, including population structure.
Three parameters have been established to be im-
portant in quantitatively predicting the spread of CI-
inducing endosymbionts in a host population. First, the
transmission rate gives the proportion of offspring
produced by an infected mother that is also infected by
the bacteria. Transmission rates are often close to one (for
example, Rasgon and Scott, 2003; Narita et al., 2007;
Perlman et al., 2008), but they may also be o95% (Poinsot
et al., 2000). Second, the CI mortality (or CI level) is the
proportion of offspring that dies in incompatible crosses.
CI mortality varies widely (from zero to almost one)
between different strains of bacteria (Drosophila strains
reviewed in Merc¸ot and Charlat, 2004) and it may also
decline with the age of males (Clark et al., 2002; Reynolds
and Hoffmann, 2002). Finally, CI-inducing bacteria may
have direct effects on female fitness, necessitating a third
parameter. For example, female fecundity can be
decreased (for example, Hoffmann and Turelli, 1988;
Perlman et al., 2008) or increased (Dobson et al., 2004) by
the bacterial infection, but often, no effect on fecundity is
seen (for example, Giordano et al., 1995; Bordenstein and
Werren, 2000). It is noted that selection acting on the
bacteria may also increase the fecundity of infected
females over relatively short time spans and to the extent
where infected females eventually have a higher fecund-
ity than uninfected females (Weeks et al., 2007). As
fecundity is the best-studied fitness component directly
influenced by CI-inducing microbes, most theoretical
models incorporate a parameter for fecundity; however,
other fitness components may also be important and may
require separate treatment in the models.
Several models for the infection dynamics of CI have
been developed that incorporate some or all of these
parameters (Caspari and Watson, 1959; Fine, 1978;
Hoffmann et al., 1990; Hurst, 1991; Turelli, 1994). Discrete
generations and random mating between hosts are
generally assumed, and bacteria infecting a host are
treated as a single genetic entity that can either be
present or absent. In Box 1, we present a mathematical
formulation and solutions of these models. The most
important result is that because of the frequency-
dependent selection, there may be an invasion threshold
for CI, that is, an infection frequency below which the
bacteria become extinct and above which they spread.
This invasion threshold exists whenever infected
females have (1) a reduced fecundity and/or (2) when
transmission is imperfect (and this is not sufficiently
compensated for by increased fecundity). Provided the
invasion threshold is reached, the infection is expected
to spread to a high polymorphic equilibrium frequency
or—with perfect transmission or CI mortality—to
fixation.
Population cage experiments with flies and mosqui-
toes have confirmed the qualitative predictions of the
above models. Both Nigro and Prout (1990) and Dobson
et al. (2002b) consistently observed an increasing infec-
tion frequency of CI-inducing Wolbachia over a few
generations. In addition, Xi et al. (2005), using an
artificially established Wolbachia infection in Aedes aegypti
that led to a strong fecundity reduction of infected
females, also reported the extinction of Wolbachia when it
was introduced at a low initial infection frequency. This
observation is in line with the invasion threshold of
CI-inducing bacteria that have deleterious effects on their
female hosts.
Extensions of the null model
Although the main focus of this review is the impact of
population structure on the infection dynamics of CI, we
will also give a short overview in this section of other
factors that are expected to influence these dynamics.
It is currently not understood how the invasion
threshold is overcome in natural populations, but
stochastic effects (that is, random genetic drift) are likely
to play an important role (Rousset and Raymond, 1991).
Analytical approximations (Rigaud and Rousset, 1996;
Jansen et al., 2008) and simulations (Egas et al., 2002;
Jansen et al., 2008) indicate that the probability of CI
spread starting from a singly infected female is generally
rather low, particularly with large populations and high
invasion thresholds. However, even in the face of an
invasion threshold, the spread of CI was often found to
be more likely than that of a comparable neutral genetic
CI and host population structure
J Engelsta¨dter and A Telschow
198
Heredity

element, suggesting that repeated exposure of a popula-
tion to CI-inducing bacteria through horizontal transmis-
sion may produce a reasonable likelihood of eventual
invasion (Jansen et al., 2008).
When a single panmictic population is infected with
more than one strain of bacteria that induce bidirectional
CI, it is crucial to distinguish whether multiple infections
occur at the level of individual hosts or not. In the latter
case, modelling predicts that one of the strains will
eventually drive the other(s) extinct, and which of the
strains prevails will depend both on the parameters and
on the initial frequencies of each strain (Rousset et al.,
1991). When there are multiply infected females in the
population, the population may remain polymorphic
(Frank, 1998). More precisely, a stable polymorphism of
several CI-inducing strains can only be maintained in a
panmictic population if a subset of the population is
infected with all of these strains. This is because only
females infected with all strains of bacteria are compa-
tible with all males and therefore enjoy the highest
fitness in the population. Female hosts carrying only a
subset of bacterial strains have lower fitness but may be
maintained in the population through imperfect mater-
nal transmission.
Other complications of CI concern haplodiploid
species. First, males develop from unfertilized eggs in
haplodiploid species, and so that their production is not
affected by incompatible matings. Second, as CI involves
a loss of the paternal set of chromosomes, diploid
zygotes arising from incompatible matings may survive
as haploid males. This type of CI has been observed in
the wasp N. vitripennis (Breeuwer and Werren, 1990) and
is termed the male development (MD) type of CI. Most
haplodiploid species, however, seem to show the female
mortality (FM) type of CI, in which fertilized eggs from
incompatible crosses fail to hatch as in diplodiploid
species (for example, Breeuwer, 1997; Vavre et al., 2000).
It has been shown theoretically that all else being equal,
Box 1 A simple mathematical model for CI in panmictic populations
In what follows, we describe a model for CI-infection dynamics that has first been derived (using different notation) by Hoffmann et al.
(1990). Let us denote by tthe transmission efficiency of the CI-inducing bacteria (proportion of infected offspring produced by infected
mothers), by l
CI
the CI-mortality (proportion of offspring killed in incompatible matings) and by fthe relative fertility of infected
females. The proportion pof infected females in the population then changes from one generation to the next by
Dp¼pft
1pð1fÞplCI½1pð1fþftÞ p:ð1Þ
This recursion equation has three equilibria, given by
^
p1¼0;
^
p2¼1
AlCI þf1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð1flCIÞ22Að1ftÞ
q

;
^
p3¼1
AlCI þf1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð1flCIÞ22Að1ftÞ
q

;
ð2Þ
where A¼2l
CI
(1f+ft). It can be demonstrated that provided all equilibria exist, equilibria p
ˆ
1
and p
ˆ
3
are stable, and p
ˆ
2
is unstable. The
latter fixed point, p
ˆ
2
, is often referred to as the invasion threshold in the literature, as this is the frequency that the
CI-inducing bacteria have to overcome initially in order to spread in the population. This threshold exists whenever fto1. It can also be
seen that p
ˆ
3
¼1 if either t¼1orl
CI
¼1. In other words, following invasion the bacteria will reach fixation if they have perfect maternal
transmission or induce complete CI. Figure B1 illustrates the recursion equation (1), indicating also the three fixed points and their
stability. Examples for the dynamics of the system are shown in Figure B2.
-0.025
0
0.025
0.05
0.075
Δp
p
ˆ
p1
ˆ
p2ˆ
p3
00.2
0.4 0.6 0.8 1
0
p
0.2
0.4
0.6
0.8
1
generation
invasion threshold
0 20406080
Figure B2 Dynamics of infection frequency pfor different initial
frequencies. Depending on whether the initial frequency is below
or above the invasion threshold (p
ˆ
2
), the CI-inducing bacteria
become extinct (p
ˆ
1
¼0) or established in the population (p
ˆ
3
).
Parameters are the same as in Figure B1.
Figure B1 Change in frequency of CI-inducing endosymbionts,
Dp, depending on the frequency pin the present generation. Stable
equilibria are shown as black circles, and the unstable equilibrium
(‘invasion threshold’) is shown as a white circle. Parameters take
the values t¼0.98, f¼0.9 and l¼0.5.
CI and host population structure
J Engelsta¨dter and A Telschow
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the invasion threshold for CI is highest for the MD type
of CI, followed by the FM type and the diplodiploid type
of CI (Vavre et al., 2000). Conversely, the stable
equilibrium frequency is highest in diplodiploid species
and lowest with the MD type of CI in haplodiploid
species.
Finally, infection dynamics may be influenced by a
number of other factors that have been studied theore-
tically, but which we can only briefly mention here.
These factors include paternal transmission of the
bacteria (Nigro and Prout, 1990), host nuclear genes
suppressing CI action (Rousset et al., 1991; Turelli, 1994;
Koehnke et al., 2009), competition within a brood of
siblings (Freeland and McCabe, 1997), the presence of
other maternally inherited bacteria that induce a sex-
ratio distortion (Freeland and McCabe, 1997; Engelsta
¨d-
ter et al., 2004), age-structured host populations (Rasgon
and Scott, 2004) and sperm competition (Hoffmann and
Turelli, 1997; Champion de Crespigny et al., 2008).
The dynamics of CI in structured
host populations
Roughly speaking, three different types of models with
host population structure have been constructed, which
are illustrated in Figure 2. These types of models are (1)
deterministic models of continuously structured (‘vis-
cous’) populations, (2) deterministic models with dis-
crete subpopulations and (3) stochastic models with
discrete subpopulations (‘deme-structured’ populations).
We will discuss these different classes of models in turn
and aim at clarifying how they produce different
outcomes and sometimes even opposing predictions.
Before entering this discussion, however, we would
like to briefly examine how inbreeding and outbreeding
influence the spread of CI. Inbreeding and outbreeding
are deviations from panmixis that may result from
spatial subdivision of populations, but may also repre-
sent a form of population structure that only extends to
mating (for example, through behavioural inbreeding
avoidance) without actual spatial subdivision. To date, a
systematic investigation of the impact of inbreeding and
outbreeding on CI dynamics is still lacking. Numerical
analyses of a model with sibmating or sibmating
avoidance indicate that substantial inbreeding can
increase the invasion threshold and decrease the stable
equilibrium frequency of the CI-inducing microbes
(Engelsta
¨dter et al., 2006). This is because with increasing
levels of inbreeding, incompatible matings become
increasingly unlikely, thus diminishing selection for the
CI microbes. When the level of inbreeding is above a
certain threshold, CI invasion and persistence can even
become impossible. Sibmating avoidance (outbreeding),
on the other hand, did not seem to have an effect on the
infection dynamics (Engelsta
¨dter et al., 2006). This is
because even when females never mate with their
brothers, this hardly affects the probability of mating
with an uninfected or infected male when the population
is reasonably large.
Continuous ‘viscous’ populations
This class of models was originally motivated by the
observation of an ongoing spread of CI-inducing
Wolbachia through a Californian D. simulans population,
documented in detail by Turelli, Hoffmann and collea-
gues (Hoffmann et al., 1986; Hoffmann and Turelli, 1988;
Turelli and Hoffmann, 1991; Turelli et al., 1992). The
spread was described mathematically using a PDE that
was originally developed for the analysis of hybrid zones
(Barton, 1979; Turelli and Hoffmann, 1991). To test the
model, the authors measured the three main parameters
for the CI dynamics (transmission rate, CI level,
fecundity), and combined them in the model with rather
phenomenological assumptions about the underlying
insect dispersal mode (Turelli and Hoffmann, 1991). As a
result, the model describes the spread of Wolbachia
qualitatively well but fails to make accurate predictions
about the invasion speed. As the authors acknowledge,
Figure 2 Illustration of three types of approaches to model
population structure. In each model, red and black colours
represent different infection states of individuals, for example,
infected and uninfected. (a) Models with continuous spatial
distribution of individuals, employing partial differential equations.
(b) Models with migration between two infinitely large subpopula-
tions. Migration may occur in both directions (two-islands model)
or in one direction only (mainland–island model). (c) Models with a
number of demes of small to intermediate size. Migration may
occur between all demes with equal probability (Wright’s island
model) or in a geographically restricted way (for example, stepping-
stone model).
CI and host population structure
J Engelsta¨dter and A Telschow
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this is most likely because of the lack of knowledge about
the actual range of migration in D. simulans.
In a more recent theoretical study, Schofield (2002)
investigated the role of insect dispersal on the spatio-
temporal spread of unidirectional CI. The underlying
PDEs are based on Turelli and Hoffmann (1991). Two
types of PDE were analysed: reaction-diffusion and
integro-difference equations. These models differ with
respect to the mode of migration. In the former, dispersal
is treated as a diffusion process and dispersal distance
modelled by a normal distribution, whereas the latter
uses a leptokurtic distribution that allows for rare long-
range dispersal of hosts. Model analysis was carried out
by computer simulations, and parameters were chosen to
match the D. simulans system. The main result of this
study was that long-range migration results in faster
spread of CI and that including such dispersal provided
a better description of CI spread in D. simulans. The merit
of Schofield’s study is to point out that the actual mode
of insect dispersal plays a crucial role in the speed of
spread as well as the shape of the infection wave.
However, as with most theoretical studies based purely
on computer simulations, the lack of analytical results
and the limited range of parameters for which simula-
tions were performed make it difficult to generalize the
results.
Given the close relationship between models of hybrid
zones and those of CI in continuous populations,
Barton’s classical study (Barton, 1979) may provide clues
on factors that can be expected to affect the spatial spread
of symbionts. The equations analysed by Barton (1979)
model hybrid zones caused by underdominant chromo-
somal rearrangements. From a mathematical point of
view, an underdominant locus is almost equivalent to
symmetric bidirectional CI (that is, the degree of CI is
equal in both directions). It might therefore be worth
investigating to what extent previous predictions about
hybrid zones, including results on spatial heterogeneity,
hold true for bidirectional CI. In particular, the theore-
tical analysis of hybrid zones indicates that spatial
heterogeneity in population density plays a crucial role
in wave speed and cline stability; regions with low
population density are obstacles that can prevent the
spread and lead, under certain circumstances, to stable
clines. An extension of Schofield’s model could reveal a
similar effect; the spread of a CI-inducing microbe
might be impeded or prevented in regions with low
population density. Stochastic effects, however, might
lead to an opposite effect. This is because with low
population density, random genetic drift becomes more
important, which was shown to promote the spread of
unidirectional CI (Reuter et al., 2008; also see discussion
below).
We close this subsection with a general remark on
spatial models. In PDEs, space is considered as a
continuous variable, whereas in lattice or stepping-stone
models, space consists of discrete units. Both types of
models are often too complicated for analytical analysis,
making the use of numerical methods necessary. When
interpreting numerical results, however, it is important
to recall that computers, in general, allow only discrete
mathematical calculations; computational methods for
solving PDEs do not generate solutions of the PDE, but
only give approximations of such solutions. The results
presented by Schofield (2002) are therefore, in a strict
mathematical sense, the solutions of a stepping-stone
model with a very high number of subpopulations. This
should be kept in mind when comparing studies based
on discrete models with those based on PDEs.
Deterministic models with discrete subpopulations
We next consider deterministic models with a discrete
number of subpopulations that are connected by migra-
tion. The main question underlying these models is
under which conditions coexistence of differentially
infected subpopulations is possible. We discuss the
following three models in detail: (1) unidirectional CI
in a two-population model (Flor et al., 2007), (2)
bidirectional CI in a two-population model (Telschow
et al., 2005b) and (3) bidirectional CI in a lattice model
(Keeling et al., 2003). The basic idea behind all three
studies is the same (and goes back to Nigro and Prout
(1990) and Rousset et al. (1991)): frequency-dependent
selection on CI creates a situation where bistability does
not allow stable coexistence in a panmictic population
but does allow coexistence in different subpopulations if
migration is below a critical value.
The dynamics of bacterial infections causing unidirec-
tional CI in a two-population model was investigated by
Flor et al. (2007). Infected and (mainly) uninfected host
populations can coexist stably in this model if migration
is below a critical value. The critical migration rates were
determined analytically for mainland–island models and
it was shown that these solutions are lower-bound
estimates for critical migration rates in the general model
with two-way migration. In general, critical migration
rates exist if either the bacteria cause fecundity reduc-
tions in infected female hosts or bacterial transmission is
imperfect. In the case of symmetric two-way migration,
infection polymorphism is most stable for intermediate
levels of CI.
A similar analysis was carried out for two bacterial
strains causing bidirectional CI (Telschow et al., 2005b). It
was shown analytically for a two-population model that
the stability could be fully described in terms of the
critical migration rate, which is here defined as the
highest migration rate below which a stable coexistence
of the two bacterial strains is possible. The main finding
of the study is that bidirectional CI can persist stably in
the face of high migration rates. For example, CI in Culex
and Nasonia is nearly complete (Perrot-Minnot et al.,
1996; Rasgon and Scott, 2003), resulting in a critical
migration rate of 19% per generation, whereas CI in
Drosophila is more variable, ranging from 0.3 to 0.7
(Merc¸ot and Charlat, 2004), which causes critical migra-
tion rates between 5 and 13%. These values are roughly
one order of magnitude higher than for unidirectional CI,
indicating that bidirectional CI may result in substan-
tially more stable infection polymorphisms.
The studies of Flor et al. (2007) and Telschow et al.
(2005b) do not take into account host nuclear back-
ground. We mention in this context that local adaptation
in hosts significantly increases the stability of infection
polymorphism and critical migration rates (Telschow
et al., 2002a, b, 2007). Moreover, it was shown that other
reproductive parasites (male-killing bacteria) can pre-
vent the spread of CI to a certain extent, thereby
increasing the respective critical migration rates (Engel-
sta
¨dter et al., 2008).
CI and host population structure
J Engelsta¨dter and A Telschow
201
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Finally, Keeling et al. (2003) investigated the coex-
istence of two bacterial strains causing bidirectional CI in
a (one- or two-dimensional) lattice model. The authors
used a purely numerical approach, and in contrast to the
above-discussed models, infection dynamics in each
subpopulation were described by ordinary differential
equations reflecting overlapping host generations. The
main result of Keeling et al. (2003) is that stable
coexistence of the two strains is possible if migration is
below a threshold. This is in line with the above-
discussed critical migration rates. Coexistence of strains
comes about through the formation of different patches
within the entire population that are occupied predomi-
nantly by one or the other strain. In addition, the study
points out the role of founder control in determining the
eventual infection status of a subpopulation.
Stochastic models of deme-structured populations
The final class of models that we discuss assumes that
the host population is subdivided into a number of
‘demes’ of finite size, thus incorporating random genetic
drift into the models. A first analysis of this type of
model was presented by Wade and Stevens (1994). Here,
it was assumed that mating takes place within demes,
but all offspring disperse and compete at the level of the
entire population before again forming demes for
mating. Thus, this model assumes hard selection, that
is, complete population mixture and global competition
in each generation. It was shown that this scenario slows
the spread of CI-inducing microbes. This result can be
understood by examining the effect of the model setup
on the frequency of incompatible matings, which
determines the selective advantage of CI. In a panmictic
population, incompatible matings occur with a prob-
ability equal to the variance in infection status (see also
Box 1). In the model by Wade and Stevens (1994), the
variance in infection status in the entire population is
partitioned into the variance in infection frequency
between demes and the average variance of infection
status within demes. As the latter determines the overall
mortality, it can be seen that the higher the variance in
infection frequency across demes, the fewer the offspring
that will be killed, so that selection for the CI microbes is
reduced.
A recent, more explicit analysis has come to rather
different conclusions (Reuter et al., 2008). In this model,
competition occurs locally and only a fraction of the
offspring disperses from their natal deme. Using a
combination of analytical methods and simulations, the
authors showed that the deme structure can substantially
facilitate the spread of CI compared with a panmictic
population. Specifically, it was shown that the spread of
CI is most likely when migration rates are low and
demes are of intermediate size. Under these conditions,
the amount of local random drift maximizes the
frequency of incompatible matings and is therefore most
conducive to the spread of the CI microbes. The
frequency of incompatible matings is lower (and condi-
tions less favourable for CI) when demes are very small
or large, because then random genetic drift is either so
strong that it homogenizes infection within demes or so
weak that it does not allow for stochastic increases in
infection frequency within demes, leading to essentially
deterministic dynamics. These results appear to hold
qualitatively both with a migrant pool and a stepping-
stone type of migration model. Furthermore, the in-
vestigation of sex-specific dispersal rates revealed that
the likelihood of CI spread was mainly determined by
the female dispersal rate, but that it did also decrease
with increasing male dispersal rate.
The divergent predictions of the two models de-
scribed—impeded or facilitated spread of CI through
population subdivision in Wade and Stevens (1994) and
Reuter et al. (2008), respectively—indicate that the
selection regime applied is decisive for the impact of
population structure on the spread of CI: global
competition combined with complete mixing of the
population disfavours the spread of CI-inducing mi-
crobes. On the other hand, local competition appears to
generally favour the spread of CI, although this effect is
strong only with low migration rates and intermediate
deme size. This latter result may appear puzzling on first
sight when compared with the results concerning the
critical migration rate discussed in the previous section.
Here, low migration rates impeded the spread of CI
microbes into an adjacent population. It is important to
realize that not only is the underlying model different (it
assumes infinitely large subpopulations without random
genetic drift), but also the questions addressed. Whilst
the deme-structured models aim to study the likelihood
of CI spread and its expected velocity in populations
with a more ‘local’ structure, the deterministic models
investigate under what conditions a stable polymorph-
ism can be maintained in populations structured on a
larger geographical scale. The deterministic models
assume infinitely large subpopulations and, conse-
quently, CI spread relies on high migration rates to
overcome the invasion threshold. In the deme-structured
models, by contrast, spread relies on stochastic increases
of infection frequency above the invasion threshold,
which requires low migration (little dilution) and genetic
drift.
Implications of population structure
Host gene flow
It is a well-known result in population genetics that
genetic influx into a population often does not corre-
spond to the real migration rate (m) of individuals,
owing to some class structure within the population.
Examples of class structure include different sexes, allelic
classes, age or infection status. The concept of effective
migration rate (m
e
) was developed to measure gene flow
in such situations (Barton and Bengtsson, 1986; Kobaya-
shi et al., 2008). The ratio of the effective migration rate to
the real migration rate (m
e
/m) is called gene flow factor
and represents the degree of gene flow modification. In a
class-structured population with mainland–island popu-
lation structure, the gene flow factor is in good
approximation equal to the mean reproductive value of
immigrants (Kobayashi et al., 2008).
The concept of effective migration rate allows the
determination of the impact of CI on host gene flow
(Telschow et al., 2002a, b, 2007; Engelsta
¨dter et al., 2008). It
was shown that both uni- and bidirectional CI causes
gene flow reduction between host populations that differ
in their infection status. Using the methods described in
CI and host population structure
J Engelsta¨dter and A Telschow
202
Heredity

Kobayashi and Telschow (2008), the gene flow factor can
be calculated analytically as
me
m1lA
1þlB
:ð1Þ
In this formula, l
A
and l
A
are the mortality rates in
incompatibility matings where males are infected with
bacterial strains Aand B, respectively, and we consider
gene flow from a (mainland) population infected with
strain Ato an (island) population mainly infected with
strain B. Formula (1) shows that CI can cause strong gene
flow reduction between populations with different
infection state. For example, if half of the offspring are
killed through CI (l
A
¼l
B
¼0.5), gene flow is reduced by
two-third (m
e
/mE1/3), and in the extreme case of
complete CI (l
A
¼l
B
¼1), gene flow is reduced to zero,
m
e
/mE0.
By setting l
B
¼0, formula (1) can also be applied to
unidirectional CI. An interesting implication of formula
(1) then is that unidirectional CI causes an asymmetrical
gene flow reduction: gene flow from an uninfected
population to an infected population is reduced by
1/(1 þl
A
),whereas gene flow in the opposite direction is
reduced by 1l
A
. As 1/(1 þl
A
)41l
A
for l
A
40, this
shows that gene flow is less strongly reduced towards
the CI-infected population than towards the uninfected
population. Thus, CI converts infected populations into
population genetic ‘sinks’ (that is, larger genetic influx
than outflux), whereas their neighbouring uninfected
populations are converted into genetic ‘sources’. This
might have important implications for the evolutionary
process of both host and symbiont.
Premating isolation and speciation
The idea that CI could facilitate speciation of hosts is
nearly as old as CI’s discovery (Laven, 1959), and has
generated some controversy over the last few decades
(Hurst and Schilthuizen, 1998; Werren, 1998; Bordenstein
et al., 2001; Wade, 2001; Telschow et al., 2007). The role of
CI would be to reduce gene flow between populations,
allowing genetic divergence for locally adaptive traits,
and to select for premating isolation. Above, we have
summarized the effect of CI on host gene flow. Here, we
discuss how population structure creates circumstances
for CI to select for female mating preferences. We
constrain ourselves to discussing theoretical results and
refer to the review by Bordenstein (2003) for a detailed
discussion of empirical patterns.
To date, three different models exist that investigate
how CI could select for premating isolation: (1) unidirec-
tional CI in a panmictic population (Champion de
Crespigny et al., 2005), (2) unidirectional CI in a main-
land–island model (Telschow et al., 2007) and (3)
bidirectional CI in a two-population model (Telschow
et al., 2005a). The basic idea is the same in all three
scenarios: mating preference is adaptive when it reduces
the risk of getting involved in an incompatibility mating.
Champion de Crespigny et al. (2005) considered a
panmictic host population to investigate the evolution of
female mating preference in the presence of unidirec-
tional CI. Their model shows that during the spread of
CI, a mutant allele that leads female carriers to
preferentially mate with uninfected males can increase
in frequency. However, this study may be criticized on
two grounds. First, the results depend crucially on the
assumption that females can choose between infected
and uninfected males. This is, to our knowledge, not
supported by any empirical data. Second, the increase in
mutant allele frequency was observed only during the
spread of CI, but not after CI has spread to fixation.
Given that the spread of CI-inducing bacteria is
potentially very rapid, this obviously limits the range
under which CI can select for mating preference. Both
critics raise serious doubts whether unidirectional CI can
select for female mating preference in a panmictic host
population.
A different picture emerges when population structure
is considered. As reviewed above, stable infection
polymorphisms are possible for both uni- and bidirec-
tional CI if migration is below a critical rate (Telschow
et al., 2005b; Flor et al., 2007). These infection polymorph-
isms create situations where females face an ongoing
threat of being involved in incompatibility matings.
Combining numerical and analytical approaches, it was
shown that this allows mating preference to evolve
under a broad range of circumstances (Telschow et al.,
2005a, 2007). Both models for uni- and bidirectional CI
differ from the panmictic model of Champion de
Crespigny et al. (2005) in that they do not assume mating
preference for uninfected males (or infection with a
certain bacterial strain). Instead, mating preference is for
locally adapted male traits, and mating preference alleles
spread because the male traits tend to be associated
with the respective infection states. In summary, popu-
lation structure solves both criticisms that were
raised against the panmictic model; it allows a stable
infection polymorphism as well as a polymorphism
of locally adapted male traits that females may use as a
preference cue.
Evolutionary dynamics of CI
How new CI types evolve and how CI arose in the first
place is currently not understood, in part because the
mechanistic and genetic bases of CI remain elusive.
Assuming that the modification (mod) and rescue (resc)
aspects of CI are genetically independent (for empirical
justification of this assumption, see Poinsot et al., 2003), a
crucial feature of CI is that in panmictic populations,
there is no selection on mod. This means that, provided
they still retain the original resc function, mutant strains
of bacteria that cannot induce modification in males or
induce a different mod are selectively neutral relative to
the ancestral strain (Prout, 1994; Charlat et al., 2001).
Therefore, through random genetic drift, the bacteria
may lose their ability to induce CI and become extinct
(Turelli, 1994; Hurst and McVean, 1996), or evolve a new
CI type that is bidirectionally incompatible to the
ancestral CI type (Charlat et al., 2001, 2005a).
The neutrality of the mod function rests on the
assumption of random mating and an unstructured host
population. With inbreeding, mod or new mod variants
are selected against when there is no resc against the
new mod, whereas outbreeding (inbreeding avoidance)
favours new variants of mod that cannot be rescued
(Engelsta
¨dter and Charlat, 2006; Engelsta
¨dter et al., 2006).
On the other hand, however, selection for mod is not
influenced by in- or outbreeding if resc is always
CI and host population structure
J Engelsta¨dter and A Telschow
203
Heredity

complete (Haygood and Turelli, 2009). Moreover,
local relatedness between individuals is expected
to also lead to positive selection for mod (Frank, 1997;
Hurst, 1991). This is because bacteria that induce CI
in males will relax local competition between hosts
and thereby benefit their relatives in females. Given
that the mating patterns, the scale of competition, local
relatedness and random genetic drift are all expected
to be important factors, it seems clear that host
population structure—potentially having an impact on
all of these factors—plays a key role in the evolutionary
dynamics of CI.
A recent study investigating the impact of
population structure on the evolutionary dynamics of
CI found that selection for increased CI level was present
with local density-regulation (as predicted by Hurst
(1991) and Frank (1997)), but this effect was only weak
and transient (Haygood and Turelli, 2009). This is
because relatedness was not, as in Frank’s (1997)
treatment, a fixed parameter, but a variable quantity
that converges quickly to zero as the population becomes
homogenized through migration. The analysis by Hay-
good and Turelli thus indicates that the evolutionary
maintenance of the mod function remains a conundrum
even in subdivided populations, leading the authors to
subscribe to the notion that CI persists in the long term
only through clade selection (Hurst and McVean, 1996).
According to this view, CI persists in the long term
because clades of microorganisms that retain the ability
to induce strong CI have a higher potential to spread in
novel host species than do clades with low CI levels.
In principle, this mechanism could also work with
different populations of the same species (with migration
playing the role of interspecies transmission), but
migration rates need to be very low to prevent fast
homogenization of the populations. Clade selection for
CI as well as the evolution of new types of CI (that is,
new mod/resc pairs) in structured host populations
remains to be analysed.
CI and insect pest control
Many medically important insect species, including the
disease-transmitting mosquitoes C. pipiens and A. aegypti,
are infected with or can be artificially infected with CI-
inducing Wolbachia. Therefore, CI has been investigated
as a mechanism to control insect pest populations
(Laven, 1967; Zabalou et al., 2004), or to drive transgenes
into insect populations (Turelli and Hoffmann, 1999;
Sinkins and Godfray, 2004). In what follows, we will give
a brief overview of these strategies (for in-depth reviews,
see Sinkins and Gould, 2006; Aksoy, 2008) and discuss
how their applicability may be dependent on host
population structure.
The most straightforward method to employ CI
as a control of insect pests is to release large
quantities of infected males into an uninfected popula-
tion. These males will then result in increased mortality
among offspring, potentially reducing the population
size of the next generation. This strategy has been
successfully applied in a field study of a mosquito
(C. pipiens) population (Laven, 1967) and also in
population cage experiments with the medfly Ceratitis
capitata (Zabalou et al., 2004). As this method is
largely independent from the infection dynamics of CI,
we expect the host population structure to be important
only insofar as it restricts dispersal of the released males.
The main disadvantage of this scheme of CI-based pest
control is that large quantities of infected males need to
be produced. These males need to be sexed accurately so
that no infected females are accidentally released into the
target population, in which case the infection might
spread so that a further release of infected males has no
effect. The second strategy for reducing the host
population size by means of CI that circumvents these
problems is the CI management (CIM) strategy (Dobson
et al., 2002a). CIM consists of the repeated release of
infected individuals (males and females), combined with
a monitoring of the population for infection frequencies.
During the spread of the infection, the host population
may be reduced because of incompatible matings
(Dobson et al., 2002a). In addition, the targeted release
of other bidirectionally incompatible strains at appro-
priate times is expected to further suppress the host
population (Dobson et al., 2002a). Finally, insect species
that act as disease vectors may be controlled through CI-
inducing bacteria that reduce the life span of their hosts,
because older insects are often more likely to transmit the
disease than younger ones. An example is the mosquito
A. aegypti, which has recently been successfully transin-
fected with a life-span reducing strain of Wolbachia
(McMeniman et al., 2009).
The theoretical results discussed in the previous
sections suggest that the success of CIM may be strongly
determined by the host population structure. For
example, as population structure influences the speed
of CI spread, this in turn determines how transient
suppression of the host population is and in which time
intervals new CI strains need to be released. More
importantly, the release of bidirectionally incompatible
CI strains into a structured host population may also
lead to the establishment of stable infections in the
various subpopulations, so that there may be only few
incompatible matings and consequently little population
suppression. Further modelling investigating the impact
of CI on host population dynamics in structured
populations is needed to assess the applicability of
CIM in such populations.
As an alternative to reducing their population size,
insect pests (in particular, disease vectors) may be
controlled by driving desired genes into these popula-
tions (reviewed in Sinkins and Gould, 2006). For
example, such genes could reduce the ability of
mosquitoes to transmit Plasmodium parasites. CI-indu-
cing Wolbachia have been proposed as a candidate drive
mechanism by means of which genes can spread into the
target population that either have been transgenically
incorporated into the Wolbachia genome or that are
linked to Wolbachia (Curtis, 1994; Sinkins et al., 1997;
Turelli and Hoffmann, 1999). Again, we expect the
applicability and efficiency of this strategy to depend
on the host population structure, which may accelerate,
slow or even prevent the spread of the transgenes along
with the CI-inducing bacteria. It has also been suggested
that actively influencing the population structure may be
a promising strategy for increasing the probability of CI
spread (Reuter et al., 2008): as moderately small deme
sizes and low rates of migration favour the spread of CI,
the release of few transgenic hosts combined with the
restriction of migration can create an infection base from
CI and host population structure
J Engelsta¨dter and A Telschow
204
Heredity

which further spread through the entire host population
is facilitated.
Conclusions
Given the importance of population structure in the
fields of epidemiology, population genetics and evolu-
tionary biology, it is not surprising that population
structure is expected to have a large impact on the
dynamics of CI spread. Mathematical models with
different assumptions and addressing different questions
have produced a variety of predictions concerning the
probability and velocity of CI spread as well as the
stability of spatial polymorphisms. Depending on the
scale of competition in the population, CI spread can be
facilitated (with local competition) or impeded (with
global dispersion and competition). Infection poly-
morphisms of two bidirectional CI-inducing strains can
be very stable in structured host populations, whereas
polymorphisms of infected and uninfected populations
are stable only when migration rates are very low. Given
the disparity and the sometimes diametrically opposed
predictions of previous models, future models providing
a unifying framework and producing all of the above
outcomes with different parameters might be desirable.
On the empirical side, virtually all theoretical predic-
tions concerning CI spread in structured populations
remain untested. Data from surveys of natural popula-
tions indicate that both stable polymorphisms and
spatial spread are common, but as of date, these data
have rarely been linked quantitatively to model predic-
tions. This is largely because of inherent difficulties in
estimating demographic parameters such as migration
rates and population sizes. Population cage experiments
that emulate different kinds of population structure may
be a more feasible alternative to get a better under-
standing of how much and what aspects of reality are
captured by the various theoretical models. Such an
understanding appears particularly important if one is to
apply CI-inducing microbes to controlling insect pest
populations.
Acknowledgements
We thank Sylvain Charlat, Matthias Flor, Yutaka Kobaya-
shi, Max Reuter and two anonymous reviewers for
helpful comments on the article. AT acknowledges
support from a postdoctoral fellowship awarded by the
Volkswagen Foundation.
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