Life and Death of an Influential Passenger: Wolbachia and the Evolution of CI-Modifiers by Their Hosts

Background Wolbachia are intracellular bacteria widely distributed among arthropods and nematodes. In many insect species these bacteria induce a cytoplasmic incompatibility (CI) between sperm of infected males and eggs of uninfected females. From an evolutionary point of view, CI is puzzling: In order to induce this modification-rescue system, Wolbachia affect sperm of infected males even though Wolbachia are only transmitted maternally. Phylogenetic studies of Wolbachia and hosts show that the bacteria rarely cospeciate with their hosts, indicating that infections are lost in host species. However, the mechanisms leading to Wolbachia loss are not well understood. Results Using a population genetic model, we investigate the spread of host mutants that enhance or repress Wolbachia action by affecting either bacterial transmission or the level of CI. We show that host mutants that decrease CI-levels in males (e.g. by reducing Wolbachia-density during spermatogenesis) spread, even at cost to mutant males. Increase of these mutants can lead to loss of Wolbachia infections, either as a direct consequence of their increase or in a step-wise manner, and we derive analytically a threshold penetrance above which a mutation's spread leads to extinction of Wolbachia. Selection on host modifiers is sexually antagonistic in that, conversely, host mutants that enhance Wolbachia in females are favoured whereas suppressors are not. Conclusions Our results indicate that Wolbachia is likely to be lost from host populations on long evolutionary time scales due to reduction of CI levels in males. This can occur either by evolution of single host modifiers with large effects or through accumulation of several modifier alleles with small effects on Wolbachia action, even at cost to mutant males and even if infected hosts do not incur fecundity costs. This possibility is consistent with recent findings and may help to explain the apparent short evolutionary persistence times of Wolbachia in many host systems.


Introduction
Wolbachia are intracellular bacteria that infect a wide variety of arthropod hosts. Screenings of single individuals per species typically give estimates of around 20% infection [1][2][3], and a recent meta-analysis indicates that the global incidence of Wolbachia among insect species can be as high as 65% [4]. As intracellular bacteria inhabiting the cytoplasm, Wolbachia are transmitted vertically through female eggs and not through sperm, but can affect phenotypes in both males and females.
As part of their lifestyle as reproductive parasites, arthropod-Wolbachia show a wide array of strategies to manipulate hosts into producing higher proportions of infected female offspring. Infected females are favoured because this is the sex that transmits the bacteria to future generations through the egg cytoplasm, whereas Wolbachia are not transmitted through sperm. Mechanisms used by Wolbachia range from killing of male offspring or induction of parthenogenesis to more subtle manipulations such as generation of sperm-egg incompatibilities, called cytoplasmic incompatibility (CI) [5][6][7][8]. CI is interpreted to involve a modification-rescue system [6]: Wolbachia in infected males modify the sperm, and the same strain of Wolbachia must be present in the egg to rescue the modification, or the embryo will typically fail to complete development. Cytologically, CI is manifested as a delay in the nuclear envelope breakdown of the paternal nucleus which results in improper condensation of paternal chromatin in the embryo, typically leading to embryonic death [9][10][11].
The phylogenetic history of Wolbachia indicates that long-time phylogenetic concordance between arthropod hosts and Wolbachia is uncommon [1,6,12]. However, such phylogenetic concordance would be expected due to the vertical transmission of these bacteria typically found within a species. Comparative phylogenetic analyses of Wolbachia in nematodes do show concordance with host phylogeny indicative of long term maintenance of the bacteria [13,14], which contrasts with the pattern observed in arthropod-associated Wolbachia. However, Wolbachia in nematodes are thought to be mutualistic, whereas those found in arthropods are primarily reproductive parasites (i.e. they manipulate repro-duction of hosts to enhance their own persistence). Studies also reveal frequent horizontal transmission of Wolbachia between arthropod species on an evolutionary timescale [1,12,[15][16][17].
Comparing these patterns suggests that Wolbachia are frequently acquired by arthropod species, but often do not persist within a species sufficiently long to co-diverge with the host (but see [18] for an exception). There must thus be mechanisms of loss of Wolbachia. However, unlike typical infections, resistance to Wolbachia infections in females is expected to be selected against, at least for the predominantly found phenotype of cytoplasmic incompatibility. The reason is that infected females are ''addicted'' to Wolbachia -if they lose their parasites, they will be reproductively incompatible with infected males in the population. Therefore, mechanisms by which host species lose their Wolbachia despite these antagonistic selection pressures are still unclear, and the male-specific repression of Wolbachia that is presented here seems to be one theoretical possibility to solve this paradox.
Early studies on CI-systems elucidated the dynamics of CI-Wolbachia and the implications of maternal transmission and infected male incompatibility for the fitness of uninfected females [19,20]. Previous theoretical studies of the evolution of incompatibility-inducing systems and their dynamics have found selection among parasites and hosts to favor variants that increase the proportion of infected progeny, i.e. by increasing transmission rates [21]. Turelli [21] also addressed possible ''resistance'' mechanisms in infected or uninfected females: Without assuming mutational costs and given imperfect transmission, he found the spread of modifier alleles reducing susceptibility of infected ova to sperm from infected males [21]. In a similar spirit, previous studies on haplodiploids have examined the spread of costless modifier alleles that completely eliminate or moderately to greatly reduce CI [22,23], the latter focusing on the effect of different CI types on the spread of such mutations. The dynamics of costly modifier alleles reducing female susceptibility to modified sperm have been examined and suggested as a plausible mechanism to drive nuclear transgenes through insect populations by Sinkins and Godfray [24]. Moreover, a bacterial role in losing Wolbachia has been proposed where CI-levels are assumed to slowly degenerate through mutation [25]. CI-inducing Wolbachia could also be displaced by sex-ratio distorting mutants, but empirical and theoretical evidence supports this idea only for induction of parthenogenesis and not for male-killing [26][27][28]. However, there has not been a systematic investigation of the effects of male and female specific host modifiers on Wolbachia dynamics, particularly treatments that incorporate costs of modifying alleles and consider the consequences to persistence of Wolbachia infections.
Here we investigate the co-dynamics of sex-specific host modifiers of CI-Wolbachia to determine whether their evolution can explain the lack of persistence of CI-Wolbachia in host species. Specifically, we investigate host modifiers that either (a) decrease or increase modification of sperm or (b) decrease or increase transmission of Wolbachia through eggs. Previous studies have either focused on -for the case of male ''resistance'' -the special case of complete elimination of CI through host modification [22] or the special case of CI in haplodiploids (where CI can lead to male production) and the effect of different CI-types on the spread of CI-reducing mutations of moderate to large effect [23].
Our study systematises these approaches but focuses on the long-term fate of Wolbachia-infections in the face of host modifier evolution. Moreover, we widen the scope by considering the entire range of putative modifications with relative effects varying from 0% to 100%, and we furthermore introduce survival costs incurred by mutant individuals in order to assess the effect of such costs on the fate of the mutation. We then apply analytical and numerical methods to examine how such regulatory mutants alter Wolbachia dynamics and investigate whether such mutations may also cause local extinctions of Wolbachia. We find that mutations that decrease Wolbachia modification of sperm can often spread and go to fixation in single populations, thereby altering stable infection frequency equilibria or driving Wolbachia to extinction, even when elevated survival costs of the mutation are incurred. Moreover, we make explicit use of infection instability to deduce analytically the threshold in effect size above which the spread of a mutation leads to loss of Wolbachia. We find that fixation of sub-threshold malespecific repressive mutations (that decrease CI-levels and lower Wolbachia-prevalence) eases the conditions for the spread of subsequent mutations of similar kind, so that Wolbachia may be lost by way of sequential host adaptation. Mutations that decrease Wolbachia transmission or rescue function are disadvantageous to females and never spread for moderate fecundity-costs, while, as expected, enhancing mutations increasing transmission rates are favoured. These modelling results are then discussed within the context of current theoretical, developmental, and evolutionary studies.

Methods
We investigated the evolution of host modifiers in a single panmictic host population infected with Wolbachia that induce cytoplasmic incompatibility. Modification of Wolbachia action by the host is controlled by one nuclear locus with two alleles, one being the wild-type, the other the mutation in question. Within the employed haploid model, individuals are characterized by their sex, their genotype at the modifier locus, and their cytoplasmic infection status with Wolbachia. Consequently, eight resulting phenotypic classes of hosts are treated in the model. Host-modifier genes are generally assumed to segregate according to standard Mendelian laws. We consider the following classes of host modifiers: (a) enhancement or reduction of Wolbachia modification of sperm, (b) enhancement or reduction of Wolbachia transmission to eggs, and (c) ''mimicry'' of egg rescue or sperm modification.
We follow Fine [20] in describing the infection dynamics of Wolbachia by two parameters: the transmission rate t, and the level of cytoplasmic incompatibility l CI . The transmission rate is defined as the proportion of an infected female's gametes that contain Wolbachia. The level of cytoplasmic incompatibility refers to the non-developing proportion of zygotes that result from fusion of modified spermatozoids with uninfected oocytes. If transmission is complete then the Wolbachia-infection will go to fixation, if t,1, however, a threshold frequency will exist below which Wolbachia cannot invade. Additionally, we assume Wolbachia to inflict a fecundity cost on infected females which reduces their offspring number by a factor of 12f. To facilitate comparison with the work of Turelli [21], our transmission rate t corresponds to his 1-m, our level of CI l CI to his 1-H (or s h ), and our fecundity reduction in infected females f to his 1-F (or s f ).
The mutations under consideration may be grouped according to their sex-specificity (i.e. male-or female-specific) and their effect on Wolbachia (i.e. repression or enhancement). Within each class mutations are thought to be sex-specific. Mutations repressing or enhancing Wolbachia action in males will alter the modificationfunction of Wolbachia accordingly, while in females such mutations may similarly alter Wolbachia transmission-rates (and thereby indirectly the rescue-function of Wolbachia) or change the rescuefunction directly without affecting transmission. Mechanistically, these effects may either be achieved by affecting gonadal Wolbachia-density or by altering Wolbachia's abilities of gamete manipulation.
Moreover, enhancing Wolbachia action in the germline could also be accomplished by emulating Wolbachia's modification-or rescue-function autonomously without the presence of Wolbachia. A mutation acting in this way would then enable the host to increase modification or rescue without having to interfere directly with Wolbachia transmission or manipulation. In this paper, we shall use the term mimicry to describe such an imitation of Wolbachia effects. Table 1 outlines the different mutations, groups them according to their sex-specificity and their effect on Wolbachia, and specifies mechanistic pathways through which these effects could be achieved. Generally, hypothetical mutations active in males deviate from some previous approaches that focused on mutations decreasing female susceptibility to modified sperm [21,24]. Moreover, our approach also incorporates conceptually the developmental details of Wolbachia-positioning during gamete production and modification [29,30].
Phenotypically, we suppose any mutation active in males to result in a different number of spermatozoids being modified by Wolbachia and thus to change the effective level of CI to (12e)l CI . Similarly, mutations active in females are thought to either lead to an altered fraction (12d)t of offspring inheriting Wolbachia or to a direct change in Wolbachia's rescue function that in turn modifies the effective level of CI to (12d)l CI . The parameters d and e represent the mutation's sex-specific penetrance, that is the likelihood of the mutation generating the respective enhancing or repressing phenotype. For reasons of generality, we differentiate penetrance levels d and e only according to sex-specificity and not to the specifically induced mechanism, and use positive penetrance levels for mutations repressing Wolbachia (by reducing CI-levels or transmission rates) and negative penetrance levels for mutations of inverse effects that enhance Wolbachia actions through increased transmission rates or CI-levels.
The mutation is further assumed to inflict some costs on affected individuals (in contrast to earlier theoretical studies [21][22][23]), so that the affected sex' chance of survival to adulthood is lessened by a factor of 12c if they carry the mutated allele. Thereby, we hypothesize the mutation's effects on survival to be independent of its penetrance. This cost is motivated by the fact that interfering with bacterial activity might also have influences on the host's own metabolism and vitality -especially if vital host processes co-opted by Wolbachia such as microtubule motor protein transport via kinesin-1 [31] need to be modified to, for example, impede bacterial recruitment during gametogenesis.
As shown in the Appendix S1, this verbal description of the system under study may be formalized to give a corresponding mathematical model of eight coupled difference equations. All numbered equations in this text thus refer to the Appendix S1. We were able to deduce analytically thresholds for the penetrance levels of repressive male-specific mutations above which Wolbachia is lost, but did not treat the general model analytically. Hence, we employed computer simulations to analyse the dynamics of the model for a wide range of parameters. For every simulation, we used the analytically derived equilibria of the mutant-free system as a starting point and then introduced the respective mutation in all cytogenotypes at a combined starting frequency of 0.1%. Simulations were performed using C++ and the DevC++-compiler (Bloodshed Software), and simulations were continued until equilibria were reached where frequency changes per generation were less than 10 27 . Analytical calculations were performed by hand and using Mathematica (Wolfram Research Inc.).

Results
For computer simulations, we considered large parts of the multi-dimensional parameter space. Transmission rates are usually high in nature [32]. Here, we let transmission rate t vary between 0.9 and 1. Guided by empirical studies showing CI levels to be variable [33], we let the level of cytoplasmic incompatibility l CI take on values across the whole parameter range (i.e. between 0 and 1). We used an upper limit of 50% for the fitness cost of modifier alleles, supposing higher values as very unlikely for an effect of this kind. For the respective mutations' levels of penetrance (e in males and d in females) we chose values from the entire meaningful range.
Fixed point analysis of the system without mutants reveals a threshold CI-level relative to the transmission rate below which a Wolbachia infection cannot persist and disappears from the population (see eqs. 10-12 in Appendix S1). We replicate the results of Fine [20] in showing this threshold -in the absence of fecundity costs to infected females -to be l crit: CI~4 t 1{t ð Þ(for only then the relevant fixed points are non-negative and nonimaginary). This threshold value is pivotal in determining whether the spread of a modifier allele causes the extinction of Wolbachia and was confirmed by simulation.

Male-specific mutations
Here, we consider mutants active in male hosts that change the level of CI (i.e. by regulating Wolbachia-density during spermatogenesis or reducing Wolbachia's ability to modify sperm) and consider whether these can spread in an infected population. This concept draws on an idea already suggested by Turelli [21]. The concept of male-specific modifiers was put forward verbally by Charlat et al. [14], and the idea of host-mediated changes in CIlevels has been developed formally for the special case of complete elimination of CI by Vala et al. [22] and for different CI-types in haplodiploids by Vavre et al. [23]. Our study systematically enlarges on these concepts and shifts the focus to the evolutionary fate of Wolbachia-infections. We allow for the whole range of host modification with effects from 0% to 100% and further introduce a survival cost incurred by those males carrying the mutation in question. Further, we consider the sequential evolution of male and female modifiers on stability of the Wolbachia infection.
Repressive mutations in Males. In the absence of survival costs, male-specific repressive mutations always spread as long as transmission is imperfect (t,1; as shown analytically in eqs. 31&32 of Appendix S1). An important finding is that spread of an incompletely repressing mutation can lead directly to the elimination of the Wolbachia-infection, or to a lower equilibrium frequency, depending primarily on the penetrance e. These contrasting outcomes are illustrated in figure 1, where subfigures 1a and 1b show the mutant's invasion dynamics for different penetrance levels e. Specifically, subfigure 1a presents the case of Wolbachia-persistence at reduced prevalence levels whereas subfigure 1b depicts the scenario of Wolbachia-extinction. Generally, as the mutation spreads among infected individuals, the frequency of uninfected individuals increases as well, and the selective advantage of mutant males correlates positively with the amount of uninfected females present as well as with the value of e.
As the mutation rises in frequency, Wolbachia experience a new ''effective'' CI level that is equivalent to (12e)l CI at fixation of the mutation. Consequently, Wolbachia disappear if the mutation reduces the population's ''effective'' CI level to values below the threshold l crit: CI (as derived above) where the Wolbachia-infection cannot stably persist. Thus, a threshold for e exists relative to l CI and t above which the successful spread of a regulatory mutation drives Wolbachia to extinction. This threshold's exact value can be calculated by setting (12e)l CI equal to l crit: lCI . These analytical results were confirmed by simulation and are summarized in table 2.
When e is below this threshold, however, the repressive mutation's spread does not lower the population's ''effective'' CI level sufficiently for Wolbachia to disappear from the population. Thus, a new equilibrium of reduced Wolbachia-prevalence is attained (see figure 1a). The actual equilibrium values depend on the value of e: As e grows, a lesser proportion of mutants remains infected in the subsequent equilibrium. The exact new prevalence levels can be calculated analytically by replacing l CI in the steady states of equations 10 and 11 in Appendix S1 with l eff: CI~1 {e ð Þl CI (see equations 33 and 34 of Appendix S1).
When we introduce a survival cost c that is inflicted on mutant males, the repressive mutation's penetrance e needs to be above a certain threshold e thr for the mutation to spread. This threshold depends on the original CI-level l CI , the transmission rate t, and the survival cost c. An analytical approximation of e thr can be derived by taking into account the reduced cost of CI incurred by mutants and then projecting the population dynamics one generation into the future (see figure 2 in the main text and equation 30 of Appendix S1). However, infected mutant females, despite being phenotypically indistinguishable from the wildtype, also enjoy a reproductive advantage through indirect fitness effects due to the production of infected mutant sons. When projecting the population dynamics only one generation into the future, mutant benefits therefore are underestimated (and threshold levels e thr overestimated as a consequence, see figure 2). This estimation error can, for example, be attenuated by projecting the population dynamics one more generation into the future (see figure 1 of Appendix S1).
As in the costless case, the mutation's successful spread leads to two possible scenarios: Either it causes the extinction of Wolbachia or the mutation spreads but Wolbachia persist at reduced prevalence levels. Again, the consequences of the mutation's spread depend on the level of e: The analytical threshold value e crit. derived above is confirmed by the numerical results and does not vary with survival cost c:While costs do influence whether a mutation invades or not (see below), they do not alter the qualitative dynamics where invading mutations always go to fixation, so that e crit. remains a function of only l CI and t.
Typical dynamics of the spread of a costly mutation with Wolbachia being lost from the population are depicted in figure 3a. As in the case without costs, the repressive mutation increases in frequency until average CI levels are lowered to l crit: CI (see above). Thus, the infection becomes unstable, Wolbachia suddenly disappears, and only uninfected hosts remain. However, with all females being uninfected, the survival cost incurred by mutant males is no longer balanced by their increased reproductive success. Thus, in contrast to the costless case presented in figure 1b, the mutant allele disappears from the population (as demonstrated for a female-specific costly ''nuclear rescue construct'' by Sinkins and Godfray [24]).
If the mutation does not drive Wolbachia to extinction but only reduces the bacteria's prevalence, the resulting dynamics are qualitatively similar to the costless case presented in figures 1a and 1b. As a consequence, the costly mutation persists at a new equilibrium of infected and uninfected mutants. The exact new prevalence levels can be calculated analytically as in the costless case (this is illustrated in figure 4a). However, sex ratios are skewed when c.0, as costs are only incurred by males. Thus, the analytical predictions of equations 33 and 34 in Appendix S1 only hold for the overall prevalence of Wolbachia but not for the individual equilibria of males and females.
In general, the mutant allele's invasion success is influenced by the CI-level l CI and the mutation's penetrance e, as well as the survival cost c and the transmission rate t. Figure 2 shows the dependence of invasion success on l CI and e for different values of c. These results show that successful invasions require higher levels of penetrance as survival costs increase, since the mutational benefits need to outweigh the associated rising fitness costs. Moreover, if transmission rates rise and survival costs stay constant, then successful invasions are only possible at further increased levels of penetrance (data not shown, but compare figure 5 for the female-specific equivalent): At higher transmission rates, less uninfected females are present in the population and the reproductive advantage of mutant males shrinks accordingly. Therefore, a mutant's reproductive benefits can only offset equal survival costs at higher penetrance levels. Our results indicate that even high costs of survival may be outweighed at intermediate transmission rates, favouring establishment of the mutant allele as well as, on long evolutionary timescales, the eventual loss of Wolbachia.
For the sake of completeness, we also investigated the dynamics of a mutant allele that increases CI in males. As expected, such enhancing mutations were not observed to spread in our numerical simulations because mutant males incur higher costs of CI than corresponding wildtypes.

Female-specific Mutations
Here we consider mutants in the host that either indirectly change the level of Wolbachia's rescue function in the gamete by altering Wolbachia transmission rates (e.g. by regulating Wolbachiadensity during oogenesis or increasing bacterial transmission efficiency) or that directly adjust said rescue function. We then ask whether such mutations can spread in the population. Again, we also introduce a survival cost imposed on mutant females and analyse the two cases in turn. The dynamics are expected to be influenced by the fact that females with repressive mutations will tend to be incompatible with infected males in the population, thus incurring an additional ''cost'' due to CI.
Altering transmission rates. Turelli has shown previously that selection on hosts tends to increase transmission rates in infected females, even in the presence of fecundity costs [21]. Here, we revisit these results with a special focus on the long-term persistence of Wolbachia, thereby extending Turelli's work by including in our consideration survival costs incurred by mutant hosts. Figure 3b shows a typical example of a cost-free mutation's dynamics: The original equilibrium between infected and uninfected individuals is left and the prevalence of Wolbachia covaries with the mutation's rise in frequency until a new equilibrium between infected and uninfected mutants is reached. At equilibrium, the new ''effective'' transmission rate is equivalent to (12d)t. Therefore, as in the male case, the resulting equilibrium prevalences can be calculated by replacing t in equation 10 and 11 in Appendix S1 with t eff. = (12d)t (see figure 4b for a graphical example and equations 35 and 36 of the Appendix S1).
In general, whether the mutant allele can invade is influenced by level of CI l CI , the mutation's penetrance 2d, transmission rate t, and the survival cost c. Figures 5a and 5b show the dependence of invasion success on l CI and 2d for different values of c and t. These results demonstrate that, as expected, cost-free mutations increasing transmission rates can invade and spread through an infected population over nearly the entire parameter space. This is due to the fact that mutant females produce more infected female offspring that can mate compatibly with infected males, which offsets the cost of simultaneously begetting more infected males that are subject to CI in mating with uninfected females.    l CI where a male-specific repressive mutation can spread in the population, and how this affects the persistence of Wolbachia. In 2a the survival cost was set to c = 0 and the mutation could always spread. In 2b and 2c the survival cost was set to c = 0.01 and c = 0.05, respectively. Dashed lines mark the critical penetrance e crit. as approximated analytically in eq.30 of Appendix S1. Other parameters were t = 0.9, d = 0, and f = 0. doi:10.1371/journal.pone.0004425.g002 Prior treatments did not consider the influence of costs to enhancing female mutations. Introducing such costs complicates the matter in that reproductive benefits enjoyed by mutant females must now offset these costs in order for the mutation to spread. As a result, the parameter subspace where the mutation can invade successfully shrinks for elevated survival costs c (see figures 5a and 5b). Still, if the mutation does spread, the resulting elevated prevalence levels can be calculated as in the costless case (see Figure 4. Altered Wolbachia-prevalence after spread of repressive and enhancing mutations. Shown in 4a is the reduced prevalence of Wolbachia after successful spread of a male-specific repressive mutation. Prevalence is shown as a function of the mutation's penetrance e for different values of l CI (as indicated in the graph) and with t = 0.95. Figure 4b shows the elevated prevalence of Wolbachia after fixation of a female-specific enhancing mutation as a function of the mutation's penetrance 2d for different values of t (as indicated) with l CI = 0.5. All plots are based on the analytical results of eqs. 33&34 and eqs. 35&36 respectively, all in Appendix S1. In 4a, e was varied between e = 0 and e = e crit. for each case. At higher values of e, the spread of the mutation reduces Wolbachia's prevalence to zero. In 4b, 2d was varied between 2d = 0 and {d~1 t {1, as larger values of 2d all lead to t eff. = 1. Other parameters were c = 0 and f = 0. doi:10.1371/journal.pone.0004425.g004 Figure 5. Parameter regions of spread of female-specific enhancing mutations. Shown are the parameter regions of the mutation's penetrance levels d and the level of CI l CI where a femalespecific enhancing mutation that either increases transmission rates (5a above and figure 4b). However, since sex ratios are skewed when c.0 (as costs are only incurred by females), the analytical predictions of equations 35 and 36 in Appendix S1 only hold for the overall prevalence of Wolbachia but not for the individual equilibria of males and females.
For the sake of completeness, we also investigated the fate of female-specific repressive mutations that lower transmission rates. As expected, these were not observed to spread since mutant females incur the cost of receiving more uninfected daughters that cannot mate compatibly with infected males. Therefore, mutant females are at a fitness disadvantage to corresponding wildtypes that beget more infected offspring -a manifestation of the addiction-character of Wolbachia. Moreover, even the potential prior spread of a male-specific repressor only changes the situation qualitatively (i.e. repressive female mutants would now encounter lowered CI-levels) and thus still precludes the subsequent spread of female repressors.
Hypothetical fecundity costs incurred by infected females might be expected to change the general situation, as lowering transmission rates would then harbour the benefit of reducing average fecundity costs since more uninfected offspring are produced. Nevertheless, even in the presence of moderate fecundity costs of up to 10%, such a mutation was never observed to spread during our numerical simulations. This may be due to the fact that fecundity costs decrease the prevalence of Wolbachia at equal transmission rates and CI-levels because of the reduced fitness of infected females (see eqs. 13-18 of Appendix S1). Therefore, the infection becomes unstable already at larger critical CI-levels (see eq.19 of Appendix S1), and the critical penetrance levels e crit and d crit required for loss of Wolbachia shrink accordingly. It seems that, as a result, the reduction of fecundity costs in uninfected female offspring does not suffice to offset the increased costs of CI incurred by mutant females.
For similar reasons, we observed little effect of fecundity costs when examining the success of female-specific enhancing mutations that increase transmission in situations with varying fecundity costs. At first glance, we would expect mutant benefits of receiving more infected offspring (that are not subject to CI) to trade-off with fecundity reduction of said infected offspring. However, as the presence of fecundity costs results in a larger proportion of uninfected hosts (see above), this increases the reproductive benefits enjoyed by mutant females, whereas the costs of fecundity reduction remain unaltered. As a result, threshold levels of penetrance above which the mutation may invade and spread are not shifted upwards, as intuition might suggest, but the entire curve is shifted to the right -that is, not higher penetrance thresholds at similar CI-levels, but higher penetrance thresholds at correspondingly higher levels of CI are the result of the introduction of fecundity costs (see figure 2 in Appendix S1 for an illustration).
Changing the rescue function directly. Enhancement of Wolbachia action in females could also occur if mutant females increase the rescue function directly without affecting transmission rates. In theory such an effect could be achieved if a (hypothetical) Wolbachia rescue gene were to be transferred to the host's nucleus. This is similar to the 'nuclear rescue construct' of Sinkins and Godfray [24] and has been considered theoretically for cost-free mutations reducing the susceptibility of uninfected ova by Turelli [21], albeit without the focus on potentially resulting infection instabilities and loss of Wolbachia. Here, we add costs to the mutations and determine the effects on infection stability.
Generally, the consequences are reminiscent of a male-specific repressive mutation: The mutation induces an autonomous rescuefunction in the host (irrespective of whether mutant females are infected with Wolbachia) that leads to a decrease in population CIlevels. These may in turn cause the extinction of Wolbachia if penetrance levels are above a threshold d crit: . (equivalent to e crit: as derived above). If penetrance levels are below this threshold, new equilibria of reduced Wolbachia prevalence are attained.
As in the male case, such a mutation always spreads to fixation if it carries no cost for female mutants. However, if mutant females' survival chances are reduced, then penetrance levels need to be above certain thresholds for the mutation to spread (see figure 5c). Interestingly, these thresholds are up to 100% higher than for a male-specific repressive mutation (compare to figure 2). This is due to the fact that mutant males only benefit from a repressive mutation if they are infected and thus would otherwise incur the cost of CI if mated with uninfected females. Mutant females, however, only benefit from enhancing mutations mimicking Wolbachia's rescue function if they are, in fact, uninfected with Wolbachia -otherwise their matings would not be subject to CI anyway. These results stress the importance of considering both male-and female-specific CI-reducing mutations and demonstrate that the two scenarios can, in fact, result in qualitatively different dynamics for similar parameter settings.
In contrast, the analogous mutation in females that autonomously lowers the rescue function irrespective of infection status (i.e. an ''inverse mimic'') was not successful: Similar to the case of a male-specific enhancing mutation, mutants incur a higher cost of CI due to lowered rescue-levels. Thus, they suffer a fitness disadvantage relative to the wildtype, so that the mutation is not expected to spread (and was not observed to do so in our simulations).

Non sex-specific mutations
We also examined the fate of a repressive mutation that is equally active in females and in males (with d = e) so that transmission rates and Wolbachia's modification of sperm are reduced simultaneously. As discussed above, female-specific mutations reducing transmission rates were never observed to spread. Moreover, mutations that simultaneously repress Wolbachia manipulation of gametes in males could not spread either. As the results with effects only on females did not differ numerically from those with equal effects on both sexes, it seems that the reproductive costs and benefits of reduced transmission rates are the limiting factor for the spread of any mutation that affects transmission (and thus gametogenesis) also (or only) in females. Note that this would effectively limit the evolution of repressive host modifier alleles as long as their effect -for example on reduction of Wolbachia density during gametogenesis -is symmetric in both sexes.

Sequential Evolution
Hypothetically, several mutations affecting Wolbachia action in the host could also arise subsequently within one population (be it through occasional migrational influx or through actual local and b) or increases the rescue function autonomously (5c) can spread in the population. Transmission rates were varied between t = 0.9 (5a and c) and t = 0.95 (5b). The survival cost c was varied as indicated, and the mutation could invade (and spread to fixation) above the depicted threshold lines. In 5a and c, costless mutations could always invade. Penetrance levels in 5a and b (where they take on negative values in order to increase transmission rates) were varied between 2d = 0 and {d~1 t {1 (where t eff. becomes 1) and between 0 and 1 in subfigure c. The grey line in 5c depicts the critical penetrance level d crit. above which Wolbachia is driven to extinction by the mutation's spread. Other parameters were e = 0 and f = 0. doi:10.1371/journal.pone.0004425.g005 mutation). Their fate then depends on local values of l CI , t, e, d, and c, as well as on the timing of mutational events: If a costly male mutant arrives first, spreads, and Wolbachia disappears as a result, then future mutations enhancing Wolbachia action (whether through increased transmission rate, increased rescue-function, or a 'nuclear rescue construct') necessarily are of no effect. However, if the male-specific repressive mutation's penetrance is lower, then Wolbachia will persist, albeit at lower prevalence as a result of the mutation's spread. As a consequence, invasion conditions for female-specific enhancing mutations are rendered more restrictive as the spread of the male mutation lowers the effective level of CI to (12e)l CI (compare figure 5 where threshold values of 2d rise with lower l CI ). In contrast, conditions for the subsequent spread of additional male-specific repressive modifiers are eased (i.e. threshold levels of e fall with lower l CI ).
To explore these predictions further, we examined cascades of mutations of equally small effect and found that these can lead to gradual meltdown of CI and long-term frequency decline and loss of Wolbachia.We know from our analyses that cost-free malespecific repressors will spread to fixation for all penetrance levels, thereby driving the earlier predominating wildtype to extinction. Moreover, we can calculate the ''effective'' CI-level that Wolbachia are exposed to after fixation of a host-modifier. As a result, we can approximate the fitness benefits enjoyed by a new mutation that we introduce after a previous male-specific modifier has reached fixation (see eq.38 of Appendix S1). For the cascade of mutations, we repeatedly calculate the fitness benefits of two such subsequent mutations until the mutations' cumulative effects have reduced CI-levels to l crit. and Wolbachia goes to extinction. The results show that the benefit enjoyed by subsequent male-specific repressors grows with the number of preceding mutations of similar effect (see. figure 6a). As predicted, successive mutations act synergistically and ease their reciprocal spread until the final stop of Wolbachia-extinction is reached. Moreover, we can use infection stability to calculate analytically the critical number of repressive mutations of equal effect that is necessary to drive Wolbachia to extinction (see eq.37 of Appendix S1). Figure 6b shows these critical numbers to vary greatly depending on the mutation's penetrance as well transmission rates and CI-levels, but for certain parameter values (e.g. t = 0.9, e = 2.5%) few consecutive mutations suffice to reach the cascade's final stop.
Female enhancers that increase Wolbachia's rescue function also lower effective CI-levels and are thus expected to produce qualitatively similar results as male repressors: Either Wolbachia disappears (if d$d crit. ) and subsequent male-specific repressive mutations are of no relevance, or Wolbachia persists at reduced prevalence levels so that conditions for subsequent male-specific repressive mutations are eased due to lowered CI-levels. As noted before, prior fixation of CI-reducing mutations in males or females does not produce conditions conducive to the spread of female specific repressors lowering transmission rates, even in the presence of fecundity costs.
Conversely, if a female-specific enhancing mutation that increases transmission rates arises first and is able to spread, then elevated effective transmission rates will restrict conditions under which costly male mutants may invade (since threshold values of e rise with higher t). Moreover, such preceding female-specific mutations with a penetrance of {d § 1 t {1 would raise local transmission rates to 1 so that subsequent male-specific repressive mutations cannot spread since they require imperfect transmission. However, perfect transmission is only reached in the absence of fecundity costs. If fecundity costs are present (i.e. f.0), then effective transmission rates remain below 1 so that subsequent spread of male-specific repressive mutations is still possible.
Furthermore, even under complete transmission and without female fecundity costs, male repressors are expected to invade when there is a male fecundity or survival cost to being infected (which we did not explicitly consider in our model). This is because mutant males are then equally compatible with females whether they have the infection or not, and loss of Wolbachia increases fitness. In turn, this would lead to either reduced equilibrium levels Figure 6. Cascades of male-specific repressive mutations and loss of Wolbachia. Shown in 6a are the increasing fitness advantages during a cascade of male-specific repressive mutations of equally small effect. The percentage fitness benefits of an additional mutation relative to the predominating genotype are plotted against the currently fixed number of n mutations. Fitness benefits are approximated using eqs. 27-28 of Appendix S1. Each dot represents one mutational step in the cascade; stars indicate the final stop of loss of Wolbachia where cumulative effects reach the threshold penetrance e thr. . Parameters are e = 0.025 and l CI = 0.4 with transmission rates varied as indicated. Shown in 6b are the critical numbers of male-specific repressive mutations n crit. of equal effect that are necessary to drive Wolbachia to extinction in such a cascade of mutations. These thresholds were calculated analytically using eq.37 of Appendix S1 and are plotted as a function of l CI with t varied as indicated and e = 0.025. Other parameters for both graphs are c = 0 and f = 0. doi:10.1371/journal.pone.0004425.g006 or elimination of Wolbachia, as before. Moreover, the presence of fecundity costs generally leads to an increase in the critical CI-level below which the infection becomes unstable and Wolbachia disappears (see above and eq.19 of Appendix S1). As a result, critical penetrance levels e crit. shrink accordingly, so that the cumulative evolution of male-specific repressors can lead to quicker loss of Wolbachia.
Note that, although not explicitly considered in our study, there also is selection on Wolbachia to counter host adaptation, e.g. by increasing transmission rates or increasing CI-levels (as modeled in ref. 21). Such Wolbachia adaptations could result in very high symbiont-mediated transmission rates that, in turn, would weaken selection on hosts for reduced sperm modification. However, while perfect transmission has indeed been recorded under laboratory conditions (e.g. [34]), earlier studies suggest that transmission rates can be lower in the field [35]. Also, as mentioned previously, even if complete transmission occurs, selection for male repressors of Wolbachia will be favored in the infection imposes a survival or fertility cost in males.
In summary, the outcome of selection can be the consequence of two competing processes -selection for enhanced transmission through females and selection for reduced modification in males, where consecutive mutations work synergistically within each class (that is, they ease the spread of future mutations of similar effect) and antagonistically between classes. While individual outcomes naturally depend on the specific costs and effects of the two classes of mutation, we generally expect cascades of male-specific repressors to outweigh the effect of female-specific enhancers on long evolutionary time scales. This is motivated by the fact that the presence of fecundity costs discourages the emergence of hostmediated perfect transmission. Still, even if transmission is complete, male-specific repressors would be selectively favored if Wolbachia impose a fertilitiy or survival cost on infected males. As a result, we expect this sequential sexually antagonistic process to lead to long-term loss of Wolbachia.

Discussion
Wolbachia are among the most widespread and abundant infections known. They are inherited maternally within species and also move laterally between host taxa. The bacteria spread within host species due to the reproductive alterations they induce, such as cytoplasmic incompatibility, feminization, parthenogenesis, or male-killing. Phylogenetic comparisons of hosts and Wolbachia indicate that these bacteria do not persist over long time periods within most arthropod taxa [1,6,12]. That is, rarely does one find concordant phylogenies of the bacteria and their hosts. Therefore, the infections are relatively quickly lost on evolutionary time scales, such that they infrequently persist within a taxon across speciation events. However, in the case of CI bacteria, infection loss would appear to be difficult because elimination of the infection in females would lead to ''sterility'' of these females in crosses with infected males, due to CI. This has presented a paradox -why and how are Wolbachia infections lost in species.
Our study is an attempt to investigate this question. The results show that sex-specific host repressors of Wolbachia in males can readily spread, even at cost to mutant males, and either result in elimination of Wolbachia infections or reduced infection levels within a population. Conversely, enhancers of Wolbachia transmission in females are favoured under a broad range of conditions, because they enhance the probability of female eggs being compatible with sperm from infected males. Hence selection for host modifiers works antagonistically in the two sexes. The outcome of these processes may be complex, although in general, we expect that successive selection for male repressors of Wolbachia can lead to long-term elimination of infections.
There is some empirical support for the notion that malespecific reduction of CI modification occurs. In Drosophila melanogaster, Wolbachia are effective at inducing CI only in young males, and the infection level declines and can be lost in testes over time [30]. In the cricket species Gryllus firmus and G. pennsylvaticus, Wolbachia are absent from testes, despite the presence of somatic infections [36]. These results may be consistent with selection for sex specific reduction or exclusion of Wolbachia from testes. Moreover, introgression experiments demonstrate an effect of host genetic background on level of CI and thus the apparent coevolution of host and reproductive parasite regarding regulation of Wolbachia action [30].
Host-induced changes not in the density of Wolbachia but in the efficiency of their action also seem to occur: In the parasitoid wasp Nasonia vitripennis, complete CI occurs despite very low Wolbachiadensity in all tissues including the gonads -even if Wolbachia is present not in the spermatocysts but only in the adjacent sheet cells [37]. When compared to the situation in Drosophila where Wolbachia-placement in sheet cells is not sufficient to cause CI [30], these findings suggest host-parasite interactions that alter Wolbachia's efficiency.
The potential role of host suppressor genes has repeatedly been mentioned in the literature (e.g. Stouthamer [38] with regard to Wolbachia-induced parthenogenesis) and there is empirical evidence for host-suppression of male-killing as well as parthenogenesis-inducing Wolbachia [39][40][41][42]. Earlier theoretical analyses [21] found host selection to favor increased transmission rates as well as increased compatibility between infected males and uninfected females. However, these treatments did not consider costs to such modifiers, and therefore expected uninfected females from polymorphic populations to generally evolve resistance to incompatibility [21]. Mathematically, the consequences of a mutant female's reduced susceptibility are similar to those of a mutant's males reduced sperm-modification: both lower the effective level of CI. However, our study shows that male-specific repressive mutations lowering CI will spread for a wider range of conditions than will female-specific mutations lowering CI (i.e. a 'nuclear rescue construct', sensu Sinkins and Godfray [24]). This difference is due to CI-reduction differentially affecting both sexes regarding their infection status -in mutant females uninfected individuals benefit more, whereas among mutant males infected individuals enjoy greater benefits.
Our study further demonstrates that even complete suppressors of Wolbachia-growth (i.e. e = 1) can increase within populations at a stable infection frequency equilibrium when they are male-specific. This contrasts with some earlier predictions that did not take into account the possibility of sex-specific host modification of Wolbachia action [21], specifically repression of Wolbachia in male gonads. Later modelling work that did include sex-specific host modifications and focused on the special case of complete elimination of CI found such mutations to spread easily [22]. Similarly, a theoretical study concentrating on the effect of CItypes in haplodiploids demonstrates the spread of CI-reducing host modifiers with moderate to large effects [23]. However, both these studies do not investigate systematically the fate of mutations of varying effect size, fitness costs to the repressors, and the mutations' consequences for the long-term persistence or extinction of Wolbachia. Further verbal arguments of sex-specific ''resistance'' expected nuclear genes increasing transmission rates in females to spread if Wolbachia-prevalence is higher than 50%, while male resistance was expected to spread if less than 100% are infected [14]. Our formal model then confirms these predictions but also shows that male suppressors may spread at initial infection frequencies of 100% (i.e. for l CI = 1 and t,1, where uninfected zygotes are produced but fail to develop due to perfect CI).
Generally, our study systematically extends the scope of possible mutations to the entire range of host modifications (i.e. from 0% to 100%). By explicitly considering the consequences for infection instability, we were able to deduce analytically those critical penetrance levels above which the spread of a modifier leads to loss of Wolbachia . Additionally, host modifications with small effect on, for example, Wolbachia gonadal density, seem to be biologically more plausible than the direct elimination of CI altogether. Overall, we show that spread of a male repressor can lead to loss of the Wolbachia under a broad range of clearly-specifiable conditions. Moreover, spread of sub-threshold male repressors eases invasion conditions for subsequent mutations of similar kind, so that Wolbachia may be lost in a step-wise manner. As a result, increase of such sex-specific repressors may be one process explaining why CI-Wolbachia do not persist within host taxa on evolutionary timescales.
Despite Wolbachia's lifestyle as an intracellular parasite, the expected phylogenetic congruence between hosts and Wolbachia is absent [1,[6][7][8]12,15,17]. Our model suggests these data to be interpreted as the result of repeated loss of CI-inducing Wolbachia through the spread of host modifiers and subsequent reinfection by horizontal transfer. Earlier studies point out that invasion of nonmodifying Wolbachia into infected populations could also account for the subsequent loss of Wolbachia [25]. However, this explanation requires a direct cost of Wolbachia to be imposed on infected females in order for Wolbachia to be lost through selection. Within our model, however, a hypothetical moderate fecundity cost f that lowers infected females' fecundity levels to 12f had no effect on invasion success. Assuming such direct costs of Wolbachia is thus unnecessary for Wolbachia to be lost from the population through the mechanisms proposed by our model. This stands in contrast to previous theoretical studies of suppression of CIinducing Wolbachia [22,23] that did not separately consider scenarios without fecundity costs incurred by infected females.
Empirical studies have shown two types of CI to exist in haplodiploid insects where CI-affected offspring either die (female mortality, FM) or develop as males (male development, MD; [43]). Previous studies show that, in contrast to the typical FM-CI, the MD-type selects for females to decrease transmission rates [23]. While we did not explicitly consider this CI-type in our own modelling, this fact nonetheless substantiates the possibility of Wolbachia loss. Moreover, empirical results suggest that dosage effects of Wolbachia-induced damage to paternal DNA may account for these differential CI-types: In simplified terms, greater damage leads to haploid embryos (and thus the MD-type in haplodiploids) whereas smaller damage allows for some paternal chromosomes to survive the first mitosis, which results in aneuploid embryos and failure of development (the FM-type; [44,45]). As a result, host-mediated changes in bacterial density might lead to changes in CI-type, as observed by Breeuwer and Werren [44]. Thus, the host modifiers examined in our studyespecially those that have small effects on bacterial action and lead to reduced prevalence, not extinction of Wolbachia -may provide a host-mediated pathway between different CI-types. Note that, however, even though the MD-type is more prone to host modification than the FM-type (see above and [23]), the type of CI will only have a quantitative influence on the evolution of Wolbachia-suppression, not a qualitative one: It may increase fixation times for an allele reducing CI-levels in FM-relative to MD-populations, but it does not affect the evolutionary potential of such modifier alleles on long evolutionary time scales.
Finally, given our results of the easily-observable loss of Wolbachia-infection, the details of the host-symbiont system under study here can be regarded as not stable but in fact circular: Any uninfected and unregulatory host-population could be infected by CI-Wolbachia (given high enough values of t and l CI ), thus leading to spread of the infection. Subsequent selection on the host for sexspecific repressors would lead to eventual loss of the Wolbachia. Once the repressors declined due to mutation or selection against a costly repressor in the absence of Wolbachia, the species would be vulnerable to reinfection by CI inducing Wolbachia. Thus infections could be cyclical within a host clade over evolutionary time. In the spirit of previous work [46], infection with CI-inducing Wolbachia does not seem to be a veritable ''final stop'' for any insect host population.

Supporting Information
Appendix S1 Appendix S1 contains mathematical formulae and derivations as well as additional figures.