Wolbachia-induced unidirectional cytoplasmic incompatibility and the stability of infection polymorphism in parapatric host populations

Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes

This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensional models. The conditions for the durable coexistence of Wolbachia-carrying and wild mosquitoes are expressed using the model's parameters in a compact closed form. When the Wolbachia bacterium is locally established, the size of the remanent wild population can be assessed by a direct formula derived from the model. The model was tested for four Wolbachia strains undergoing laboratory and field trials to control mosquito-borne diseases: wMel, wMelPop, wAlbB, and wAu. As all these bacterial strains affect the individual fitness of mosquito hosts differently and exhibit different levels of resistance to temperature variations, the model helped to conclude that: (1) the wMel strain spreads faster in wild mosquito populations; (2) the wMelPop exhibits lower resilience but also guarantees the smallest size of the remanent wild population; (3) the wAlbB strain performs better at higher ambient temperatures than others; (4) the wAu strain is not sustainable and cannot persist in the wild mosquito population despite its resistance to high temperatures.

Modelling the ecological dynamics of mosquito populations with multiple co-circulating Wolbachia strains

Wolbachia intracellular bacteria successfully reduce the transmissibility of arthropod-borne viruses (arboviruses) when introduced into virus-carrying vectors such as mosquitoes. Despite the progress made by introducing Wolbachia bacteria into the Aedes aegypti wild-type population to control arboviral infections, reports suggest that heat-induced loss-of-Wolbachia-infection as a result of climate change may reverse these gains. Novel, supplemental Wolbachia strains that are more resilient to increased temperatures may circumvent these concerns, and could potentially act synergistically with existing variants. In this article, we model the ecological dynamics among three distinct mosquito (sub)populations: a wild-type population free of any Wolbachia infection; an invading population infected with a particular Wolbachia strain; and a second invading population infected with a distinct Wolbachia strain from that of the first invader. We explore how the range of possible characteristics of each Wolbachia strain impacts mosquito prevalence. Further, we analyse the differential system governing the mosquito populations and the Wolbachia infection dynamics by computing the full set of basic and invasive reproduction numbers and use these to establish stability of identified equilibria. Our results show that releasing mosquitoes with two different strains of Wolbachia did not increase their prevalence, compared with a single-strain Wolbachia-infected mosquito introduction and only delayed Wolbachia dominance.

Cytoplasmic incompatibility in hybrid zones: infection dynamics and resistance evolution

Cytoplasmic incompatibility is an endosymbiont-induced mating incompatibility common in arthropods. Unidirectional cytoplasmic incompatibility impairs crosses between infected males and uninfected females, whereas bidirectional cytoplasmic incompatibility occurs when two host lineages are infected with reciprocally in compatible endosymbionts. Bidirectional cytoplasmic incompatibility is unstable in unstructured populations, but may be stable in hybrid zones. Stable coexistence of incompatible host lineages should generate frequent incompatible crosses. Therefore, hosts are expected to be under selection to resist their endosymbionts. Here, we for mulate a mathematical model of hybrid zones where two bidirectionally incompatible host lineages meet. We expand this model to consider the invasion of a hypothetical resistance allele. To corroborate our mathematical predictions, we test each prediction with stochastic, individual-based simulations. Our models suggest that hybrid zones may sustain stable coinfections of bidirectionally incompatible endosymbiont strains. Over a range of conditions, host are under selection for resistance against cytoplasmic incompatibility. Under asymetric migration, a resistance allele can facilitate infection turnover and subsequently either persist or become lost. The predictions we present may inform our understanding of the cophylogenetic relationship between the endosym biont Wolbachia and its hosts.

Molecular Evidence Suggests That Wolbachia pipientis (Rickettsiales: Anaplasmataceae) is Widely Associated With South American Sand Flies (Diptera: Psychodidae)

Wolbachia pipientis (Hertig) is an endosymbiotic microorganism widespread among arthropods and other invertebrate hosts, and employed in strategies to reduce the incidence of arthropod-borne diseases. Here, we used a PCR-based approach for 16S RNA and wsp genes to investigate the prevalence, geographical distribution, and strains of Wolbachia in sand flies (Diptera: Psychodidae: Phlebotominae), the main vectors of the causative agents of leishmaniasis, from three biomes in Brazil: Amazon, Cerrado, and Caatinga. We found that: 1) Wolbachia DNA is present in most (66.7%) of the sampled sand fly species, including vectors of Leishmania spp. (Ross, Trypanosomatida: Trypanosomatidae), 2) the prevalence of Wolbachia DNA varies among species and populations, 3) some strains of Wolbachia may have wider geographical and host range in South America, and 4) two phylogenetic distinct wsp sequences might represent two novel strains for Wolbachia in South America sand flies. Those findings increase the basic knowledge about Wolbachia in South American sand flies and might foster further researches on its use to reduce the transmission of sand fly-borne parasites.

Greenhead (Tabanus nigrovittatus) Wolbachia and Its Microbiome: A Preliminary Study

Endosymbiotic Wolbachia bacteria are known to influence the host physiology, microbiota composition, and dissemination of pathogens. We surveyed a population of Tabanus nigrovittatus, commonly referred to as "greenheads," from Crane Beach (Ipswich, MA, USA) for the presence of the alphaproteobacterial symbiont Wolbachia. We studied the COI (mitochondrial cytochrome oxidase) marker gene to evaluate the phylogenetic diversity of the studied specimens. The DNA sequences show strong similarity (between 99.9 and 98%) among the collected specimens but lower similarity to closely related entries in the NCBI database (only between 96.3 and 94.7%), suggesting a more distant relatedness. Low levels of Wolbachia presence necessitated a nested PCR approach, and using 5 markers (ftsZ, fbpA, dnaA, coxA, and gatB), we determined that two recognized "supergroups" of Wolbachia species were represented in the studied specimens, members of clades A and B. Using next-generation sequencing, we also surveyed the insect gut microbiomes of a subset of flies, using Illumina and PacBio 16S rRNA gene sequencing with barcoded primers. The composition of Proteobacteria also varied from fly to fly, with components belonging to Gammaproteobacteria making up the largest percentage of organisms (30 to 70%) among the microbiome samples. Most of the samples showed the presence of Spiroplasma, a member of the phylum Mollicutes, although the frequency of its presence was variable, ranging from 2 to 57%. Another noteworthy bacterial phylum consistently identified was Firmicutes, though the read abundances were typically below 10%. Of interest is an association between Wolbachia presence and higher Alphaproteobacteria representation in the microbiomes, suggesting that the presence of Wolbachia affects the host microbiome. IMPORTANCE Tabanus nigrovittatus greenhead populations contain two supergroups of Wolbachia endosymbionts, members of supergroups A and B. Analysis of the greenhead microbiome using next-generation sequencing revealed that the majority of bacterial species detected belonged to Gammaproteobacteria, with most of the samples also showing the presence of Spiroplasma, a member of the Mollicutes phylum also known to infect insects. An association between Wolbachia presence and higher Alphaproteobacteria representation in the microbiomes suggests that Wolbachia presence affects the host microbiome composition.

Testing the potential contribution of Wolbachia to speciation when cytoplasmic incompatibility becomes associated with host-related reproductive isolation

Endosymbiont‐induced cytoplasmic incompatibility (CI) may play an important role in arthropod speciation. However, whether CI consistently becomes associated or coupled with other host‐related forms of reproductive isolation (RI) to impede the transfer of endosymbionts between hybridizing populations and further the divergence process remains an open question. Here, we show that varying degrees of pre‐ and postmating RI exist among allopatric populations of two interbreeding cherry‐infesting tephritid fruit flies (Rhagoletis cingulata and R. indifferens) across North America. These flies display allochronic and sexual isolation among populations, as well as unidirectional reductions in egg hatch in hybrid crosses involving southwestern USA males. All populations are infected by a Wolbachia strain, wCin2, whereas a second strain, wCin3, only co‐infects flies from the southwest USA and Mexico. Strain wCin3 is associated with a unique mitochondrial DNA haplotype and unidirectional postmating RI, implicating the strain as the cause of CI. When coupled with nonendosymbiont RI barriers, we estimate the strength of CI associated with wCin3 would not prevent the strain from introgressing from infected southwestern to uninfected populations elsewhere in the USA if populations were to come into secondary contact and hybridize. In contrast, cytoplasmic–nuclear coupling may impede the transfer of wCin3 if Mexican and USA populations were to come into contact. We discuss our results in the context of the general paucity of examples demonstrating stable Wolbachia hybrid zones and whether the spread of Wolbachia among taxa can be constrained in natural hybrid zones long enough for the endosymbiont to participate in speciation.

Wolbachia affects mitochondrial population structure in two systems of closely related Palaearctic blue butterflies

The bacterium Wolbachia infects many insect species and spreads by diverse vertical and horizontal means. As co-inherited organisms, these bacteria often cause problems in mitochondrial phylogeny inference. The phylogenetic relationships of many closely related Palaearctic blue butterflies (Lepidoptera: Lycaenidae: Polyommatinae) are ambiguous. We considered the patterns of Wolbachia infection and mitochondrial diversity in two systems: Aricia agestis/Aricia artaxerxes and the Pseudophilotes baton species complex. We sampled butterflies across their distribution ranges and sequenced one butterfly mitochondrial gene and two Wolbachia genes. Both butterfly systems had uninfected and infected populations, and harboured several Wolbachia strains. Wolbachia was highly prevalent in A. artaxerxes and the host's mitochondrial structure was shallow, in contrast to A. agestis. Similar bacterial alleles infected both Aricia species from nearby sites, pointing to a possible horizontal transfer. Mitochondrial history of the P. baton species complex mirrored its Wolbachia infection and not the taxonomical division. Pseudophilotes baton and P. vicrama formed a hybrid zone in Europe. Wolbachia could obscure mitochondrial history, but knowledge on the infection helps us to understand the observed patterns. Testing for Wolbachia should be routine in mitochondrial DNA studies.

A Review: Aedes-Borne Arboviral Infections, Controls and Wolbachia-Based Strategies

Arthropod-borne viruses (Arboviruses) continue to generate significant health and economic burdens for people living in endemic regions. Of these viruses, some of the most important (e.g., dengue, Zika, chikungunya, and yellow fever virus), are transmitted mainly by Aedes mosquitoes. Over the years, viral infection control has targeted vector population reduction and inhibition of arboviral replication and transmission. This control includes the vector control methods which are classified into chemical, environmental, and biological methods. Some of these control methods may be largely experimental (both field and laboratory investigations) or widely practised. Perceptively, one of the biological methods of vector control, in particular, Wolbachia-based control, shows a promising control strategy for eradicating Aedes-borne arboviruses. This can either be through the artificial introduction of Wolbachia, a naturally present bacterium that impedes viral growth in mosquitoes into heterologous Aedes aegypti mosquito vectors (vectors that are not natural hosts of Wolbachia) thereby limiting arboviral transmission or via Aedes albopictus mosquitoes, which naturally harbour Wolbachia infection. These strategies are potentially undermined by the tendency of mosquitoes to lose Wolbachia infection in unfavourable weather conditions (e.g., high temperature) and the inhibitory competitive dynamics among co-circulating Wolbachia strains. The main objective of this review was to critically appraise published articles on vector control strategies and specifically highlight the use of Wolbachia-based control to suppress vector population growth or disrupt viral transmission. We retrieved studies on the control strategies for arboviral transmissions via arthropod vectors and discussed the use of Wolbachia control strategies for eradicating arboviral diseases to identify literature gaps that will be instrumental in developing models to estimate the impact of these control strategies and, in essence, the use of different Wolbachia strains and features.

Geographic and Temporal Variation of Distinct Intracellular Endosymbiont Strains of Wolbachia sp. in the Grasshopper Chorthippus parallelus: a Frequency-Dependent Mechanism?

Wolbachia is an intracellular endosymbiont that can produce a range of effects on host fitness, but the temporal dynamics of Wolbachia strains have rarely been experimentally evaluated. We compare interannual strain frequencies along a geographical region for understanding the forces that shape Wolbachia strain frequency in natural populations of its host, Chorthippus parallelus (Orthoptera, Acrididae). General linear models show that strain frequency changes significantly across geographical and temporal scales. Computer simulation allows to reject the compatibility of the observed patterns with either genetic drift or sampling errors. We use consecutive years to estimate total Wolbachia strain fitness. Our estimation of Wolbachia fitness is significant in most cases, within locality and between consecutive years, following a negatively frequency-dependent trend. Wolbachia spp. B and F strains show a temporal pattern of variation that is compatible with a negative frequency-dependent natural selection mechanism. Our results suggest that such a mechanism should be at least considered in future experimental and theoretical research strategies that attempt to understand Wolbachia biodiversity.

Cytogenetic and symbiont analysis of five members of the B. dorsalis complex (Diptera, Tephritidae): no evidence of chromosomal or symbiont-based speciation events

The Bactroceradorsalis species complex, currently comprising about 90 entities has received much attention. During the last decades, considerable effort has been devoted to delimiting the species of the complex. This information is of great importance for agriculture and world trade, since the complex harbours several pest species of major economic importance and other species that could evolve into global threats. Speciation in Diptera is usually accompanied by chromosomal rearrangements, particularly inversions that are assumed to reduce/eliminate gene flow. Other candidates currently receiving much attention regarding their possible involvement in speciation are reproductive symbionts, such as Wolbachia, Spiroplasma, Arsenophonus, Rickettsia and Cardinium. Such symbionts tend to spread quickly through natural populations and can cause a variety of phenotypes that promote pre-mating and/or post-mating isolation and, in addition, can affect the biology, physiology, ecology and evolution of their insect hosts in various ways. Considering all these aspects, we present: (a) a summary of the recently gained knowledge on the cytogenetics of five members of the Bactroceradorsalis complex, namely Bactroceradorsaliss.s., Bactrocerainvadens, Bactroceraphilippinensis, Bactrocerapapayae and Bactroceracarambolae, supplemented by additional data from a Bactroceradorsaliss.s. colony from China, as well as by a cytogenetic comparison between the dorsalis complex and the genetically close species, Bactroceratryoni, and, (b) a reproductive symbiont screening of 18 different colonized populations of these five taxa. Our analysis did not reveal any chromosomal rearrangements that could differentiate among them. Moreover, screening for reproductive symbionts was negative for all colonies derived from different geographic origins and/or hosts. There are many different factors that can lead to speciation, and our data do not support chromosomal and/or symbiotic-based speciation phenomena in the taxa under study.

A computer simulation model of Wolbachia invasion for disease vector population modification

BACKGROUND

Wolbachia invasion has been proved to be a promising alternative for controlling vector-borne diseases, particularly Dengue fever. Creating computer models that can provide insight into how vector population modification can be achieved under different conditions would be most valuable for assessing the efficacy of control strategies for this disease.

METHODS

In this paper, we present a computer model that simulates the behavior of native mosquito populations after the introduction of mosquitoes infected with the Wolbachia bacteria. We studied how different factors such as fecundity, fitness cost of infection, migration rates, number of populations, population size, and number of introduced infected mosquitoes affect the spread of the Wolbachia bacteria among native mosquito populations.

RESULTS

Two main scenarios of the island model are presented in this paper, with infected mosquitoes introduced into the largest source population and peripheral populations. Overall, the results are promising; Wolbachia infection spreads among native populations and the computer model is capable of reproducing the results obtained by mathematical models and field experiments.

CONCLUSIONS

Computer models can be very useful for gaining insight into how Wolbachia invasion works and are a promising alternative for complementing experimental and mathematical approaches for vector-borne disease control.

Stable coexistence of incompatible Wolbachia along a narrow contact zone in mosquito field populations

In arthropods, the intracellular bacteria Wolbachia often induce cytoplasmic incompatibility (CI) between sperm and egg, which causes conditional embryonic death and promotes the spatial spread of Wolbachia infections into host populations. The ability of Wolbachia to spread in natural populations through CI has attracted attention for using these bacteria in vector-borne disease control. The dynamics of incompatible Wolbachia infections have been deeply investigated theoretically, whereas in natural populations, there are only few examples described, especially among incompatible infected hosts. Here, we have surveyed the distribution of two molecular Wolbachia strains (wPip11 and wPip31) infecting the mosquito Culex pipiens in Tunisia. We delineated a clear spatial structure of both infections, with a sharp contact zone separating their distribution areas. Crossing experiments with isofemale lines from different localities showed three crossing types: wPip11-infected males always sterilize wPip31-infected females; however, while most wPip31-infected males were compatible with wPip11-infected females, a few completely sterilize them. The wPip11 strain was thus expected to spread, but temporal dynamics over 7 years of monitoring shows the stability of the contact zone. We examined which factors may contribute to the observed stability, both theoretically and empirically. Population cage experiments, field samples and modelling did not support significant impacts of local adaptation or assortative mating on the stability of wPip infection structure. By contrast, low dispersal probability and metapopulation dynamics in the host Cx. pipiens probably play major roles. This study highlights the need of understanding CI dynamics in natural populations to design effective and sustainable Wolbachia-based control strategies.

Dobzhansky-muller and wolbachia-induced incompatibilities in a diploid genetic system

Genetic incompatibilities are supposed to play an important role in speciation. A general (theoretical) problem is to explain the persistence of genetic diversity after secondary contact. Previous theoretical work has pointed out that Dobzhansky-Muller incompatibilities (DMI) are not stable in the face of migration unless local selection acts on the alleles involved in incompatibility. With local selection, genetic variability exists up to a critical migration rate but is lost when migration exceeds this threshold value. Here, we investigate the effect of intracellular bacteria Wolbachia on the stability of hybrid zones formed after the Dobzhansky Muller model. Wolbachia are known to cause a cytoplasmic incompatibility (CI) within and between species. Incorporating intracellular bacteria Wolbachia can lead to a significant increase of critical migration rates and maintenance of divergence, primarily because Wolbachia-induced incompatibility acts to reduce frequencies of F1 hybrids. Wolbachia infect up to two-thirds of all insect species and it is therefore likely that CI co-occurs with DMI in nature. The results indicate that both isolating mechanisms strengthen each other and under some circumstances act synergistically. Thus they can drive speciation processes more forcefully than either when acting alone.

Equilibrium frequency of endosymbionts in multiple infections based on the balance between vertical transmission and cytoplasmic incompatibility

Cytoplasmic incompatibility (CI)-inducing endosymbiotic bacteria, such as Wolbachia and Cardinium, have been well studied through field data and validations on the basis of numerical simulations. However, the analytically derived equilibrium frequency of multiple infections has not yet been determined, although the equilibrium for cases of single infection has been reported. In this study, we considered the difference equation for endosymbionts using three parameters: the probability of the failure of vertical transmission (), CI strength (), and the level of host inbreeding (). To analyze this model, we particularly focused on , i.e., the frequency of host individuals completely infected with all -bacterial strains in the population. , at the equilibrium state, was analytically calculated in the cases where and is any arbitrary value. We found that can be described using two parameters: and , which is identical to . has a larger value in a system with a smaller . In addition, determines the maximum number of strains that infect a single host. Our results revealed the following: i) three parameters can be reduced to a single parameter, i.e., and ii) the threshold of the maximum number of infections is defined by , which prevents additional invasions by endosymbionts.

Wolbachia association with the tsetse fly, Glossina fuscipes fuscipes, reveals high levels of genetic diversity and complex evolutionary dynamics

Background

Wolbachia pipientis, a diverse group of α-proteobacteria, can alter arthropod host reproduction and confer a reproductive advantage to Wolbachia-infected females (cytoplasmic incompatibility (CI)). This advantage can alter host population genetics because Wolbachia-infected females produce more offspring with their own mitochondrial DNA (mtDNA) haplotypes than uninfected females. Thus, these host haplotypes become common or fixed (selective sweep). Although simulations suggest that for a CI-mediated sweep to occur, there must be a transient phase with repeated initial infections of multiple individual hosts by different Wolbachia strains, this has not been observed empirically. Wolbachia has been found in the tsetse fly, Glossina fuscipes fuscipes, but it is not limited to a single host haplotype, suggesting that CI did not impact its population structure. However, host population genetic differentiation could have been generated if multiple Wolbachia strains interacted in some populations. Here, we investigated Wolbachia genetic variation in G. f. fuscipes populations of known host genetic composition in Uganda. We tested for the presence of multiple Wolbachia strains using Multi-Locus Sequence Typing (MLST) and for an association between geographic region and host mtDNA haplotype using Wolbachia DNA sequence from a variable locus, groEL (heat shock protein 60).

Results

MLST demonstrated that some G. f. fuscipes carry Wolbachia strains from two lineages. GroEL revealed high levels of sequence diversity within and between individuals (Haplotype diversity = 0.945). We found Wolbachia associated with 26 host mtDNA haplotypes, an unprecedented result. We observed a geographical association of one Wolbachia lineage with southern host mtDNA haplotypes, but it was non-significant (p = 0.16). Though most Wolbachia-infected host haplotypes were those found in the contact region between host mtDNA groups, this association was non-significant (p = 0.17).

Conclusions

High Wolbachia sequence diversity and the association of Wolbachia with multiple host haplotypes suggest that different Wolbachia strains infected G. f. fuscipes multiple times independently. We suggest that these observations reflect a transient phase in Wolbachia evolution that is influenced by the long gestation and low reproductive output of tsetse. Although G. f. fuscipes is superinfected with Wolbachia, our data does not support that bidirectional CI has influenced host genetic diversity in Uganda.

Modelling the spread of Wolbachia in spatially heterogeneous environments

The endosymbiont Wolbachia infects a large number of insect species and is capable of rapid spread when introduced into a novel host population. The bacteria spread by manipulating their hosts' reproduction, and their dynamics are influenced by the demographic structure of the host population and patterns of contact between individuals. Reaction-diffusion models of the spatial spread of Wolbachia provide a simple analytical description of their spatial dynamics but do not account for significant details of host population dynamics. We develop a metapopulation model describing the spatial dynamics of Wolbachia in an age-structured host insect population regulated by juvenile density-dependent competition. The model produces similar dynamics to the reaction-diffusion model in the limiting case where the host's habitat quality is spatially homogeneous and Wolbachia has a small effect on host fitness. When habitat quality varies spatially, Wolbachia spread is usually much slower, and the conditions necessary for local invasion are strongly affected by immigration of insects from surrounding regions. Spread is most difficult when variation in habitat quality is spatially correlated. The results show that spatial variation in the density-dependent competition experienced by juvenile host insects can strongly affect the spread of Wolbachia infections, which is important to the use of Wolbachia to control insect vectors of human disease and other pests.

Speciation history of three closely related oak gall wasps, Andricus mukaigawae, A. kashiwaphilus, and A. pseudoflos (Hymenoptera: Cynipidae) inferred from nuclear and mitochondrial DNA sequences

The Andricus mukaigawae complex of oak gall wasps is composed of cyclically parthenogenetic species: A. mukaigawae and Andricus kashiwaphilus, and a parthenogenetic species, Andricus pseudoflos. The component species differ in life history, host plant, karyotype, and asexual gall shape, although little difference is found in the external morphology of asexual adults. To understand the speciation history of this species complex, DNA sequences of one mitochondrial region and nine nuclear gene regions were investigated. The genetic relationship among the species suggested that a loss of sex occurred after host shift. Unexpectedly, two or three distinct groups in the parthenogenetic species, A. pseudoflos, were revealed by both mitochondrial and nuclear DNA data. Gene flow in nuclear genes from the species not infected by Wolbachia (A. kashiwaphilus) to the species infected by it (A. mukaigawae) was suggested by a method based on coalescent simulations. On the other hand, gene flow in mitochondrial genes was suggested to be in the opposite direction. These findings indicate possible involvement of Wolbachia infection in the speciation process of the A. mukaigawae complex.

Spatial waves of advance with bistable dynamics: cytoplasmic and genetic analogues of Allee effects

Unlike unconditionally advantageous "Fisherian" variants that tend to spread throughout a species range once introduced anywhere, "bistable" variants, such as chromosome translocations, have two alternative stable frequencies, absence and (near) fixation. Analogous to populations with Allee effects, bistable variants tend to increase locally only once they become sufficiently common, and their spread depends on their rate of increase averaged over all frequencies. Several proposed manipulations of insect populations, such as using Wolbachia or "engineered underdominance" to suppress vector-borne diseases, produce bistable rather than Fisherian dynamics. We synthesize and extend theoretical analyses concerning three features of their spatial behavior: rate of spread, conditions to initiate spread from a localized introduction, and wave stopping caused by variation in population densities or dispersal rates. Unlike Fisherian variants, bistable variants tend to spread spatially only for particular parameter combinations and initial conditions. Wave initiation requires introduction over an extended region, while subsequent spatial spread is slower than for Fisherian waves and can easily be halted by local spatial inhomogeneities. We present several new results, including robust sufficient conditions to initiate (and stop) spread, using a one-parameter cubic approximation applicable to several models. The results have both basic and applied implications.

Confinement of gene drive systems to local populations: a comparative analysis

Mosquito-borne diseases such as malaria and dengue fever pose a major health problem through much of the world. One approach to disease prevention involves the use of selfish genetic elements to drive disease-refractory genes into wild mosquito populations. Recently engineered synthetic drive systems have provided encouragement for this strategy; but at the same time have been greeted with caution over the concern that transgenes may spread into countries and communities without their consent. Consequently, there is also interest in gene drive systems that, while strong enough to bring about local population replacement, are unable to establish themselves beyond a partially isolated release site, at least during the testing phase. Here, we develop simple deterministic and stochastic models to compare the confinement properties of a variety of gene drive systems. Our results highlight several systems with desirable features for confinement-a high migration rate required to become established in neighboring populations, and low-frequency persistence in neighboring populations for moderate migration rates. Single-allele underdominance and single-locus engineered underdominance have the strongest confinement properties, but are difficult to engineer and require a high introduction frequency, respectively. Toxin-antidote systems such as Semele, Merea and two-locus engineered underdominance show promising confinement properties and require lower introduction frequencies. Killer-rescue is self-limiting in time, but is able to disperse to significant levels in neighboring populations. We discuss the significance of these results in the context of a phased release of transgenic mosquitoes, and the need for characterization of local ecology prior to a release.

Population dynamic models of the spread of Wolbachia

Wolbachia are endosymbionts that are found in many insect species and can spread rapidly when introduced into a naive host population. Most Wolbachia spread when their infection frequency exceeds a threshold normally calculated using purely population genetic models. However, spread may also depend on the population dynamics of the insect host. We develop models to explore interactions between host population dynamics and Wolbachia infection frequency for an age-structured insect population regulated by larval density dependence. We first derive a new expression for the threshold frequency that extends existing theory to incorporate important details of the insect's life history. In the presence of immigration and emigration, the threshold also depends on the form of density-dependent regulation. We show how the type of immigration (constant or pulsed) and the temporal dynamics of the host population can strongly affect the spread of Wolbachia. The results help understand the natural dynamics of Wolbachia infections and aid the design of programs to introduce Wolbachia to control insects that are disease vectors or pests.

A new model and method for understanding Wolbachia-induced cytoplasmic incompatibility

Wolbachia are intracellular bacteria transmitted almost exclusively vertically through eggs. In response to this mode of transmission, Wolbachia strategically manipulate their insect hosts' reproduction. In the most common manipulation type, cytoplasmic incompatibility, infected males can only mate with infected females, but infected females can mate with all males. The mechanism of cytoplasmic incompatibility is unknown; theoretical and empirical findings need to converge to broaden our understanding of this phenomenon. For this purpose, two prominent models have been proposed: the mistiming-model and the lock-key-model. The former states that Wolbachia manipulate sperm of infected males to induce a fatal delay of the male pronucleus during the first embryonic division, but that the bacteria can compensate the delay by slowing down mitosis in fertilized eggs. The latter states that Wolbachia deposit damaging "locks" on sperm DNA of infected males, but can also provide matching "keys" in infected eggs to undo the damage. The lock-key-model, however, needs to assume a large number of locks and keys to explain all existing incompatibility patterns. The mistiming-model requires fewer assumptions but has been contradicted by empirical results. We therefore expand the mistiming-model by one quantitative dimension to create the new, so-called goalkeeper-model. Using a method based on formal logic, we show that both lock-key- and goalkeeper-model are consistent with existing data. Compared to the lock-key-model, however, the goalkeeper-model assumes only two factors and provides an idea of the evolutionary emergence of cytoplasmic incompatibility. Available cytological evidence suggests that the hypothesized second factor of the goalkeeper-model may indeed exist. Finally, we suggest empirical tests that would allow to distinguish between the models. Generalizing our results might prove interesting for the study of the mechanism and evolution of other host-parasite interactions.

The spread of incompatibility-inducing parasites in sub-divided host populations

BACKGROUND

Maternally transmitted symbionts have evolved a variety of ways to promote their spread through host populations. One strategy is to hamper the reproduction of uninfected females by a mechanism called cytoplasmic incompatibility (CI). CI occurs in crosses between infected males and uninfected females and leads to partial to near-complete infertility. CI-infections are under positive frequency-dependent selection and require genetic drift to overcome the range of low frequencies where they are counter-selected. Given the importance of drift, population sub-division would be expected to facilitate the spread of CI. Nevertheless, a previous model concluded that variance in infection between competing groups of breeding individuals impedes the spread of CI.

RESULTS

In this paper we derive a model on the spread of CI-infections in populations composed of demes linked by restricted migration. Our model shows that population sub-division facilitates the invasion of CI. While host philopatry (low migration) favours the spread of infection, deme size has a non-monotonous effect, with CI-invasion being most likely at intermediate deme size. Individual-based simulations confirm these predictions and show that high levels of local drift speed up invasion but prevent high levels of prevalence across the entire population. Additional simulations with sex-specific migration rates further show that low migration rates of both sexes are required to facilitate the spread of CI.

CONCLUSION

Our analyses show that population structure facilitates the invasion of CI-infections. Since some level of sub-division is likely to occur in most natural populations, our results help to explain the high incidence of CI-infections across species of arthropods. Furthermore, our work has important implications for the use of CI-systems in order to genetically modify natural populations of disease vectors.

How many species are infected with Wolbachia?--A statistical analysis of current data

Wolbachia are intracellular bacteria found in many species of arthropods and nematodes. They manipulate the reproduction of their arthropod hosts in various ways, may play a role in host speciation and have potential applications in biological pest control. Estimates suggest that at least 20% of all insect species are infected with Wolbachia. These estimates result from several Wolbachia screenings in which numerous species were tested for infection; however, tests were mostly performed on only one to two individuals per species. The actual percent of species infected will depend on the distribution of infection frequencies among species. We present a meta-analysis that estimates percentage of infected species based on data on the distribution of infection levels among species. We used a beta-binomial model that describes the distribution of infection frequencies of Wolbachia, shedding light on the overall infection rate as well as on the infection frequency within species. Our main findings are that (1) the proportion of Wolbachia-infected species is estimated to be 66%, and that (2) within species the infection frequency follows a ‘most-or-few’ infection pattern in a sense that the Wolbachia infection frequency within one species is typically either very high (>90%) or very low (<10%).

Coexistence of cytoplasmic incompatibility and male-killing-inducing endosymbionts, and their impact on host gene flow

Male-killing (MK) and cytoplasmic incompatibility (CI) inducing bacteria are among the most common endosymbionts of arthropods. Previous theoretical research has demonstrated that these two types of endosymbionts cannot stably coexist within a single unstructured host population if no doubly infected host individuals occur. Here, we analyse a model of two host subpopulations connected by migration. We demonstrate that coexistence of MK- and CI-inducing endosymbionts is possible if migration rates are sufficiently low. In particular, our results suggest that for coexistence to be possible, migration rates into the subpopulation infected predominantly with MK-inducing endosymbionts must be considerably low, while migration rates from the MK- to the CI-infected subpopulation can be very high. We also analyse how the presence of MK- and CI-inducing endosymbionts affects host gene flow between the two subpopulations. Employing the concept of the 'effective migration rate', we demonstrate that compared with an uninfected subdivided population, gene flow is increased towards the MK-infected island, but decreased towards the CI-infected island. We discuss our results with respect to the butterfly Hypolimnas bolina, in which infection polymorphism of CI- and MK-inducing Wolbachia has been reported across South-Pacific island populations.

Wolbachia-induced unidirectional cytoplasmic incompatibility and speciation: mainland-island model

Bacteria of the genus Wolbachia are among the most common endosymbionts in the world. In many insect species these bacteria induce a sperm-egg incompatibility between the gametes of infected males and uninfected females, commonly called unidirectional cytoplasmic incompatibility (CI). It is generally believed that unidirectional CI cannot promote speciation in hosts because infection differences between populations will be unstable and subsequent gene flow will eliminate genetic differences between diverging populations. In the present study we investigate this question theoretically in a mainland-island model with migration from mainland to island. Our analysis shows that (a) the infection polymorphism is stable below a critical migration rate, (b) an (initially) uninfected “island” can better maintain divergence at a selected locus (e.g. can adapt locally) in the presence of CI, and (c) unidirectional CI selects for premating isolation in (initially) uninfected island populations if they receive migration from a Wolbachia-infected mainland. Interestingly, premating isolation is most likely to evolve if levels of incompatibility are intermediate and if either the infection causes fecundity reductions or Wolbachia transmission is incomplete. This is because under these circumstances an infection pattern with an infected mainland and a mostly uninfected island can persist in the face of comparably high migration. We present analytical results for all three findings: (a) a lower estimation of the critical migration rate in the presence of local adaptation, (b) an analytical approximation for the gene flow reduction caused by unidirectional CI, and (c) a heuristic formula describing the invasion success of mutants at a mate preference locus. These findings generally suggest that Wolbachia-induced unidirectional CI can be a factor in divergence and speciation of hosts.