Anticipating the occurrence and type of critical transitions

Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition. However, no effective method allows to establish practical threshold indicating the condition when the critical transition is most likely to occur. Here, we introduce a powerful EWS, named dynamical eigenvalue (DEV), that is rooted in bifurcation theory of dynamical systems to estimate the dominant eigenvalue of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, while its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and also test the DEV approach on various critical transitions in real-world systems.

Fasting blood glucose in a Ghanaian adult is causally affected by malaria parasite load: a mechanistic case study using convergent cross mapping

BACKGROUND

Adults with diabetes mellitus (DM) in malaria-endemic areas might be more susceptible to Plasmodium infection than healthy individuals. Herein, the study was aimed at verifying the hypothesis that increased fasting blood glucose (FBG) promotes parasite growth as reflected by increased parasite density.

METHODS

Seven adults without DM were recruited in rural Ghana to determine the relationships between FBG and malaria parasite load. Socio-economic data were recorded in questionnaire-based interviews. Over a period of 6 weeks, FBG and Plasmodium sp. Infection were measured in peripheral blood samples photometrically and by polymerase chain reaction (PCR)-assays, respectively. Daily physical activity and weather data were documented via smartphone recording. For the complex natural systems of homeostatic glucose control and Plasmodium sp. life cycle, empirical dynamic modelling was applied.

RESULTS

At baseline, four men and three women (median age, 33 years; interquartile range, 30-48) showed a median FBG of 5.5 (5.1-6.0 mmol/L); one participant had an asymptomatic Plasmodium sp. infection (parasite density: 240/µL). In this participant, convergent cross mapping (CCM) for 34 consecutive days, showed that FBG was causally affected by parasite density (p < 0.02), while the reciprocal relationship was not discernible (p > 0.05). Additionally, daily ambient temperature affected parasite density (p < 0.01).

CONCLUSION

In this study population living in a malaria-endemic area, time series analyses were successfully piloted for the relationships between FBG and Plasmodium sp. density. Longer observation periods and larger samples are required to confirm these findings and determine the direction of causality.

Evolutionary stability of plant-pollinator networks: efficient communities and a pollination dilemma

Mutualistic interactions between species are ubiquitous in nature and essential for ecosystem functioning. Often dozens or even hundreds of species with different degrees of specialisation form complex networks. How this complexity evolves is a fundamental question in ecology. Here, we present a new game theoretical approach to model complex coevolutionary processes and apply it to pollination networks. A theoretical analysis reveals multiple evolutionary stable network structures that depend on the availability of pollination service. In particular, we find efficient communities, in which a high percentage of pollen are transported conspecifically, to evolve only when plant and pollinator abundances are well balanced. Both pollinator shortage and oversupply select for more inefficient network structures. The results suggest that availability of pollination services is a key factor structuring pollination networks and may offer a new explanation for geographical differences in pollination communities that have long been recognised by ecologists.

Theory of coevolution of cytoplasmic male-sterility, nuclear restorer and selfing

Gynodioecy is a sexual polymorphism in angiosperms, where hermaphroditic and female individuals coexist. This is often caused by a cytoplasmic genetic element (CGE) that destroys male functions, which is called cytoplasmic male-sterility (CMS). On the other hand, nuclear genes tend to evolve the ability to restore male function. The coevolutionary process of CMS and the restoration has been studied theoretically. Recently, a theoretical study suggested that these coevolutionary dynamics could be influenced by the rate of selfing within populations, although it assumed that the selfing rate of a population was a fixed parameter. Accordingly, we theoretically study the coevolution of three traits in this paper: CMS, nuclear restorer and selfing rate, in which we hypothesize that selfing evolution can suppress CMS evolution under some conditions. The analysis indicates three significant properties of the system; (1) CMS-restorer evolution can result in bistability under a given selfing rate, (2) the coevolution of three traits can realize intermediate levels of selfing, and (3) the evolution of high levels of selfing is conditionally associated with no CMS and/or no restoration, which may support our hypothesis.

Spatial spread of Wolbachia in Rhagoletis cerasi populations

The bacterial endosymbiont Wolbachia has been used to control insect pests owing to its ability to manipulate their life history and suppress infectious diseases. Therefore, knowledge on Wolbachia dynamics in natural populations is fundamental. The European cherry fruit fly, Rhagoletis cerasi, is infected with the Wolbachia strain wCer2, mainly present in southern and central European populations, and is currently spreading into wCer2-uninfected populations driven by high unidirectional cytoplasmic incompatibility. Here, we describe the distribution of wCer2 along two transition zones where the infection is spreading into wCer2-uninfected R. cerasi populations. Fine-scale sampling of 19 populations in the Czech Republic showed a smooth decrease of wCer2 frequency from south to north within a distance of less than 20 km. Sampling of 12 Hungarian populations, however, showed a sharp decline of wCer2 infection frequency within a few kilometres. We fitted a standard wave equation to our empirical data and estimated a Wolbachia wave speed of 1.9 km yr⁻¹ in the Czech Republic and 1.0 km yr⁻¹ in Hungary. Considering the univoltine life cycle and limited dispersal ability of R. cerasi, our study highlights a rapid Wolbachia spread in natural host populations.

Genetic Incompatibilities Between Mitochondria and Nuclear Genes: Effect on Gene Flow and Speciation

The process of speciation is, according to the biological species concept, the reduction in gene flow between genetically diverging populations. Most of the previous theoretical studies analyzed the effect of nuclear genetic incompatibilities on gene flow. There is, however, an increasing number of empirical examples suggesting that cytoplasmically inherited genetic elements play an important role in speciation. Here, we present a theoretical analysis of mitochondrial driven speciation, in which genetic incompatibilities occur between mitochondrial haplotypes and nuclear alleles. Four population genetic models with mainland-island structure were analyzed that differ with respect to the type of incompatibility and the underlying genetics. Gene flow reduction was measured on selectively neutral alleles of an unlinked locus and quantified by the effective migration rate. Analytical formulae for the different scenarios were derived using the fitness graph method. For the models with haploid genetics, we found that mito-nuclear incompatibilities (MtNI) are as strong as nuclear-nuclear incompatibilities (NNI) in reducing gene flow at the unlinked locus, but only if males and females migrate in equal number. For models with diploid genetics, we found that MtNI reduce gene flow stronger than NNI when incompatibilities are recessive, but weaker when they are dominant. For both haploid and diploid MtNI, we found that gene flow reduction is stronger if females are the migrating sex, but weaker than NNI when males are the migrating sex. These results encourage further examination on the role of mitochondria on genetic divergence and speciation and point toward specific factors (e.g., migrating sex) that could be the focus of an empirical test.

Empirical Dynamic Modelling Identifies different Responses of Aedes Polynesiensis Subpopulations to Natural Environmental Variables

To control mosquito populations for managing vector-borne diseases, a critical need is to identify and predict their response to causal environmental variables. However, most existing attempts rely on linear approaches based on correlation, which cannot apply in complex, nonlinear natural systems, because correlation is neither a necessary nor sufficient condition for causation. Applying empirical dynamic modelling that acknowledges nonlinear dynamics on nine subpopulations of tiger mosquitos from three neighbouring reef islets of the Raiatea atoll, we identified temperature, precipitation, dew point, air pressure, and mean tide level as causal environmental variables. Interestingly, responses of subpopulations in close proximity (100–500 m) differed with respect to their causal environmental variables and the time delay of effect, highlighting complexity in mosquito-environment causality network. Moreover, we demonstrated how to explore the effects of changing environmental variables on number and strength of mosquito outbreaks, providing a new framework for pest control and disease vector ecology.

Assortment of Flowering Time and Immunity Alleles in Natural Arabidopsis thaliana Populations Suggests Immunity and Vegetative Lifespan Strategies Coevolve

The selective impact of pathogen epidemics on host defenses can be strong but remains transient. By contrast, life-history shifts can durably and continuously modify the balance between costs and benefits of immunity, which arbitrates the evolution of host defenses. Their impact on the evolutionary dynamics of host immunity, however, has seldom been documented. Optimal investment into immunity is expected to decrease with shortening lifespan, because a shorter life decreases the probability to encounter pathogens or enemies. Here, we document that in natural populations of Arabidopsis thaliana, the expression levels of immunity genes correlate positively with flowering time, which in annual species is a proxy for lifespan. Using a novel genetic strategy based on bulk-segregants, we partitioned flowering time-dependent from -independent immunity genes and could demonstrate that this positive covariation can be genetically separated. It is therefore not explained by the pleiotropic action of some major regulatory genes controlling both immunity and lifespan. Moreover, we find that immunity genes containing variants reported to impact fitness in natural field conditions are among the genes whose expression covaries most strongly with flowering time. Taken together, these analyses reveal that natural selection has likely assorted alleles promoting lower expression of immunity genes with alleles that decrease the duration of vegetative lifespan in A. thaliana and vice versa. This is the first study documenting a pattern of variation consistent with the impact that selection on flowering time is predicted to have on diversity in host immunity.

Infections of Wolbachia may destabilize mosquito population dynamics

Recent efforts in controlling mosquito-borne diseases focus on biocontrol strategies that incapacitate pathogens inside mosquitoes by altering the mosquito's microbiome. A case in point is the introduction of Wolbachia into natural mosquito populations in order to eliminate Dengue virus. However, whether this strategy can successfully control vector-borne diseases is debated; particularly, how artificial infection affects population dynamics of hosts remains unclear. Here, we show that natural Wolbachia infections are associated with unstable mosquito population dynamics by contrasting Wolbachia-infected versus uninfected cage populations of the Asian tiger mosquito (Aedes albopictus). By analyzing weekly data of adult mosquito abundances, we found that the variability of the infected populations is significantly higher than that of the uninfected. The elevated population variability is explained by increased instability in dynamics, as quantified by system nonlinearity (i.e., state-dependence). In addition, predictability of infected populations is substantially lower. A mathematical model analysis suggests that Wolbachia may alter mosquito population dynamics by modifying larval competition of hosts. These results encourage examination for effects of artificial Wolbachia establishment on mosquito populations, because an enhancement of population variability with reduced predictability could pose challenges in management. Our findings have implications for application of microbiome alterations in biocontrol programs.

A Comparison of Wolbachia Infection Frequencies in Varroa With Prevalence of Deformed Wing Virus

Wolbachia are widely distributed bacterial endosymbionts of arthropods and filarial nematodes. These bacteria can affect host fitness in a variety of ways, such as protecting hosts against viruses and other pathogens. Here, we investigate the possible role of Wolbachia in the prevalence of the deformed wing virus (DWV), a highly virulent pathogen of honey bees (Apis mellifera) that is transmitted by parasitic Varroa mites (Varroa destructor). About 180 Varroa mites from 18 beehives were tested for infection with Wolbachia and DWV. We first screened for Wolbachia using two standard primers (wsp and 16S rDNA), and found 26% of the mites to be positive for Wolbachia using the wsp primer and 64% of the mites to be positive using the 16S rDNA primer. Using these intermediate Wolbachia frequencies, we then tested for statistical correlations with virus infection frequencies. The analysis revealed a significant positive correlation between DWV and Wolbachia using the wsp primer, but no significant association between DWV and Wolbachia using the 16S rDNA primer. In conclusion, there is no evidence for an anti-pathogenic effect of Wolbachia in V. destructor, but weak evidence for a pro-pathogenic effect. These results encourage further examination of Wolbachia-virus interactions in Varroa mites since an increased vector competence of the mites may significantly impact disease outbreaks in honey bees.

Geographical variation in the heterogeneity of mutualistic networks

Plant-animal mutualistic networks are characterized by highly heterogeneous degree distributions. The majority of species interact with few partner species, while a small number are highly connected to form network hubs that are proposed to play an important role in community stability. It has not been investigated, however, if or how the degree distributions vary among types of mutualisms or communities, or between plants and animals in the same network. Here, we evaluate the degree distributions of pollination and seed-dispersal networks, which are two major types of mutualistic networks that have often been discussed in parallel, using an index based on Pielou's evenness. Among 56 pollination networks we found strong negative correlation of the heterogeneity between plants and animals, and geographical shifts of network hubs from plants in temperate regions to animals in the tropics. For 28 seed-dispersal networks, by contrast, the correlation was positive, and there is no comparable geographical pattern. These results may be explained by evolution towards specialization in the presence of context-dependent costs that occur if plants share the animal species as interaction partner. How the identity of network hubs affects the stability and resilience of the community is an important question for future studies.

Experimental evolution in silico: a custom-designed mathematical model for virulence evolution of Bacillus thuringiensis

Most mathematical models on the evolution of virulence are based on epidemiological models that assume parasite transmission follows the mass action principle. In experimental evolution, however, mass action is often violated due to controlled infection protocols. This "theory-experiment mismatch" raises the question whether there is a need for new mathematical models to accommodate the particular characteristics of experimental evolution. Here, we explore the experimental evolution model system of Bacillus thuringiensis as a parasite and Caenorhabditis elegans as a host. Recent experimental studies with strict control of parasite transmission revealed that one-sided adaptation of B. thuringiensis with non-evolving hosts selects for intermediate or no virulence, sometimes coupled with parasite extinction. In contrast, host-parasite coevolution selects for high virulence and for hosts with strong resistance against B. thuringiensis. In order to explain the empirical results, we propose a new mathematical model that mimics the basic experimental set-up. The key assumptions are: (i) controlled parasite transmission (no mass action), (ii) discrete host generations, and (iii) context-dependent cost of toxin production. Our model analysis revealed the same basic trends as found in the experiments. Especially, we could show that resistant hosts select for highly virulent bacterial strains. Moreover, we found (i) that the evolved level of virulence is independent of the initial level of virulence, and (ii) that the average amount of bacteria ingested significantly affects the evolution of virulence with fewer bacteria ingested selecting for highly virulent strains. These predictions can be tested in future experiments. This study highlights the usefulness of custom-designed mathematical models in the analysis and interpretation of empirical results from experimental evolution.

The hitchhiker's guide to Europe: the infection dynamics of an ongoing Wolbachia invasion and mitochondrial selective sweep in Rhagoletis cerasi

Wolbachia is a maternally inherited and ubiquitous endosymbiont of insects. It can hijack host reproduction by manipulations such as cytoplasmic incompatibility (CI) to enhance vertical transmission. Horizontal transmission of Wolbachia can also result in the colonization of new mitochondrial lineages. In this study, we present a 15‐year‐long survey of Wolbachia in the cherry fruit fly Rhagoletis cerasi across Europe and the spatiotemporal distribution of two prevalent strains, wCer1 and wCer2, and associated mitochondrial haplotypes in Germany. Across most of Europe, populations consisted of either 100% singly (wCer1) infected individuals with haplotype HT1, or 100% doubly (wCer1&2) infected individuals with haplotype HT2, differentiated only by a single nucleotide polymorphism. In central Germany, singly infected populations were surrounded by transitional populations, consisting of both singly and doubly infected individuals, sandwiched between populations fixed for wCer1&2. Populations with fixed infection status showed perfect association of infection and mitochondria, suggesting a recent CI‐driven selective sweep of wCer2 linked with HT2. Spatial analysis revealed a range expansion for wCer2 and a large transition zone in which wCer2 splashes appeared to coalesce into doubly infected populations. Unexpectedly, the transition zone contained a large proportion (22%) of wCer1&2 individuals with HT1, suggesting frequent intraspecific horizontal transmission. However, this horizontal transmission did not break the strict association between infection types and haplotypes in populations outside the transition zone, suggesting that this horizontally acquired Wolbachia infection may be transient. Our study provides new insights into the rarely studied Wolbachia invasion dynamics in field populations.

Host-Pathogen Coevolution: The Selective Advantage of Bacillus thuringiensis Virulence and Its Cry Toxin Genes

Reciprocal coevolution between host and pathogen is widely seen as a major driver of evolution and biological innovation. Yet, to date, the underlying genetic mechanisms and associated trait functions that are unique to rapid coevolutionary change are generally unknown. We here combined experimental evolution of the bacterial biocontrol agent Bacillus thuringiensis and its nematode host Caenorhabditis elegans with large-scale phenotyping, whole genome analysis, and functional genetics to demonstrate the selective benefit of pathogen virulence and the underlying toxin genes during the adaptation process. We show that: (i) high virulence was specifically favoured during pathogen-host coevolution rather than pathogen one-sided adaptation to a nonchanging host or to an environment without host; (ii) the pathogen genotype BT-679 with known nematocidal toxin genes and high virulence specifically swept to fixation in all of the independent replicate populations under coevolution but only some under one-sided adaptation; (iii) high virulence in the BT-679-dominated populations correlated with elevated copy numbers of the plasmid containing the nematocidal toxin genes; (iv) loss of virulence in a toxin-plasmid lacking BT-679 isolate was reconstituted by genetic reintroduction or external addition of the toxins. We conclude that sustained coevolution is distinct from unidirectional selection in shaping the pathogen's genome and life history characteristics. To our knowledge, this study is the first to characterize the pathogen genes involved in coevolutionary adaptation in an animal host-pathogen interaction system.

Modeling the indirect effect of Wolbachia on the infection dynamics of horizontally transmitted viruses

Intracellular bacteria of the genus Wolbachia are widely distributed in arthropods. There is growing empirical evidence that Wolbachia directly interacts with viruses and other parasites inside the arthropod host, sometimes resulting in low or no pathogen replication. Previous theoretical studies showed that this direct effect of Wolbachia can result in a reduced virus prevalence (within the population), suggesting that Wolbachia could be used in the biological control of vector-borne diseases (e.g., dengue fever). However, Wolbachia might also indirectly affect virus dynamics because Wolbachia-induced reproductive phenotypes (cytoplasmic incompatibility or male killing) increase the larval mortality of hosts and thus alter the age structure of populations. We investigated this indirect effect using mathematical models with overlapping generations, and found the results to depend strongly on the host's life history. In general, the indirect effect can result in two different outcomes: (1) reduced virus prevalence and virus invasion ability, and (2) increased virus prevalence and virus invasion ability. The former occurs for host species with larval competition and undercompensation, the latter for hosts with either adult competition or larval competition and overcompensation. These findings suggest that the effect of Wolbachia on a specific virus is sensitive to the host's life history. We discuss the results with respect to biocontrol programs using Wolbachia.

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.

Effects of wolbachia on genetic divergence between populations: mainland-island model

Cytoplasmic incompatibility (CI) induced by intracellular bacteria is a possible mechanism for speciation. Growing empirical evidence suggests that bacteria of the group Wolbachia may indeed act as isolating factors in recent insect speciation. Wolbachia are cytoplasmically transmitted and can cause uni- or bidirectional CI. We present a mainland-island model to investigate how much impact Wolbachia can have on genetic divergence between populations. In the first scenario we assume that the island population has diverged at a selected locus and ask whether genetic divergence will be maintained after introduction of migration from the mainland. In the second we explore whether divergence will originate under migration. For simplicity, the host organisms are modeled as haploid sexuals. Simulations show that if each population is initially infected with a different strain of Wolbachia, then higher levels of divergence occur at the locally selected locus than in the absence of Wolbachia. A weaker effect is seen when there is only unidirectional CI caused by a single strain of Wolbachia on the island. CI increases divergence because it reduces effective migration between mainland and island. Migrants suffer from being confronted with the wrong CI system and this also applies to their matrilineal descendants. Moreover, there is a strong linkage disequilibrium between host genotype and infection state, which helps to maintain Wolbachia differences between the populations in the face of migration A sex bias in migration can either increase or decrease the effect of Wolbachia on divergence. Results support the view that Wolbachia has the potential for increasing divergence between populations and thus could enhance probabilities of speciation.

Population Dynamics of Borrelia burgdorferi in Lyme Disease

Many chronic inflammatory diseases are known to be caused by persistent bacterial or viral infections. A well-studied example is the tick-borne infection by the gram-negative spirochaetes of the genus Borrelia in humans and other mammals, causing severe symptoms of chronic inflammation and subsequent tissue damage (Lyme Disease), particularly in large joints and the central nervous system, but also in the heart and other tissues of untreated patients. Although killed efficiently by human phagocytic cells in vitro, Borrelia exhibits a remarkably high infectivity in mice and men. In experimentally infected mice, the first immune response almost clears the infection. However, approximately 1 week post infection, the bacterial population recovers and reaches an even larger size before entering the chronic phase. We developed a mathematical model describing the bacterial growth and the immune response against Borrelia burgdorferi in the C3H mouse strain that has been established as an experimental model for Lyme disease. The peculiar dynamics of the infection exclude two possible mechanistic explanations for the regrowth of the almost cleared bacteria. Neither the hypothesis of bacterial dissemination to different tissues nor a limitation of phagocytic capacity were compatible with experiment. The mathematical model predicts that Borrelia recovers from the strong initial immune response by the regrowth of an immune-resistant sub-population of the bacteria. The chronic phase appears as an equilibration of bacterial growth and adaptive immunity. This result has major implications for the development of the chronic phase of Borrelia infections as well as on potential protective clinical interventions.

Effect of parasitic sex-ratio distorters on host gene frequencies in a mainland-island context

It was previously argued that infection by parasitic sex-ratio distorters can enhance both random genetic drift and genetic influx from outside the population. However, these two enhancement effects have been studied independently. Here, we study the equilibrium frequencies of alleles (neutral and selected) in a mainland-island scenario where both genetic drift and genetic influx are enhanced due to infection by a cytoplasmic feminizing element. Interestingly, our model reveals that at neutral loci, the two effects almost exactly cancel each other out, such that infection has only a very minor effect on the equilibrium frequency distributions of alleles. At selected loci, in contrast, the two effects are unbalanced and infection has conspicuous effects. Despite the cryptic effects of infection at neutral loci, we demonstrate that temporally spaced data can be used to evaluate the effect of infection on genetic drift and that on gene flow separately.

The concept of effective recombination rate and its application in speciation theory

The goal of this study is to develop a unifying theoretical framework to quantify the strength of reproductive isolation. We propose the use of the "effective recombination rate," which measures how fast associations of genes are broken by interlocus recombination. Applying the well-established theory of the effective migration rate, we derive two techniques to investigate the effective recombination rate in models of speciation: the weak migration approximation for parapatric scenarios and the weak recombination approximation for sympatric scenarios. We illustrate the use of these two methods by two examples each: (1) single-locus genetic incompatibility and (2) two-locus genetic incompatibility for the first method, and (3) assortative mating and (4) assortative mating combined with disruptive selection for the second method. An advantage of the effective recombination rate over previous approaches is that it integrates gene flow in both directions into a single index measuring the strength of isolation. This enables straightforward comparisons of speciation scenarios with the same or different geographic histories. The method also allows us to evaluate the relative contributions of F2 hybrid deficiency or linkage between multiple barriers in reproductive isolation.

Transmission dynamics of an emerging infectious disease in wildlife through host reproductive cycles

Emerging infectious diseases are major threats to wildlife populations. To enhance our understanding of the dynamics of these diseases, we investigated how host reproductive behavior and seasonal temperature variation drive transmission of infections among wild hosts, using the model system of cyprinid herpesvirus 3 (CyHV-3) disease in common carp. Our main findings were as follows: (1) a seroprevalence survey showed that CyHV-3 infection occurred mostly in adult hosts, (2) a quantitative assay for CyHV-3 in a host population demonstrated that CyHV-3 was most abundant in the spring when host reproduction occurred and water temperature increased simultaneously and (3) an analysis of the dynamics of CyHV-3 in water revealed that CyHV-3 concentration increased markedly in breeding habitats during host group mating. These results indicate that breeding habitats can become hot spots for transmission of infectious diseases if hosts aggregate for mating and the activation of pathogens occurs during the host breeding season.

Evolution of cytoplasmic sex ratio distorters: Effect of paternal transmission

Eukaryotic organisms carry various genetic factors the so-called cytoplasmic genetic elements (CGEs), in their cytoplasm. Numerous examples are known in which CGEs possess the ability to control sex determination of their host organisms and cause sex ratio distortion (SRD). In general, CGEs are inherited maternally from female hosts, via egg cytoplasm to offspring. Thus, the elements tend to evolve abilities to avoid entrance into "dead-end" males. Previous theoretical studies have revealed that, as long as maternal transmission is perfect, CGEs evolve the highest levels of ability to cause SRD. However, it is recently reported that some CGEs transmit from male to offspring through infection to female in mating. This raises the question of how such a paternal contribution alters selective forces and SRD evolution. In the present study, the evolutionary process of SRD ability of CGEs was analyzed theoretically. The main finding is that paternal transmission results in evolution towards intermediate levels of SRD. Further, coexistence was observed of different CGEs inducing different levels of SRD. These results point to the importance of paternal transmission in the evolution of CGEs.

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.

The effect of Wolbachia on genetic divergence between populations: models with two-way migration

Wolbachia are intracellular bacteria that cause various reproduction alterations in their hosts, including cytoplasmic incompatibility (CI), an incompatibility between sperm and egg that typically results in embryonic death. We investigate theoretically the effects of Wolbachia-induced bidirectional CI on levels of divergence between two populations, where there is migration in both directions and differential selection at a single locus. The main findings are as follows: Wolbachia differences in the two populations are maintained up to a threshold migration rate, above which the system collapses to a single Wolbachia type; differential selection at a nuclear locus increases the threshold migration rate below which Wolbachia polymorphisms are maintained; Wolbachia differences between the populations enhance their genetic divergence at the selected locus by reducing the "effective migration rate," and even moderate levels of CI can cause large population differences in allele frequencies; and asymmetric CI can induce strong asymmetries in effective migration rate and dramatically alter the pattern of genetic divergence compared with the No Wolbachia situation. We derive an analytical approximation for the effective migration rate, which matches the simulation results for most parameter values. These results generally support the view that CI Wolbachia can contribute to genetic divergence between populations.

The neutral effective migration rate in a mainland-island context

Genetic influx into a population often does not correspond to the real migration rate (m) of individuals, due to class structure within the population. The effective migration rate (m(e)) is a concept to measure gene flow in such a situation. The ratio of the effective migration rate to the real migration rate (m(e)/m) is called the gene flow factor, and represents the degree of gene flow modification. Prior authors proposed different definitions of the effective migration rate. These may be categorized into two groups: the neutral effective migration rate and the selective effective migration rate. In this article, we construct a general model of a class-structured population with a mainland-island structure. Using the model, we prove that the gene flow factor of the neutral effective migration rate converges to the mean reproductive value of immigrants if the limit is taken with the real migration rate converging to zero. This limit theorem provides a novel interpretation of gene flow and can be used to derive approximation formulae of the neutral effective migration rate. We illustrate this method analyzing two examples, sex ratio distortion due to extrinsic factors and hybrid zones with underdominance.

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.

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

Wolbachia are intracellular, maternally inherited bacteria that are widespread among arthropods and commonly induce a reproductive incompatibility between infected male and uninfected female hosts known as unidirectional cytoplasmic incompatibility (CI). If infected and uninfected populations occur parapatrically, CI acts as a post-zygotic isolation barrier. We investigate the stability of such infection polymorphisms in a mathematical model with two populations linked by migration. We determine critical migration rates below which infected and uninfected populations can coexist. Analytical solutions of the critical migration rate are presented for mainland-island models. These serve as lower estimations for a more general model with two-way migration. The critical migration rate is positive if either Wolbachia causes a fecundity reduction in infected female hosts or its transmission is incomplete, and is highest for intermediate levels of CI. We discuss our results with respect to local adaptations of the Wolbachia host, speciation, and pest control.

Asymmetric gene flow and constraints on adaptation caused by sex ratio distorters

Asymmetric gene flow is generally believed to oppose natural selection and potentially impede adaptation. Whilst the cause of asymmetric gene flow has been seen largely in terms of variation in population density over space, asymmetric gene flow can also result from varying sex ratios across subpopulations with similar population sizes. We model the process of adaptation in a scenario in which two adjacent subpopulations have different sex ratios, associated with different levels of infection with maternally inherited endosymbionts that selectively kill male hosts. Two models are analyzed in detail. First, we consider one host locus with two alleles, each of which possesses a selective advantage in one of the subpopulations. We found that local adaptation can strongly be impeded in the subpopulation with the more female biased population sex ratio. Second, we analyze host alleles that provide resistance against the male-killing (MK) endosymbionts and show that asymmetric gene flow can prevent the spread of such alleles under certain conditions. These results might have important implications for the coevolution of MK bacteria and their hosts.

Bidirectional cytoplasmic incompatibility and the stable coexistence of two Wolbachia strains in parapatric host populations

Wolbachiaare intracellular bacteria which are very widely distributed among arthropods. In many insect species Wolbachiaare known to induce cytoplasmic mating incompatibility (CI). It has been suggested that Wolbachiacould promote speciation in their hosts if parapatric host populations are infected with two different Wolbachiastrains causing bidirectional mating incompatibilities. A necessary condition for this speciation scenario to work is that the two Wolbachiastrains can stably coexist. The following study investigates this problem analysing a mathematical model with two host populations and migration between them. We show that the stability of bidirectional CI can be fully described in terms of a critical migration rate which is defined as the highest migration below which a stable coexistence of two Wolbachiastrains is possible. For some special cases we could derive analytical solutions for the critical migration rate; for the general case estimations of the critical migration rate are given. Our main finding is that bidirectional CI can stably persist in the face of high migration and can be as high as over 15% per generation for CI levels observed in nature. These results have implications for the potential of Wolbachiato promote genetic divergence and speciation in their hosts.

The effect of Wolbachia versus genetic incompatibilities on reinforcement and speciation

Wolbachia is a widespread group of intracellular bacteria commonly found in arthropods. In many insect species, Wolbachia induce a cytoplasmic mating incompatibility (CI). If different Wolbachia infections occur in the same host species, bidirectional CI is often induced. Bidirectional CI acts as a postzygotic isolation mechanism if parapatric host populations are infected with different Wolbachia strains. Therefore, it has been suggested that Wolbachia could promote speciation in their hosts. In this article we investigate theoretically whether Wolbachia-induced bidirectional CI selects for premating isolation and therefore reinforces genetic divergence between parapatric host populations. To achieve this we combined models for Wolbachia dynamics with a well-studied reinforcement model. This new model allows us to compare the effect of bidirectional CI on the evolution of female mating preferences with a situation in which postzygotic isolation is caused by nuclear genetic incompatibilities (NI). We distinguish between nuclear incompatibilities caused by two loci with epistatic interactions, and a single locus with incompatibility among heterozygotes in the diploid phase. Our main findings are: (1) bidirectional CI and single locus NI select for premating isolation with a higher speed and for a wider parameter range than epistatic NI; (2) under certain parameter values, runaway sexual selection leads to the increase of an introduced female preference allele and fixation of its preferred male trait allele in both populations, whereas under others it leads to divergence in the two populations in preference and trait alleles; and (3) bidirectional CI and single locus NI can stably persist up to migration rates that are two times higher than seen for epistatic NI. The latter finding is important because the speed with which mutants at the preference locus spread increases exponentially with the migration rate. In summary, our results show that bidirectional CI selects for rapid premating isolation and so generally support the view that Wolbachia can promote speciation in their hosts.

Infection dynamics of different Wolbachia-types within one host population

Wolbachia are widespread intracellular symbionts of arthropods which are known to cause several reproductive manipulations in their hosts, the commonest of which being cytoplasmic incompatibility (CI), male killing (MK), and the induction of parthenogenesis (PI). Strains of endosymbionts inducing one of these effects can be referred to as 'Wolbachia-types'. Here, we try to ascertain whether two of these Wolbachia-types can stably coexist within one population. We investigate this question by means of two discrete-time mathematical models which describe the dynamics of an infection of a host population with either CI- and MK- or CI- and PI-Wolbachia. We derive analytical solutions for two special cases of each model showing that stable coexistence of the respective Wolbachia-types is not possible if no doubly infected individuals occur within the population and that stable coexistence is possible when doubly infected hosts do exist and transmission of the endosymbionts is perfect. Moreover, we show that a population infected with either CI- or MK-Wolbachia at equilibrium can resist invasion of the respective other Wolbachia-type as a single infection. In contrast, a population infected with CI-Wolbachia can be invaded by PI-Wolbachia as a single infection with the CI-Wolbachia going extinct. Computer simulations confirmed these findings for the general models. We discuss our results with respect to the prevalence of the Wolbachia-types considered here and the emergence of PI- from CI-Wolbachia.