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.     

Evolution of early male-killing in horizontally transmitted parasites

Early male-killing (MK) bacteria are vertically transmitted reproductive parasites which kill male offspring that inherit them. Whereas their incidence is well documented, characteristics allowing originally non-MK bacteria to gradually evolve MK ability remain unclear. We show that horizontal transmission is a mechanism enabling vertically transmitted bacteria to evolve fully efficient MK under a wide range of host and parasite characteristics, especially when the efficacy of vertical transmission is high. We also show that an almost 100% vertically transmitted and 100% effective male-killer may evolve from a purely horizontally transmitted non-MK ancestor, and that a 100% efficient male-killer can form a stable coexistence only with a non-MK bacterial strain. Our findings are in line with the empirical evidence on current MK bacteria, explain their high efficacy in killing infected male embryos and their variability within and across insect taxa, and suggest that they may have evolved independently in phylogenetically distinct species.     

Evolutionarily stable mixed mating in a variety of genetic systems

Many species display a mixture of close inbreeding and outbreeding which is referred to as mixed mating. For selfing species, models predict that such mixed mating systems can be stable. Conversely, models considering separate sex species have not been able to explain mixed mating systems. This failure may be a result of the unrealistic assumption that recurrent inbreeding does not increase the inbreeding coefficient. Here we show that mixed mating is expected in separate sex systems when recurrent inbreeding is taken into account. A female that allows her brother to sibmate with her gives an extra mating opportunity to said brother. This kin selective advantage should be strongest in genetic systems where the male is more related to the female. In support of this idea, we find that inbreeding evolves most easily in selfers, followed by diploid sibmating, followed by haplodiploid sibmating. Consideration of published values for the regression of fitness on inbreeding coefficient suggests that many species fall in a range where some selfing/sibmating is optimal.     

Tropical Drosophila pandora carry Wolbachia infections causing cytoplasmic incompatibility or male killing

Wolbachia infections have been described in several Drosophila species, but relatively few have been assessed for phenotypic effects. Cytoplasmic incompatibility (CI) is the most common phenotypic effect that has been detected, while some infections cause male killing or feminization, and many Wolbachia infections have few host effects. Here, we describe two new infections in a recently described species, Drosophila pandora, one of which causes near‐complete CI and near‐perfect maternal transmission (the “CI” strain). The other infection is a male killer (the “MK” strain), which we confirm by observing reinitiation of male production following tetracycline treatment. No incompatibility was detected in crosses between CI strain males and MK strain females, and rare MK males do not cause CI. Molecular analyses indicate that the CI and MK infections are distantly related and the CI infection is closely related to the wRi infection of Drosophila simulans. Two population surveys indicate that all individuals are infected with Wolbachia, but the MK infection is uncommon. Given patterns of incompatibility among the strains, the infection dynamics is expected to be governed by the relative fitness of the females, suggesting that the CI infection should have a higher fitness. This was evidenced by changes in infection frequencies and sex ratios in population cages initiated at different starting frequencies of the infections.     

Invasion of sibmating genes in diploid and haplodiploid populations

Summary Existing genetic models of the evolution of sibmating behaviour in diploids incorporate inbreeding depression in terms of reduced fecundity of consanguineous mating pairs rather than reduced survival or fecundity of the progeny of such matings. Here we derive a model to correct this deficiency and extend the model to haplodiploids where differential effects of inbreeding in males and females is a crucial consideration. Our analyses indicate that sibmating can readily evolve in both diploids and haplodiploids in which male mating costs and inbreeding depression are reasonably low, provided there is some mechanism to permit sibmating such as siblings being reared in nests or other forms of aggregation. Our analyses also indicate that once sibmating invades, it typically will go to fixation, although sib-/randommating polymorphisms can persist in both diploids and haplodiploids if male mating costs are close to zero and inbreeding depression reduces survival by around one-third. The conditions favouring sibmating are slightly more restrictive in haplodiploids than in diploids. In light of this we may ask why we see intense sibmating in many haplodiploids such as parasitic wasps, fig wasps, ants, bark beetles and mites, and only rarely in diploid animals. The common factor could be certain kinds of aggregation behaviour that are a prerequisite for sibmating in the absence of kin recognition. Another possibility is that inbreeding depression is likely to be more severe in diploids than in haplodiploids because deleterious recessives are purged from haplodiploid populations when expressed by haploid males. Thus, lower levels of inbreeding depression might be one important reason why sibmating appears to arise more frequently in haplodiploids than diploids. Phylogenetic analysis of groups, such as bark beetles and mites, exhibiting both diploid and haplodiploid populations may be useful in elucidating the relative importance of gregarious behaviour and haplodiploidy in facilitating sibmating systems.     

Space and the persistence of male-killing endosymbionts in insect populations

Male-killing bacteria are bacteria that are transmitted vertically through the females of their insect hosts. They can distort the sex ratio of their hosts by killing infected male offspring. In nature, male-killing endosymbionts (male killers) often have a 100% efficient vertical transmission, and multiple male-killing bacteria infecting a single population are observed. We use different model formalisms to study these observations. In mean-field models a male killer with perfect transmission drives the host population to extinction, and coexistence between multiple male killers within one population is impossible; however, in spatially explicit models, both phenomena are readily observed. We show how the spatial pattern formation underlies these results. In the case of high transmission efficiencies, waves with a high density of male killers alternate with waves of mainly wild-type hosts. The male killers cause local extinction, but this creates an opportunity for uninfected hosts to re-invade these areas. Spatial pattern formation also creates an opportunity for two male killers to coexist within one population: different strains create spatial regions that are qualitatively different; these areas then serve as different niches, making coexistence possible.     

Coexistence and specialization of pathogen strains on contact networks

The coexistence of different pathogen strains has implications for pathogen variability and disease control and has been explained in a number of different ways. We use contact networks, which represent interactions between individuals through which infection could be transmitted, to investigate strain coexistence. For sexually transmitted diseases the structure of contact networks has received detailed study and has been shown to be a vital determinant of the epidemiological dynamics. By using analytical pairwise models and stochastic simulations, we demonstrate that network structure also has a profound influence on the interaction between pathogen strains. In particular, when the population is serially monogamous, fully cross-reactive strains can coexist, with different strains dominating in network regions with different characteristics. Furthermore, we observe specialization of different strains in different risk groups within the network, suggesting the existence of diverging evolutionary pressures.     

HOW SPECIFICITY AND EPIDEMIOLOGY DRIVE THE COEVOLUTION OF STATIC TRAIT DIVERSITY IN HOSTS AND PARASITES

There is typically considerable variation in the level of infectivity of parasites and the degree of resistance of hosts within populations. This trait variation is critical not only to the evolutionary dynamics but also to the epidemiology, and potentially the control of infectious disease. However, we lack an understanding of the processes that generate and maintain this trait diversity. We examine theoretically how epidemiological feedbacks and the characteristics of the interaction between host types and parasites strains determine the coevolution of host–parasite diversity. The interactions include continuous characterizations of the key phenotypic features of classic gene‐for‐gene and matching allele models. We show that when there are costs to resistance in the hosts and infectivity in the parasite, epidemiological feedbacks may generate diversity but this is limited to dimorphism, often of extreme types, in a broad range of realistic infection scenarios. For trait polymorphism, there needs to be both specificity of infection between host types and parasite strains as well as incompatibility between particular strains and types. We emphasize that although the high specificity is well known to promote temporal “Red Queen” diversity, it is costs and combinations of hosts and parasites that cannot infect that will promote static trait diversity.     

Sex ratio genetics and the competitiveness of parasitic wasps

In the first part of the paper we analyse dynamics of the genetic mechanisms responsible for maintaining biased sex ratios in host-parasitoid interactions. We begin by reviewing recent results relating to the maintenance of sibmating in haplo-diploid populations. We then investigate the evolutionary stable sex ratio in populations in which all or some of the females mate with their brothers. In particular, we derive a diallelic one-locus model for studying evolutionary stable sex ratios in partially sibmating haplo-diploid populations. In the second part of the paper we review the impact of sex ratio on host-parasitoid populations. We then analyse how the sex ratio strategy of one parasitoid species may affect its interaction with another parasitoid species competing for the same host. In particular we show that, although a female biased sex ratio may enhance the inherent competitiveness of one species, it may also destabilize the ecological interaction of the three species so that all become extinct.     

Mixed inoculation alters infection success of strains of the endophyte Epichloë bromicola on its grass host Bromus erectus

Within-host competition in multiply infected hosts is considered an important component of host-parasite interactions, but experimental studies on the dynamics of multiple infections are still rare. We measured the infection frequencies of four strains of the fungal endophyte Epichloë bromicola on two genotypes of its host plant Bromus erectus after single- and double-strain inoculation. Double-strain inoculations resulted in fewer double, but more single, infections than expected on the basis of infection frequencies in single-strain inoculations. In most cases, only one of the two strains established an infection, and strains differed in their overall competitive ability. This pattern resembles the mutual exclusion scenarios in some theoretical models of parasite evolution. In addition, competitive ability varied with host genotype, which may represent a mechanism for the coexistence of strains in a population. Hence, considering the genetic variation in both host and parasite may be important for a better understanding of within-host dynamics and their role in epidemiology or (co)evolution.     

EVOLUTION OF THE NUMBER OF SEXES

In sexually reproducing isogamous organisms, gametes (or diploid cells in ciliates) are classified into two or more groups called sexes, and mating occurs only between cells of different sexes. We have studied the evolutionary stability of the number of sexes maintained in a population by examining population-genetic models. For models in which the diploid genome determines the sex of conjugal cells, a one-locus system with three alleles of pecking-order dominance is assumed. Unlike traditional bisexual models, the genetic dynamics then depend on a rule, called mating kinetics, which determines the proportion of matings between each pair of sexes for given proportions of cells of the three sexes. The evolutionary consequences greatly depend on the mating kinetics assumed. Of the four mating kinetics examined, two give a large advantage to rare sexes whose cells quickly find heterosexual partners, which implies an evolutionary increase in the number of sexes. In contrast, the other two mating kinetics, in which gametes wait for suitable mates without being eliminated from the gamete pool during this waiting period, produce neutrally stable dynamics with curves or a surface of equilibria. Then random drift or differential fitness among sexes would result in the loss of sex alleles until only two remain in the population. This suggests a turnover of sexes; a new sex invades and replaces resident sexes after temporary coexistence. Similar results are obtained in models with haploid sex-determination and with autogamy. These two processes, however, may help to maintain many sexes indirectly by preventing the accumulation of recessive lethal mutations on sex chromosomes. The relationship of these models to models of self-sterility factors in plants and sex factors in honeybees is discussed. To summarize, the number of sexes should increase when conjugal cells must find mates during a limited period of time, otherwise a two-sex system should evolve. We conclude that there may be more isogamous species with three or more sexes than are currently known.     

ON THE EVOLUTION OF PSEUDOGAMY

A. density- and frequency-dependent model for the evolution and maintenance of pseudogamous females is developed and analyzed. Ecological as well as evolutionary aspects of pseudogamy are discussed. Criteria are described for the stable coexistence of sexual females and pseudogamous females under natural conditions. The conditions for invasion of a normal bisexual population by pseudogamous females are less stringent than the conditions for stable coexistence. Hence, we expect that some populations will be characterized by unstable sex ratios over time (with the resulting local extinction due to lack of males) while other populations will be characterized by stable sex ratios over time. If high population sex ratios (i.e., many females to few males) are to be stable, the net population growth rate must be large, and there can be no successful male preference for sexual females.     

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.     

Interactions between frequency-dependent and vertical transmission in host-parasite systems.

We investigate host-pathogen dynamics and conditions for coexistence in two models incorporating frequency-dependent horizontal transmission in conjunction with vertical transmission. The first model combines frequency-dependent and uniparental vertical transmission, while the second addresses parasites transmitted vertically via both parents. For the first model, we ask how the addition of vertical transmission changes the coexistence criteria for parasites transmitted by a frequency-dependent horizontal route, and show that vertical transmission significantly broadens the conditions for parasite invasion. Host-parasite coexistence is further affected by the form of density-dependent host regulation. Numerical analyses demonstrate that within a host population, a parasite strain with horizontal frequency-dependent transmission can be driven to extinction by a parasite strain that is additionally transmitted vertically for a wide range of parameters. Although models of asexual host populations predict that vertical transmission alone cannot maintain a parasite over time, analysis of our second model shows that vertical transmission via both male and female parents can maintain a parasite at a stable equilibrium. These results correspond with the frequent co-occurrence of vertical with sexual transmission in nature and suggest that these transmission modes can lead to host-pathogen coexistence for a wide range of systems involving hosts with high reproductive rates.     

The effects of females’ susceptibility on the coexistence of multiple pathogen strains of sexually transmitted diseases

 We study the dynamics of sexually transmitted pathogens in a heterosexually active population, where females are divided into two different groups based on their susceptibility to two distinct pathogenic strains. It is assumed that a host cannot be invaded simultaneously by both disease agents and that when symptoms appear – a function of the pathogen, strain, virulence, and an individual’s degree of susceptibility – then individuals are treated and/or recover. Heterogeneity in susceptibility to the acquisition of infection and/or in variability in the length of the infection period of the female subpopulations is incorporated. Pathogens’ coexistence is highly unlikely on homogeneously mixing female and male populations with no heterogeneity among individuals of either gender. Variability in susceptibility in the female subpopulation makes coexistence possible albeit under a complex set of circumstances that must include differences in contact/mixing rates between the groups of females and the male population as well as differences in the lengths of their average periods of infectiousness for the three groups. Received 25 July 1995; received in revised form 6 May 1996     

Latent Coinfection and the Maintenance of Strain Diversity

Technologies for strain differentiation and typing have made it possible to detect genetic diversity of pathogens, both within individual hosts and within communities. Coinfection of a host by more than one pathogen strain may affect the relative frequency of these strains at the population level through complex within- and between-host interactions; in infectious diseases that have a long latent period, interstrain competition during latency is likely to play an important role in disease dynamics. We show that SEIR models that include a class of latently coinfected individuals can have markedly different long-term dynamics than models without coinfection, and that coinfection can greatly facilitate the stable coexistence of strains. We demonstrate these dynamics using a model relevant to tuberculosis in which people may experience latent coinfection with both drug sensitive and drug resistant strains. Using this model, we show that the existence of a latent coinfected state allows the possibility that disease control interventions that target latency may facilitate the emergence of drug resistance.     

Competitive exclusion and coexistence of pathogens in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population has been studied completely by Jiang and Chai in (J Math Biol 56:373-390, 2008). In this paper, we give a analysis for a SIS STD with two competing strains, where populations are divided into three differential groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterizes competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability about these equilibria under some assumptions. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium, that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability, the coexistence equilibrium is globally stable or unstable if and only if the two boundary equilibria are both unstable or both stable.     

Sex and space destabilize intransitive competition within and between species

Organisms ranging from bacteria and corals to plants and vertebrates can form intransitive competitive networks, in which coexistence can be maintained because no one species or genotype is superior to all others. However, in the simplest case with three competing types, the long-term outcome may not be so clear if two of the three represent the ends of a continuous heritable trait distribution within one species, as has been recently demonstrated empirically in a short-term experiment with plants. Using simulation models of this scenario, results with asexual reproduction confirm previous studies which showed that local interactions promote coexistence. However, with sexual reproduction, genetic variance is reduced because selection fluctuates between favouring the two extremes during population cycles, while sex continually produces intermediates. Sex thus slows the response to selection when it is the strongest and therefore slows the recovery from extreme abundances, creating larger abundance fluctuations. Local interactions do not stabilize dynamics with sex because the resultant spatial patches of one species are genetically heterogeneous, such that particular phenotypes do not benefit from spatial refuges. In sharp contrast to previous models suggesting that sex or local interactions stabilize population dynamics, here sex and local interactions destabilize dynamics and increase extinction risk.     

Effect of pathogen-resistant vectors on the transmission dynamics of a vector-borne disease

A model is introduced for the transmission dynamics of a vector-borne disease with two vector strains, one wild and one pathogen-resistant; resistance comes at the cost of reduced reproductive fitness. The model, which assumes that vector reproduction can lead to the transmission or loss of resistance (reversion), is analyzed in a particular case with specified forms for the birth and force of infection functions. The vector component can have, in the absence of disease, a coexistence equilibrium where both strains survive. In the case where reversion is possible, this coexistence equilibrium is globally asymptotically stable when it exists. This equilibrium is still present in the full vector-host system, leading to a reduction of the associated reproduction number, thereby making elimination of the disease more feasible. When reversion is not possible, there can exist an additional equilibrium with only resistant vectors.     

From elaborate to compact seasonal plant epidemic models and back: is competitive exclusion in the details?

Seasonality, or periodic host absence, is a central feature in plant epidemiology. In this respect, seasonal plant epidemic models take into account the way the parasite overwinters and generates new infections. These are termed primary infections. In the literature, one finds two classes of models: high-dimensional elaborate models and low-dimensional compact models, where primary infection dynamics are explicit and implicit, respectively. Investigating a compact model allowed previous authors to show the existence of a competitive exclusion principle. However, the way compact models derive from elaborate models has not been made explicit yet. This makes it unclear whether results such as competitive exclusion extend to elaborate models as well. Here, we show that assuming primary infection dynamics are fast in a standard elaborate model translates into a compact form. Yet, it is not that usually found in the literature. Moreover, we numerically show that coexistence is possible in this original compact form. Reversing the question, we show that the usual compact form approximates an alternate elaborate model, which differs from the earlier one in that primary infection dynamics are density dependent. We discuss to which extent these results shed light on coexistence within soil- and air-borne plant parasites, such as within the take-all disease of wheat and the grapevine powdery mildew cryptic species complexes, respectively.