Stochastic spread of Wolbachia

Wolbachia are very common, maternally transmitted endosymbionts of insects. They often spread by a mechanism termed cytoplasmic incompatibility (CI) that involves reduced egg hatch when Wolbachia-free ova are fertilized by sperm from Wolbachia-infected males. Because the progeny of Wolbachia-infected females generally do not suffer CI-induced mortality, infected females are often at a reproductive advantage in polymorphic populations. Deterministic models show that Wolbachia that impose no costs on their hosts and have perfect maternal transmission will spread from arbitrarily low frequencies (though initially very slowly); otherwise, there will be a threshold frequency below which Wolbachia frequencies decline to extinction and above which they increase to fixation or a high stable equilibrium. Stochastic theory was used to calculate the probability of fixation in populations of different size for arbitrary current frequencies of Wolbachia, with special attention paid to the case of spread after the arrival of a single infected female. Exact results are given based on a Moran process that assumes a specific demographic model, and approximate results are obtained using the more general Wright-Fisher theory. A new analytical approximation for the probability of fixation is derived, which performs well for small population sizes. The significance of stochastic effects in the natural spread of Wolbachia and their relevance to the use of Wolbachia as a drive mechanism in vector and pest management are discussed.     

Modeling the spread of invasive species using dynamic network models

Spread dynamics of biological invasions are influenced by both the availability and spatial arrangement of suitable habitat. As such, invasive spread can be considered to occur across a network of nodes, representing patches of suitable habitat, with linkages representing the potential for movement between habitat patches. While static network models can provide valuable insight into the potential framework of nodes and linkages across which spread could occur, they offer little information on the actual spatiotemporal dynamics of range expansion processes. Here, we explore the development and application of dynamic network models (DNMs) to model the spread of invasive species. DNMs accommodate temporal dynamics in the utilization of nodes and the connections between them and can flexibly perform simulations at the spatial scales of observational data. As case studies, we develop DNMs to simulate the spread of a generalist forest pathogen and the hemlock woolly adelgid (Adelges tsugae Annand). We highlight the utility of DNMs for identifying habitat patches that contribute most to spread across the landscape and for visualizing emergent spread dynamics. While currently underutilized in ecology as compared to static network models, DNMs are potentially applicable to numerous research and management questions relevant to biological invasions and the more general phenomena of range expansion.     

Effectiveness of dynamic quarantines against pathogen spread in models of the horticultural trade network

The live plant nursery trade is a potential vector for pests and pathogens, which can spread to natural and developed environments with unintended ecosystem consequences. Simulated, approximately scale-free, tiered horticultural trade networks consisting of growers, wholesalers, and retailers were used to study the efficacy of quarantine inspection and isolation procedures for reducing the spread of infected materials to consumers. The quarantine algorithm temporarily isolated infected nurseries from the rest of the trade network, rewiring the affected trade connections to unquarantined nodes, until the infection was reduced below the detection threshold, at which time the formerly infected nursery was reincorporated into the trade network.Nodes were inspected for infection at regular intervals. Increasing the inspection interval resulted in higher levels of infection with large, system-wide oscillations whose period that matched the inspection interval. The timing of quarantine inspections of the largest hub in the grower tier drove the dynamics of the entire network. Increasing the proportion of growers or wholesalers increased infection level in most networks. Increasing the connectivity within the grower and wholesaler tiers led to large increases in mean infection levels. Focusing quarantine inspection efforts on hubs in the grower and wholesaler tiers may be the most efficient method for reducing the level of infected plant material sold by retailers in real plant trade networks.     

Population structure and the spread of disease

A common assumption of many mathematical models for the spread of disease is that there is random mixing among all individuals in the host population. This paper analyzes and develops a model for the spread of disease in a population consisting of several interacting subpopulations. The model considers 2 different types of interactions between individuals: 1) within a subpopulation because of geographic proximity, and 2) of the same or different subpopulations because of attendance at common social functions. A stability analysis performed on the equilibria of the model shows 2 stable states: 1) a population composed solely of susceptible individuals with no disease present, and 2) an interior point where there are susceptible, infective, and recovered individuals present at all times. The analysis shows that the threshold for disease maintenance is more easily exceed in centers that are members of a small local cluster than in randomly mixing centers, but that the spread of the disease throughout the population occurs more rapidly when the initial case attends a randomly mixing center. The conditions under which a disease will become established are dependent upon the transmission rate for the disease, the birth and death rate in each neighborhood, the recovery rate from the disease in each neighborhood, and the movement patterns of the individuals in the population. The study of the spread of disease in a population by means of mathematical models provides a valuable addition to the statistical data analyzed by epidemiologists. This model is relevant any time there is a division of the population into several interacting groups in which the probability of disease spread is a function both of neighborhood contact because of geographic proximity and of social interactions between groups.     

Rapid spread of male‐killing Wolbachia in the butterfly Hypolimnas bolina

Reproductive parasites such as Wolbachia can spread through uninfected host populations by increasing the relative fitness of the infected maternal lineage. However, empirical estimates of how fast this process occurs are limited. Here we use nucleotide sequences of male‐killing Wolbachia bacteria and co‐inherited mitochondria to address this issue in the island butterfly Hypolimnas bolina. We show that infected specimens scattered throughout the species range harbour the same Wolbachia and mitochondrial DNA as inferred from 6337 bp of the bacterial genome and 2985 bp of the mitochondrial genome, suggesting this strain of Wolbachia has spread across the South Pacific Islands at most 3000 years ago, and probably much more recently.     

Population Genomics of the Wolbachia Endosymbiont in Drosophila melanogaster

Wolbachia are maternally inherited symbiotic bacteria, commonly found in arthropods, which are able to manipulate the reproduction of their host in order to maximise their transmission. The evolutionary history of endosymbionts like Wolbachia can be revealed by integrating information on infection status in natural populations with patterns of sequence variation in Wolbachia and host mitochondrial genomes. Here we use whole-genome resequencing data from 290 lines of Drosophila melanogaster from North America, Europe, and Africa to predict Wolbachia infection status, estimate relative cytoplasmic genome copy number, and reconstruct Wolbachia and mitochondrial genome sequences. Overall, 63% of Drosophila strains were predicted to be infected with Wolbachia by our in silico analysis pipeline, which shows 99% concordance with infection status determined by diagnostic PCR. Complete Wolbachia and mitochondrial genomes show congruent phylogenies, consistent with strict vertical transmission through the maternal cytoplasm and imperfect transmission of Wolbachia. Bayesian phylogenetic analysis reveals that the most recent common ancestor of all Wolbachia and mitochondrial genomes in D. melanogaster dates to around 8,000 years ago. We find evidence for a recent global replacement of ancestral Wolbachia and mtDNA lineages, but our data suggest that the derived wMel lineage arose several thousand years ago, not in the 20th century as previously proposed. Our data also provide evidence that this global replacement event is incomplete and is likely to be one of several similar incomplete replacement events that have occurred since the out-of-Africa migration that allowed D. melanogaster to colonize worldwide habitats. This study provides a complete genomic analysis of the evolutionary mode and temporal dynamics of the D. melanogaster–Wolbachia symbiosis, as well as important resources for further analyses of the impact of Wolbachia on host biology.     

Population differentiation and Wolbachia phylogeny in mosquitoes of the Aedes scutellaris group

Mosquito species of the Aedes (Stegomyia) scutellaris (Walker) group (Diptera: Culicidae) are distributed across many islands of the South Pacific and include major regional vectors of filariasis, such as Aedes polynesiensis (Marks). Analysis of populations of Ae. polynesiensis at the extremes of its range, from Fiji and from Moorea, French Polynesia, using the rDNA ITS2 (internal transcribed spacer 2) region and six microsatellite markers showed considerable genetic differentiation between them (F(ST) = 0.298-0.357). Phylogenetic analysis of the Wolbachia endosymbionts in three members of the complex revealed that based on the wsp gene they are all very similar and belong to the Mel subgroup of the A clade, closely related to the Wolbachia strain present in the gall wasp Callyrhytis glandium (Giraud) (Hymenoptera: Cynipidae). By contrast they are only distantly related to the A-clade Wolbachia in Aedes albopictus (Skuse), a species closely allied to the Ae. scutellaris group. There was very low differentiation between the Wolbachia in the Moorea and Fiji populations of Ae. polynesiensis.     

Spatially explicit models of Turelli-Hoffmann Wolbachia invasive wave fronts

This paper examines different mathematical models of insect dispersal and infection spread and compares these with field data. Reaction-diffusion and integro-difference equation models are used to model the spatio-temporal spread of Wolbachia in Drosophila simulans populations. The models include cytoplasmic incompatibility between infected females and uninfected males that creates a threshold density, similar to an Allee effect, preventing increase from low incidence of infection in the host population. The model builds on an earlier model (Turelli & Hoffmann, 1991) by incorporating imperfect maternal transmission. The results of simulations of the models using the same parameter values produce different dynamics for each model. These differences become very marked in the integro-difference equation models when insect dispersal patterns are assumed to be non-Gaussian. The success or failure of invasion by Wolbachia in the simulations may be attributed to the insect dispersal mechanism used in the model rather than the parameter values. As the models predict very different outcomes for the integro-difference models depending on the underlying assumptions of insect dispersal patterns, this emphasizes that good field data on real (rather than idealized) dispersal patterns need to be collected before models such as these can be used for predictive purposes.     

Population dynamics of the Wolbachia infection causing cytoplasmic incompatibility in Drosophila melanogaster.

Field populations of Drosophila melanogaster are often infected with Wolbachia, a vertically transmitted microorganism. Under laboratory conditions the infection causes partial incompatibility in crosses between infected males and uninfected females. Here we examine factors influencing the distribution of the infection in natural populations. We show that the level of incompatibility under field conditions was much weaker than in the laboratory. The infection was not transmitted with complete fidelity under field conditions, while field males did not transmit the infection to uninfected females and Wolbachia did not influence sperm competition. There was no association between field fitness as measured by fluctuating asymmetry and the infection status of adults. Infected field females were smaller than uninfecteds in some collections from a subtropical location, but not in other collections from the same location. Laboratory cage studies showed that the infection did not change in frequency when populations were maintained at a low larval density, but it decreased in frequency at a high larval density. Monitoring of infection frequencies in natural populations indicated stable frequencies in some populations but marked fluctuations in others. Simple models suggest that the infection probably provides a fitness benefit for the host in order to persist in populations. The exact nature of this benefit remains elusive.     

Making (good) use of Wolbachia: what the models say

Wolbachia, probably the most common animal endosymbiont, infects a wide range of arthropods as well as filarial nematodes. Generally vertically transmitted from mothers to offspring, it has evolved various strategies, ranging from brutal male-killing to mutualism, which facilitate invasion and persistence of the infections within host populations. Current interest in Wolbachia as a potential control agent against harmful nematodes and arthropods makes it important to be able to predict Wolbachia epidemiology and evolutionary trajectory. Here we highlight recent theoretical developments and suggest future modelling and empirical directions for basic and applied research in this domain.     

Developing dynamic mechanistic species distribution models: predicting bird-mediated spread of invasive plants across northeastern North America

Species distribution models are a fundamental tool in ecology, conservation biology, and biogeography and typically identify potential species distributions using static phenomenological models. We demonstrate the importance of complementing these popular models with spatially explicit, dynamic mechanistic models that link potential and realized distributions. We develop general grid-based, pattern-oriented spread models incorporating three mechanisms--plant population growth, local dispersal, and long-distance dispersal--to predict broadscale spread patterns in heterogeneous landscapes. We use the model to examine the spread of the invasive Celastrus orbiculatus (Oriental bittersweet) by Sturnus vulgaris (European starling) across northeastern North America. We find excellent quantitative agreement with historical spread records over the last century that are critically linked to the geometry of heterogeneous landscapes and each of the explanatory mechanisms considered. Spread of bittersweet before 1960 was primarily driven by high growth rates in developed and agricultural landscapes, while subsequent spread was mediated by expansion into deciduous and coniferous forests. Large, continuous patches of coniferous forests may substantially impede invasion. The success of C. orbiculatus and its potential mutualism with S. vulgaris suggest troubling predictions for the spread of other invasive, fleshy-fruited plant species across northeastern North America.     

Analytic models for the patchy spread of plant disease

Plant epidemiologists have long been concerned with the patchy nature of plant disease epidemics. This paper presents a new analytical model for patchy plant epidemics (and patchy dynamics in general), using a second-order approximation to capture the spatial dynamics in terms of the densities and spatial covariances of healthy and infected hosts. Using these spatial moment equations helps us to explain the dynamic growth of patchiness during the early phase of the epidemic, and how the patchiness feeds back on the growth rate of the epidemic. Both underlying heterogeneity in the host spatial arrangement and dynamically generated heterogeneity in the spatial arrangement of infected plants initially accelerate but later decelerate the epidemic.     

Wolbachia Infection in a Natural Parasitoid Wasp Population

The maternally transmitted bacterium Wolbachia pipientis is well known for spreading and persisting in insect populations through manipulation of the fitness of its host. Here, we identify three new Wolbachia pipientis strains, wHho, wHho2 and wHho3, infecting Hyposoter horticola, a specialist wasp parasitoid of the Glanville fritillary butterfly. The wHho strain (ST435) infects about 50% of the individuals in the Åland islands in Finland, with a different infection rate in the two mitochondrial (COI) haplotypes of the wasp. The vertical transmission rate of Wolbachia is imperfect, and lower in the haplotype with lower infection rate, suggesting a fitness trade-off. We found no association of the wHho infection with fecundity, longevity or dispersal ability of the parasitoid host. However, preliminary results convey spatial associations between Wolbachia infection, host mitochondrial haplotype and parasitism of H. horticola by its hyperparasitoid, Mesochorus cf. stigmaticus. We discuss the possibility that Wolbachia infection protects H. horticola against hyperparasitism.     

Population structure in relation to host-plant ecology and Wolbachia infestation in the comma butterfly

Experimental work on Polygonia c‐album, a temperate polyphagous butterfly species, has shown that Swedish, Belgian, Norwegian and Estonian females are generalists with respect to host‐plant preference, whereas females from UK and Spain are specialized on Urticaceae. Female preference is known to have a strong genetic component. We test whether the specialist and generalist populations form respective genetic clusters using data from mitochondrial sequences and 10 microsatellite loci. Results do not support this hypothesis, suggesting that the specialist and generalist traits have evolved more than once independently. Mitochondrial DNA variation suggests a rapid expansion scenario, with a single widespread haplotype occurring in high frequency, whereas microsatellite data indicate strong differentiation of the Moroccan population. Based on a comparison of polymorphism in the mitochondrial data and sequences from a nuclear gene, we show that the diversity in the former is significantly less than that expected under neutral evolution. Furthermore, we found that almost all butterfly samples were infected with a single strain of Wolbachia, a maternally inherited bacterium. We reason that indirect selection on the mitochondrial genome mediated by a recent sweep of Wolbachia infection has depleted variability in the mitochondrial sequences. We also surmise that P. c‐album could have expanded out of a single glacial refugium and colonized Morocco recently.     

Population models of sperm-dependent parthenogenesis

Organisms that reproduce by sperm-dependent parthenogenesis are asexual clones that require sperm of a sexual host to initiate egg production, without the genome of the sperm contributing genetic information to the zygote. Although sperm-dependent parthenogenesis has some of the disadvantages of sex (requiring a mate) without the counterbalancing advantages (mixing of parental genotypes), it appears amongst a wide variety of species. We develop initial models for the density-dependent dynamics of animal populations with sperm-dependent parthenogenesis (pseudogamy or gynogenesis), based on the known biology of the common Enchytraeid worm Lumbricillus lineatus. Its sperm-dependent parthenogenetic populations are reproductive parasites of the hermaphrodite sexual form. Our logistic models reveal two alternative requirements for coexistence at density-dependent equilibria: (i) If the two forms differ in competitive ability, the form with the lower intrinsic birth rate must be compensated by a more than proportionately lower competitive impact from the other, relative to intraspecific competition, (ii) If the two forms differ in their intrinsic capacity to exploit resources, the sperm-dependent parthenogen must be superior in this respect and must have a lower intrinsic birth rate. In general for crowded environments we expect a sperm-dependent parthenogen to compete strongly for limiting resources with the sexual sibling species. Its competitive impact is likely to be weakened by its genetic uniformity, however, and this may suffice to cancel any advantage of higher intrinsic growth rate obtained from reproductive investment only in egg production. We discuss likely thresholds of coexistence for other sperm-dependent parthenogens. The fish Poeciliopsis monacha-lucida likewise obtains an intrinsic growth advantage from reduced investment in male gametes, and so its persistence is likely to depend on it being a poor competitor. The planarian Schmidtea polychroa obtains no such intrinsic benefit because it produces fertile sperm, and its persistence may depend on superior resource exploitation.     

Oscillations in epidemic models with spread of awareness

Journal of Mathematical Biology - We study ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models...     

Population replacement strategies for controlling vector populations and the use of Wolbachia pipientis for genetic drive

In this video, Jason Rasgon discusses population replacement strategies to control vector-borne diseases such as malaria and dengue. "Population replacement" is the replacement of wild vector populations (that are competent to transmit pathogens) with those that are not competent to transmit pathogens. There are several theoretical strategies to accomplish this. One is to exploit the maternally-inherited symbiotic bacteria Wolbachia pipientis. Wolbachia is a widespread reproductive parasite that spreads in a selfish manner at the extent of its host's fitness. Jason Rasgon discusses, in detail, the basic biology of this bacterial symbiont and various ways to use it for control of vector-borne diseases.     

Male-killing Wolbachia in a live-bearing arthropod: brood abortion as a constraint on the spread of a selfish microbe

Maternally inherited, cellular endosymbionts can enhance their fitness by biasing host sex ratio in favor of females. Male killing (MK), an extreme form of sex-ratio manipulation, is selectively advantageous, if the death of males results in increased microbe transmission through female siblings. In live-bearing hosts, females typically produce more embryos than are brought to term, and reproductive compensation through maternal resource reallocation from dead male embryos to female siblings provides a direct, physiological mechanism that could increase the number of daughters born to infected females, thereby promoting MK endosymbiont spread. In this study, a Wolbachia-infected line and an uninfected line of the viviparous pseudoscorpion, Cordylochernes scorpioides were genetically homogenized for nuclear DNA by repeated backcrossing of the infected line with the uninfected, laboratory population. Photomicroscopy of early-stage embryos demonstrated that female C. scorpioides invariably produced an excess of embryos, with Wolbachia-infected females producing as many early-stage embryos as uninfected female controls. However, Wolbachia-infected females that successfully carried broods to term gave birth to significantly fewer offspring, indicating that the extreme female bias characteristic of their broods results from the killing rather than the feminization of male embryos. Infected females that carried broods to term gave birth to significantly larger nymphs and did produce 10% more female offspring than uninfected females. However, the slight transmission advantage that the MK Wolbachia accrued from this reproductive compensation appears to be heavily outweighed by the high rate of spontaneous brood abortion suffered by infected females.     

Population dynamic consequences of allee effects

We take a well-known dynamic model of an isolated, unstructured population and modify this to include a factor that allows for a reduction in fitness due to declining population sizes, often termed an Allee effect. Analysis of the behaviour of this model is carried out on two fronts - determining the equilibrium values and examining the stability of these equilibria. Our results point to the stabilising effect on population dynamics of the Allee effect and an unexpected increase in stability with increased competition due to the interaction between competitive and Allee effects.     

Population dynamic theory of size-dependent cannibalism

Cannibalism is characterized by four aspects: killing victims, gaining energy from victims, size-dependent interactions and intraspecific competition. In this review of mathematical models of cannibalistic populations, we relate the predicted population dynamic consequences of cannibalism to its four defining aspects. We distinguish five classes of effects of cannibalism: (i) regulation of population size; (ii) destabilization resulting in population cycles or chaos; (iii) stabilization by damping population cycles caused by other interactions; (iv) bistability such that, depending on the initial conditions, the population converges to one of two possible stable states; and (v) modification of the population size structure. The same effects of cannibalism may be caused by different combinations of aspects of cannibalism. By contrast, the same combination of aspects may lead to different effects. For particular cannibalistic species, the consequences of cannibalism will depend on the presence and details of the four defining aspects. Empirical evidence for the emerged theory of cannibalism is discussed briefly. The implications of the described dynamic effects of cannibalism are discussed in the context of community structure, making a comparison with the community effects of intraguild predation.