Dynamics of a feline retrovirus (FeLV) in host populations with variable spatial structure.

The predictions of epidemic models are remarkably affected by the underlying assumptions concerning host population dynamics and the relation between host density and disease transmission. Furthermore, hypotheses underlying distinct models are rarely tested. Domestic cats (Felis catus) can be used to compare models and test their predictions, because cat populations show variable spatial structure that probably results in variability in the relation between density and disease transmission. Cat populations also exhibit various dynamics. We compare four epidemiological models of Feline Leukaemia Virus (FeLV). We use two different incidence terms, i.e. proportionate mixing and pseudo-mass action. Population dynamics are modelled as logistic or exponential growth. Compared with proportionate mixing, mass action incidence with logistic growth results in a threshold population size under which the virus cannot persist in the population. Exponential growth of host populations results in systems where FeLV persistence at a steady prevalence and depression of host population growth are biologically unlikely to occur. Predictions of our models account for presently available data on FeLV dynamics in various populations of cats. Thus, host population dynamics and spatial structure can be determinant parameters in parasite transmission, host population depression, and disease control.     

Density-structured models for plant population dynamics

Density-structured models are structured population models in which the state variable is the proportion of populations or sites in a small number of discrete density states. Although such models have rarely been used, they have the advantage that they are straightforward to parameterize, make few assumptions about population dynamics, and permit rapid data collection using coarse density assessment. In this article, we highlight their use in relating population dynamics to environmental variation and their robustness to measurement error. We show that density-structured models are able to accurately represent population dynamics under a wide range of conditions. We look at the effects of including a persistent seedbank and describe numerical approximations for the mean and variance of population size. For simulated data, we determine the extent to which the underlying continuous process may be inferred from density-structured data. Finally, we discuss issues of parameter estimation and applications for which these types of models may be useful.     

Effects of Bacteriophages on the Population Dynamics of Four Strains of Pelagic Marine Bacteria

Viral lysis of specific bacterial populations has been suggested to be an important factor for structuring marine bacterioplankton communities. In the present study, the influence of bacteriophages on the diversity and population dynamics of four marine bacterial phage-host systems was studied experimentally in continuous cultures and theoretically by a mathematical model. By use of whole genome DNA hybridization toward community DNA, we analyzed the dynamics of individual bacterial host populations in response to the addition of their specific phage in continuous cultures of mixed bacterial assemblages. In these experiments, viral lysis had only temporary effects on the dynamics and diversity of the individual bacterial host species. Following the initial lysis of sensitive host cells, growth of phage-resistant clones of the added bacteria resulted in a distribution of bacterial strains in the phage-enriched culture that was similar to that in the control culture without phages after about 50-60 h incubation. Consequently, after a time frame of 5-10 generations after lysis, it was the interspecies competition rather than viral lysis of specific bacterial strains that was the driving force in the regulation of bacterial species composition in these experiments. The clonal diversity, on the other hand, was strongly influenced by viral activity, since the clonal composition of the four species in the phage-enriched culture changed completely from phage-sensitive to phage-resistant clones. The model simulation predicted that viral lysis had a strong impact on the population dynamics, the species composition, and the clonal composition of the bacterial community over longer time scales (weeks). However, according to the model, the overall density of bacteria in the system was not affected by phages, since resistant clones complemented the fluctuations caused by viral lysis. Based on the model analysis, we therefore suggest that viral lysis can have a strong influence on the dynamics of bacterial populations in planktonic marine systems.     

Transmission assumptions generate conflicting predictions in host-vector disease models: a case study in West Nile virus

This review synthesizes the conflicting outbreak predictions generated by different biological assumptions in host–vector disease models. It is motivated by the North American outbreak of West Nile virus, an emerging infectious disease that has prompted at least five dynamical modelling studies. Mathematical models have long proven successful in investigating the dynamics and control of infectious disease systems. The underlying assumptions in these epidemiological models determine their mathematical structure, and therefore influence their predictions. A crucial assumption is the host–vector interaction encapsulated in the disease-transmission term, and a key prediction is the basic reproduction number, R ₀. We connect these two model elements by demonstrating how the choice of transmission term qualitatively and quantitatively alters R ₀ and therefore alters predicted disease dynamics and control implications. Whereas some transmission terms predict that reducing the host population will reduce disease outbreaks, others predict that this will exacerbate infection risk. These conflicting predictions are reconciled by understanding that different transmission terms apply biologically only at certain population densities, outside which they can generate erroneous predictions. For West Nile virus, R ₀ estimates for six common North American bird species indicate that all would be effective outbreak hosts.     

Ecological and genetic determinants of multiple infection and aggregation in a microbial host-parasite system

The number of parasites colonizing a host (termed 'multiple infection') is an important determinant of host-parasite interactions. In theory, multiple infection is determined by random mass action in genetically and spatially homogeneous populations of host and parasite. In real populations, deviations from these assumptions may strongly influence levels of multiple infection. We carried out inoculation experiments in microcosms of the freshwater protozoan Paramecium caudatum and its bacterial parasite Holospora undulata. Increasing parasite dose produced higher levels of (multiple) infection; more susceptible host genotypes also were more multiply infected. An overall pattern of parasite aggregation (excess of uninfected individuals and of individuals carrying larger numbers of parasites) indicated deviations from random mass-action transmission. Homogenizing spatial distributions of parasite and host in our microcosms did not affect aggregation, whereas aggregation was more pronounced in old than in new host clones. Thus, variation in susceptibility may arise over time within clonal populations. When sequentially inoculated, already established infections increased the probability of additional infection in generally resistant host clones, but decreased it in more susceptible clones. Hence, the role of multiple infection as a driver of epidemiological or evolutionary processes may vary among populations, depending on their precise genetic composition or infection history.     

Food limitation and insect outbreaks: complex dynamics in plant-herbivore models

1. The population dynamics of many herbivorous insects are characterized by rapid outbreaks, during which the insects severely defoliate their host plants. These outbreaks are separated by periods of low insect density and little defoliation. In many cases, the underlying cause of these outbreaks is unknown. 2. Mechanistic models are an important tool for understanding population outbreaks, but existing consumer-resource models predict that severe defoliation should happen much more often than is seen in nature. 3. We develop new models to describe the population dynamics of plants and insect herbivores. Our models show that outbreaking insects may be resource-limited without inflicting unrealistic levels of defoliation. 4. We tested our models against two different types of field data. The models successfully predict many major features of natural outbreaks. Our results demonstrate that insect outbreaks can be explained by a combination of food limitation in the herbivore and defoliation and intraspecific competition in the host plant.     

Temporal dynamics of genotypic diversity reveal strong clonal selection in the aphid Myzus persicae

Parthenogenetic organisms often harbour substantial genotypic diversity. This diversity may be the result of recurrent formations of new clones, or it may be maintained by environmental heterogeneity acting on ecological differences among clones. In aphids, both processes may be important because obligate and cyclical parthenogens can form mixed populations. Using microsatellites, I analysed the temporal dynamics of clonal diversity in such a population of the aphid Myzus persicae over a 1-year period. The frequency distribution of clonal genotypes was very skewed, with many rare and few common clones. The relative frequencies of common clones underwent strong and rapid changes indicative of intense clonal selection. Differences in their host associations suggest that these shifts may partly be caused by changes in the abundance of annual host plants. Other selective factors of potential importance are also discussed. New, sexually produced genotypes made a minor contribution to clonal diversity, consistent with the observed heterozygote excess characteristic of predominantly asexual populations in M. persicae.     

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.     

Bimodal trait distributions with large variances question the reliability of trait-based aggregate models

Functionally diverse communities can adjust their species composition to altered environmental conditions, which may influence food web dynamics. Trait-based aggregate models cope with this complexity by ignoring details about species identities and focusing on their functional characteristics (traits). They describe the temporal changes of the aggregate properties of entire communities, including their total biomasses, mean trait values, and trait variances. The applicability of aggregate models depends on the validity of their underlying assumptions that trait distributions are normal and exhibit small variances. We investigated to what extent this can be expected to work by comparing an innovative model that accounts for the full trait distributions of predator and prey communities to a corresponding aggregate model. We used a food web structure with well-established trade-offs among traits promoting mutual adjustments between prey edibility and predator selectivity in response to selection. We altered the shape of the trade-offs to compare the outcome of the two models under different selection regimes, leading to trait distributions increasingly deviating from normality. Their biomass and trait dynamics agreed very well for stabilizing selection and reasonably well for directional selection, under which different trait values are favored at different times. However, for disruptive selection, the results of the aggregate model strongly deviated from the full trait distribution model that showed bimodal trait distributions with large variances. Hence, the outcome of aggregate models is reliable under ideal conditions but has to be questioned when confronted with more complex selection regimes and trait distributions, which are commonly observed in nature.     

Coliform dynamics and the implications for source tracking

In many parts of the world, coliform counts in recreational waters are unacceptably high. In an attempt to rectify this problem, programmes are under way to develop methods that will allow the sources of the faecal contamination thought to be responsible for these elevated counts to be identified. The success of these efforts depends on the validity of several assumptions that underlie many of the proposed methods. One of the critical assumptions is that the clonal composition of the coliform species being monitored in a water body reflects the clonal composition of the species in the host populations responsible for the faecal inputs into that water body. To determine the extent to which among-strain variation in a coliform species might invalidate this assumption, a series of simple mathematical models was proposed and analysed. The first series of models assumed that all cells of species were identical. The question posed was - is the density of a coliform species in a body of water linearly related to the rate at which cells of the species enter the water body via faecal production? The results of these models suggest that, over a wide range of conditions, cell densities in the water body are linearly related to the rate at which cells enter the water body as a result of faecal contamination. This outcome occurs whether or not cells are capable of division in the external environment. When the rate of cell division depends on the concentration of available nutrients then, when nutrient input rates are 'high' and rates of faecal contamination are 'low', this linear relationship does not hold. The second series of models assumed that the coliform species consists of different strains and that these strains differ in their performance in the external environment. The results of these multistrain models show that the relative abundance of strains in the external environment is unlikely to reflect their relative abundance in the faecal inputs to the environment. Consequently, statements such as - domestic animals are responsible for 30% and wildlife for 70% of the faecal inputs to a water body - may well be meaningless.     

Evaluating the contributions of purifying selection and progeny-skew in dictating within-host Mycobacterium tuberculosis evolution

The within-host evolutionary dynamics of tuberculosis (TB) remain unclear, and underlying biological characteristics render standard population genetic approaches based upon the Wright-Fisher model largely inappropriate. In addition, the compact genome combined with an absence of recombination is expected to result in strong purifying selection effects. Thus, it is imperative to establish a biologically relevant evolutionary framework incorporating these factors in order to enable an accurate study of this important human pathogen. Further, such a model is critical for inferring fundamental evolutionary parameters related to patient treatment, including mutation rates and the severity of infection bottlenecks. We here implement such a model and infer the underlying evolutionary parameters governing within-patient evolutionary dynamics. Results demonstrate that the progeny skew associated with the clonal nature of TB severely reduces genetic diversity and that the neglect of this parameter in previous studies has led to significant mis-inference of mutation rates. As such, our results suggest an underlying de novo mutation rate that is considerably faster than previously inferred, and a progeny distribution differing significantly from Wright-Fisher assumptions. This inference represents a more appropriate evolutionary null model, against which the periodic effects of positive selection, associated with drug-resistance for example, may be better assessed.     

The evolution of covert,silent infection as a parasite strategy

Many parasites and pathogens cause silent/covert infections in addition to the more obvious infectious disease-causing pathology. Here, we consider how assumptions concerning superinfection, protection and seasonal host birth and transmission rates affect the evolution of such covert infections as a parasite strategy. Regardless of whether there is vertical infection or effects on sterility, overt infection is always disadvantageous in relatively constant host populations unless it provides protection from superinfection. If covert infections are protective, all individuals will enter the covert stage if there is enough vertical transmission, and revert to overt infections after a ‘latent’ period (susceptible, exposed, infected epidemiology). Seasonal variation in transmission rates selects for non-protective covert infections in relatively long-lived hosts with low birth rates typical of many mammals. Variable host population density caused by seasonal birth rates may also select for covert transmission, but in this case it is most likely in short-lived fecund hosts. The covert infections of some insects may therefore be explained by their outbreak population dynamics. However, our models consistently predict proportions of covert infection, which are lower than some of those observed in nature. Higher proportions of covert infection may occur if there is a direct link between covert infection and overt transmission success, the covert infection is protective or the covert state is the result of suppression by the host. Relatively low proportions of covert transmission may, however, be explained as a parasite strategy when transmission opportunities vary.     

克隆和有性亲体效应及其调控机制

植物表型受自身基因型、所处环境及其亲体所经历环境的共同影响;其中,亲体环境对子代表型的影响被称为亲体效应。亲体效应不仅可通过有性繁殖产生的种子传递给后代(即有性亲体效应),也可以通过克隆生长等无性繁殖产生的分株传递给后代(即克隆亲体效应)。亲体效应对植物种群,特别是对有性繁殖受限、缺乏遗传变异的克隆植物种群的长期进化可能发挥着极其重要的作用,因此,对亲体效应研究进展的梳理非常必要。对克隆亲体效应和有性亲体效应的内涵进行了阐释,并论述了克隆和有性亲体效应对子代表型、适合度、种内/种间竞争能力以及种群/群落结构和功能的潜在影响;阐述了亲体效应的潜在调控机制,包括供给机制、代谢物质调控机制、表观遗传机制等;论述了克隆亲体效应在克隆植物适应进化中的作用。未来可以就克隆亲体效应的遗传稳定性及其对克隆生活史性状变异的贡献程度,以及克隆和有性亲体效应引起的表型多样性对种内/种间关系、种群/群落多样性及生态系统结构、功能和稳定性的影响开展深入研究。     

Evaluation of natural enemies for biological control: A behavioral approach

The success of biological pest control has stimulated the development of analytical models that explore the dynamics of natural enemies and their hosts or prey. These models seek to identify those general characteristics o f the natural enemy, host or prey population that lead to economic pest control. Because the models are strategic in nature, they are of limited value in identifying the specific attributes of an effective biological control agent prior to its introduction. Empirically developed criteria have also been of limited predictive value because they too provide only general guidelines. Behavioral ecology and foraging and sexratio theories may be useful adjuncts to these approaches, by identifying the evolutionary constraints and thus helping to define better the attributes of an effective natural enemy.     

Comparing vector–host and SIR models for dengue transmission

Various simple mathematical models have been used to investigate dengue transmission. Some of these models explicitly model the mosquito population, while others model the mosquitoes implicitly in the transmission term. We study the impact of modeling assumptions on the dynamics of dengue in Thailand by fitting dengue hemorrhagic fever (DHF) data to simple vector–host and SIR models using Bayesian Markov chain Monte Carlo estimation. The parameter estimates obtained for both models were consistent with previous studies. Most importantly, model selection found that the SIR model was substantially better than the vector–host model for the DHF data from Thailand. Therefore, explicitly incorporating the mosquito population may not be necessary in modeling dengue transmission for some populations.     

Investigation of bacteriophage MS2 viral dynamics using model discrimination analysis and the implications for phage therapy

Lytic phages infect their bacterial hosts, use the host machinery to replicate, and finally lyse and kill their hosts, releasing progeny phages. Various mathematical models have been developed that describe these phage-host viral dynamics. The aim of this study was to determine which of these models best describes the viral dynamics of lytic RNA phage MS2 and its host Escherichia coli C-3000. Experimental data consisted of uninfected and infected bacterial cell densities, free phage density, and substrate concentration. Parameters of various models were either determined directly through other experimental techniques or estimated using regression analysis of the experimental data. The models were evaluated using a Bayesian-based model discrimination technique. Through model discrimination it was shown that phage-resistant cells inhibited the growth of phage population. It was also shown that the uninfected bacterial population was a quasispecies consisting of phage-sensitive and phage-resistant bacterial cells. When there was a phage attack the phage-sensitive cells died out and the phage-resistant cells were selected for and became the dominant strain of the bacterial population.     

Density-dependent parasitoid recruitment per parasitized host: effects on parasitoid-host dynamics

Models of parasitoid-host dynamics are analyzed that include direct density dependence in the host population and either parasitoid- or host-density-dependent variation in parasitoid recruitment per parasitized host (parasitoid "yield"). The principal question addressed is how these forms of density dependence in parasitoid dynamics combine with aggregated parasitism to affect the stability of the models, in relation to suppression of host abundance. When parasitoid yield is an overcompensating function of either parasitoid or host density, stability is enhanced for systems with host equilibria suppressed far below the host carrying capacity. Substantially less aggregation of parasitism is required for stability in this situation than in previous models assuming parasitoid yield is constant. However, this density dependence in parasitoid yield also reduces stability when the host equilibrium is suppressed only moderately below carrying capacity; this is especially true when parasitoid yield is more strongly decreased by high host density than is host per capita reproduction. At present there is little empirical evidence concerning the relationships of parasitoid recruitment to parasitoid and host densities. The substantial effects shown in these models suggest that these relationships should be considered in empirical studies.     

Variation in and correlation between intrinsic rate of increase and carrying capacity

Intrinsic population growth rate and density dependence are fundamental components of population dynamics. Theory suggests that variation in and correlations between these parameters among patches within a population can influence overall population size, but data on the degree of variation and correlation are rare. Replicate populations of a specialist aphid (Chaetosiphon fragaefolii) were followed on 11 genotypes of host plant (Fragaria chiloensis) in the greenhouse. Population models fit to these census data provide estimates of intrinsic growth rate and carrying capacity for aphid populations on each plant genotype. Growth rate and carrying capacity varied substantially among plant genotypes, and these two parameters were not significantly correlated. These results support the existence of spatial variation in population dynamic parameters; data on frequency distributions and correlations of these parameters in natural populations are needed for evaluation of the importance of variation in growth rate and density dependence for population dynamics in the field.     

Ecological dynamics of the bivalve-killing dinoflagellate Heterocapsa circularisquama and its infectious viruses in different locations of western Japan

We studied the ecological relationships between the bloom-forming dinoflagellate Heterocapsa circularisquama and its infectious viruses in field surveys conducted in western Japan. The occurrence of H. circularisquama blooms in Imari Bay during 2002 and in Ago Bay during 2002 and 2004 was accompanied by specific increase in abundance of viruses lytic to H. circularisquama. Using northern dot-blot analysis, approximately 96% of the clonal virus isolates collected in the field surveys positively reacted with a molecular probe specific for HcRNAV (H. circularisquama RNA virus); hence, viral impacts on H. circularisquama population observed in these field surveys are considered largely due to HcRNAV and/or its closely related viruses. The dynamics of type UA viruses and type CY viruses having complementary host ranges to H. circularisquama clones were different in each survey and considered to reflect fluctuations in abundance of their suitable host cells in situ. The dynamics of H. circularisquama and its viruses in Ago Bay from 2002 to 2004 suggests the concentration of HcRNAV in the sediment prior to the host's blooming season is a significant factor in determining the size and length of the H. circularisquama blooms. These results support the hypothesis that HcRNAV infection is one of the significant factors affecting the population dynamics of H. circularisquama in both quantity (biomass) and quality (clonal composition).