BackgroundRegardless of the growing interest in detecting population structures in malarial parasites, there have been limited discussions on how to use this concept in control programmes. In such context, the effects of the parasite population structures will depend on interventions’ spatial or temporal scales. This investigation explores the problem of identifying genetic markers, in this case microsatellites, to unveil Plasmodium genetic structures that could affect decisions in the context of elimination. The study was performed in a low-transmission area, which offers a good proxy to better understand problems associated with surveillance at the final stages of malaria elimination.MethodsPlasmodium vivax samples collected in Tumeremo, Venezuela, between March 2003 and November 2004 were analysed. Since Plasmodium falciparum also circulates in many low endemic areas, P. falciparum samples from the same locality and time period were included for comparison. Plasmodium vivax samples were assayed for an original set of 25 microsatellites and P. falciparum samples were assayed for 12 microsatellites.ResultsNot all microsatellite loci assayed offered reliable local data. A complex temporal-cluster dynamics is found in both P. vivax and P. falciparum. Such dynamics affect the numbers and the type of microsatellites required for identifying individual parasites or parasite clusters when performing cross-sectional studies. The minimum number of microsatellites required to differentiate circulating P. vivax clusters differs from the minimum number of hyper-variable microsatellites required to distinguish individuals within these clusters. Regardless the extended number of microsatellites used in P. vivax, it was not possible to separate all individual infections.ConclusionsMolecular surveillance has great potential; however, it requires preliminary local studies in order to properly interpret the emerging patterns in the context of elimination. Clonal expansions and clusters turnovers need to be taken into account when using molecular markers. Those affect the number and type of microsatellite markers, as well as, the expected genetic patterns in the context of operational investigations. By considering the local dynamics, elimination programmes could cost-effectively use molecular markers. However, population level studies need to consider the local limitations of a given set of loci in terms of providing epidemiologically relevant information.

The destabilizing effect of endodontic treatment upon teeth is still controversial. The purpose of this study was to investigate the effects of different steps of endodontic treatments upon the rigidity of teeth. Extracted untreated central maxillary anterior teeth were loaded (3.75 N), and deformations of the root were assessed by Speckle pattern interferometry. The following treatments (with subsequent determination of deformability) were conducted sequentially: access preparation, manual instrumentation (Kerr files ISO-40, ISO-60, ISO-80, ISO-110), and tapered and parallel-sided post preparation. It was found that the teeth were increasingly destabilized by any treatment. While the increased deformability was not significant with the manual enlargement (p > 0.05), we found a significant destabilization after access preparation and post preparation (p < 0.05). A corresponding difference was found after conversion of the post preparation from tapered to parallel-sided (p < 0.05). Both substance loss and modifications of the natural root canal geometry play an important role in tooth rigidity.

The number of co-infections of a pathogen (multiplicity of infection or MOI) is a relevant parameter in epidemiology as it relates to transmission intensity. Notably, such quantities can be built into a metric in the context of disease control and prevention. Having applications to malaria in mind, we develop here a maximum-likelihood (ML) framework to estimate the quantities of interest at low computational and no additional costs to study designs or data collection. We show how the ML estimate for the quantities of interest and corresponding confidence-regions are obtained from multiple genetic loci. Assuming specifically that infections are rare and independent events, the number of infections per host follows a conditional Poisson distribution. Under this assumption, we show that a unique ML estimate for the parameter () describing MOI exists which is found by a simple recursion. Moreover, we provide explicit formulas for asymptotic confidence intervals, and show that profile-likelihood-based confidence intervals exist, which are found by a simple two-dimensional recursion. Based on the confidence intervals we provide alternative statistical tests for the MOI parameter. Finally, we illustrate the methods on three malaria data sets. The statistical framework however is not limited to malaria.

It has been shown theoretically that sympatric speciation can occur if intraspecific competition is strong enough to induce disruptive selection. However, the plausibility of the involved processes is under debate, and many questions on the conditions for speciation remain unresolved. For instance, is strong disruptive selection sufficient for speciation? Which roles do genetic architecture and initial composition of the population play? How strong must assortative mating be before a population can split in two? These are some of the issues we address here. We investigate a diploid multilocus model of a quantitative trait that is under frequency-dependent selection caused by a balance of intraspecific competition and frequency-independent stabilizing selection. This trait also acts as mating character for assortment. It has been established previously that speciation can occur only if competition is strong enough to induce disruptive selection. We find that speciation becomes more difficult for very strong competition, because then extremely strong assortment is required. Thus, speciation is most likely for intermediate strengths of competition, where it requires strong, but not extremely strong, assortment. For this range of parameters, however, it is not obvious how assortment can evolve from low to high levels, because with moderately strong assortment less genetic variation is maintained than under weak or strong assortment-sometimes none at all. In addition to the strength of frequency-dependent competition and assortative mating, the roles of the number of loci, the distribution of allelic effects, the initial conditions, costs to being choosy, the strength of stabilizing selection, and the particular choice of the fitness function are explored. A multitude of possible evolutionary outcomes is observed, including loss of all genetic variation, splitting in two to five species, as well as very short and extremely long stable limit cycles. On the methodological side, we propose quantitative measures for deciding whether a given distribution reflects two (or more) reproductively isolated clusters.

Most models of sympatric speciation have assumed that assortative mating has no costs. A few studies, however, have shown that the costs for being choosy can prevent such speciation. Here, we investigate the role of the strength of assortment and of the costs for being choosy for a simple genetic model of a single (‘magic’) trait that mediates both intraspecific competition for a continuum of resources and assortative mating, which is induced by choosy females who preferentially mate with males of similar phenotype. Choosiness may be costly if it is difficult to find a mating partner. Such magic trait models are considered to be most conducive of sympatric speciation. We consider a sexually reproducing population of haploid individuals that is density regulated. The trait is determined by a single locus with multiple alleles. The strength of stabilizing selection (caused by a unimodal resource distribution), the strength of competition, the degree of assortment and the costs for being choosy are independent parameters. We investigate analytically and numerically how these parameters determine the equilibrium and stability structure. In particular, we identify conditions under which no polymorphism at all is maintained as well as conditions under which strong competitive divergence occurs, or the population even splits into two reproductively isolated classes of highly diverse phenotypes. If costs are absent or moderate, genetic variability tends to be minimized at intermediate strengths of assortment, and reproductively isolated classes of phenotypes are a likely result of evolution only for intermediate or strong competition and for very strong assortment. The likelihood of divergence depends relatively weakly on the costs as long as they are not high. With high costs, however, increasingly strong assortment rapidly depletes all genetic variation, and strong competitive divergence is prevented.

BackgroundUnderstanding the origin and spread of mutations associated with drug resistance, especially in the context of combination therapy, will help guide strategies to halt and prevent the emergence of resistance. Unfortunately, studies have assessed these complex processes when resistance is already highly prevalent. Even further, information on the evolutionary dynamics leading to multidrug-resistant parasites is scattered and limited to areas with low or seasonal malaria transmission. This study describes the dynamics of strong selection for mutations conferring resistance against sulphadoxine-pyrimethamine (SP), a combination therapy, in western Kenya between 1992 and 1999, just before SP became first-line therapy (1999). Importantly, the study is based on longitudinal data, which allows for a comprehensive analysis that contrasts with previous cross-sectional studies carried out in other endemic regions.MethodsThis study used 236 blood samples collected between 1992 and 1999 in the Asembo Bay area of Kenya. Pyrosequencing was used to determine the alleles of dihydrofolate reductase (dhfr) and dihydropterote synthase (dhps) genes. Microsatellite alleles spanning 138 kb around dhfr and dhps, as well as, neutral markers spanning approximately 100 kb on chromosomes 2 and 3 were characterized.ResultsBy 1992, the South-Asian dhfr triple mutant was already spreading, albeit in low frequency, in this holoendemic Kenyan population, prior to the use of SP as a first-line therapy. Additionally, dhfr triple mutant alleles that originated independently from the predominant Southeast Asian lineage were present in the sample set. Likewise, dhps double mutants were already present as early as 1992. There is evidence for soft selective sweeps of two dhfr mutant alleles and the possible emergence of a selective sweep of double mutant dhps alleles between 1992 and 1997. The longitudinal structure of the dataset allowed estimation of selection pressures on various dhfr and dhps mutants relative to each other based on a theoretical model tailored to P. falciparum. The data indicate that drug selection acted differently on the resistant alleles of dhfr and dhps, as evidenced by fitness differences. Thus a combination drug therapy such as SP, by itself, does not appear to select for "multidrug"-resistant parasites in areas with high recombination rate.ConclusionsThe complexity of these observations emphasizes the importance of population-based studies to evaluate the effects of strong drug selection on Plasmodium falciparum populations.

We analytically study a deterministic model for the spread of drug resistance among human malaria parasites. The model incorporates all major characteristics of the complex malaria-transmission cycle and accounts for the fact that only a fraction α of infected hosts receive drug treatment. Furthermore, the model incorporates that hosts can be co-infected. The number m of parasites co-infecting a host is either a constant or, more generally, follows a given frequency distribution. Although the model is formulated in a multilocus setup, for our results we assume that drug resistance is caused by a single locus with two alleles - a sensitive one and a resistant one. We assume that the resistant allele has a selective advantage only in treated hosts and pays metabolic costs, which causes this allele to be deleterious in untreated hosts. We provide necessary and sufficient conditions for the fixation of the resistant allele. Moreover, provided the resistant allele will sweep through the population, we derive a formula for the time until it reaches a given frequency and in particular for the time until quasi-fixation. Furthermore, we establish an analytical solution for allele frequency changes at a linked neutral biallelic locus due to the rapid increase in frequency of the resistant allele. Our solution describes a local reduction in heterozygosity among parasite chromosomes around the resistant allele, the effect commonly referred to as the hitchhiking effect, as a function of α and m. The result therefore allows the investigation of selective sweep patterns under specific demographic settings. We find that the hitchhiking effect is similar but different from the standard model of genetic hitchhiking that assumes random mating and homogeneous selection. In particular, the process of recombination and selection cannot be decoupled. We further explain why standard hitchhiking theory cannot be applied to drug resistance in malaria. Furthermore, we will show that a genome-wide reduction in relative heterozygosity can occur provided a fraction of hosts is infected by a single parasite haplotype. Finally, we show how to incorporate host heterogeneity, and generalize our results to this bio logically more realistic case.

Reliable measures of transmission intensities can be incorporated into metrics for monitoring disease-control interventions. Genetic (molecular) measures like multiplicity of infection (MOI) have several advantages compared with traditional measures, e.g., R0. Here, we investigate the properties of a maximum-likelihood approach to estimate MOI and pathogen-lineage frequencies. By verifying regulatory conditions, we prove asymptotical unbiasedness, consistency and efficiency of the estimator. Finite sample properties concerning bias and variance are evaluated over a comprehensive parameter range by a systematic simulation study. Moreover, the estimator’s sensitivity to model violations is studied. The estimator performs well for realistic sample sizes and parameter ranges. In particular, the lineage-frequency estimates are almost unbiased independently of sample size. The MOI estimate’s bias vanishes with increasing sample size, but might be substantial if sample size is too small. The estimator’s variance matrix agrees well with the Cramér-Rao lower bound, even for small sample size. The numerical and analytical results of this study can be used for study design. This is exemplified by a malaria data set from Venezuela. It is shown how the results can be used to determine the necessary sample size to achieve certain performance goals. An implementation of the likelihood method and a simulation algorithm for study design, implemented as an R script, is available as S1 File alongside a documentation (S2 File) and example data (S3 File).