On cytoadhesion of Plasmodium vivax: raison d'être?

It is generally accepted that Plasmodium vivax, the most widely distributed human malaria parasite, causes mild disease and that this species does not sequester in the deep capillaries of internal organs. Recent evidence, however, has demonstrated that there is severe disease, sometimes resulting in death, exclusively associated with P. vivax and that P. vivax-infected reticulocytes are able to cytoadhere in vitro to different endothelial cells and placental cryosections. Here, we review the scarce and preliminary data on cytoadherence in P. vivax, reinforcing the importance of this phenomenon in this species and highlighting the avenues that it opens for our understanding of the pathology of this neglected human malaria parasite.     

Diversity in the circumsporozoite protein of Plasmodium vivax: Does it matter?

Since the gene encoding the malarial circumsporozoite surface protein was characterized a decade ago, the corresponding protein has been considered an important vaccine candidate. Victoria Mann, Michael Good and Allan Saul here discuss molecular variation in the circumsporozoite surface protein of Plasmodium vivax in this context. There is still doubt about the degree and importance of polymorphisms in non-repetitive regions of the molecule. The degree of polymorphisms and data on naturally occurring protective responses suggests there has been minimal immunological pressure; the authors contend that antigenic diversity is unlikely to be a major factor in the use of this antigen as a vaccine for P. vivax.     

Is Plasmodium vivax Malaria a Severe Malaria?: A Systematic Review and Meta-Analysis

Background

Plasmodium vivax is one of the major species of malaria infecting humans. Although emphasis on P. falciparum is appropriate, the burden of vivax malaria should be given due attention. This study aimed to synthesize the evidence on severe malaria in P. vivax infection compared with that in P. falciparum infection.

Methods/Principal Findings

We searched relevant studies in electronic databases. The main outcomes required for inclusion in the review were mortality, severe malaria (SM) and severe anaemia (SA). The methodological quality of the included studies was assessed using the Newcastle-Ottawa Scale. Overall, 26 studies were included. The main meta-analysis was restricted to the high quality studies. Eight studies (n = 27490) compared the incidence of SM between P. vivax infection and P. falciparum mono-infection; a comparable incidence was found in infants (OR: 0.45, 95% CI:0.04–5.68, I ²:98%), under 5 year age group (OR: 2.06, 95% CI: 0.83–5.1, I ²:83%), the 5–15 year-age group (OR: 0.6, 95% CI: 0.31–1.16, I ²:81%) and adults (OR: 0.83, 95% CI: 0.67–1.03, I ²:25%). Six studies reported the incidences of SA in P. vivax infection and P. falciparum mono-infection; a comparable incidence of SA was found among infants (OR: 3.47, 95%:0.64–18.94, I ²: 92%), the 5–15 year-age group (OR:0.71, 95% CI: 0.06–8.57, I ²:82%). This was significantly lower in adults (OR:0.75, 95% CI: 0.62–0.92, I ²:0%). Five studies (n = 71079) compared the mortality rate between vivax malaria and falciparum malaria. A lower rate of mortality was found in infants with vivax malaria (OR:0.61, 95% CI:0.5–0.76, I ²:0%), while this was comparable in the 5–15 year- age group (OR: 0.43, 95% CI:0.06–2.91, I ²:84%) and the children of unspecified-age group (OR: 0.77, 95% CI:0.59–1.01, I ²:0%).

Conclusion

Overall, the present analysis identified that the incidence of SM in patients infected with P. vivax was considerable, indicating that P. vivax is a major cause of SM. Awareness of the clinical manifestations of vivax malaria should prompt early detection. Subsequent treatment and monitoring of complications can be life-saving.     

Plasmodium vivax in Africa: hidden in plain sight?

People who live in tropical Africa, south of the Sahara, are predominantly negative for the Duffy blood-group antigen, which mediates invasion of reticulocytes by Plasmodium vivax. Recent reports of a parasite that was molecularly diagnosed as P. vivax from populations who are suspected, or known, to be Duffy negative confound a large body of evidence that states that invasion of P. vivax requires the Duffy antigen. If confirmed, one of several possible explanations is that P. vivax, which originated in Asia, is now evolving to exploit alternate invasion receptors in Africa.     

Adaptation to environmental stress: a rare or frequent driver of speciation?

Recent results of evolutionary genomics and other research programmes indicate an important role for environment-dependent selection in speciation, but the conceptual frameworks of speciation genetics and environmental stress physiology have not been fully integrated. Only a small number of model systems have been established for cross-disciplinary studies of this type in animals and plants. In these taxa (e.g. Drosophila and Arabidopsis/Arabis), studies of the mechanistic basis of various stress responses are increasingly combined with attempts to understand their evolutionary consequences. Our understanding of the role of environmental stress in speciation would benefit from studies of a larger variety of taxa. We pinpoint areas for future study and predict that in many taxa 'broad' hybrid zones maintained by ecological selection will be valuable venues for addressing the link between environmental stress, adaptation, and speciation.     

Asymptomatic infection with Plasmodium falciparum and Plasmodium vivax in the Brazilian Amazon Basin: to treat or not to treat?

In this study, we determined whether the treatment of asymptomatic parasites carriers (APCs), which are frequently found in the riverside localities of the Brazilian Amazon that are highly endemic for malaria, would decrease the local malaria incidence by decreasing the overall pool of parasites available to infect mosquitoes. In one village, the treatment of the 19 Plasmodium falciparum-infected APCs identified among the 270 residents led to a clear reduction (Z = -2.39, p = 0.017) in the incidence of clinical cases, suggesting that treatment of APCs is useful for controlling falciparum malaria. For vivax malaria, 120 APCs were identified among the 716 residents living in five villages. Comparing the monthly incidence of vivax malaria in two villages where the APCs were treated with the incidence in two villages where APCs were not treated yielded contradictory results and no clear differences in the incidence were observed (Z = -0.09, p = 0.933). Interestingly, a follow-up study showed that the frequency of clinical relapse in both the treated and untreated APCs was similar to the frequency seen in patients treated for primary clinical infections, thus indicating that vivax clinical immunity in the population is not species specific but only strain specific.     

Cytokine Balance in Human Malaria: Does Plasmodium vivax Elicit More Inflammatory Responses than Plasmodium falciparum?

Background

The mechanisms by which humans regulate pro- and anti-inflammatory responses on exposure to different malaria parasites remains unclear. Although Plasmodium vivax usually causes a relatively benign disease, this parasite has been suggested to elicit more host inflammation per parasitized red blood cell than P. falciparum.

Methodology/Principal Findings

We measured plasma concentrations of seven cytokines and two soluble tumor necrosis factor (TNF)-α receptors, and evaluated clinical and laboratory outcomes, in Brazilians with acute uncomplicated infections with P. vivax (n = 85), P. falciparum (n = 30), or both species (n = 12), and in 45 asymptomatic carriers of low-density P. vivax infection. Symptomatic vivax malaria patients, compared to those infected with P. falciparum or both species, had more intense paroxysms, but they had no clear association with a pro-inflammatory imbalance. To the contrary, these patients had higher levels of the regulatory cytokine interleukin (IL)-10, which correlated positively with parasite density, and elevated IL-10/TNF-α, IL-10/interferon (IFN)-γ, IL-10/IL-6 and sTNFRII/TNF-α ratios, compared to falciparum or mixed-species malaria patient groups. Vivax malaria patients had the highest levels of circulating soluble TNF-α receptor sTNFRII. Levels of regulatory cytokines returned to normal values 28 days after P. vivax clearance following chemotherapy. Finally, asymptomatic carriers of low P. vivax parasitemias had substantially lower levels of both inflammatory and regulatory cytokines than did patients with clinical malaria due to either species.

Conclusions

Controlling fast-multiplying P. falciparum blood stages requires a strong inflammatory response to prevent fulminant infections, while reducing inflammation-related tissue damage with early regulatory cytokine responses may be a more cost-effective strategy in infections with the less virulent P. vivax parasite. The early induction of regulatory cytokines may be a critical mechanism protecting vivax malaria patients from severe clinical complications.     

Line Orientation Adaptation: Local or Global?

Prolonged exposure to an oriented line shifts the perceived orientation of a subsequently observed line in the opposite direction, a phenomenon known as the tilt aftereffect (TAE). Here we consider whether the TAE for line stimuli is mediated by a mechanism that integrates the local parts of the line into a single global entity prior to the site of adaptation, or the result of the sum of local TAEs acting separately on the parts of the line. To test between these two alternatives we used the fact the TAE transfers almost completely across luminance contrast polarity [1]. We measured the TAE using adaptor and test lines that (1) either alternated in luminance polarity or were of a single polarity, and (2) either alternated in local orientation or were of a single orientation. We reasoned that if the TAE was agnostic to luminance polarity and was parts-based, we should obtain large TAEs using alternating-polarity adaptors with single-polarity tests. However we found that (i) TAEs using one-alternating-polarity adaptors with all-white tests were relatively small, increased slightly for two-alternating-polarity adaptors, and were largest with all-white or all-black adaptors. (ii) however TAEs were relatively large when the test was one-alternating polarity, irrespective of the adaptor type. (iii) The results with orientation closely mirrored those obtained with polarity with the difference that the TAE transfer across orthogonal orientations was weak. Taken together, our results demonstrate that the TAE for lines is mediated by a global shape mechanism that integrates the parts of lines into whole prior to the site of orientation adaptation. The asymmetry in the magnitude of TAE depending on whether the alternating-polarity lines was the adaptor or test can be explained by an imbalance in the population of neurons sensitive to 1^st-and 2^nd-order lines, with the 2^nd-order lines being encoded by a subset of the mechanisms sensitive to 1^st-order lines.     

Modelling the Incidence of Plasmodium vivax and Plasmodium falciparum Malaria in Afghanistan 2006–2009

Background

Identifying areas that support high malaria risks and where populations lack access to health care is central to reducing the burden in Afghanistan. This study investigated the incidence of Plasmodium vivax and Plasmodium falciparum using routine data to help focus malaria interventions.

Methods

To estimate incidence, the study modelled utilisation of the public health sector using fever treatment data from the 2012 national Malaria Indicator Survey. A probabilistic measure of attendance was applied to population density metrics to define the proportion of the population within catchment of a public health facility. Malaria data were used in a Bayesian spatio-temporal conditional-autoregressive model with ecological or environmental covariates, to examine the spatial and temporal variation of incidence.

Findings

From the analysis of healthcare utilisation, over 80% of the population was within 2 hours’ travel of the nearest public health facility, while 64.4% were within 30 minutes’ travel. The mean incidence of P. vivax in 2009 was 5.4 (95% Crl 3.2–9.2) cases per 1000 population compared to 1.2 (95% Crl 0.4–2.9) cases per 1000 population for P. falciparum. P. vivax peaked in August while P. falciparum peaked in November. 32% of the estimated 30.5 million people lived in regions where annual incidence was at least 1 case per 1,000 population of P. vivax; 23.7% of the population lived in areas where annual P. falciparum case incidence was at least 1 per 1000.

Conclusion

This study showed how routine data can be combined with household survey data to model malaria incidence. The incidence of both P. vivax and P. falciparum in Afghanistan remain low but the co-distribution of both parasites and the lag in their peak season provides challenges to malaria control in Afghanistan. Future improved case definition to determine levels of imported risks may be useful for the elimination ambitions in Afghanistan.     

Parallel Adaptation: One or Many Waves of Advance of an Advantageous Allele?

Models for detecting the effect of adaptation on population genomic diversity are often predicated on a single newly arisen mutation sweeping rapidly to fixation. However, a population can also adapt to a new environment by multiple mutations of similar phenotypic effect that arise in parallel, at the same locus or different loci. These mutations can each quickly reach intermediate frequency, preventing any single one from rapidly sweeping to fixation globally, leading to a “soft” sweep in the population. Here we study various models of parallel mutation in a continuous, geographically spread population adapting to a global selection pressure. The slow geographic spread of a selected allele due to limited dispersal can allow other selected alleles to arise and start to spread elsewhere in the species range. When these different selected alleles meet, their spread can slow dramatically and so initially form a geographic patchwork, a random tessellation, which could be mistaken for a signal of local adaptation. This spatial tessellation will dissipate over time due to mixing by migration, leaving a set of partial sweeps within the global population. We show that the spatial tessellation initially formed by mutational types is closely connected to Poisson process models of crystallization, which we extend. We find that the probability of parallel mutation and the spatial scale on which parallel mutation occurs are captured by a single compound parameter, a characteristic length, which reflects the expected distance a spreading allele travels before it encounters a different spreading allele. This characteristic length depends on the mutation rate, the dispersal parameter, the effective local density of individuals, and to a much lesser extent the strength of selection. While our knowledge of these parameters is poor, we argue that even in widely dispersing species, such parallel geographic sweeps may be surprisingly common. Thus, we predict that as more data become available, many more examples of intraspecies parallel adaptation will be uncovered.THERE are many dramatic examples of convergent evolution across distantly related species, where a phenotype independently evolves via parallel changes at orthologous genetic loci (Wood et al. 2005b; Arendt and Reznick 2008), indicating that adaptation can be strongly shaped by pleiotropic constraints (Haldane 1932; Orr 2005; Stern and Orgogozo 2008; Kopp 2009). There are also a growing number of examples of the parallel evolution of a phenotype within a species due to independent mutations at the same gene (Arendt and Reznick 2008) (which are sometimes referred to as genetically redundant). Some of the best-studied examples come from the repeated evolution of resistance to insecticides within several insect species (Ffrench Constant et al. 2000) and the resistance of malaria to antimalarial drugs (Anderson and Roper 2005; Pearce et al. 2009). Another example is the loss of pigmentation in Drosophlia santomea through at least three independent mutations at a cis-regulatory element (Jeong et al. 2008), while the evolution of pigmentation within vertebrate species provides further examples (Protas et al. 2006; Gross et al. 2009; Kingsley et al. 2009). There are also a number of examples of parallel evolution within our own species (Novembre and Di Rienzo 2009). For example, various G6PD mutations have spread in parallel in response to malaria (Tishkoff et al. 2001; Louicharoen et al. 2009), and lactase persistence has evolved independently in at least three different pastoral populations (Tishkoff et al. 2007; Enattah et al. 2008). A particularly impressive example in humans is offered by the sickle cell allele at the β-globin gene that confers malaria resistance, where multiple changes have putatively occurred at a single base pair (see Flint et al. 1998, for discussion). In each of these examples, multiple, independent mutations have led to the same or a functionally equivalent adaptive phenotype, although they differ in the degree to which the functional consequences and equivalences of the different mutations have been explored. Such repeated adaptive evolution via similar changes within a species, which we term parallel adaptation, may therefore be common. As we also address repeated evolution of a similar phenotype via changes at different genetic loci, this could more broadly be termed “convergent adaptation” (Arendt and Reznick 2008).In many of these examples the selection pressure is patchy and rates of gene flow are low, increasing the chance of parallel adaptation. However, parallel adaptation can occur even in a panmictic population. For example, adaptation may occur from multiple independent copies of the selected allele present in standing variation at mutation–selection balance within the population (Orr and Betancourt 2001; Hermisson and Pennings 2005). Even when there is no standing variation for a trait in a panmictic population, a selected allele could arise independently several times during the course of a selective sweep, if mutation is sufficiently fast relative to the spread of the selected allele. This idea was formalized by Pennings and Hermisson (2006a,b), who showed that such soft sweeps may be expected when the population scaled mutation rate (the product of the effective population size and mutation rate) toward the adaptive allele is >1. Thus, repeated mutation may be quite common for species with large populations or where the mutation target is large, e.g., knocking out of a gene. Pennings and Hermisson (2006a) showed that the number of independently arisen selected alleles in a sample has approximately a Ewens distribution, and properties of neutral variation at a closely linked site can be derived from this (Pennings and Hermisson 2006b). Such a selective sweep has been termed a soft sweep, as the population can adapt without the dramatic reduction in diversity at linked selected sites that is usually associated with a full sweep (Maynard Smith and Haigh 1974); see Pennings and Hermisson (2006a,b), Hermisson and Pfaffelhuber (2008), and Pritchard et al. (2010) for discussion and Schlenke and Begun (2005) or Jeong et al. (2008) for potential examples.Clearly, if parallel mutations can occur during adaptation in a large panmictic population, then limited dispersal should further increase the chance of parallel adaptation, as other mutations can arise and spread during the time it takes one to move across the species range. Intuitively, a low rate of dispersal and a large mutational target should increase the chance of parallel adaptation (as in Coop et al. 2009; Novembre and Di Rienzo 2009), but it is unclear exactly how other dispersal, population, and mutational parameters play into the probability of parallel adaptation. However, in the absence of a formal model, many simple questions remain: Does parallel adaptation occur only in species with strong population structure? Weak selection pressures lead to slowly spreading mutations. Is parallel adaptation more likely in this case? This leaves us unable to understand the likelihood of parallel adaptation in particular examples (such as Flint et al. 1998) and more generally its role in geographic patterns of adaptation (such as Coop et al. 2009).Here we study parallel adaptation in a homogeneous, geographically spread population. We focus on the case where a population is exposed to a novel selection regime throughout a homogeneous species range, and the population is initially entirely devoid of standing variation for the trait, assumptions that favor the fixation of only a single new allele in the population. We use simple approximations to derive theoretical results for the properties of parallel adaptation in a continuous spatial population with strong migration for a range of dispersal distributions (also called dispersal kernels, including fat-tailed examples). We are able to describe fairly completely the resulting patterns and show that they are well captured by a single compound parameter combining the rate of mutation and the speed at which the mutation spreads. For an introduction to the patterns of genetic diversity that can be expected from such geographic structure at both neutral and selected loci, see Lenormand (2002), Charlesworth et al. (2003), and Novembre and Di Rienzo (2009).We show that when population sizes are sufficiently large and dispersal distances are small compared to the species range, parallel adaptation within a species is likely to be common, and quantify this relationship. Furthermore, we describe how separately arisen mutations will—at least for some time—leave behind a spatial pattern reflecting their separate origins.The structure of this article is as follows: In methods we introduce and analyze our model of a continuous population, first in the classical context and then in a more general context that allows for accelerating waves (arising from fat-tailed dispersal distributions). In Simulations we present the results of some simulations of the continuous process, intended to assess the robustness of our results to deviations from the assumptions. In Biological parameters and the characteristic length and Applications we present and discuss the theoretical results in a few biologically reasonable contexts, providing numerical results to illustrate how the different parameters play into the probability of parallel adaptation. In the discussion we discuss consequences and extensions. Some mathematical arguments are postponed until the appendixes.

Modeling assumptions:

Here we describe the assumptions behind our model and give some background, before introducing in methods the model we analyze. First, we assume each mutation under consideration confers a selective advantage such that, upon appearing in the population, it quickly rises locally to some equilibrium frequency. Second, there is significant spatial structure; namely, migration is weak enough that the selected trait reaches an equilibrium frequency locally before spreading to the entire population. Third, the parallel mutations are distinguishable and confer the same selective benefit. Fourth, these mutations are neutral relative to each other, in the sense that in a population at equilibrium frequency (e.g., fixation) for any collection of these mutations, the dynamics of their relative proportions occur on a longer timescale than their dynamics in the original background (examples are given below). We call this last assumption allelic exclusion, since it implies that areas fixed for one adaptive allele will not be rapidly overtaken by another.Under these assumptions, a newly arisen advantageous mutation, if it is initially successful, will spread through the population in a more-or-less wavelike manner (more on this later). If another allele conferring the same advantage arises in a location the first has not yet reached, then the two waves spread toward each other and will at some point collide. What happens when they collide will generally depend on the details of their epistatic interaction or, if they occur at a single site, on their dominance interaction. However, by our assumption of allelic exclusion, the dynamics are slower than the spread of the selected alleles. This allows us to neglect the slower mixing of types and genetic drift that will happen in this phase, instead focusing on the first process by which independently arisen alleles partition the population.In Figure 1 we show a cartoon to illustrate our model, and in Figures 5 and ​and66 we show the results of a simulation (described in Simulations).Open in a separate windowFigure 1.—A cartoon representation of our model of spatial parallel mutation. In the top row, each panel represents a two-dimensional (2D) species range with time increasing from the left to the right panel. In the bottom row, a 1D species range is represented by the vertical axis and time is the horizontal axis, with more recent times closer to the right side of the page. Stars represent a new mutation arising and escaping drift. The three colors represent the area occupied by three different alleles. Note that I and II are not different views of the same process, although they are similar.Open in a separate windowFigure 5.—A space–time plot of a single run of a simulation on a linear array of 500 demes each of size 100 over 20,000 generations. The parameters were s = 0.1, m = 0.01, and μ = 4 × 10⁻⁶, and migration was nearest neighbor. Time runs down the plot; different colors label different types, and areas occupied by more than one type are colored by a mixture of the colors (local drift is strong in this simulation, so most demes have only one type). Each distinct “cone” has a unique type despite similarities in color choice. Note that types expand at roughly constant speed until encountering another type, and that mixing, while present, happens on a longer timescale. Types that appear where the advantageous type is already fixed (e.g., the orange bit between the purple and blue regions on the left) are unlikely to survive, even if they locally escape drift.Open in a separate windowFigure 6.—Six time slices of an example simulation in a two-dimensional range, showing initial establishment and expansion of types and the beginning of mixing (which happens much slower than expansion). The population was composed of a 60 × 60 grid of demes with 1000 individuals in each. Different colors correspond to different types, and white is the ancestral type; when more than one color occupies a deme, the colors are mixed, so that eventually, if all colors spread to all demes, the entire population will be gray.

Allelic exclusion:

The allelic exclusion assumption is fundamental to our approach. It will hold, for instance, if there is a single advantageous mutation, and we treat each time it arises independently as a distinct allele, identifiable by examination of linked neutral variation. It will also hold if mutations at multiple sites within a gene are genetically redundant, such as loss-of-function mutations, and no additional selective benefit is conferred by having a mutation at more than one site (though this may be an approximation, since even loss-of-function changes within the same gene may differ in their characteristics, as in Rosenblum et al. 2010).Another important consequence of allelic exclusion is that a mutation occurring in a location where the advantageous allele already exists in large numbers is unlikely to persist or achieve high frequency—indeed, if the interaction is neutral and 999 other individuals already exist in the same location with the selected trait, then a new mutation will contribute on average only 0.001 of the future population and has high probability of being lost from the population by drift. This fact allows us to ignore all new mutations that occur after any selected allele has risen in that location to a nonzero frequency. In particular, the shape of the wave front will not be important, only how its leading edge spreads. Below, for convenience we often talk about the probability or rate of local fixation, but it follows from this observation that we need require only that the allele escapes loss from the population by drift and that some intermediate equilibrium frequency is reached, as would occur in the case of overdominance.

Selection:

We also assume that the advantageous, derived alleles have a reproductive advantage of (1 + s) relative to the ancestral type. In practice, in a diploid model with dominance or epistasis, or in the presence of density dependence, we require that both the manner in which a new mutation escapes drift and the way that it subsequently spreads through the population be well approximated by the simple haploid (or additive) model. Roughly speaking, this holds if the growth and spread of the allele are driven by growth where the allele is at very low frequency (and primarily occurring in heterozygotes). This implies that the probability a new mutation escapes drift is well approximated by 2s divided by the variance in offspring number [which is quite robust to the details of spatial structure (Maruyama 1970, 1974)] and that per-capita growth is fastest when at low frequency. In the usual formulation of diploid systems (Aronson and Weinberger 1978), this is satisfied if the fitness advantage of the homozygote is no more than twice the fitness advantage of the heterozygote. In other cases, e.g., an Allee effect, the behavior can be quite different; see Stokes (1976).

Background on the wave of advance:

We model the spread of a selected allele by making use of existing work on traveling waves, a link first established independently by Fisher (1937) and by Kolmogorov, Petrovskii, and Piscunov (KPP) (Kolmogorov et al. 1937). We introduce and review the wave of advance literature here, as much of the subsequent development has occurred in fields other than population genetics. Suppose that individuals produce a random number of offspring with mean r and that offspring disperse a random distance with standard deviation σ, and let p(t, x) be the expected proportion of mutants at time t and location x. Suppose also that the selection coefficient s is small and the advantage is additive and that the population density ρ is fairly large. Both articles argued that if the dispersal distance is Gaussian, or if σ is small (so that the “long-time” dispersal distribution is Gaussian), then barring the appearance of new mutations, the time evolution of p is well described by the reaction–diffusion equation now known as the Fisher–KPP equation,(1)where d is the dimension of the species range. They furthermore showed in d = 1 that a “wave of advance” occurs as the solution to this equation and that for initial conditions where the allele is only polymorphic within a spatially bounded region, the solution moved asymptotically with speed . Kolmogorov et al. (1937) also covered the more general case in which p(x, t)(1 − p(x, t)) is replaced by F(p(x, t)) for an appropriate function F, which gives the density-dependent growth rate of the selected type, subject to certain conditions.For many other choices of dispersal distribution and growth function F the advancing front of a new type also approaches a constant wave shape that advances at constant speed through time—a “traveling wave” solution, but with a speed not given by the same formula. Then the frequency of individuals of the selected type at x  at time t  can be expressed p(x, t) = h(x − νt), where h(·) gives the shape of the wave and ν is its speed. These traveling wave solutions have been studied for the Fisher–KPP equation for a range of appropriate F (Aronson and Weinberger 1975); the speed can often be found more easily than the wave shape (Hadeler and Rothe 1975). Radially symmetric solutions also exist, in which the new type travels outward from an initial origin; the behavior of such radially spreading waves depends on initial conditions, but will asymptotically move with the same constant speed and fixed wave shape as in one dimension.Since the introduction of the Fisher–KPP equation, traveling wave solutions to reaction–diffusion equations have been studied in the ecological literature as a model of invading species (Skellam 1951; Kot et al. 1996), as well as in a range of other fields. See Aronson and Weinberger (1978) for some classical theory, general discussion, and context or Volpert et al. (1994) for a more extensive reference. Related models, using integrodifference or integrodifferential equations have been used by various authors to include various important biological factors such as age structure and fluctuating environments (Neubert and Caswell 2000; Neubert et al. 2000; Kot and Neubert 2008); see Hastings et al. (2005) or Zhao (2009) for a review. Density regulation is often discussed in these models, but important behaviors can usually be determined by a linearization, on the basis of how the new type grows when rare. Common to these models is the existence of traveling wave solutions, whose forms and speeds are often known only implicitly; most natural models of the spread of a new selected type can be translated into one of these frameworks. There is also a fruitful connection of these Fisher–KPP models to branching random walks that is beyond the scope of this article; see McKean (1975), Biggins (1979, 1995), and Kot et al. (2004). A similar model, the contact process, has also been widely studied in the probabilistic literature; see Bramson et al. (1989).The qualitative behavior of the spread of an organism or an allele in a population can depend on the organism''s dispersal kernel, defined as the probability density of the distance between mother and child''s birth locations (see Shigesada and Kawasaki 1997 or Cousens et al. 2008 for discussion). Most mathematical models of invasions assume that the dispersal kernel has tails bounded by an exponential and obtain a constant wave speed. In some species this is appropriate, while in others, rare, long-distance migration events are important (Shigesada and Kawasaki 1997). In such organisms, dispersal may be better modeled by a kernel that is not bounded by an exponential (i.e., a “fat-tailed” kernel), although there is generally insufficient evidence so far (Cousens et al. 2008, Chap. 5). Mollison (1972) showed that in a certain model, if the kernel is fat tailed, the range occupied by the expanding type will be patchy and will grow faster than linearly: the spread accelerates and eventually moves faster than any constant-speed traveling wave. Moreover, Lewis and Pacala (2000) established a link between leptokurtic kernels (kernels whose kurtosis exceeds that of the standard Gaussian) and patchy invasion dynamics. Leptokurtic but exponentially bounded kernels can lead to waves that initially accelerate but settle to a constant speed. We shall see that the important behavior of the model is not determined by the asymptotic, long-time speed of the wave, but rather by its behavior at intermediate times. Therefore, kernels that have similar short-time behavior but different long-time behavior can give rise to similar dynamics on the scale we are interested in. Consideration of other wave behaviors leads to a more general model, which we study in The general case.The models reviewed above are haploid models; traveling waves in diploid models have been much less studied. Aronson and Weinberger (1975) show that in the diploid analog to Equation 1, if the difference in selection coefficient is small, then allele frequency dynamics are approximately governed by (1). If local populations are in Hardy–Weinberg equilibrium, then more general results apply, demonstrating the existence of traveling waves (Weinberger 1982; Zhao 2009). If dispersal occurs over a distance comparable to the width of the wave, then this will no longer be the case, and while recently developed general theory (Zhao 2009) might be applied, the existence and characterization of traveling waves in other diploid models is to our knowledge an open question. However, we certainly expect the behavior to be wavelike, and since our theory takes wave behavior as an input, we have no qualms about using our model to discuss the diploid organisms in Biological parameters and the characteristic length.     

Contemporaneous and successive mixed Plasmodium falciparum and Plasmodium vivax infections are associated with Ascaris lumbricoides: an immunomodulating effect?

Following an investigation suggesting a protective role for Ascaris against cerebral malaria, possibly through immunomodulation, we examined whether Ascaris had any impact on mixed Plasmodium falciparum and Plasmodium vivax infections. We studied a cross section of 928 patient files between 1991 and 1999. Forty patients had contemporaneous mixed infections and 40 patients had P. falciparum infections, followed by P. vivax infections. There was a significant association between Ascaris infection and risk of having both contemporaneous or successive mixed P. falciparum and P. vivax infections (adjusted odds ratios respectively 6 [2-18] P = 0.001 and 3.6 [1.2-11.1] P = 0.02). There was a positive linear trend between the burden of Ascaris and the risk of mixed infections P < 0.0001. These results suggested the possibility that pre-existing Ascaris infection may increase tolerance of the host to different Plasmodium spp., thus facilitating their coexistence.