The influence of host demography, pathogen virulence, and relationships with pathogen virulence on the evolution of pathogen transmission in a spatial context

A major challenge in evolutionary ecology is to explain extensive natural variation in transmission rates and virulence across pathogens. Host and pathogen ecology is a potentially important source of that variation. Theory of its effects has been developed through the study of non-spatial models, but host population spatial structure has been shown to influence evolutionary outcomes. To date, the effects of basic host and pathogen demography on pathogen evolution have not been thoroughly explored in a spatial context. Here we use simulations to show that space produces novel predictions of the influence of the shape of the pathogen’s transmission–virulence tradeoff, as well as host reproduction and mortality, on the pathogen’s evolutionary stable transmission rate. Importantly, non-spatial models predict that neither the slope of linear transmission–virulence relationships, nor the host reproduction rate will influence pathogen evolution, and that host mortality will only influence it when there is a transmission–virulence tradeoff. We show that this is not the case in a spatial context, and identify the ecological conditions under which spatial effects are most influential. Thus, these results may help explain observed natural variation among pathogens unexplainable by non-spatial models, and provide guidance about when space should be considered. We additionally evaluate the ability of existing analytical approaches to predict the influence of ecology, namely spatial moment equations closed with an improved pair approximation (IPA). The IPA is known to have limited accuracy, but here we show that in the context of pathogens the limitations are substantial: in many cases, IPA incorrectly predicts evolution to pathogen-driven extinction. Despite these limitations, we suggest that the impact of ecology can still be understood within the conceptual framework arising from spatial moment equations, that of “self-shading’’, whereby the spread of highly transmissible pathogens is impeded by local depletion of susceptible hosts.     

Crayfish population size under different routes of pathogen transmission

We present an epidemiological model for the crayfish plague, a disease caused by an invasive oomycete Aphanomyces astaci, and its general susceptible freshwater crayfish host. The pathogen shows high virulence with resulting high mortality rates in freshwater crayfishes native to Europe, Asia, Australia, and South America. The crayfish plague occurrence shows complicated dynamics due to the several types of possible infection routes, which include cannibalism and necrophagy. We explore this complexity by addressing the roles of host cannibalism and the multiple routes of transmission through (1) environment, (2) contact, (3) cannibalism, and (4) scavenging of infected carcasses. We describe a compartment model having six classes of crayfish and a pool of crayfish plague spores from a single nonevolving strain. We show that environmental transmission is the decisive factor in the development of epidemics. Compared with a pathogen-free crayfish population, the presence of the pathogen with a low environmental transmission rate, regardless of the contact transmission rate, decreases the crayfish population size with a low risk of extinction. Conversely, a high transmission rate could drive both the crayfish and pathogen populations to extinction. High contact transmission rate with a low but nonzero environmental transmission rate can have mixed outcomes from extinction to large healthy population, depending on the initial values. Scavenging and cannibalism have a relevant role only when the environmental transmission rate is low, but scavenging can destabilize the system by transmitting the pathogen from a dead to a susceptible host. To the contrary, cannibalism stabilizes the dynamics by decreasing the proportion of infected population. Our model provides a simple tool for further analysis of complex host parasite dynamics and for the general understanding of crayfish disease dynamics in the wild.     

The evolution of parasite virulence and transmission rate in a spatially structured population

If the transmission occurs through local contact of the individuals in a spatially structured population, the evolutionarily stable (ESS) traits of parasite might be quite different from what the classical theory with complete mixing predicts. In this paper, we theoretically study the ESS virulence and transmission rate of a parasite in a lattice-structured host population, in which the host can send progeny only to its neighboring vacant site, and the transmission occurs only in between the infected and the susceptible in the nearest-neighbor sites. Infected host is assumed to be infertile. The analysis based on the pair approximation and the Monte Carlo simulation reveal that the ESS transmission rate and virulence in a lattice-structured population are greatly reduced from those in completely mixing population. Unlike completely mixing populations, the spread of parasite can drive the host to extinction, because the local density of the susceptible next to the infected can remain high even when the global density of host becomes very low. This demographic viscosity and group selection between self-organized spatial clusters of host individuals then leads to an intermediate ESS transmission rate even if there is no tradeoff between transmission rate and virulence. The ESS transmission rate is below the region of parasite-driven extinction by a finite amount for moderately large reproductive rate of host; whereas, the evolution of transmission rate leads to the fade out of parasite for small reproductive rate, and the extinction of host for very large reproductive rate.     

Species coexistence and pathogens with frequency-dependent transmission

Pathogens that infect multiple hosts are commonly transmitted by vectors, and their transmission rate is often thought to depend on the proportion of hosts or vectors infected (i.e., frequency dependence). A model of a two-host, one-pathogen system with frequency-dependent transmission is used to investigate how sharing a pathogen with an alternative host influences pathogen-mediated extinction. The results show that if there is frequency-dependent transmission, a host can be rescued from pathogen-mediated extinction by the presence of a second host with which it shares a pathogen. The study provides an important conceptual counterexample to the idea that shared pathogens necessarily result in apparent competition by showing that shared pathogens can mediate apparent mutualism. We distinguish two types of dilution effect (pathogen reduction with increasing host diversity), each resulting from different underlying pathogen transmission processes and host density effects. These results have important consequences for understanding the role of pathogens in species interactions and in maintaining host species diversity.     

Resistance,tolerance and environmental transmission dynamics determine host extinction risk in a load‐dependent amphibian disease

While disease‐induced extinction is generally considered rare, a number of recently emerging infectious diseases with load‐dependent pathology have led to extinction in wildlife populations. Transmission is a critical factor affecting disease‐induced extinction, but the relative importance of transmission compared to load‐dependent host resistance and tolerance is currently unknown. Using a combination of models and experiments on an amphibian species suffering extirpations from the fungal pathogen Batrachochytrium dendrobatidis (Bd), we show that while transmission from an environmental Bd reservoir increased the ability of Bd to invade an amphibian population and the extinction risk of that population, Bd‐induced extinction dynamics were far more sensitive to host resistance and tolerance than to Bd transmission. We demonstrate that this is a general result for load‐dependent pathogens, where non‐linear resistance and tolerance functions can interact such that small changes in these functions lead to drastic changes in extinction dynamics.     

A stochastic model for transmission,extinction and outbreak of Escherichia coli O157:H7 in cattle as affected by ambient temperature and cleaning practices

Many infectious agents transmitting through a contaminated environment are able to persist in the environment depending on the temperature and sanitation determined rates of their replication and clearance, respectively. There is a need to elucidate the effect of these factors on the infection transmission dynamics in terms of infection outbreaks and extinction while accounting for the random nature of the process. Also, it is important to distinguish between the true and apparent extinction, where the former means pathogen extinction in both the host and the environment while the latter means extinction only in the host population. This study proposes a stochastic-differential equation model as an approximation to a Markov jump process model, using Escherichia coli O157:H7 in cattle as a model system. In the model, the host population infection dynamics are described using the standard susceptible-infected-susceptible framework, and the E. coli O157:H7 population in the environment is represented by an additional variable. The backward Kolmogorov equations that determine the probability distribution and the expectation of the first passage time are provided in a general setting. The outbreak and apparent extinction of infection are investigated by numerically solving the Kolmogorov equations for the probability density function of the associated process and the expectation of the associated stopping time. The results provide insight into E. coli O157:H7 transmission and apparent extinction, and suggest ways for controlling the spread of infection in a cattle herd. Specifically, this study highlights the importance of ambient temperature and sanitation, especially during summer.     

Competition and evolutionary stability of plants in a spatially structured habitat

We modelled the population dynamics of two types of plants with limited dispersal living in a lattice structured habitat. Each site of the square lattice model was either occupied by an individual or vacant. Each individual reproduced to its neighbors. We derived a criterion for the invasion of a rare type into a population composed of a resident type based on a pair-approximation method, in which the dynamics of both average densities and the nearest neighbor correlations were considered. Based on this invasibility criterion, we showed that, when there is a tradeoff between birth and death rates, the evolutionarily stable type is the one that has the highest ratio of birth rate to mortality. If these types are different species, they form segregated spatial patterns in the lattice model in which intraspecific competitive interactions occur more frequently than interspecific interactions. However, stable coexistence is not possible in the lattice model contrary to results from completely mixed population models. This clearly shows that the casual conclusion, based on traditional well mixed population models, that different species can coexist if intraspecific competition is stronger than interspecific competition, does not hold for spatially structured population models.     

Fatal or Harmless: Extreme Bistability Induced by Sterilizing,Sexually Transmitted Pathogens

Models of sexually transmitted infections have become a fixture of mathematical epidemiology. A common attribute of all these models is treating reproduction and mating, and hence pathogen transmission, as uncoupled events. This is fine for humans, for example, where only a tiny fraction of sexual intercourses ends up with having a baby. But it can be a deficiency for animals in which mating and giving birth are tightly coupled, and mating thus mediates both reproduction and pathogen transmission. Here, we model dynamics of sterilizing, sexually transmitted infections in such animals, assuming structural consistency between the processes of reproduction and pathogen transmission. We show that highly sterilizing, sexually transmitted pathogens trigger bistability in the host population. In particular, the host population can end up in two extreme alternative states, disease-free persistence and pathogen-driven extinction, depending on its initial state. Given that sterilizing, sexually transmitted infections that affect animals are abundant, our results might implicate an effective pest control tactic that consists of releasing the corresponding pathogens, possibly after genetically enhancing their sterilization power.     

Imperfect vaccines and the evolution of pathogens causing acute infections in vertebrates

A study by Gandon et al. (2001) considered the potential ways pathogens may evolve in response to vaccination with imperfect vaccines. In this paper, by focusing on acute infections of vertebrate hosts, we examine whether imperfect vaccines that do not completely block a pathogen's replication (antigrowth) or transmission (antitransmission) may lead to evolution of more or less virulent pathogen strains. To address this question, we use models of the within-host dynamics of the pathogen and the host's immune responses. One advantage of the use of this within-host approach is that vaccination can be easily incorporated in the models and the trade-offs between pathogen transmissibility, host recovery, and virulence that drive evolution of pathogens in these models can be easily estimated. We find that the use of either antigrowth or antitransmission vaccines leads to the evolution of pathogens with an increased within-host growth rate; infection of unvaccinated hosts with such evolved pathogens results in high host mortality and low pathogen transmission. Vaccination of only a fraction of hosts with antigrowth vaccines may prevent pathogens from evolving high virulence due to pathogen adaptation to unvaccinated hosts and thus protection of vaccinated hosts from pathogen-induced disease. In contrast, antitransmission vaccines may be beneficial only if they are effective enough to cause pathogen extinction. Our results suggest that particular mechanisms of action of vaccines and their efficacy are crucial in predicting longterm evolutionary consequences of the use of imperfect vaccines.     

Harvesting can increase severity of wildlife disease epidemics

Theoretical studies of wildlife population dynamics have proved insightful for sustainable management, where the principal aim is to maximize short-term yield, without risking population extinction. Surprisingly, infectious diseases have not been accounted for in harvest models, which is a major oversight because the consequences of parasites for host population dynamics are well-established. Here, we present a simple general model for a host species subject to density dependent reproduction and seasonal demography. We assume this host species is subject to infection by a strongly immunizing, directly transmitted pathogen. In this context, we show that the interaction between density dependent effects and harvesting can substantially increase both disease prevalence and the absolute number of infectious individuals. This effect clearly increases the risk of cross-species disease transmission into domestic and livestock populations. In addition, if the disease is associated with a risk of mortality, then the synergistic interaction between hunting and disease-induced death can increase the probability of host population extinction.     

Too much of a good thing: resource provisioning alters infectious disease dynamics in wildlife

Provisioning of abundant food resources in human-altered landscapes can have profound effects on wildlife ecology, with important implications for pathogen transmission. While empirical studies have quantified the effects of provisioning on host behaviour and immunology, the net interactive effect of these components on host–pathogen dynamics is unknown. We use simple compartmental models to investigate how provisioning-induced changes to host demography, contact behaviour and immune defence influence pathogen invasion and persistence. We show that pathogen invasion success and equilibrium prevalence depend critically on how provisioning affects host immune defence and that moderate levels of provisioning can lead to drastically different outcomes of pathogen extinction or maximizing prevalence. These results highlight the need for further empirical studies to fully understand how provisioning affects pathogen transmission in urbanized environments.     

Modelling Fungal (Neozygites cf. Floridana) Epizootics in Local Populations of Cassava Green Mites (Mononychellus Tanajoa)

The fungus, Neozygitis cf. floridana is parasitic on the cassava green mite, Mononychellus tanajoa (Bondar) (Acari: Tetranychidae) in South America and may be considered for classical biological control of cassava green mites in Africa, where cassava is an important subsistence crop, cassava green mites are an imported pest and specific natural enemies are lacking. Spider mites generally have a viscous structure of local populations, a trait that would normally hamper the spread of a fungus that is transmitted by the contact of susceptible hosts with the halo of capilliconidia surrounding an infectious host. However, if infected mites search and settle to produce capilliconidia on sites where they are surrounded by susceptible mites before becoming infectious, then the conditions for maximal transmission in a viscous host population are met. Because the ratio between spider mites and the leaf area they occupy is constant, parasite-induced host searching behaviour leads to a constant per capita transmission rate. Hence, the transmission rate only depends on the number of infectious hosts. These assumptions on parasite-induced host search and constant host density lead to a simple, analytically tractable model that can be used to estimate the maximal capacity of the fungus to decimate local populations of the cassava green mite. By estimating the parameters of this model (host density, per capita transmission rate and duration of infected and infectious state) it was shown that the fungal pathogen can reduce the population growth of M. tanajoa, but cannot drive local mite populations to extinction. Only when the initial ratio of infectious to susceptible mites exceeds unity or the effective growth rate of the mite population is sufficiently reduced by other factors than the fungus (e.g. lower food quality of the host plant, dislodgement and death by rain and wind and predation), will the fungal pathogen be capable of decimating the cassava green mite population. Under realistic field conditions, where all of these growth-reducing factors are likely to operate, there may well be room for effective control by the parasitic fungus. This revised version was published online in November 2006 with corrections to the Cover Date.     

Effects of host heterogeneity on pathogen diversity and evolution

Phenotypic variation is common in most pathogens, yet the mechanisms that maintain this diversity are still poorly understood. We asked whether continuous host variation in susceptibility helps maintain phenotypic variation, using experiments conducted with a baculovirus that infects gypsy moth (Lymantria dispar) larvae. We found that an empirically observed tradeoff between mean transmission rate and variation in transmission, which results from host heterogeneity, promotes long‐term coexistence of two pathogen types in simulations of a population model. This tradeoff introduces an alternative strategy for the pathogen: a low‐transmission, low‐variability type can coexist with the high‐transmission type favoured by classical non‐heterogeneity models. In addition, this tradeoff can help explain the extensive phenotypic variation we observed in field‐collected pathogen isolates, in traits affecting virus fitness including transmission and environmental persistence. Similar heterogeneity tradeoffs might be a general mechanism promoting phenotypic variation in any pathogen for which hosts vary continuously in susceptibility.     

Allee threshold and extinction threshold for spatially explicit metapopulation dynamics with Allee effects

In this paper, we investigate a spatially explicit metapopulation model with Allee effects. We refer to the patch occupancy model introduced by Levins (Bull Entomol Soc Am 15:237–240, 1969) as a spatially implicit metapopulation model, i.e., each local patch is either occupied or vacant and a vacant patch can be recolonized by a randomly chosen occupied patch from anywhere in the metapopulation. When we transform the model into a spatially explicit one by using a lattice model, the obtained model becomes theoretically equivalent to a “lattice logistic model” or a “basic contact process”. One of the most popular or standard metapopulation models with Allee effects, developed by Amarasekare (Am Nat 152:298–302, 1998), supposes that those effects are introduced formally by means of a logistic equation. However, it is easier to understand the ecological meaning of associating Allee effects with this model if we suppose that only the logistic colonization term directly suffers from Allee effects. The resulting model is also well defined, and therefore we can naturally examine it by Monte Carlo simulation and by doublet and triplet decoupling approximation. We then obtain the following specific features of one-dimensional lattice space: (1) the metapopulation as a whole does not have an Allee threshold for initial population size even when each local population follows the Allee effects; and (2) a metapopulation goes extinct when the extinction rate of a local population is lower than that in the spatially implicit model. The real ecological metapopulation lies between two extremes: completely mixing interactions between patches on the one hand and, on the other, nearest neighboring interactions with only two nearest neighbors. Thus, it is important to identify the metapopulation structure when we consider the problems of invasion species such as establishment or the speed of expansion.     

The effect of heterogeneity on invasion in spatial epidemics: from theory to experimental evidence in a model system

Heterogeneity in host populations is an important factor affecting the ability of a pathogen to invade, yet the quantitative investigation of its effects on epidemic spread is still an open problem. In this paper, we test recent theoretical results, which extend the established "percolation paradigm" to the spread of a pathogen in discrete heterogeneous host populations. In particular, we test the hypothesis that the probability of epidemic invasion decreases when host heterogeneity is increased. We use replicated experimental microcosms, in which the ubiquitous pathogenic fungus Rhizoctonia solani grows through a population of discrete nutrient sites on a lattice, with nutrient sites representing hosts. The degree of host heterogeneity within different populations is adjusted by changing the proportion and the nutrient concentration of nutrient sites. The experimental data are analysed via Bayesian inference methods, estimating pathogen transmission parameters for each individual population. We find a significant, negative correlation between heterogeneity and the probability of pathogen invasion, thereby validating the theory. The value of the correlation is also in remarkably good agreement with the theoretical predictions. We briefly discuss how our results can be exploited in the design and implementation of disease control strategies.     

How do pathogen evolution and host heterogeneity interact in disease emergence?

Heterogeneity in the parameters governing the spread of infectious diseases is a common feature of real-world epidemics. It has been suggested that for pathogens with basic reproductive number R(0)>1, increasing heterogeneity makes extinction of disease more likely during the early rounds of transmission. The basic reproductive number R(0) of the introduced pathogen may, however, be less than 1 after the introduction, and evolutionary changes are then required for R(0) to increase to above 1 and the pathogen to emerge. In this paper, we consider how host heterogeneity influences the emergence of both non-evolving pathogens and those that must undergo adaptive changes to spread in the host population. In contrast to previous results, we find that heterogeneity does not always make extinction more likely and that if adaptation is required for emergence, the effect of host heterogeneity is relatively small. We discuss the application of these ideas to vaccination strategies.     

Effects of phenotypic plasticity on pathogen transmission in the field in a Lepidoptera-NPV system

In models of insect–pathogen interactions, the transmission parameter (ν) is the term that describes the efficiency with which pathogens are transmitted between hosts. There are two components to the transmission parameter, namely the rate at which the host encounters pathogens (contact rate) and the rate at which contact between host and pathogen results in infection (host susceptibility). Here it is shown that in larvae of Spodoptera exempta (Lepidoptera: Noctuidae), in which rearing density triggers the expression of one of two alternative phenotypes, the high-density morph is associated with an increase in larval activity. This response is likely to result in an increase in the contact rate between hosts and pathogens. Rearing density is also known to affect susceptibility of S. exempta to pathogens, with the high-density morph showing increased resistance to a baculovirus. In order to determine whether density-dependent differences observed in the laboratory might affect transmission in the wild, a field trial was carried out to estimate the transmission parameter for S. exempta and its nuclear polyhedrosis virus (NPV). The transmission parameter was found to be significantly higher among larvae reared in isolation than among those reared in crowds. Models of insect–pathogen interactions, in which the transmission parameter is assumed to be constant, will therefore not fully describe the S. exempta-NPV system. The finding that crowding can influence transmission in this way has major implications for both the long-term population dynamics and the invasion dynamics of insect–pathogen systems. Received: 14 June 1999 / Accepted: 22 March 2000     

Niche‐based host extinction increases prevalence of an environmentally acquired pathogen

Understanding the ecology of environmentally acquired and multi‐host pathogens affecting humans and wildlife has been elusive in part because fluctuations in the abundance of host and pathogen species may feed back onto pathogen transmission. Complexity of pathogen‐host dynamics emerges from processes driving local extinction of the pathogen, its hosts and non‐hosts. While the extinction of species may entail losses in pathogen–host interactions and decrease the proportion of hosts infected by a pathogen (prevalence), some studies suggest the opposite pattern. Niche‐based extinction, based on the species tolerance to environmental conditions, may increase prevalence of infection because the pathogen and its hosts persist, while other species go extinct. Hence, understanding prevalence of infection requires disentangling random‐ and niche‐based extinction processes occurring simultaneously. To contribute to this exercise, we analysed the prevalence of an environmentally acquired, multi‐host pathogen, Mycobacterium ulcerans (MU), in a unique dataset of 16 communities of freshwater animals, surveyed during 12 months in Akonolinga, Cameroon in equatorial Africa. Two different ecosystems were identified: rivers (lotic) and swamps and flooded areas (lentic). Increased prevalence of MU infection was correlated with niche‐based extinction of aquatic host invertebrates and vertebrates in the lentic ecosystems, whereas decreased prevalence was associated with random disassembly of the lotic ecosystems. This finding suggests that random and niche‐based extinction of host taxa are key to assessing the effect of local extinction of species on the ecology of environmentally acquired and multi‐host pathogens.     

Circular dichroism of double-helical oligoribonucleotides

The ultraviolet circular dichroism and absorption of 15 double-stranded helical oligoribonucleotides have been measured. These molecules of chain-length 6 to 12 contain all 10 possible nearest neighbors of Watson-Crick base pairs. They are thus good models for short double-stranded regions in RNA molecules. The contribution to the circular dichroism of each of the nearest neighbor base pairs has been obtained. The circular dichroism is found to be very sequence-dependent and may be useful in distinguishing possible secondary structures. However, the nearest neighbor approximation for circular dichroism fails to give a quantitative measure of the circular dichroism of double-strand regions.