Experimental manipulation of immune-mediated disease and its fitness costs for rodent malaria parasites

Background  

Explaining parasite virulence (harm to the host) represents a major challenge for evolutionary and biomedical scientists alike. Most theoretical models of virulence evolution assume that virulence arises as a direct consequence of host exploitation, the process whereby parasites convert host resources into transmission opportunities. However, infection-induced disease can be immune-mediated (immunopathology). Little is known about how immunopathology affects parasite fitness, or how it will affect the evolution of parasite virulence. Here we studied the effects of immunopathology on infection-induced host mortality rate and lifetime transmission potential – key components of parasite fitness – using the rodent malaria model, Plasmodium chabaudi chabaudi.     

Population extinction and quasi-stationary behavior in stochastic density-dependent structured models

Density-independent and density-dependent, stochastic and deterministic, discrete-time, structured models are formulated, analysed and numerically simulated. A special case of the deterministic, density-independent, structured model is the well-known Leslie age-structured model. The stochastic, density-independent model is a multitype branching process. A review of linear, density-independent models is given first, then nonlinear, density-dependent models are discussed. In the linear, density-independent structured models, transitions between states are independent of time and state. Population extinction is determined by the dominant eigenvalue λ of the transition matrix. If λ ≤ 1, then extinction occurs with probability one in the stochastic and deterministic models. However, if λ > 1, then the deterministic model has exponential growth, but in the stochastic model there is a positive probability of extinction which depends on the fixed point of the system of probability generating functions. The linear, density-independent, stochastic model is generalized to a nonlinear, density-dependent one. The dependence on state is in terms of a weighted total population size. It is shown for small initial population sizes that the density-dependent, stochastic model can be approximated by the density-independent, stochastic model and thus, the extinction behavior exhibited by the linear model occurs in the nonlinear model. In the deterministic models there is a unique stable equilibrium. Given the population does not go extinct, it is shown that the stochastic model has a quasi-stationary distribution with mean close to the stable equilibrium, provided the population size is sufficiently large. For small values of the population size, complete extinction can be observed in the simulations. However, the persistence time increases rapidly with the population size. This author received partial support by the National Science Foundation grant # DMS-9626417.     

Dynamics of two electrically coupled chaotic neurons: Experimental observations and model analysis

Conductance-based models of neurons from the lobster stomatogastric ganglion (STG) have been developed to understand the observed chaotic behavior of individual STG neurons. These models identify an additional slow dynamical process – calcium exchange and storage in the endoplasmic reticulum – as a biologically plausible source for the observed chaos in the oscillations of these cells. In this paper we test these ideas further by exploring the dynamical behavior when two model neurons are coupled by electrical or gap junction connections. We compare in detail the model results to the laboratory measurements of electrically-coupled neurons that we reported earlier. The experiments on the biological neurons varied the strength of the effective coupling by applying a parallel, artificial synapse, which changed both the magnitude and polarity of the conductance between the neurons. We observed a sequence of bifurcations that took the neurons from strongly synchronized in-phase behavior, through uncorrelated chaotic oscillations to strongly synchronized – and now regular – out-of-phase behavior. The model calculations reproduce these observations quantitatively, indicating that slow subcellular processes could account for the mechanisms involved in the synchronization and regularization of the otherwise individual chaotic activities. Received: 28 June 1999 / Accepted in revised form: 30 June 2000     

Disease-induced stabilization of predator-prey oscillations

Parasites are an integral part of virtually all food webs and species communities. Here we consider the invasion of a resident predator-prey system by an infectious disease with frequency-dependent transmission spreading within the predator population. We derive biologically plausible and insightful quantities (demographic and epizootiological reproduction numbers) that allow us to completely determine community composition. Successful disease invasion can have two contrary effects in driving its host population to extinction or in stabilizing predator-prey cycles. Our findings contradict predictions from previous models suggesting a destabilizing effect of parasites. We show that predator infection counteracts the paradox of enrichment. In turn, parasite removal from food webs can have catastrophic effects. We discuss the implications for biological control and resource management on more than one trophic level.     

Predator-prey models with delay and prey harvesting

It is known that predator-prey systems with constant rate harvesting exhibit very rich dynamics. On the other hand, incorporating time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying the combined effects of the harvesting rate and the time delay on the dynamics of the generalized Gause-type predator-prey models and the Wangersky-Cunningham model. It is shown that in these models the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities, while the harvesting rate has a stabilizing effect on the equilibrium if it is under the critical harvesting level. In particular, one of these models loses stability when the delay varies and then regains its stability when the harvesting rate is increased. Computer simulations are carried to explain the mathematical conclusions. Received: 1 March 2000 / Revised version: 7 September 2000 /?Published online: 21 August 2001     

A numerical method for renal models that represent tubules with abrupt changes in membrane properties

 The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method. Received: 13 November 2001 / Revised version: 28 June 2002 / Published online: 26 September 2002 This work was supported in part by the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney Diseases, grant DK-42091.) Mathematics Subject Classification (2000): 65-04, 65M12, 65M25, 92-04, 92C35, 35-04, 35L45 Keywords or phrases: Mathematical models – Differential equations – Mathematical biology – Kidney – Renal medulla – Semi-Lagrangian semi-implicit     

Stochastic epidemics: the probability of extinction of an infectious disease at the end of a major outbreak

 The aim of this study is to derive an asymptotic expression for the probability that an infectious disease will disappear from a population at the end of a major outbreak (‘fade-out’). The study deals with a stochastic SIR-model. Local asymptotic expansions are constructed for the deterministic trajectories of the corresponding deterministic system, in particular for the deterministic trajectory starting in the saddle point. The analytical expression for the probability of extinction is derived by asymptotically solving a boundary value problem based on the Fokker-Planck equation for the stochastic system. The asymptotic results are compared with results obtained by random walk simulations. Received 20 July 1995; received in revised form 6 May 1996     

Individual-based vs deterministic models for macroparasites: host cycles and extinction

Our understanding of the qualitative dynamics of host-macroparasite systems is mainly based on deterministic models. We study here an individual-based stochastic model that incorporates the same assumptions as the classical deterministic model. Stochastic simulations, using parameter values based on some case studies, preserve many features of the deterministic model, like the average value of the variables and the approximate length of the cycles.An important difference is that, even when deterministic models yield damped oscillations, stochastic simulations yield apparently sustained oscillations. The amplitude of such oscillations may be so large to threaten parasites' persistence.With density-dependence in parasite demographic traits, persistence increases somewhat. Allowing instead for infections from an external parasite reservoir, we found that host extinction may easily occur. However, the extinction probability is almost independent of the level of external infection over a wide intermediate parameter region.     

Does the early frog catch the worm? Disentangling potential drivers of a parasite age–intensity relationship in tadpoles

The manner in which parasite intensity and aggregation varies with host age can provide insights into parasite dynamics and help identify potential means of controlling infections in humans and wildlife. A significant challenge is to distinguish among competing mechanistic hypotheses for the relationship between age and parasite intensity or aggregation. Because different mechanisms can generate similar relationships, testing among competing hypotheses can be difficult, particularly in wildlife hosts, and often requires a combination of experimental and model fitting approaches. We used field data, experiments, and model fitting to distinguish among ten plausible drivers of a curvilinear age–intensity relationship and increasing aggregation with host age for echinostome trematode infections of green frogs. We found little support for most of these proposed drivers but did find that the parsimonious explanation for the observed age–intensity relationship was seasonal exposure to echinostomes. The parsimonious explanation for the aggregated distribution of parasites in this host population was heterogeneity in exposure. A predictive model incorporating seasonal exposure indicated that tadpoles hatching early or late in the breeding season should have lower trematode burdens at metamorphosis, particularly with simulated warmer climates. Application of this multi-pronged approach (field surveys, lab experiments, and modeling) to additional parasite–host systems could lead to discovery of general patterns in the drivers of parasite age–intensity and age–distribution relationships.     

Isotopic insight into host–endosymbiont relationships in Liolaemid lizards

Nitrogen isotopes have been widely used to investigate trophic levels in ecological systems. Isotopic enrichment of 2–5‰ occurs with trophic level increases in food webs. Host–parasite relationships deviate from traditional food webs in that parasites are minimally enriched relative to their hosts. Although this host–parasite enrichment pattern has been shown in multiple systems, few studies have used isotopic relationships to examine other potential symbioses. We examined the relationship between two gut-nematodes and their lizard hosts. One species, Physaloptera retusa, is a documented parasite in the stomach, whereas the relationship of the other species, Parapharyngodon riojensis (pinworms), to the host is putatively commensalistic or mutualistic. Based on the established trophic enrichments, we predicted that, relative to host tissue, parasitic nematodes would be minimally enriched (0–1‰), whereas pinworms, either as commensals or mutualists, would be significantly enriched by 2–5‰. We measured the ¹⁵N values of food, digesta, gut tissue, and nematodes of eight lizard species in the family Liolaemidae. Parasitic worms were enriched 1±0.2‰ relative to host tissue, while the average enrichment value for pinworms relative to gut tissue was 6.7±0.2‰. The results support previous findings that isotopic fractionation in a host–parasite system is lower than traditional food webs. Additionally, the larger enrichment of pinworms relative to known parasites suggests that they are not parasitic and may be several trophic levels beyond the host.     

A new species, Parupeneus procerigena, from the Saya de Malha Bank in the western Indian Ocean (Perciformes: Mullidae)

A new mullid fish, Parupeneus procerigena, is described on the basis of 13 specimens (118.9–198.4 mm SL) from depths of 92–148 m off the Saya de Malha Bank in the western Indian Ocean. This species resembles P. chrysopleuron and P. heptacanthus in color pattern without black stripes or spots, but it differs from them in having more gill rakers, two scales in lachrymal region, deeper body, deeper cheek, and longer distance between nostrils. Received: April 4, 2000 / Revised: July 27, 2000 / Accepted: August 27, 2000     

Why do parasitized hosts look different? Resolving the “chicken-egg” dilemma

Phenotypic differences between infected and non-infected hosts are often assumed to be the consequence of parasite infection. However, pre-existing differences in hosts’ phenotypes may promote differential susceptibility to infection. The phenotypic variability observed within the host population may therefore be a cause rather than a consequence of infection. In this study, we aimed at disentangling the causes and the consequences of parasite infection by calculating the value of a phenotypic trait (i.e., the growth rate) of the hosts both before and after infection occurred. That procedure was applied to two natural systems of host–parasite interactions. In the first system, the infection level of an ectoparasite (Tracheliastes polycolpus) decreases the growth rate of its fish host (the rostrum dace, Leuciscus leuciscus). Reciprocally, this same phenotypic trait before infection modulated the future level of host sensitivity to the direct pathogenic effect of the parasite, namely the level of fin degradation. In the second model, causes and consequences linked the growth rate of the fish host (the rainbow smelt, Osmerus mordax) and the level of endoparasite infection (Proteocephalus tetrastomus). Indeed, the host’s growth rate before infection determined the number of parasites later in life, and the parasite biovolume then decreased the host’s growth rate of heavily infected hosts. We demonstrated that reciprocal effects between host phenotypes and parasite infection can occur simultaneously in the wild, and that the observed variation in the host phenotype population was not necessarily a consequence of parasite infection. Disentangling the causality of host–parasite interactions should contribute substantially to evaluating the role of parasites in ecological and evolutionary processes. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The onset of oscillatory dynamics in models of multiple disease strains

 We examine a generalised SIR model for the infection dynamics of four competing disease strains. This model contains four previously-studied models as special cases. The different strains interact indirectly by the mechanism of cross-immunity; individuals in the host population may become immune to infection by a particular strain even if they have only been infected with different but closely related strains. Several different models of cross-immunity are compared in the limit where the death rate is much smaller than the rate of recovery from infection. In this limit an asymptotic analysis of the dynamics of the models is possible, and we are able to compute the location and nature of the Takens–Bogdanov bifurcation associated with the presence of oscillatory dynamics observed by previous authors. Received: 5 December 2001 / Revised version: 5 May 2002 / Published online: 17 October 2002 Keywords or phrases: Infection – Pathogen – Epidemiology – Multiple strains – Cross-immunity – Oscillations – Dynamics – Bifurcations     

Evolutionary tradeoff and equilibrium in an aquatic predator-prey system

Due to the conventional distinction between ecological (rapid) and evolutionary (slow) timescales, ecological and population models have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has been recently established and may be critical to understanding how populations persist in changing environments. In this paper we examine the relationship between ecological and evolutionary dynamics, focusing on a well-studied experimental aquatic predator-prey system (Fussmann et al., 2000, Science, 290, 1358–1360; Shertzer et al., 2002, J. Anim. Ecol., 71, 802–815; Yoshida et al., 2003, Nature, 424, 303–306). Major properties of predator-prey cycles in this system are determined by ongoing evolutionary dynamics in the prey population. Under some conditions, however, the populations tend to apparently stable steady-state densities. These are the subject of the present paper. We examine a previously developed model for the system, to determine how evolution shapes properties of the equilibria, in particular the number and identity of coexisting prey genotypes. We then apply these results to explore how evolutionary dynamics can shape the responses of the system to ‘management’: externally imposed alterations in conditions. Specifically, we compare the behavior of the system including evolutionary dynamics, with predictions that would be made if the potential for rapid evolutionary change is neglected. Finally, we posit some simple experiments to verify our prediction that evolution can have significant qualitative effects on observed population-level responses to changing conditions.     

A new zoarcid, Lycodes mcallisteri, from eastern Arctic Canada (Teleostei: Perciformes)

A new zoarcid fish, Lycodes mcallisteri, is described on the basis of nine specimens (230–375 mm SL) from eastern Arctic Canada, Nunavut (Hudson Strait, 298 m; Cumberland Sound and Baffin Bay, 579 m). It resembles about 15 other Lycodes spp. in having a long tail and a "ventromediolateral" type of lateral line. It is distinguished from Arctic members of this group (Lycodes marisalbi, L. palearis, and L. sagittarius) by the high number of pectoral fin rays (22–23), short pelvic fins, low submental crests, and coloration (6–10 light patches dorsally). It resembles two Pacific species (L. macrochir and L. soldatovi) by the high number of pectoral fin rays, but differs by coloration, meristics, and shape of the pectoral fin. Received: April 13, 2000 / Revised: September 7, 2000 / Accepted: January 11, 2001     

Rich dynamics of a ratio-dependent one-prey two-predators model

The objective of this paper is to systematically study the qualitative properties of a ratio-dependent one-prey two-predator model. We show that the dynamics outcome of the interactions are very sensitive to parameter values and initial data. Specifically, we show the interactions can lead to all the following possible outcomes: 1) competitive exclusion; 2) total extinction, i.e., collapse of the whole system; 3) coexistence in the form of positive steady state; 4) coexistence in the form of oscillatory solutions; and 5) introducing a friendly and better competitor can save a otherwise doomed prey species. These results reveal far richer dynamics compared to similar prey dependent models. Biological implications of these results are discussed. Received: 14 November 2000 / Revised version: 18 February 2001 / Published online: 19 September 2001     

The dynamics of infection of Tribolium confusum by Hymenolepis diminuta: the influence of infective-stage density and spatial distribution

The mean parasite burden of a population of Tribolium confusum is shown to rise to a plateau as the exposure density of infective eggs of Hymenolepis diminuta increases. The level of this plateau is shown to be dependent on the nutritional status of the host population, being depressed from approximately 18 cysticeroids/beetle in hosts which have been starved prior to experimentation, to approximately 2 cysticercoids/beetle in satiated hosts. A simple model is used to describe the shape of this infection functional response in terms of the predator-prey interaction between hosts (T. confusum) and parasite infective stages (H. diminuta eggs). The distribution of successful infections/host is shown to be over-dispersed, even when hosts are exposed to infective stages arranged in a uniform spatial pattern. The over-dispersion of parasite numbers/host is shown to become more severe as the spatial pattern of infective stages changes from under-dispersed, through random, to over-dispersed. Experimental results are discussed in relation to the dynamics of parasite-host interactions, in which infection takes place by host ingestion of a free-living infective stage.     

Detection of sinusoidal gratings by pattern-specific detectors: further evidence for the correlation principle in human vision

 The detection of compound sinusoidal gratings of various spatial frequency separations and four different grating sizes has been studied using the summation-to-threshold paradigm. Contrast interrelation functions have been measured and spatial frequency tuning estimates, based on the slope of the contrast interrelation function at two definite points, were derived using the “negative gradient technique” proposed by Logvinenko [Logvinenko (1995) Biol Cybern 73: 547–552]. It is shown that compound grating detection can be modelled by assuming pattern-specific sensory mechanisms for each of the spatial frequency components, which adapt to the periodicity and the size of the stimulus but not to its envelope function. Further, it is shown that relative sensitivity for a given spatial frequency separation can be predicted with good accuracy by the correlation of the grating components used for superposition. It is suggested that the most plausible implementation of the pattern correlation principle in human grating detection is the “grating cell” model. Received: 10 March 2000 / Accepted in revised form: 4 December 2000     

Noise-induced transition in excitable neuron models

 We studied the influence of noisy stimulation on the Hodgkin-Huxley neuron model. Rather than examining the noise-related variability of the discharge times of the model – as has been done previously – our study focused on the effect of noise on the stationary distributions of the membrane potential and gating variables of the model. We observed that a gradual increase in the noise intensity did not result in a gradual change of the distributions. Instead, we could identify a critical intermediate noise range in which the shapes of the distributions underwent a drastic qualitative change. Namely, they moved from narrow unimodal Gaussian-like shapes associated with low noise intensities to ones that spread widely at large noise intensities. In particular, for the membrane potential and the sodium activation variable, the distributions changed from unimodal to bimodal. Thus, our investigation revealed a noise-induced transition in the Hodgkin-Huxley model. In order to further characterize this phenomenon, we considered a reduced one-dimensional model of an excitable system, namely the active rotator. For this model, our analysis indicated that the noise-induced transition is associated with a deterministic bifurcation of approximate equations governing the dynamics of the mean and variance of the state variable. Finally, we shed light on the possible functional importance of this noise-induced transition in neuronal coding by determining its effect on the spike timing precision in models of neuronal ensembles. Received: 19 September 2000 / Accepted in revised form: 4 March 2001     

Effect of starvation on parasite-induced mortality in a freshwater snail (Potamopyrgus antipodarum)

The level of host exploitation is expected, under theory, to be selected to maximise (subject to constraints) the lifetime reproductive success of the parasite. Here we studied the effect of two castrating trematode species on their intermediate snail host, Potamopyrgus antipodarum. One of the trematode species, Microphallus sp., encysts in the snail host and the encysted larvae “hatch” following ingestion of infected snails by birds. The other species, Notocotylus gippyensis, by contrast, releases swimming larvae; ingestion of the snail host is not required for, and does not aid, transmission to the final host. We isolated field-collected snails for 3 months in the laboratory, and followed the survival of infected and uninfected snails under two conditions: not fed and fed ad libitum. Mortality of the infected hosts was higher than mortality of the uninfected ones, but the response to starvation treatment was parasite species specific. N. gippyensis induced significantly higher mortality in starved snails than did Microphallus. Based on these results, we suggest that host exploitation by different species of trematodes may depend on the type of transmission. Encysting in the snail host may select for a reduced rate of host exploitation so as to increase the probability of transmission to the final host. Received: 29 July 1998 / Accepted: 1 February 1999