The effect of delayed host self-regulation on host-pathogen population cycles in forest insects

Delayed host self-regulation using a Beverton-Holt function and delayed logistic self-regulation are included in a host-pathogen model with free-living infective stages (Anderson and May's model G) with the purpose of investigating whether adding the relatively complex self-regulations decrease the likelihood of population cycles. The main results indicate that adding delayed self-regulation to the baseline model increases the likelihood of population cycles. The dynamics display some of the key features seen in the field, such as cycle peak density exceeding the carrying capacity and a locally stable equilibrium coexisting with a stable cycle (bistability). Numerical studies show that the model with more complex forms of self-regulation can generate cycles which match most aspects of the cycles observed in nature.     

Pathogen-Driven Outbreaks in Forest Defoliators Revisited: Building Models from Experimental Data

Models of outbreaks in forest-defoliating insects are typically built from a priori considerations and tested only with long time series of abundances. We instead present a model built from experimental data on the gypsy moth and its nuclear polyhedrosis virus, which has been extensively tested with epidemic data. These data have identified key details of the gypsy moth-virus interaction that are missing from earlier models, including seasonality in host reproduction, delays between host infection and death, and heterogeneity among hosts in their susceptibility to the virus. Allowing for these details produces models in which annual epidemics are followed by bouts of reproduction among surviving hosts and leads to quite different conclusions than earlier models. First, these models suggest that pathogen-driven outbreaks in forest defoliators occur partly because newly hatched insect larvae have higher average susceptibility than do older larvae. Second, the models show that a combination of seasonality and delays between infection and death can lead to unstable cycles in the absence of a stabilizing mechanism; these cycles, however, are stabilized by the levels of heterogeneity in susceptibility that we have observed in our experimental data. Moreover, our experimental estimates of virus transmission rates and levels of heterogeneity in susceptibility in gypsy moth populations give model dynamics that closely approximate the dynamics of real gypsy moth populations. Although we built our models from data for gypsy moth, our models are, nevertheless, quite general. Our conclusions are therefore likely to be true, not just for other defoliator-pathogen interactions, but for many host-pathogen interactions in which seasonality plays an important role. Our models thus give qualitative insight into the dynamics of host-pathogen interactions, while providing a quantitative interpretation of our gypsy moth-virus data.     

The impact of non-lethal synergists on the population and evolutionary dynamics of host-pathogen interactions

Multiple pathogenic infections can influence disease transmission and virulence, and have important consequences for understanding the community ecology and epidemiology of host-pathogen interactions. Here the population and evolutionary dynamics of a host-pathogen interaction with free-living stages are explored in the presence of a non-lethal synergist that hosts must tolerate. Through the coupled effects on pathogen transmission, host mass gain and allometry it is shown how investing in tolerance to a non-lethal synergist can lead to a broad range of different population dynamics. The effects of the synergist on pathogen fitness are explored through a series of life-history trait trade-offs. Coupling trade-offs between pathogen yield and pathogen speed of kill and the presence of a synergist favour parasites that have faster speeds of kill. This evolutionary change in pathogen characteristics is predicted to lead to stable population dynamics. Evolutionary analysis of tolerance of the synergist (strength of synergy) and lethal pathogen yield show that decreasing tolerance allows alternative pathogen strategies to invade and replace extant strategies. This evolutionary change is likely to destabilise the host-pathogen interaction leading to population cycles. Correlated trait effects between speed of kill and tolerance (strength of synergy) show how these traits can interact to affect the potential for the coexistence of multiple pathogen strategies. Understanding the consequences of these evolutionary relationships is important for the both the evolutionary and population dynamics of host-pathogen interactions.     

Variable prey development time suppresses predator–prey cycles and enhances stability

Although theoretical models have demonstrated that predator–prey population dynamics can depend critically on age (stage) structure and the duration and variability in development times of different life stages, experimental support for this theory is non‐existent. We conducted an experiment with a host–parasitoid system to test the prediction that increased variability in the development time of the vulnerable host stage can promote interaction stability. Host–parasitoid microcosms were subjected to two treatments: Normal and High variance in the duration of the vulnerable host stage. In control and Normal‐variance microcosms, hosts and parasitoids exhibited distinct population cycles. In contrast, insect abundances were 18–24% less variable in High‐ than Normal‐variance microcosms. More significantly, periodicity in host–parasitoid population dynamics disappeared in the High‐variance microcosms. Simulation models confirmed that stability in High‐variance microcosms was sufficient to prevent extinction. We conclude that developmental variability is critical to predator–prey population dynamics and could be exploited in pest‐management programs.     

Positive and negative density-dependence and boom-bust dynamics in enemy-victim populations: a mountain pine beetle case study

Negative density-dependent population regulation in exploitative species is well studied. Positive density-dependence can arise if exploiters must cooperate to obtain access to well-defended resources. Most studies, however, focus on the first type of density-dependence at the expense of the other. Using a parasitoid-host model, we explored how positive density-dependence driven by host defenses in combination with negative density-dependence due to competition for resources impact transient population dynamics. Inspired by interactions between the mountain pine beetle and its pine hosts, we formulated a model of enemy-victim interactions in discrete-time in which the victim is capable of deadly self-defense against exploitation. We fitted the model to data and then analyzed its non-equilibrium dynamics to determine what conditions promote boom-bust dynamics. When present together, strong Allee effects and overcompensating competition for resources among exploiters can cause their populations to irrupt and then crash even though many exploitable resources remain. Accelerating population irruptions followed by precipitous collapse occur for realistic parameter values of our model of mountain pine beetle dynamics. Insect dynamics are often dominated by sudden irruptions and collapses on short time scales. Population crashes in exploitative species often happen enigmatically even when exploitable resources are not depleted. Herein, we argue that strong Allee effects in combination with overcompensation provide a plausible explanation for these boom-bust dynamics in some species.     

Outside-Host Growth of Pathogens Attenuates Epidemiological Outbreaks

Opportunist saprotrophic pathogens differ from obligatory pathogens due to their capability in host-independent growth in environmental reservoirs. Thus, the outside-host environment potentially influences host-pathogen dynamics. Despite the socio-economical importance of these pathogens, theory on their dynamics is practically missing. We analyzed a novel epidemiological model that couples outside-host density-dependent growth to host-pathogen dynamics. Parameterization was based on columnaris disease, a major hazard in fresh water fish farms caused by saprotrophic Flavobacterium columnare. Stability analysis and numerical simulations revealed that the outside-host growth maintains high proportion of infected individuals, and under some conditions can drive host extinct. The model can show stable or cyclic dynamics, and the outside-host growth regulates the frequency and intensity of outbreaks. This result emerges because the density-dependence stabilizes dynamics. Our analysis demonstrates that coupling of outside-host growth and traditional host-pathogen dynamics has profound influence on disease prevalence and dynamics. This also has implications on the control of these diseases.     

Population dynamic consequences of parasitised-larval competition in stage-structured host–parasitoid systems

Parasitism can influence many aspects of the host's behaviour and physiology, which in turn can have a profound impact on their population and evolutionary ecology. In many host–parasite interactions there is often a time lag between infection and the death of the host, yet little is known, experimentally or theoretically, about the effects that intra-class competition between parasitised and unparasitised hosts have on the host–parasite population dynamics.
In this article we address this gap in our understanding using a stage-structured mathematical model for a host–parasitoid interaction, which has been parameterised for the Plodia–Venturia experimental system.
In the case where parasitised larvae do not compete and do not cannibalise unparasitised larvae, our model predicts a wide range of host–parasitoid dynamics, ranging from host–parasitoid generation cycles, to host generation cycles with parasitoid half-generation cycles, to host–parasitoid equilibria, to host generation cycles with parasitoid extinction.
However, when parasitised larvae can compete with their unparasitised larvae counterparts, the host–parasitoid population dynamics can dramatically change. In particular, we show that high levels of competition exerted by unparasitised larvae upon parasitised larvae is more likely to lead to parasitoid extinction.
In addition, we demonstrate that unparasitised host larvae that are sufficiently susceptible to intra-class competition, or parasitised host larvae that are sufficiently strong competitors, can have a stabilising effect on the host–parasitoid population dynamics.
The implications of these theoretical results are discussed in light of our understanding of host–parasitoid interactions and host–parasite systems in general.     

Parasite-mediated and direct competition in a two-host shared macroparasite system

This paper investigates the local dynamical behaviour of a deterministic model describing two host species experiencing three forms of competition: direct competition, apparent competition mediated by macroparasites, and intra-specific (density-dependent) competition. The problem of algebraic intractability is sidestepped by adopting a geometric approach, in which an array of maps is constructed in parameter space, each structured by bifurcation surfaces which mark qualitative changes in system behaviour. The maps provide both a succinct and a comprehensive overview of the stability and feasibility structure of the system equilibria, from which can be deduced the possible modes of local dynamical behaviour. A detailed examination of these maps shows that (i) the system is highly sensitive to the effect of infection on fecundity with synchronous sustained cycles readily generated by Hopf bifurcations; (ii) for a broad range of parameter values, pertinent to actual biological systems, apparent competition mediated by macroparasites is sufficient, on its own, to explain host exclusion; (iii) direct competition reinforces parasite-mediated competition to expand the host exclusion region; and (iv) the condition for host exclusion can be expressed simply in a form which holds for both micro- and macroparasite models and which involves just two key indices, measuring tolerance to the infection and the strength of direct competition. The techniques used in this paper are not restricted to the analysis of host-parasite systems but can be applied to a wide range of nonlinear population models. They are therefore as relevant to the analysis of such general issues as exploitative competition and trophic interactions as they are to specific epidemiological problems.     

Population biology of multispecies helminth infection: competition and coexistence

The role that interspecific interactions play in shaping parasite communities is uncertain. To date, models of competition between helminth species have assumed that interaction occurs through parasite-induced host death. To our knowledge, there has been no theoretical exploration of other forms of competition. We examine models in which competition acts at the point of establishment within the host, and at the time of egg production by the adult worm. The models used are stochastic and we allow hosts to vary in their rate of exposure to infective larvae. We derive the Lotka-Volterra model of competition when exposure is homogenous and thus demonstrate that two helminth species cannot coexist on a single limiting resource. We show that coexistence of species is promoted by heterogeneity in host exposure provided that the rates of exposure to the two species are not perfectly correlated, and, if they are positively correlated, provided that the degree of heterogeneity in host exposure is similar for the two competing helminth species. These results are robust to the mechanism of competition.     

Effects of deterministic and random refuge in a prey-predator model with parasite infection

Most natural ecosystem populations suffer from various infectious diseases and the resulting host-pathogen dynamics is dependent on host's characteristics. On the other hand, empirical evidences show that for most host pathogen systems, a part of the host population always forms a refuge. To study the role of refuge on the host-pathogen interaction, we study a predator-prey-pathogen model where the susceptible and the infected prey can undergo refugia of constant size to evade predator attack. The stability aspects of the model system is investigated from a local and global perspective. The study reveals that the refuge sizes for the susceptible and the infected prey are the key parameters that control possible predator extinction as well as species co-existence. Next we perform a global study of the model system using Lyapunov functions and show the existence of a global attractor. Finally we perform a stochastic extension of the basic model to study the phenomenon of random refuge arising from various intrinsic, habitat-related and environmental factors. The stochastic model is analyzed for exponential mean square stability. Numerical study of the stochastic model shows that increasing the refuge rates has a stabilizing effect on the stochastic dynamics.     

具有综合控制策略的离散宿主病原体模型(英文)

研究了具有综合控制策略的离散宿主病原体模型,并考虑了固定时刻脉冲效应和状态依赖脉冲效应对综合控制策略的影响.对于固定时刻脉冲的模型,分析了宿主根除、宿主病原体共存以及宿主爆发周期解的存在性和稳定性,并给出了宿主根除周期解全局稳定的充分条件.对于状态依赖的脉冲离散模型,数值研究说明宿主最大振幅不超过经济临界值的周期解的存在性以及相应动态行为的复杂性.     

Incorporating spatial variation in density enhances the stability of simple population dynamics models

Simple discrete time models of population growth admit a wide variety of dynamic behaviors, including population cycles and chaos. Yet studies of natural and laboratory populations typically reveal their dynamics to be relatively stable. Many explanations for the apparent rarity of unstable or chaotic behavior in real populations have been developed, including the possible stabilizing roles of migration, refugia, abrupt density-dependence, and genetic variation in sensitivity to density. We develop a theoretical framework for incorporating random spatial variation in density into simple models of population growth, and apply this approach to two commonly used models in ecology: the Ricker and Hassell maps. We show that the incorporation of spatial density variation into both these models has a strong stabilizing influence on their dynamic behavior, and leads to their exhibiting stable point equilibria or stable limit cycles over a relatively much larger range of parameter values. We suggest that one reason why chaotic population dynamics are less common than the simple models indicate is, these models typically neglect the potentially stabilizing role of spatial variation in density.     

Enrichment can damp population cycles: a balance of inflexible and flexible interactions

Destabilization of one predator–one prey systems with an increase in nutrient input has been viewed as a paradox. We report that enrichment can damp population cycles by a food‐web structure that balances inflexible and flexible interaction links (i.e. specialist and generalist predators). We modeled six predator–prey systems involving three or four species in which the predators practice optimal foraging based on prey profitability determined by handling time. In all models, the balance of interaction links simultaneously decreased the amplitude of population oscillations and increased the minimum density with increasing enrichment, leading to a potential theoretical resolution of the paradox of enrichment in non‐equilibrium dynamics. The stabilization mechanism was common to all of the models. Important previous studies on the stability of food webs have also demonstrated that a balance of interaction strengths stabilizes systems, suggesting a general rule of ecosystem stability.     

Pathogen interactions, population cycles, and phase shifts

Interspecific pathogen interactions can profoundly affect pathogen population dynamics and the efficacy of control strategies. However, many pathogens exhibit cyclic abundance patterns (e.g., seasonality), and temporal asynchrony between interacting pathogens could reduce the impact of those interactions. Here we use an extension of our previously published model to investigate the effects of cycles on pathogen interaction. We demonstrate that host immune memory can maintain the impact of an interaction, even when the effector pathogen abundance is low or the pathogen is absent. Paradoxically, immune memory can result in pathogens interacting more strongly when temporally out of phase. We find that interactions between species can result in changes to the temporal pattern of the affected species. We further demonstrate that this may be observed in a natural host-pathogen system. Given the continuing debate regarding the relevance of pathogen interactions in natural systems and increasing concern about treatment strategies for coinfections, both the discovery of a shift in cycle in empirical data and the mechanism by which we identified it are important. Finally, because the model structure used here is analogous to models of a simple predator-prey system, we also consider the consequences of these findings in the context of that system.     

The role of mathematical models of host-pathogen interactions for livestock health and production - a review

Compared with the application of mathematical models to study human diseases, models that describe animal responses to pathogen challenges are relatively rare. The aim of this review is to explain and show the role of mathematical host-pathogen interaction models in providing underpinning knowledge for improving animal health and sustaining livestock production. Existing host-pathogen interaction models can be assigned to one of three categories: (i) models of the infection and immune system dynamics, (ii) models that describe the impact of pathogen challenge on health, survival and production and (iii) models that consider the co-evolution of host and pathogen. State-of-the-art approaches are presented and discussed for models belonging to the first two categories only, as they concentrate on the host-pathogen dynamics within individuals. Models of the third category fall more into the class of epidemiological models, which deserve a review by themselves. An extensive review of published models reveals a rich spectrum of methodologies and approaches adopted in different modelling studies, and a strong discrepancy between models concerning diseases in animals and models aimed at tackling diseases in humans (most of which belong to the first category), with the latter being generally more sophisticated. The importance of accounting for the impact of infection not only on health but also on production poses a considerable challenge to the study of host-pathogen interactions in livestock. This has led to relatively simplistic representations of host-pathogen interaction in existing models for livestock diseases. Although these have proven appropriate for investigating hypotheses concerning the relationships between health and production traits, they do not provide predictions of an animal's response to pathogen challenge of sufficient accuracy that would be required for the design of appropriate disease control strategies. A synthesis between the modelling methodologies adopted in categories 1 and 2 would therefore be desirable. The progress achieved in mathematical modelling to study immunological processes relevant to human diseases, together with the current advances in the generation and analysis of biological data related to animal diseases, offers a great opportunity to develop a new generation of host-pathogen interaction models that take on a fundamental role in the study and control of disease in livestock.     

A nutritive view on the host-pathogen interplay

The interaction between pathogenic microbes and their host is determined by survival strategies on both sides, including competition for essential nutrients. During evolution, pathogenic microbes developed ways to access certain nutrients from the host, which, by contrast, can be exploited by the host for defence by restricting the availability of these nutrients. In this article, we review ecological aspects of the host-pathogen relationship and describe examples for competitive nutrient usage. We also discuss the beneficial probiotic microbes of the mammalian gut, which influence their environment including inflammatory host responses, and how they might be supported by prebiotic diets.     

Disentangling the interaction among host resources,the immune system and pathogens

The interaction between the immune system and pathogens is often characterised as a predator–prey interaction. This characterisation ignores the fact that both require host resources to reproduce. Here, we propose novel theory that considers how these resource requirements can modify the interaction between the immune system and pathogens. We derive a series of models to describe the energetic interaction between the immune system and pathogens, from fully independent resources to direct competition for the same resource. We show that increasing within‐host resource supply has qualitatively distinct effects under these different scenarios. In particular, we show the conditions for which pathogen load is expected to increase, decrease or even peak at intermediate resource supply. We survey the empirical literature and find evidence for all three patterns. These patterns are not explained by previous theory, suggesting that competition for host resources can have a strong influence on the outcome of disease.     

Costs of aggregation: shadow competition in a sit-and-wait predator

The role of top-down (e.g. parasitism) and bottom-up (e.g. resource competition) processes is of fundamental importance for the stability and persistence of insect herbivore populations. Although emphasis has often focused on single regulatory agents, the processes underpinning tri-trophic interactions may actually be more pluralistic. Recently, further complexities involved in the regulation of tri-trophic systems have been highlighted. In particular, life history characteristics may have a concomitant role when coupled with the regulatory effects of resource competition and/or parasitism. Here we present an age-structured model to investigate the effects of larval development period, parasitism and resource competition on the stability and persistence of herbivore–parasitoid interactions. We show that the influence of weak density dependent parasitism is sufficient to stabilise the interaction when the period of host susceptibility to parasitism is short. For longer periods of host susceptibility, parasitism needs to be highly non-linear to overcome the destabilising effects of the time delays. In systems where host development is protracted through the season we predict that resource competition is likely to be the dominant process for herbivore regulation. We use this age-structured approach to explore the population dynamics of two field studies from temperate ecosystems. Predictions from these case studies show 1) that both the strength and type of competition and parasitism are important for the stability and persistence of the particular system, and 2) that the length of the developmental period of the vulnerable host is critical to understand the influence of different regulatory processes. Host demography is of overriding importance in determining whether herbivores show outbreaks, and which particular ecological processes and mechanisms are responsible for generating such overcompensatory dynamics.     

Evolution of positive and negative density-dependent dispersal

Understanding the evolution of density-dependent dispersal strategies has been a major challenge for evolutionary ecologists. Some existing models suggest that selection should favour positive and others negative density-dependence in dispersal. Here, we develop a general model that shows how and why selection may shift from positive to negative density-dependence in response to key ecological factors, in particular the temporal stability of the environment. We find that in temporally stable environments, particularly with low dispersal costs and large group sizes, habitat heterogeneity selects for negative density-dependent dispersal, whereas in temporally variable environments, particularly with high dispersal costs and small group sizes, habitat heterogeneity selects for positive density-dependent dispersal. This shift reflects the changing balance between the greater competition for breeding opportunities in more productive patches, versus the greater long-term value of offspring that establish themselves there, the latter being very sensitive to the temporal stability of the environment. In general, dispersal of individuals out of low-density patches is much more sensitive to habitat heterogeneity than is dispersal out of high-density patches.     

多种病原物混合侵染的昆虫流行病模型

两种或两种以上的病原物同时侵染昆虫寄主时,病原物之间的相互作用表现为偏利、偏害、中性及竞争等类型,寄生群体的病症可呈多种形式．根据单种病菌的重叠侵染原理,建立了多种病原物混合侵染时以温度、病原接种量、虫龄及湿度为因子的昆虫流行病模型．由模型可计算寄生群体中不同病原物的致病比率,及寄主群体的总发病率,给出了模型的参数求解算法,以及病原物相互作用类型的判定准则．这类模型可用于多种病原物混合侵染的昆虫流行病预测,也可作为多种病原物混合施用防治害虫的最优化模型．