Adaptive host preference and the dynamics of host-parasitoid interactions

Models of two independent host populations and a common parasitoid are investigated. The hosts have density-dependent population growth and only interact indirectly by their effects on parasitoid behavior and population dynamics. The parasitoid is assumed to experience a trade-off in its ability to exploit the two hosts. Three alternative types of parasitoid are investigated: (i) fixed generalists whose consumption rates are those that maximize fitness; (ii) "ideal free" parasitoids, which modify their behavior to maximize their rate of finding unparasitized hosts within a generation; and (iii) "evolving" parasitoids, whose capture rates change between generations based on quantitative genetic determination of the relative attack rates on the two hosts. The primary questions addressed are: (1) Do the different types of adaptive processes stabilize or destabilize the population dynamics? (2) Do the adaptive processes tend to equalize or to magnify differences in host densities? The models show that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.     

Coevolution across landscapes: a spatially explicit model of parasitoid-host coevolution

The geographic mosaic theory of coevolution suggests that population spatial structure may have a strong impact on coevolutionary dynamics. Therefore, coevolution must be studied across geographic scales, not just in single populations. To examine the impact of movement rate on coevolutionary dynamics, we developed a spatially explicit model of host–parasitoid coevolution. We described space as a coupled-map lattice and assumed that resistance (defined as the ability of a host to encapsulate a parasitoid egg) and virulence (defined as the successful parasitization of a host) traits were graded and costly. The model explicitly detailed population and evolutionary dynamics. When holding all parameters constant and varying only the movement rate of the host and parasitoid, profoundly different dynamics were observed. We found that fluctuations in the mean levels of resistance and virulence in the global population were greatest when the movement rate of the host and parasitoid was high. In addition, we found that the variation in resistance and virulence levels among neighboring patches was greatest when the movement rates of the host and parasitoid was low. However, as the distance among patches increased, so did the variation in resistance and virulence levels regardless of movement rate. These generalizations did not hold when spatial patterns in the distribution of resistance and virulence traits, such as spirals, were observed. Finally, we found that the evolution of resistance and virulence caused the abundance of hosts to increase and the abundance of parasitoids to decrease. As a result, the spatial distribution of hosts and parasitoids was influenced.     

Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations

In this paper we develop a general mathematical model describing the spatio-temporal dynamics of host-parasitoid systems with forced generational synchronisation, for example seasonally induced diapause. The model itself may be described as an individual-based stochastic model with the individual movement rules derived from an underlying continuum PDE model. This approach permits direct comparison between the discrete model and the continuum model. The model includes both within-generation and between-generation mechanisms for population regulation and focuses on the interactions between immobile juvenile hosts, adult hosts and adult parasitoids in a two-dimensional domain. These interactions are mediated, as they are in many such host-parasitoid systems, by the presence of a volatile semio-chemical (kairomone) emitted by the hosts or the hosts food plant. The model investigates the effects on population dynamics for different host versus parasitoid movement strategies as well as the transient dynamics leading to steady states. Despite some agreement between the individual and continuum models for certain motility parameter ranges, the model dynamics diverge when host and parasitoid motilities are unequal. The individual-based model maintains spatially heterogeneous oscillatory dynamics when the continuum model predicts a homogeneous steady state. We discuss the implications of these results for mechanistic models of phenotype evolution.P. Schofield gratefully acknowledges the financial support of the BBSRC and The Wellcome Trust.     

Adaptive Host Preference and the Dynamics of Host–Parasitoid Interactions

Models of two independent host populations and a common parasitoid are investigated. The hosts have density-dependent population growth and only interact indirectly by their effects on parasitoid behavior and population dynamics. The parasitoid is assumed to experience a trade-off in its ability to exploit the two hosts. Three alternative types of parasitoid are investigated: (i) fixed generalists whose consumption rates are those that maximize fitness; (ii) “ideal free” parasitoids, which modify their behavior to maximize their rate of finding unparasitized hosts within a generation; and (iii) “evolving” parasitoids, whose capture rates change between generations based on quantitative genetic determination of the relative attack rates on the two hosts. The primary questions addressed are: (1) Do the different types of adaptive processes stabilize or destabilize the population dynamics? (2) Do the adaptive processes tend to equalize or to magnify differences in host densities? The models show that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.     

Temporal variation and the evolution of a parasitoid foraging cue

This work details theory in which selection favors generalists in a more variable environment. Specifically, in a two-host-one-parasitoid model, temporal variation in host abundances alters the optimal searching strategy and leads to the evolution of more generalist parasitoid strategies. Consistent with empirical observations, parasitoids learn host/plant odors, and use them as a cue to search for oviposition sites. The amount of unsuccessful search time required before a parasitoid alters its searching cues (the "giving-up time") is modeled in order to understand the evolutionarily optimal giving-up times under a variety of conditions. When host abundances vary across time, a generalist parasitoid strategy evolves with short giving-up times as it is likely that the host initially favored by a parasitoid will now have a low abundance. In contrast, when populations reach stable dynamics across time, giving-up times typically evolve to longer times, i.e. parasitoids remain specialized longer. The effect of temporal fluctuations is consistent across variation caused by endogenous population interactions and, to some degree, by environmental stochasticity. The conclusions are robust in that there is a strong degree of concordance between the results of a stochastic, individual-based model and a deterministic, numerical model. As an extension, spatial variation in hosts that leads to unequal tradeoffs between generalist parasitoids and specialist parasitoids may also result in the evolution of reduced giving-up times.     

Strange limits of stability in host-parasitoid systems

The classical Nicholson-Bailey model for a two species host-parasitoid system with discrete generations assumes random distributions of both hosts and parasitoids, randomly searching parasitoids, and random encounters between the individuals of the two species. Although unstable, this model induced many investigations into more complex host-parasitoid systems. Local linearized stability analysis shows that equilibria of host parasitoid systems within the framework of a generalized Nicholson-Bailey model are generally unstable. Stability is only possible if host fertility does not exceede ⁴=54.5982 and if superparasitism is unsuccessful. This special situation has already been discovered by Hassell et al. (1983) in their study of the effects of variable sex ratios on host parasitoid dynamics. We discuss global behaviour of the Hassell-Waage-May model using KAM-theory and illustrate its sensitivity to small perturbations, which can give rise to radically different patterns of the population dynamics of interacting hosts and parasitoids.     

Host-feeding and oviposition by parasitoids in relation to host stage: Consequences for parasitoid-host population dynamics

Among parasitoids which host-feed destructively, there is a tendency for females to partition their feeding and oviposition behaviour in relation to different host stages, feeding preferentially or exclusively on earlier host stages and ovipositing preferentially or exclusively in (or on) later ones. We explored the dynamic implications of this behaviour for parasitoid-host population dynamics, using modifications of the age-structured simulation models of Kidd and Jervis (1989, 1991). Using the new versions of the models, we compared the situation where parasitoids practice host stage discrimination with respect to feeding and oviposition, with the situation where they do not. Additionally, we examined the effects of host stage discrimination on populations by (a) having generations either discrete or overlapping, (b) varying initial age structure, (c) having varying degrees of density dependence acting on host adult mortality, and (d) varying parasitoid develoment times in relation to the length of host development. With either discrete or overlapping generations of the host population, a reduction in the parasitoid development time had a destabilizing influence on the parasitoid-host population interaction. With discrete generations stage discrimination had no effect on the risk of extinction, irrespective of either the degree of density dependence acting on the host population, or the initial age structure of the host population. When parasitoid search was uncoupled from the insect's adult energy requirements, the interaction was always unstable. With continuous generations, stage discrimination affected stability at certain parasitoid development times, but not at others. The relative lengths of parasitoid and host development times also influenced the tendency of the host population to show discrete or overlapping generations.     

An integrative approach to understanding host–parasitoid population dynamics in real landscapes

Many of our advances regarding the spatial ecology of predators and prey have been attributed to research with insect parasitoids and their hosts. Host–parasitoid systems are ideal for spatial-ecological studies because of the small size of the organisms, the often discrete distribution of their resources, and the relative ease with which host mortality from parasitoids can be determined. We outline an integrated approach to studying host–parasitoid interactions in heterogeneous natural landscapes. This approach involves conducting experiments to obtain critically important information on dispersal and boundary behavior of the host and parasitoid, large-scale manipulations of landscape structure to reveal the impacts of landscape change on host–parasitoid interactions and temporal population dynamics, and the development of spatially realistic, behavior-based landscape models. The dividends from such an integrative approach are far reaching, as is illustrated in our research on the prairie planthopper Prokelisia crocea and its egg parasitoid Anagrus columbi that occurs in the tall-grass prairies of North America. Here, we describe the population structure of this system which is based on a long-term survey of planthoppers and parasitoids among host–plant patches. We also outline novel approaches to experimentally quantify and model the movement and boundary behavior of animals in general. The value of this information is revealed in a landscape-level field experiment that was designed to test predictions about how landscape change affects the spatial and temporal population dynamics of the host and parasitoid. Finally, with these empirical data as the foundation, we describe novel simulation models that are spatially realistic and behavior based. Drawing from this integrated approach and case study, we identify key research questions for the future.     

An implicit approach to model plant infestation by insect pests

Various spatial approaches were developed to study the effect of spatial heterogeneities on population dynamics. We present in this paper a flux-based model to describe an aphid-parasitoid system in a closed and spatially structured environment, i.e. a greenhouse. Derived from previous work and adapted to host-parasitoid interactions, our model represents the level of plant infestation as a continuous variable corresponding to the number of plants bearing a given density of pests at a given time. The variation of this variable is described by a partial differential equation. It is coupled to an ordinary differential equation and a delay-differential equation that describe the parasitized host population and the parasitoid population, respectively. We have applied our approach to the pest Aphis gossypii and to one of its parasitoids, Lysiphlebus testaceipes, in a melon greenhouse. Numerical simulations showed that, regardless of the number and distribution of hosts in the greenhouse, the aphid population is slightly larger if parasitoids display a type III rather than a type II functional response. However, the population dynamics depend on the initial distribution of hosts and the initial density of parasitoids released, which is interesting for biological control strategies. Sensitivity analysis showed that the delay in the parasitoid equation and the growth rate of the pest population are crucial parameters for predicting the dynamics. We demonstrate here that such a flux-based approach generates relevant predictions with a more synthetic formalism than a common plant-by-plant model. We also explain how this approach can be better adapted to test different management strategies and to manage crops of several greenhouses.     

Population dynamics and sex ratio of a parasitoid altered by fungal-infected diet of host butterfly

Variation of host quality affects population dynamics of parasitoids, even at the landscape scale. What causes host quality to vary and the subsequent mechanisms by which parasitoid population dynamics are affected can be complex. Here, we examine the indirect interaction of a plant pathogen with a parasitoid wasp. Under laboratory conditions, parasitoids from hosts fed fungus-infected plants weighed less than those from hosts fed uninfected plants, indicating that the fungus causes the hosts to be of poor quality. However, parasitoids reared from hosts fed fungal-infected diet also tended to be female, a characteristic associated with high host quality. The pathogen, herbivore and parasitoid persist regionally as metapopulations in a shared landscape in Aland, Finland. In an analysis of the metapopulation dynamics of the parasitoid over 6 years, the probability of colonization of a host population increased by more than twofold in patches occupied by the plant pathogen. While we cannot determine that the relationship is causal, a compelling explanation is that the plant pathogen facilitates the establishment by the parasitoid by increasing the fraction of female offspring. This is a novel mechanism of spatial multi-trophic level interactions.     

Searching for Food or Hosts: The Influence of Parasitoids Behavior on Host–Parasitoid Dynamics

A host–parasitoid system with overlapping generations is considered. The dynamics of the system is described by differential equations with a control parameter describing the behavior of the parasitoids. The control parameter models how the parasitoids split their time between searching for hosts and searching for non-host food. The choice of the control parameter is based on the assumption that each parasitoid maximizes the instantaneous growth rate of the number of copies of its genotype. It is shown that optimal individual behavior of parasitoids, with respect to time sharing between hosts and food searching, may have a stabilizing effect on the host–parasitoid dynamics.     

Emergence of global behaviour in a host–parasitoid model with density-dependent dispersal in a chain of patches

We present a time discrete spatial host–parasitoid model. The environment is a chain of patches connected by dispersal events. Dispersal of parasitoids is host-density dependent. When the host density is small (resp. high), the proportion of migrant parasitoids is close to unity (resp. to zero). We assume fast patch to patch dispersal with respect to local interactions. Local host–parasitoid interactions are described by the classical Nicholson–Bailey model. By using time scales separation methods (or aggregation methods), we obtain a reduced model that governs the total host and parasitoid densities (obtained by addition over all patches). The aggregated model describes the time evolution of the total number of hosts and parasitoids of the system of patches. This global model is useful to make predictions of emerging behaviour regarding the dynamics of the complete system. We study the effects of number of patches and host density-dependent parasitoid dispersal on the overall stability of the host–parasitoid system. We finally compare our stability results with the CV² > 1 rule.     

A dynamic refuge model and population regulation by insect parasitoids

1. The population dynamic effects of refuges, which hosts enter and leave by diffusive movement, in host–parasitoid interactions are explored using simple models in continuous time.
2. This type of refuge has a stabilizing effect on a host–parasitoid interaction, which is contrary to the implications of some previous models.
3. Stability can be explained by considering how depletion processes lead to a refuge proportion (proportion of hosts protected at a given instant) that increases as parasitoid density increases. This effect is synonymous with pseudointerference in the context of the model.
4. Very high rates of movement of host larvae largely destroy this stability process. Stability is greatest at intermediate levels of movement.
5. Density-dependent host movement can alter the effect of these refuges such that they are either more stabilizing, or tend to destabilize, the dynamics of host–parasitoid systems, depending on the type of density dependence assumed. The conclusion that intermediate movement rates are likely to generate stability with this general type of refuge is not altered in the presence of any type of density dependence, unless the density dependence is at levels which we consider unrealistically high and unlikely to be encountered in nature.
6. It is the assumption that larvae do not move into the refuge prior to becoming vulnerable to parasitism that ensures top-down population control in the model. Thus, parasitoids attacking very early instars make good candidates for biological control when faced with a structural refuge.     

Can hyperparasitoids cause large‐scale outbreaks of insect herbivores?

Synchronous population fluctuations occur in many species and have large economic impacts, but remain poorly understood. Dispersal, climate and natural enemies have been hypothesized to cause synchronous population fluctuations across large areas. For example, insect herbivores cause extensive forest defoliation and have many natural enemies, such as parasitoids, that may cause landscape‐scale changes in density. Between outbreaks, parasitoid‐caused mortality of hosts/herbivores is high, but it drops substantially during outbreak episodes. Because of their essential role in regulating herbivore populations, we need to include parasitoids in spatial modelling approaches to more effectively manage insect defoliation. However, classic host‐parasitoid population models predict parasitoid density, and parasitoid density is difficult to relate to host‐level observations of parasitoid‐caused mortality. We constructed a novel model to study how parasitoids affect insect outbreaks at the landscape scale. The model represents metacommunity dynamics, in which herbivore regulation, colonisation and extinction are driven by interactions with the forest, primary parasitoids and hyperparasitoids. The model suggests that parasitoid spatial dynamics can produce landscape‐scale outbreaks. Our results propose the testable prediction that hyperparasitoid prevalence should increase just before the onset of an outbreak because of hyperparasitoid overexploitation. If verified empirically, hyperparasitoid distribution could provide a biotic indicator that an outbreak will occur.     

Competitive Interactions between Parasitoids Provide New Insight into Host Suppression

Understanding the dynamics of potential inter- and intraspecific competition in parasitoid communities is crucial in the screening of efficient parasitoid species and for utilization of the best parasitoid species combinations. In this respect, the host-parasitoid systems, Bemisia tabaci and two parasitoids, Eretmocerus hayati (exotic) and Encarsia sophia (existing) were studied under laboratory conditions to investigate whether interference competition between the exotic and existing species occurs as well as the influence of potential interference competition on the suppression of the host B. tabaci. Studies on interspecific-, intraspecific- and self-interference competition in two parasitoid species were conducted under both rich and limited host resource conditions. Results showed that (1) both parasitoid species negatively affect the progeny production of the other under both rich and limited host resource conditions; (2) both parasitoid species interfered intraspecifically on conspecific parasitized hosts when the available hosts are scarce and; 3) the mortality of B. tabaci induced by parasitoids via parasitism, host-feeding or both parasitism and host-feeding together varied among treatments under different host resource conditions, but showed promise for optimizing control strategies. As a result of our current findings, we suggest a need to investigate the interactions between the two parasitoids on continuous generations.     

Migration frequency and the persistence of host-parasitoid interactions

This paper analyses the effect of migration frequency on the stability and persistence of a host-parasitoid system in a two-patch environment. The hosts and parasitoids are allowed to move from one patch to the other a certain number of times within a generation. When this number is low, i.e. when the time-scales associated with migration and demography are of the same order, host-parasitoid interactions are usually not persistent. When this number is high, however, persistence is more likely. Moreover, in this situation, aggregation methods can be used to simplify the proposed initial model into an aggregated model describing the dynamics of both the total host and parasitoid populations. Analysis of the aggregated model shows that the system reaches a stable steady state for some regions of the parameter domain. Persistence occurs when the movement of the parasitoids is asymmetrical, i.e. they move preferentially to one of the two patches. We show that the growth rate of the host population is a key parameter in determining which migration strategies of the parasitoids lead to persistent host-parasitoid interactions.     

A simulation study of population interaction between the greenhouse whitefly,Trialeurodes vaporariorum Westwood (Homoptera: Aleyrodidae) and the parasitoidEncarsia formosa Gahan (Hymenoptera: Aphelinidae) II. Simulation analysis of population dynamics and strategy of biological control

Simulation studies were performed to analyze factors affecting the population dynamics of the system with the greenhouse whitefly (Trialeurodes vaporariorumWestwood ) and the parasitoid Encarsia formosaGahan and to develop strategies for the introduction of E. formosa. The reduction of parasitization efficiency with an increase in parasitoid density promotes the stability of the system, which coincides with the prediction from current theory. The stability of the system is also shown to be promoted by the effect of host feeding. The population levels of the system are remarkably suppressed with an increase in searching efficiency and a decrease in host oviposition. The control effect of the parasitoids is enhanced when the number of parasitoids is divided among many introductions. An optimal time, an optimal density ratio of parasitoids to hosts and optimal densities of hosts and parasitoids exist in the introduction programme of parasitoids.     

A two-component model of host-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control

A two-component differential equation model is formulated for a host-parasitoid interaction. Transient dynamics and population crashes of this system are analysed using differential inequalities. Two different cases can be distinguished: either the intrinsic growth rate of the host population is smaller than the maximum growth rate of the parasitoid or vice versa. In the latter case, the initial ratio of parasitoids to hosts should exceed a given threshold, in order to (temporarily) halt the growth of the host population. When not only oviposition but also host-feeding occurs the dynamics do not change qualitatively. In the case that the maximum growth rate of the parasitoid population is smaller than the intrinsic growth rate of the host, a threshold still exists for the number of parasitoids in an inundative release in order to limit the growth of the host population. The size of an inundative release of parasitoids, which is necessary to keep the host population below a certain level, can be determined from the two-component model. When parameter values for hosts and parasitoids are known, an effective control of pests can be found. First it is determined whether the parasitoids are able to suppress their hosts fully. Moreover, using our simple rule of thumb it can be assessed whether suppression is also possible when the relative growth rate of the host population exceeds that of the parasitoid population. With a numerical investigation of our simple system the design of parasitoid release strategies for specific situations can be computed.     

Host–parasitoid spatial models: the interplay of demographic stochasticity and dynamics

Host–parasitoid metapopulation models have typically been deterministic models formulated with population numbers as a continuous variable. Spatial heterogeneity in local population abundance is a typical (and often essential) feature of these models and means that, even when average population density is high, some patches have small population sizes. In addition, large temporal population fluctuations are characteristic of many of these models, and this also results in periodically small local population sizes. Whenever population abundances are small, demographic stochasticity can become important in several ways. To investigate this problem, we have reformulated a deterministic, host–parasitoid metapopulation as an integer-based model in which encounters between hosts and parasitoids, and the fecundity of individuals are modelled as stochastic processes. This has a number of important consequences: (1) stochastic fluctuations at small population sizes tend to be amplified by the dynamics to cause massive population variability, i.e. the demographic stochasticity has a destabilizing effect; (2) the spatial patterns of local abundance observed in the deterministic counterpart are largely maintained (although the area of ''spatial chaos'' is extended); (3) at small population sizes, dispersal by discrete individuals leads to a smaller fraction of new patches being colonized, so that parasitoids with small dispersal rates have a greater tendency for extinction and higher dispersal rates have a larger competitive advantage; and (4) competing parasitoids that could coexist in the deterministic model due to spatial segregation cannot now coexist for any combination of parameters.     

Effects of climate warming on host–parasitoid interactions

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