Modelling the spatio-temporal dynamics of multi-species host-parasitoid interactions: heterogeneous patterns and ecological implications

A mathematical model of the spatio-temporal dynamics of a two host, two parasitoid system is presented. There is a coupling of the four species through parasitism of both hosts by one of the parasitoids. The model comprises a system of four reaction-diffusion equations. The underlying system of ordinary differential equations, modelling the host-parasitoid population dynamics, has a unique positive steady state and is shown to be capable of undergoing Hopf bifurcations, leading to limit cycle kinetics which give rise to oscillatory temporal dynamics. The stability of the positive steady state has a fundamental impact on the spatio-temporal dynamics: stable travelling waves of parasitoid invasion exhibit increasingly irregular periodic travelling wave behaviour when key parameter values are increased beyond their Hopf bifurcation point. These irregular periodic travelling waves give rise to heterogeneous spatio-temporal patterns of host and parasitoid abundance. The generation of heterogeneous patterns has ecological implications and the concepts of temporary host refuge and niche formation are considered.     

Influence of parasitized adult reproduction on host-parasitoid dynamics: an age-structured model

In this work, we develop an age-structured model (based on delay-differential equations) to investigate the dynamics of host-parasitoid systems in which adults are the target of parasitism. The rare previous work dealing with such interactions assumes that hosts are functionally dead as soon as they are attacked. We relax this assumption and show that low reproduction rates of parasitized hosts can promote stability at the expense of cyclic behavior (either long term or generation cycles). Higher reproduction rates make the regulation of the host population by parasitoids impossible. As it is the case in models in which adults are subjected to attacks but do not reproduce, our model generates generation cycles for a larger set of parameter values than in models in which juveniles are attacked.     

Host-parasitoid dynamics of a generalized Thompson model

A discrete-time host-parasitoid model including host-density dependence and a generalized Thompson escape function is analyzed. This model assumes that parasitoids are egg-limited but not search-limited, and is proven to exhibit five types of dynamics: host failure in which the host goes extinct in the parasitoid's presence or absence, unconditional parasitoid failure in which the parasitoid always goes extinct while the host persists, conditional parasitoid failure in the host and the parasitoid go extinct or coexist depending on the initial host-parasitoid ratio, parasitoid driven extinction in which the parasitoid invariably drives the host to extinction, and coexistence in which the host and parasitoid coexist about a global attractor. The latter two dynamics only occur when the parasitoid's maximal rate of growth exceeds the host's maximal rate of growth. Moreover, coexistence requires parasitism events to be sufficiently aggregated. Small additive noise is proven to alter the dynamical outcomes in two ways. The addition of noise to parasitoid driven extinction results in random outbreaks of the host and parasitoid with varying intensity. Additive noise converts conditional parasitoid failure to unconditional parasitoid failure. Implications for classical biological control are discussed.     

Prolonged diapause and the stability of host-parasitoid interactions

We investigated the effect on host-parasitoid dynamics of prolonged diapause, a feature of the life history of many animals living in unpredictable environments, by modifying the classical May (J. Anim. Ecol. 47 (1978) 833) host-parasitoid model. We considered three patterns of development of host and parasitoid: (a) prolonged parasitoid diapause controlled by host physiology, (b) parasitoid interference in host development, preventing parasitized hosts from prolonging diapause, and (c) host diapause independent of parasitoid attack. We found that single-year prolonged diapause shifted the boundaries of the May model towards a slight increase in stability. Longer periods of diapause prolongation had a stronger influence, but this influence remained modest if we considered realistic parameter values. In contrast to other recent studies, our results suggest that prolonged diapause does not necessarily compensate for the destabilizing effects of time lags on the influence of parasitoids on population dynamics.     

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.     

Models for integrated pest control and their biological implications

Successful integrated pest management (IPM) control programmes depend on many factors which include host-parasitoid ratios, starting densities, timings of parasitoid releases, dosages and timings of insecticide applications and levels of host-feeding and parasitism. Mathematical models can help us to clarify and predict the effects of such factors on the stability of host-parasitoid systems, which we illustrate here by extending the classical continuous and discrete host-parasitoid models to include an IPM control programme. The results indicate that one of three control methods can maintain the host level below the economic threshold (ET) in relation to different ET levels, initial densities of host and parasitoid populations and host-parasitoid ratios. The effects of host intrinsic growth rate and parasitoid searching efficiency on host mean outbreak period can be calculated numerically from the models presented. The instantaneous pest killing rate of an insecticide application is also estimated from the models. The results imply that the modelling methods described can help in the design of appropriate control strategies and assist management decision-making. The results also indicate that a high initial density of parasitoids (such as in inundative releases) and high parasitoid inter-generational survival rates will lead to more frequent host outbreaks and, therefore, greater economic damage. The biological implications of this counter intuitive result are discussed.     

Evolutionary character changes and population responses in an insect host-parasitoid experimental system

In an insect host (the cowpea weevilCallosobruchus maculatus)- parasitoidHeterospilus prosopidis) experimental system, the population densities of the component species oscillated for the first 20 generations and then abruptly stabilized as the parasitoid density decreased. Examination of the host and parasitoid after the 40th generation in the long-term experiment showed that (1) host larvae exhibited contest-type competition (killing other larvae inhabiting the same bean), in contrast to the founder population being scramble-type competitors and (2) the parasitoid attack rate on the host did not change. There was also an evolutionary trade-off between body size and the rates of larval survival and development, suggesting a cost of contest competition on larval survivorship and development. I tested model predictions (Tuda and Iwasa 1998) that (1) host equilibrium population size should gradually decrease as the proportion of the contest type increases and that (2) random attacks of the parasitoid on the host should reduce the rate of increase in proportion of the contest type, and the effect should become manifest especially during the first 20 generations. Two of three host-only replicates showed significant decrease in population sizes. Although the density of emerging adults per bean did not differ between replicates of the host-only and host-parasitoid systems, comparison of the host body size between them on day 270 (at the 13th generation) showed that the host was more contest-type in the host-only system than in the host-parasitoid system, as the model predicted, and later on day 650 the effect of the parasitoid had disappeared.     

The dynamical consequences of developmental variability and demographic stochasticity for host-parasitoid interactions

Few age-structured models of species dynamics incorporate variability and uncertainty in population processes. Motivated by laboratory data for an insect and its parasitoid, we investigate whether such assumptions are appropriate when considering the population dynamics of a single species and its interaction with a natural enemy. Specifically, we examine the effects of developmental variability and demographic stochasticity on different types of cyclic dynamics predicted by traditional models. We show that predictions based on the deterministic fixed-development approach are differentially sensitive to variability and noise in key life stages. In particular, we find that the demonstration of half-generation cycles in the single-species model and the multigeneration cycles in the host-parasitoid model are sensitive to the introduction of developmental variability and noise, whereas generation cycles are robust to the intrinsic variability and uncertainty that may be found in nature.     

Host suitability of a gregarious parasitoid on beetle hosts: flexibility between fitness of adult and offspring

Behavioral tactics play a crucial role in the evolution of species and are likely to be found in host-parasitoid interactions where host quality may differ between host developmental stages. We investigated foraging decisions, parasitism and related fitness in a gregarious ectoparasitoid, Sclerodermus harmandi in relation to two distinct host developmental stages: larvae and pupae. Two colonies of parasitoids were reared on larvae of Monochamus alternatus and Saperda populnea (Cerambycidae: Lamiinae). Paired-choice and non-choice experiments were used to evaluate the preference and performance of S. harmandi on larvae and pupae of the two species. Foraging decisions and offspring fitness-related consequences of S. harmandi led to the selection of the most profitable host stage for parasitoid development. Adult females from the two colonies oviposited more quickly on pupae as compared to larvae of M. alternatus. Subsequently, their offspring development time was faster and they gained higher body weight on the pupal hosts. This study demonstrates optimal foraging of intraspecific détente that can occur during host-parasitoid interactions, of which the quality of the parasitism (highest fitness benefit and profitability) is related to the host developmental stage utilized. We conclude that S. harmandi is able to perfectly discriminate among host species or stages in a manner that maximizes its offspring fitness. The results indicated that foraging potential of adults may not be driven by its maternal effects, also induced flexibly with encountering prior host quality.     

Fitting host-parasitoid models with CV2 > 1 using hierarchical generalized linear models.

The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density-dependent heterogeneity (HDD) to be distinguished from between-patch, host density-independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well-known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent.     

Periodicity, persistence, and collapse in host-parasitoid systems with egg limitation

There is an emerging consensus that parasitoids are limited by the number of eggs which they can lay as well as the amount of time they can search for their hosts. Since egg limitation tends to destabilize host-parasitoid dynamics, successful control of insect pests by parasitoids requires additional stabilizing mechanisms such as heterogeneity in the distribution of parasitoid attacks and host density-dependence. To better understand how egg limitation, search limitation, heterogeneity in parasitoid attacks, and host density-dependence influence host-parasitoid dynamics, discrete time models accounting for these factors are analyzed. When parasitoids are purely egg-limited, a complete anaylsis of the host-parasitoid dynamics are possible. The analysis implies that the parasitoid can invade the host system only if the parasitoid's intrinsic fitness exceeds the host's intrinsic fitness. When the parasitoid can invade, there is a critical threshold, CV*>1, of the coefficient of variation (CV) of the distribution of parasitoid attacks that determines that outcome of the invasion. If parasitoid attacks sufficiently aggregated (i.e., CV>CV*), then the host and parasitoid coexist. Typically (in a topological sense), this coexistence is shown to occur about a periodic attractor or a stable equilibrium. If the parasitoid attacks are sufficiently random (i.e. CV1. When CV<1, the parasitoid exhibits highly oscillatory dynamics. Alternatively, when parasitoid attacks are sufficiently aggregated but not overly aggregated (i.e. CV>1 but close to 1), the host and parasitoid coexist about a stable equilibrium with low host densities. The implications of these results for classical biological control are discussed.     

Intraspecific competition and density dependence in an Ephestia kuehniella–Venturia canescens laboratory system

A model host-parasitoid system of Ephestia kuehniella and Venturia canescens was used to examine the influence of host and parasitoid density on host and parasitoid life-history parameters via a two-way factorial experimental design (5 initial host densities×3 parasitoid densities). In the absence of parasitoids, E. kuehniella experienced scramble-type competition with reduced growth, diminished adult size and a subsequent fecundity trade-off for mortality. The mortality that did occur was confined to the late larval and pupal stages. In the presence of parasitoids attacking the late larval stage, competition changed from scramble for food to contest for enemy-free space, with hosts escaping parasitism being small with low fecundity and reduced egg size, and with parasitoid adult size inversely dependent on host density. Total insect emergence (host+parasitoid), a measure of the influence of host resource competition on survivorship, exhibited a threshold effect as a function of initial host density; the threshold value was increased to a higher initial host density in the presence of parasitoids. Models of host self-limitation were fitted to the data, with the generalized Beverton-Holt model that incorporates a threshold effect providing the best fit, and the Ricker model with no threshold providing a very poor fit to the data.     

Errors associated with estimating parasitism using a modified version of Southwood's graphical method

A simulation model is used to examine the errors in estimating parasitized and nonparasitized host densities independently with Southwood's graphical technique. This technique is accurate when parasitoid attack occurs prior to the sampling period (e.g. the previous life stage of the host). When this is not the case, the parasitized host density is estimated accurately, but the unparasitized host density is over estimated by those individuals that are sampled as healthy prior to attack. This error is neglible at low levels of parasitism (<20% parasitized), but increases with increasing parasitism. Of the biological parameters tested, only the parasitoid attack pattern (shape of the parasitoid attack curve) has a significant influence on the magnitude of this error. A generalized simulation model is presented for evaluating errors in estimates of seasonal parasitism for specific host-parasitoid interactions. University of Rhode Island, Agricultural Experiment Station Journal, Article Number 2479.     

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.     

Persistent host–parasitoid interaction caused by host maturation variability

The heterogeneity of parasitism risk among host individuals is a key factor for stabilizing or sustaining host–parasitoid interactions. Host maturation variability, or the variation in the maturation times among host individuals, is the simplest source of such heterogeneity, but it has often been neglected in previous theoretical studies. We developed a configuration individual-based model (cIBM) of host–parasitoid interaction to investigate to what degree of host maturation variability promotes the persistence of host–parasitoid interactions. We ran simulations with various degrees of host maturation variability for different lengths of unsusceptible period. The result showed that low host maturation variability could sustain host–parasitoid dynamics when the host-unsusceptible period was short. Conversely, high levels of variability could sustain host–parasitoid dynamics when the host-unsusceptible period was about half of the total larval period. This suggests that the balance between variability and unsusceptible period is important for the persistence of host–parasitoid interaction. We conclude that maturation variability is a factor that can contribute to the sustainment of host–parasitoid interactions.     

Effects of patch scale on density-dependence and species-dependence in two host-parasitoid systems

Summary Data from two host-parasitoid communities were analyzed to ascertain whether patch scale affected the kinds of correlations existing between 1) spatial differences in host density and the intensity of parasitism (density-dependence) and 2) number of species of parasitoids and the intensity of parasitism (species-dependence). We concluded that parasitization rates are usually independent of both host density and number of parasitoid species present regardless of patch scale. Therefore, the responses of parasitoids to host density and the addition of parasitoid species to a community are equally unpredictable in outcome.     

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.     

A model for the coevolution of resistance and virulence in coupled host—parasitoid interactions

A coevolutionary model is developed of the interaction between a host and an internal parasitoid, where the outcome of parasitism depends upon the extent to which individual hosts invest in resistance mechanisms and individual parasitoids in countermeasures (virulence). The host and parasitoid are assumed to have coupled population dynamics (of Nicholson–Bailey form) and to be composed of a series of asexual clones with different levels of resistance and virulence. Investment in resistance and virulence mechanisms is assumed to be costly. The model has two main outcomes. First, if resistance is relatively costly compared to virulence, the host may be selected not to invest in resistance mechanisms despite parasitoid investment in virulence, in effect trading off the risks of parasitism against the savings in costs. A number of cases which appear to correspond to this result have been reported. Second, for most other feasible parameter values, an arms race occurs between host and parasitoid, until effective resistance becomes so costly that the host abandons defence. This abandonment is followed by a reduction in parasitoid virulence and the cycle begins again. These cycles may explain reports of persistent additive genetic variation in resistance and virulence, and may also contribute towards population dynamic stability.     

Host-size mediated trade-off in a parasitoid Sclerodermus harmandi

Optimality models of host-parasitoid relationships have traditionally assumed that host quality increases as a function of host size at parasitism. However, trade-offs may play a crucial role in species evolution and should be found in host-parasitoid interactions where the host quality may differ between different sizes. Here, we investigated the effects of host size differences of Monochamus alternatus larva on foraging decisions, parasitism and related fitness in a gregarious ectoparasitoid, Sclerodermus harmandi. Two-choice and non-choice experiments were conducted with M. alternatus larvae to evaluate preference and performance of S. harmandi, respectively. Results from two-choice test showed that adult females prefer to attack large larvae rather than small larvae. In no-choice tests, adult females needed more time to paralyze large larvae than small larvae before laying eggs on the body surface of M. alternatus larvae and had lower survival and parasitism rate on those large larvae. Foraging decisions of S. harmandi led to the selection of the most profitable host size for parasitoid development, which showed more offspring gained on large M. alternatus larvae than on small larvae and got higher body weight on those large hosts. This study demonstrates the existence of trade-off occurring during host-parasitoids interactions according to host size related quality.     

Metapopulation dynamics in an aphid-parasitoid system

Metapopulation theory makes a number of predictions concerning the effects of dispersal on the persistence of predator-prey or host-parasitoid systems. While the stabilising effects of dispersal have been shown in a number of laboratory studies, evidence from field studies remains scarce due to a lack of suitable model systems. I describe a host-parasitoid system that shows a classical metapopulation structure with frequent extinctions and colonisations consisting of the aphidiid Lysiphlebus hirticornisand the aphid Metopeurum fuscoviride. Both the parasitoid and the aphid are specialists on their respective hosts. I followed the dynamics of host and parasitoid on individually marked tansy (Tanacetum vulgare) plants, the host of M. fuscoviride. Dynamics of host and parasitoid populations were characterized by frequent extinctions and colonisations. Mean longevity of aphid colonies was only 3.1 weeks. Parasitism by L. hirticorniswas a main cause of extinction for the aphid as rates of parasitism often reached 100%, in particular towards the end of the field season. Patchiness in this system occurs at two spatial scales. Aphid colonies form on single tansy ramets = shoots but movements of aphid individuals among ramets within a particular tansy genet are frequent. Because aphids can persist on a genet for a large numer of generations, it is argued that local populations form on genets rather than ramets. The number of host and parasitoid extinctions described in this study exceeds the number of extinctions usually observed in field studies of host-parasitoid metapopulations. It is suggested that aphid-parasitoid systems such as the one studied in this paper may be good models to test the predictions of metapopulation theory.