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.     

Host-Parasitoid Dynamics and the Success of Biological Control When Parasitoids Are Prone to Allee Effects

In sexual organisms, low population density can result in mating failures and subsequently yields a low population growth rate and high chance of extinction. For species that are in tight interaction, as in host-parasitoid systems, population dynamics are primarily constrained by demographic interdependences, so that mating failures may have much more intricate consequences. Our main objective is to study the demographic consequences of parasitoid mating failures at low density and its consequences on the success of biological control. For this, we developed a deterministic host-parasitoid model with a mate-finding Allee effect, allowing to tackle interactions between the Allee effect and key determinants of host-parasitoid demography such as the distribution of parasitoid attacks and host competition. Our study shows that parasitoid mating failures at low density result in an extinction threshold and increase the domain of parasitoid deterministic extinction. When proned to mate finding difficulties, parasitoids with cyclic dynamics or low searching efficiency go extinct; parasitoids with high searching efficiency may either persist or go extinct, depending on host intraspecific competition. We show that parasitoids suitable as biocontrol agents for their ability to reduce host populations are particularly likely to suffer from mate-finding Allee effects. This study highlights novel perspectives for understanding of the dynamics observed in natural host-parasitoid systems and improving the success of parasitoid introductions.     

The influence of varying spatial heterogeneity on the refuge model for coexistence of specialist parasitoid assemblages

Models of host–parasitoid dynamics often assume constant levels of spatial heterogeneity in parasitoid attack rate, which tends to stabilize the interactions. Recently, authors have questioned this assumption and shown that outcomes of simple host–parasitoid models change if spatial heterogeneity is allowed to vary with parasitoid density. Here, we allow spatial heterogeneity to vary with either parasitoid density or percent parasitism in a model designed to explain specialist parasitoid coexistence on insect hosts with various levels of refuge. By examining this model we can evaluate the effect of varying spatial heterogeneity on a more complex model in which spatial heterogeneity is not considered the primary determinant of persistence. By modeling communities with one host and two parasitoid species, we show that the probability of species persistence for the competitively inferior parasitoid depends on the assumed relationship between spatial heterogeneity and both parasitoid density and percent parasitism. The probability of parasitoid coexistence is generally lower when spatial heterogeneity varies with parasitoid demographics. We conclude that the conditions for which host refuge promote specialist parasitoid coexistence are less common that proposed by the original model. Finally, we compared a model in which spatial heterogeneity varies with percent parasitism to data from laboratory trials and find a reasonable fit. We conclude that the change in spatial heterogeneity strongly influenced the outcome of the laboratory trials, and we suggest more research is necessary before researchers can assume constant spatial heterogeneity in future models.     

Coexistence of specialist parasitoids with host refuges in the laboratory and the dynamics of spatial heterogeneity in attack rate

There is a well documented relationship between parasitoid species assemblage size and host feeding niche. Parasitoid assemblage size peaks on hosts thought to have intermediate levels of physical refuge. We examined the influence of refuges on parasitoid coexistence using pairs of specialist parasitoids in a controlled laboratory environment. Using physical barriers we excluded parasitoids from 0, 25, 50 or 75% of the hosts to simulate host refuge. We found no evidence that host refuges can promote parasitoid coexistence in a simplified laboratory environment. Results were similar whether pairs of parasitoid species were competitively disparate or competitively similar. Our results suggest that spatial heterogeneity in parasitoid attack rate was not sufficient to maintain parasitoid coexistence regardless of host refuge, and we argue that the level of spatial heterogeneity necessary to promote coexistence is rare in nature. We conclude that in most systems the coexistence of specialist parasitoids cannot be explained by a host refuge effect.     

The effect of evolution on host-parasitoid systems

It is well known that a simple first-order difference equation can exhibit complex population dynamics, such as sustained oscillations and chaos. An interesting problem is whether such oscillatory dynamics are expected to occur in real populations. This paper assumes that the resident system is composed of 1-host and 1-parasitoid and that only the host is allowed to evolve, but not the parasitoid. Based on the invasibility of a host to host-parasitoid systems, we investigate the dynamics of the host-parasitoid system favored by natural selection. We consider two cases. In the first case, the host's evolution involving both the intrinsic growth rate and the sensitivity to density is considered. In the second case, the host's evolution involving both the intrinsic growth rate and the vulnerability to the parasitoid is considered. In both cases, we see that the dynamics with a stable equilibrium will not be favored by natural selection without the trade-off between the host's traits which are allowed to evolve. The host-parasitoid system with a stable equilibrium will be eventually invaded by a host type that develops an unstable equilibrium with the parasitoid. If there is a trade-off between the host's traits which are allowed to evolve, a host-parasitoid system with a stable equilibrium can be favored by natural selection.     

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.     

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.     

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.     

Temporal/spatial structure and the dynamical property of laboratory host-parasitoid systems

The effects of spatial structure in terms of local capacity, or the maximum number of larvae surviving competition at resource patches, and temporal structure in terms of the period vulnerable to parasitoid attack in host populations on the persistence of host-parasitoid systems were quantitatively evaluated by laboratory experiments and well-parameterized model analyses. One of two bruchid beetles,Callosobruchus maculatus andC. phaseoli, were used as a host with Heterospilus prosopidis used as the parasitoid.C. maculatus, in which few larvae survive competition to become adults in each bean, andC. phaseoli, in which many larvae become adults in each bean, along with two kinds of beans, the mung and the azuki, were combined to construct four (2×2) resource-herbivorous host-parasitoid systems that differed in local capacity and vulnerable period. The mung-C. maculatus system with the parasitoid was the most persistent, i.e., took the longest time for extinction of either the host or parasitoid to occur. Since this resource-herbivorous host combination exhibited the lowest local capacity and the shortest vulnerable period, these two conditions possibly promoted the persistence of the system. A model incorporating the host population structure supported the observed persistence. Furthermore, the possible contribution of the timing of density-dependent competition of the host on the host-parasitoid persistence is predicted.     

The role of transient dynamics in biological pest control: insights from a host-parasitoid community

1. Identifying natural enemies that can maintain pests at low abundances is a priority in biological control. Here, we show that experiments combined with models generate new insights into identifying effective control agents prior to their release in the field. Using a host-parasitoid community (the harlequin bug and its egg parasitoids) as a model system, we report three key findings. 2. The interplay between the host's self-limitation and the parasitoids' saturating functional response causes the long-term (steady-state) outcomes for pest suppression to differ from those of short-term (transient) dynamics. When the bug's self-limitation is moderately strong, the parasitoid with the higher attack rate and conversion efficiency (Ooencyrtus) achieves greater host suppression in the long term, but its longer handling time causes long periods of transient dynamics during which the bug can reach high abundances; when the bug's self-limitation is weak, host fluctuations amplify over time and Ooencyrtus fails at host suppression altogether. In contrast, the parasitoid with the lower attack rate and conversion efficiency but the shorter handling time (Trissolcus) induces only weak transient fluctuations of short duration and can maintain the host at low abundances regardless of the strength of the bug's self-limitation. 3. Release of multiple enemy species can compromise host suppression if an enemy that induces stronger transient fluctuations excludes one that induces weaker fluctuations. For instance, Ooencyrtus excludes Trissolcus despite having a longer handling time because of its higher conversion efficiency. The model correctly predicts the time to exclusion observed in experiments, suggesting that it captures the key biological features of the host-parasitoid interaction. 4. Intraspecific interference reduces long-term pest suppression but improves short-term pest control by reducing the magnitude and duration of transient fluctuations. 5. These results highlight the importance of transient dynamics in pest suppression. Pests are unlikely to be strongly self-limited because they attack crop monocultures. Hence, pest fluctuations are likely to dominate short-term dynamics even when the long-term outcome is a stable equilibrium. The tendency to induce strong transient fluctuations (e.g. through a long handling time) is therefore a crucial consideration when identifying effective pest control agents.     

Elevated Temperature and Drought Interact to Reduce Parasitoid Effectiveness in Suppressing Hosts

Climate change affects the abundance, distribution and activity of natural enemies that are important for suppressing herbivore crop pests. Moreover, higher mean temperatures and increased frequency of climatic extremes are expected to induce different responses across trophic levels, potentially disrupting predator-prey interactions. Using field observations, we examined the response of an aphid host-parasitoid system to variation in temperature. Temperature was positively associated with attack rates by parasitoids, but also with a non-significant trend towards increased attack rates by higher-level hyperparasitoids. Elevated hyperparasitism could partly offset any benefit of climate warming to parasitoids, and would suggest that higher trophic levels may hamper predictions of predator-prey interactions. Additionally, the mechanisms affecting host-parasitoid dynamics were examined using controlled laboratory experiments that simulated both temperature increase and drought. Parasitoid fitness and longevity responded differently when exposed to each climatic variable in isolation, compared to the interaction of both variables at once. Although temperature increase or drought tended to positively affect the ability of parasitoids to control aphid populations, these effects were significantly reversed when the drivers were expressed in concert. Additionally, separate warming and drought treatments reduced parasitoid longevity, and although temperature increased parasitoid emergence success and drought increased offspring production, combined temperature and drought produced the lowest parasitoid emergence. The non-additive effects of different climate drivers, combined with differing responses across trophic levels, suggest that predicting future pest outbreaks will be more challenging than previously imagined.     

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.     

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.     

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.     

Host-parasitoid association and diffuse coevolution: when to be a generalist?

In host-parasitoid communities, hosts are subjected to selective pressures from numerous parasitoid species, and parasitoids may attack several host species. The specificity of host resistance and parasitoid virulence is thus a key factor in host-parasitoid coevolution. A continuum of strategies exists, from strict specificity to a generalist strategy. The optimal level of specificity may differ in host and parasitoid. I investigated the optimal level of resistance specificity using a model in which the host could be attacked by two parasitoid species, with variable levels of defense specificity. The fitness of a parasitoid attacking two host species with different levels of virulence specificity was also modeled. Finally, a fluctuating environment was simulated by introducing variable probabilities of encounters between antagonistic species over several generations. If the frequency of encounters with the antagonistic species is fixed, then both host and parasitoid gain from a strategy of exclusive specialization toward the most frequent antagonist. If the frequency of encounters fluctuates between generations, generalist host resistance and partially specialist parasitoid virulence are favored. Generalist host resistance may be considered to be a bet-hedging response to an unpredictable environment. This asymmetry in host-parasitoid coevolution may account for some of the genetic structures observed in the field for host-parasitoid associations.     

Dynamical consequences of optimal host feeding on host-parasitoid population dynamics

This study examines the influence of various host-feeding patterns on host-parasitoid population dynamics. The following types of host-feeding patterns are considered: concurrent and non-destructive, non-concurrent and non-destructive, and non-concurrent and destructive. The host-parasitoid population dynamics is described by the Lotka-Volterra continuous-time model. This study shows that when parasitoids behave optimally, i.e. they maximize their fitness measured by the instantaneous per capita growth rate, the non-destructive type of host feeding stabilizes host-parasitoid dynamics. Other types of host feeding, i.e. destructive, concurrent, or non-concurrent, do not qualitatively change the neutral stability of the Lotka-Volterra model. Moreover, it is shown that the pattern of host feeding which maximizes parasitoid fitness is either non-concurrent and destructive, or concurrent and non-destructive host feeding, depending on the host abundance and parameters of the model. The effects of the adaptive choice of host-feeding patterns on host-parasitoid population dynamics are discussed.     

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.     

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. CV<CV ^*), then the parasitoid drives the host to extinction. When parasitoids are weakly search-limited as well as egg-limited, coexistence about a global attractor occurs even if CV<CV ^*. However, numerical simulations suggest that the nature of this attractor depends critically on whether CV<1 or CV>1. 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.     

The effects of parasitoid fecundity and host taxon on the biological control of insect pests: the relationship between theory and data

1. A simple, intuitive argument and the tenets of the biological control literature both suggest that, in general, parasitoids with a greater fecundity will provide better control of their hosts, and will thus be better biological control agents. 2. A model of host-parasitoid dynamics, based on the standard Thompson–Nicholson–Bailey approach and incorporating the effects of parasitoid fecundity-limitation and host density-dependence, also indicates that as parasitoid fecundity decreases so does local stability and the degree of host suppression. 3. A taxonomically diverse data set obtained from the biological control record failed to support this theoretical prediction, but at the same time indicated a strong effect of host taxon on the outcome of biological control. 4. The hypothesis that the fecundity of parasitoids is correlated positively with their ability to suppress host populations is supported by data exclusively from the host order Lepidoptera. 5. Possible explanations for the divergence between the fecundity-limitation hypothesis and the complete data set include: the ability of parasitoids to provide long-term control of pests without the presence of a stable host–parasitoid equilibrium; differences between the concepts of successful control in theory and practice; evolutionary trade-offs between fecundity and other parasitoid life-history features, such as search efficiency, leading to better pest control by parasitoids with low fecundity; and differing windows of vulnerability to parasitoid attack between host taxa.