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.     

Discrete-time host–parasitoid models with pest control

We propose a simple discrete-time host–parasitoid model to investigate the impact of external input of parasitoids upon the host–parasitoid interactions. It is proved that the input of the external parasitoids can eventually eliminate the host population if it is above a threshold and it also decreases the host population level in the unique interior equilibrium. It can simplify the host–parasitoid dynamics when the host population practices contest competition. We then consider a corresponding optimal control problem over a finite time period. We also derive an optimal control model using a chemical as a control for the hosts. Applying the forward–backward sweep method, we solve the optimal control problems numerically and compare the optimal host populations with the host populations when no control is applied. Our study concludes that applying a chemical to eliminate the hosts directly may be a more effective control strategy than using the parasitoids to indirectly suppress the hosts.     

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.     

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.     

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.     

Effects of asymmetric dispersal and environmental gradients on the stability of host–parasitoid systems

We consider host–parasitoid systems spatially distributed on a row of patches connected by dispersal. We analyze the effects of dispersal frequency, dispersal asymmetry, number of patches and environmental gradients on the stability of the host–parasitoid interactions. To take into account dispersal frequency, the hosts and parasitoids are allowed to move from one patch to a neighboring patch a certain number of times within a generation. When this number is high, 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. We show that as the number of patches increases less asymmetric parasitoid dispersal rates are required for stability. We found that the 'CV²>1 rule' is a valid approximation for stability if host growth rate is low, otherwise the general condition of stability we establish should be preferred. Environmental variability along the row of patches is introduced as gradients on host growth rate and parasitoid searching efficiency. We show that stability is more likely when parasitoids move preferentially towards patches where they have high searching efficiency or when hosts go mainly to patches where they have a low growth rate.     

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.     

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.     

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.     

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.     

Models for pest control: Complementary effects of periodic releases of sterile pests and parasitoids

Four host-parasitoid models that incorporate the simultaneous or sequential release during each generation of sterile hosts and parasitoids for control or eradication of host species are presented. The models are based on two modifications of the Nicholson-Bailey model which incorporate density regulation either in the host larvae or via parasitoid oviposition. Parasitization of host larvae and adults forms another comparison. The models indicate that the release of sterile hosts alone is more efficient than release of parasitoids alone in controlling the hosts if population regulation is in the parasitoids; otherwise, the release of parasitoids alone is more efficient. The release of both steriles and parasitoids is much more efficient than the release of either alone for either suppressing or eradicating the hosts. This greater efficiency in combination rather than separately appears to be a special case of a more general principle, which is that two pest control methods will mutually complement each other if their optimal actions in reducing host numbers are at very different host densities. This is the case for sterile releases (optimal at low host densities) and parasitoid inundation (optimal at high host densities).     

Optimized timing of parasitoid release: a mathematical model for biological control of <Emphasis Type="Italic">Drosophila suzukii</Emphasis>

We present a model for the population dynamics of the invasive fruit fly Drosophila suzukii and its pupal parasitoid Trichopria drosophilae. Seasonality of the environment is captured through a system of delay differential equations with variable delays. The model is used to explore optimal timing for releasing parasitoids in biological control programs. According to the results, releasing parasitoids is most effective between late spring and early summer when the host population begins to increase. A single parasitoid release event can be more efficient than multiple releases over a prolonged period, but multiple releases are more robust to suboptimal timing choices. The findings can be useful for optimizing parasitoid release and should be transferable for similar systems. More generally, the model is an example for stage-structured resource-consumer dynamics in a varying environment.     

Coevolution of Contrary Choices in Host-Parasitoid Systems

We investigate patch selection strategies of hosts and parasitoids in heterogeneous environments. Previous theoretical work showed that when host traits vary among patches, coevolved populations of hosts and parasitoids make congruent choices (i.e., hosts and parasitoids preferentially select the same patches) and exhibit direct density dependence in the distribution of percent parasitism. However, host-parasitoid systems in the field show a range of patterns in percent parasitism, while behavioral studies indicate that hosts and parasitoids can exhibit contrary choices (i.e., hosts avoid patches favored by the parasitoid). We extend previous theory by permitting life-history traits of the parasitoid as well as the host to vary among patches. Our analysis implies that in coevolutionarily stable populations, hosts preferentially select patches that intrinsically support higher host equilibrium numbers (i.e., the equilibrium number achieved by hosts when both populations are confined to a single patch) and that parasitoids preferentially select patches that intrinsically support higher parasitoid equilibrium numbers (i.e., the equilibrium number achieved by the parasitoids when both populations are confined to a patch). Using this result, we show how variation in life-history traits among patches leads to contrary or congruent choices or leads to direct density dependence, inverse density dependence, or density independence in the distribution of percent parasitism. In addition, we determine when populations playing the coevolutionarily stable strategies are ecologically stable. Our analysis shows that heterogeneous environments containing patches where the intrinsic rate of growth of the host and the survivorship rate of the parasitoid are low result in the coevolved populations exhibiting contrary choices and, as a result, promote ecological stability.     

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.     

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.     

Effects of the gregarious parasitoids,Apanteles ruficrus and A. Kariyai,on host growth and development

Two gregarious parasitoids, Apanteles ruficrus and A. kariyai attack larvae of the common armyworm, Pseudaletia separata. Their growth pattern and growth rate of the parasitoids were not affected by host age at the time of oviposition, even though host weight increased exponentially with age. Consequently, the maximal weight of a single parasitoid larva was nearly constant regardless of host instar parasitized. Parasitoid females laid more eggs in later-instar hosts than in earlier-instar hosts. When parasitized at the same age, heavily parasitized hosts attained a larger mass than lightly parasitized larvae. Therefore, the ratio of the maximal weight of the host to the parasitoid mass was nearly constant. These results indicate that host growth is regulated by the parasitoids.     

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.     

Egg Size, Intrinsic Competition, and Lethal Interference in the Parasitoids Encarsia pergandiella and Encarsia formosa

Recent population dynamic theory predicts that disruption of biological control may occur when one parasitoid species' superiority in intrinsic competition is associated with a lower ability to find and exploit hosts (i.e., ability in extrinsic competition). One might expect such a trade-off, for instance, if parasitoids with larger (and fewer) eggs are more likely to prevail in intrinsic competition than species with smaller (and more numerous) eggs. We tested the idea that relative egg size could be used to predict the outcome of intrinsic competition in two closely related endoparasitoids, Encarsia pergandiella Howard and Encarsia formosa Gahan. Contrary to expectation, the parasitoid species with smaller eggs, E. pergandiella, prevailed in intrinsic competition, regardless of the order that hosts were exposed to the two species. In a literature survey, we found four studies of competing pairs of endoparasitoid species for which: (a) egg size estimates were available and (b) one species was consistently superior in intrinsic competition. In three of the four studies, the small-egged species prevailed in intrinsic competition, as we also found. Although E. formosa lost in intrinsic competition, this species negatively affected E. pergandiella's progeny production by host feeding on and killing hosts containing E. pergandiella eggs. E. formosa females also host fed on conspecific-parasitized hosts. As a mechanism of both intra- and interspecific interference competition, host feeding on parasitized hosts contradicts assumptions about the nature of interference competition in existing population dynamics models.     

Intrinsic and extrinsic competitive interactions between two larval parasitoids of Heliothis virescens

1. Competition between parasitoid species may be a key factor in the community dynamics of plant–herbivore-parasitoid systems and is an important consideration in the selection and management of effective biological control agents. 2. Interspecific competition can occur between adult parasitoids searching for hosts (extrinsic competition) and between multiple parasitoid larvae developing within a single host individual (intrinsic competition). A model system comprising the lepidopteran pest Heliothis virescens and two key hymenopteran endoparasitoids, Microplitis croceipes and Cardiochiles nigriceps, was employed to explore parasitoid host-location strategies and the consequences of intrinsic and extrinsic competitive interactions between parasitoid species. 3. The less specialised of the two parasitoids, M. croceipes, was found to have a shorter hatching time and to dominate intrinsic competition, except when its oviposition followed that of the more specialised parasitoid, C. nigriceps, by 16 h or more. This interval corresponded to the differential in hatching time between the two species. 4. Cardiochiles nigriceps, however, displayed superior host-searching efficiency that may compensate for its disadvantage in intrinsic competition. This parasitoid was more effective at detecting host infestation sites via airborne odours and at locating and attacking early instar host larvae than was M. croceipes.     

Ratio dependence in the functional response of insect parasitoids: evidence from Trichogramma minutum foraging for eggs in small host patches

Abstract.  1. Despite considerable recent debate on the suitability of ratio dependence as a more general form for the functional response in consumer–victim relationships, there have been few detailed studies to experimentally determine the response of insect parasitoids to host and parasitoid density at a local scale.
2. The experimental host, Ephestia kuehniella , was used to test for host dependence and ratio dependence in the functional response of the egg parasitoid, Trichogramma minutum , a species widely used in inundative biological control. The functional response was examined through four series of experiments in which either host density, parasitoid density, or the ratio of previously parasitised to healthy hosts was manipulated.
3. The response to host density was type I for both single and simultaneously foraging parasitoids, indicating a lack of host dependence in the functional response. The upper limit to the response was estimated as 39 hosts attacked in a 24-h period, with an estimated per capita search rate of 1.32 for individual females and 0.37 for three simultaneously searching females.
4. The response to parasitoid density provided an interference constant of unity, indicating an equal sharing of hosts and thus ratio dependence in the functional response. Female parasitoids responded to the presence of conspecifically parasitised eggs with a significant increase in search rate (1.75), but with no change to the form or upper limit of the response.
5. It is suggested that ratio dependence may be more common among insect parasitoids than previously supposed, and that a type I functional response, or the absence of host dependence, may be an emergent property of phylogenetic constraint within the monophyletic grouping of Cales , Eretmocerus , and Trichogramma .