Developmental schedules and persistence of experimental host-parasitoid systems at two different temperatures

In experimental systems of a bruchid host, Callosobruchus chinensis, and a braconid parasitoid, Heterospilus prosopidis, the effects of changes in developmental schedules were examined in relation to the persistence of the system, or the time to extinction of a component species. We modified the developmental schedules by changing the temperature from 30°C to 32°C. To compare persistence, a long-term system with overlapping generations was set up and the bruchid host resource, azuki beans (Vigna angularis), were renewed every 10 days. The long-term systems showed greater persistence at 30°C than at 32°C. Parasitoid extinction was often observed. We examined differences in life-history characteristics of the component species between the two temperatures by short-term, single-generation experiments. Fecundity and egg hatchability of the host were reduced and the developmental period of the parasitoid was shortened at 32°C. The age at which the host became vulnerable to parasitoid attacks was earlier at 32°C than at 30°C. We constructed a daily based, age-structured model to analyse which life-history change(s) affected the persistence of the long-term systems. The density-dependent population growth of the host was described by a logistic equation and the attack rate of the parasitoid by a type II functional response with mutual interference. The simulation results showed greater persistence at 30°C than at 32°C. Sensitivity analysis showed that there are threshold boundaries in the length of the vulnerable period of the host beyond which system persistence drastically changes. Further, persistence at another temperature, 28°C, was predicted using a model based on short-term data on the host.     

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.     

Egg limitation in host-parasitoid dynamics: an individual-based perspective

Theoretical models of parasitoid-host dynamics predict that egg limitation in parasitoids destabilizes community dynamics. However, although egg limitation is experienced by individual parasitoids with variable success of encountering hosts, such details were neglected in previous models. This study developed an individual-based parasitoid-host model that explicitly incorporates egg limitation and host encounters of individual parasitoids. The model indicates that the combination of egg limitation and variation in the success of encountering hosts stabilizes parasitoid-host dynamics. The stabilizing mechanism emerges from Jensen’s inequality because egg limitation makes the number of offspring inherently concave down in the number of encountered hosts. Reasons for the inconsistent predictions of the effect of egg limitation between the current model and previous models are discussed.     

Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host’s intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.     

Periodic local disturbance in host-parasitoid metapopulations: host suppression and parasitoid persistence

Within many agricultural systems, insect pests and their natural enemies are forced to persist as a metapopulation, continuously recolonizing patches following disturbance through harvesting or spraying with insecticides. Despite the need to understand factors influencing biocontrol success, few theoretical studies of host-parasitoid interactions have examined the potential impact of local disturbance within a metapopulation framework. Here, we add periodic local mortality to series of classical host-parasitoid models to examine its effect on host suppression and parasitoid persistence. Using a deterministic lattice model, we show that despite the wide range of complex dynamics generated at the patch level, the region wide pattern of disturbance is the key factor influencing host suppression. The level of host suppression achieved can be understood in terms of both the strength of density dependent parasitism, and the relative amounts of host and parasitoid mixing amongst patches of different ages. Local dispersal among patches is sufficient to ensure coexistence of the host and parasitoid, though persistence is not necessarily associated with the formation of self-organized spatial structures reported in previous studies. Finally, a stochastic version of the model is developed, in order to highlight how the effects of demographic stochasticity may influence biocontrol success in highly disturbed agricultural systems.     

Egg maturation, egg resorption and the costliness of transient egg limitation in insects

Although there is widespread agreement that the cost of oviposition underlies selective oviposition in insects, there is no consensus regarding which factors mediate the cost of oviposition. Models have suggested that egg costs are often paramount in those insects that do not continue to mature eggs during the adult stage (pro-ovigenic insects). Here we address the hypothesis that egg costs are generally less significant in synovigenic insects, which can replenish oocyte supplies through continuous egg maturation. A dynamic optimization model based on the biology of a highly synovigenic parasitoid, Aphytis aonidiae, suggests that the maximum rate of egg maturation is insufficient to balance the depletion of eggs when opportunities to oviposit are abundant. Transient egg limitation therefore occurs, which imposes opportunity costs on reproducing females. Thus, whereas the most fundamental constraint acting on the lifetime reproductive success of pro-ovigenic species is the fixed total number of eggs that they carry at eclosion, the most fundamental constraint acting on a synovigenic species is the maximum rate of oocyte maturation. Furthermore, the ability of synovigenic species to reverse the flow of nutrients from the soma to oocytes (i.e. egg resorption) has a dramatic influence on the cost of oviposition. Whereas females in hostrich environments may experience oviposition-mediated egg limitation, females in host-poor environments may experience oosorption-mediated egg limitation. Both forms of egg limitation are costly. Contrary to initial expectations, the flexibility of resource allocation that typifies synovigenic reproduction actually appears to broaden the range of conditions under which costly egg limitation occurs. Egg costs appear to be fundamental in mediating the trade-off between current and future reproduction, and therefore are an important factor favouring selective insect oviposition.     

Genetic variation can promote system persistence in an experimental host-parasitoid system

We tested experimentally the effects of genetic variation in host population on the host-parasitoid system persistence. The experimental systems consisted of one parasitoid wasp species (Heterospilus prosopidis), one bean weevil species (Callosobruchus chinensis), and one bean species, of which only the host species (bean weevil) was genetically manipulated. As control treatments with low genetic heterogeneity in the host population, we used two bean weevil strains (Kyoto and Niigata strains) which have several contrasting ecological traits. For the high genetic heterogeneity treatment, hybrid bean weevils which were generated by crossbreeding the strains Kyoto and Niigata were used. In the multiple-generation experiments, all three treatments had different patterns of extinction. The control treatment with the Niigata strain was very prone to system extinction, whereas the treatment with hybrids showed coexistence of constituent species in almost all replicates and also showed stabilized population dynamics. The other control treatment, using the Kyoto strain, showed intermediate proneness. To interpret the results of multiple-generation experiments, we conducted several short-term experiments. The different persistence patterns between the two control treatments were explained by the shapes of the host-finding abilities of wasps and the growth rate of the bean weevils. The mean values of many ecological traits of hybrid lines were not different from those of the Kyoto strain, but their variability increased. These outcomes corresponded well to the prediction of models by Doebeli [J Theor Biol (1997) 188:109–120]. We discuss the mechanisms in which the variability in host species population was effective for the prolonged system persistence.     

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.     

Chemotaxis-induced spatio-temporal heterogeneity in multi-species host-parasitoid systems

When searching for hosts, parasitoids are observed to aggregate in response to chemical signalling cues emitted by plants during host feeding. In this paper we model aggregative parasitoid behaviour in a multi-species host-parasitoid community using a system of reaction-diffusion-chemotaxis equations. The stability properties of the steady-states of the model system are studied using linear stability analysis which highlights the possibility of interesting dynamical behaviour when the chemotactic response is above a certain threshold. We observe quasi-chaotic dynamic heterogeneous spatio-temporal patterns, quasi-stationary heterogeneous patterns and a destabilisation of the steady-states of the system. The generation of heterogeneous spatio-temporal patterns and destabilisation of the steady state are due to parasitoid chemotactic response to hosts. The dynamical behaviour of our system has both mathematical and ecological implications and the concepts of chemotaxis-driven instability and coexistence and ecological change are discussed. I. G. Pearce gratefully acknowledges the financial support of the NERC.     

Scale-free extinction dynamics in spatially structured host-parasitoid systems

Much of the work on extinction events has focused on external perturbations of ecosystems, such as climatic change, or anthropogenic factors. Extinction, however, can also be driven by endogenous factors, such as the ecological interactions between species in an ecosystem. Here we show that endogenously driven extinction events can have a scale-free distribution in simple spatially structured host-parasitoid systems. Due to the properties of this distribution there may be many such simple ecosystems that, although not strictly permanent, persist for arbitrarily long periods of time. We identify a critical phase transition in the parameter space of the host-parasitoid systems, and explain how this is related to the scale-free nature of the extinction process. Based on these results, we conjecture that scale-free extinction processes and critical phase transitions of the type we have found may be a characteristic feature of many spatially structured, multi-species ecosystems in nature. The necessary ingredient appears to be competition between species where the locally inferior type disperses faster in space. If this condition is satisfied then the eventual outcome depends subtly on the strength of local superiority of one species versus the dispersal rate of the other.     

Time limitation, egg limitation, the cost of oviposition, and lifetime reproduction by an insect in nature

For more than 80 years, ecologists have debated whether reproduction by female insect herbivores and parasitoids is constrained by the time needed to find hosts (time limitation) or by the finite supply of mature eggs (egg limitation). Here we present the first direct measures of permanent time limitation and egg limitation and their influences on the cost of oviposition and lifetime reproduction for an insect in nature. We studied the gall midge Rhopalomyia californica, which neither matures nor resorbs eggs during the adult stage. By sampling females soon after their death and correcting for predation effects, we demonstrate that females lay a large proportion of their total complement of eggs (multiyear mean: 82.9%). The egg supplies of 17.1% of females were completely exhausted, with the remaining 82.9% of females being time limited. As predicted by theory, we estimate that even though egg limitation is a minority condition within the population, egg costs make a substantial contribution (57% of the total) to the cost of oviposition. We conclude that insect life histories evolve to produce a balanced risk of time and egg limitation and, therefore, that both of these constraining factors have important influences on insect oviposition behavior and population dynamics.     

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.     

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.     

Egg and time limitation mediate an egg protection strategy

The number of mature eggs remaining in the ovaries and the time left for oviposition determine the reproductive decisions of the hyperdiverse guild of insects that require discrete and potentially limiting resources for oviposition (such as seeds, fruits or other insects). A female may run out of eggs before all available oviposition sites are used (egg limitation), or die before using all of her eggs (time limitation). Females are predicted to change clutch size depending on whether eggs or time is the limiting resource. We extend this framework and ask whether the same constraints influence a strategy in which females modify eggs into protective shields. In response to egg parasitism cues, female seed beetles (Mimosestes amicus) lay eggs in vertical groups of 2–4, modifying the top 1–3 eggs into shields in order to protect the bottom egg from attack by parasitoids. We made contrasting predictions of how egg and time limitation would influence egg size and the incidence and level of egg protection. By varying access to seed pods, we manipulated the number of remaining eggs a female had at the time she received a parasitism cue. Although egg size was not affected, our results confirm that egg‐limited females protected fewer eggs and time‐limited females protected more eggs. Female body size explained the number of eggs in a stack rather than host deprivation or the timing of parasitoid exposure. Our results clearly show that host availability relative to female age influences the incidence of egg protection in M. amicus. Furthermore, our study represents a novel use of life history theory to explain patterns in an unusual but compelling defensive behaviour.     

Effects of time limitation and egg limitation on lifetime reproductive success of a parasitoid in the field

We used field observations of freely foraging Aphytis aonidiae parasitoids in conjunction with results of laboratory studies of A. aonidiae and other Aphytis species to simulate lifetime patterns of behavior and reproduction. Field observations provided estimates of encounter rates with three classes of hosts, the mortality rate from predation on adult parasitoids, and host-handling times for oviposition and host feeding by adult wasps. A series of physiological parameters, including the egg maturation rate and the value of host-feeding meals, were estimated from previously published studies. Plasticity in parasitoid behavior was incorporated in two ways. For one set of simulations we used a behavioral rule derived empirically from observations of parasitoids made in the field, and for another we used a dynamic state-variable model to generate a set of behavioral rules that maximize lifetime reproductive success. As was expected, the empirically derived rule led to better matches with field observations than did simulations using the output of the dynamic model. Projections of lifetime reproductive success in the field ranged between three and 37 eggs within the 95% confidence intervals of the mortality rate and host encounter rate and depending on which behavioral rule was used. Lifetime reproductive success from the simulation with central estimates of the mortality and host encounter rates that incorporated the empirical rule was 6.25 eggs. Using the empirical versus the theoretical rule in the simulations led to a 10%-30% decline in projections of lifetime reproductive success, depending on mortality and host encounter rates. Regardless of the behavioral rule, the simulations underscored the observation that the host encounter rate was greater than the egg maturation rate. The overall oviposition rate was sufficiently high to lead to daily episodes of temporary egg limitation during which parasitoids must mature an egg before being able to oviposit.     

Patterns of 2-year population cycles in spatially extended host-parasitoid systems.

Coexisting but temporally separated cohorts of insects with a multiannual life cycle may have dissimilar average abundance, resulting in periodically fluctuating population density. In the case of the boreal moth genus Xestia with a 2-year life cycle and a distinct abundance difference between the two coexisting cohorts, empirical results and a simple model suggest that the oscillatory dynamics are maintained by interaction with a parasitoid wasp. Here we report theoretical results on a spatially extended version of the basic model and relate the modeling results to empirical observations. A spatially extended model may have domains oscillating in different phases as is the case between western and eastern Finnish Lapland. Spatial heterogeneity tends to fix the location of phase boundaries. In contrast, spatially homogeneous temporal fluctuations tend to synchronize populations in large regions.     

Stochasticity in reproductive opportunity and the evolution of egg limitation in insects

Is reproduction by adult female insects limited by the finite time available to locate hosts (time limitation) or by the finite supply of eggs (egg limitation)? An influential model predicted that stochasticity in reproductive opportunity favors elevated fecundity, rendering egg limitation sufficiently rare that its importance would be greatly diminished. Here, I use models to explore how stochasticity shapes fecundity, the likelihood of egg limitation, and the ecological importance of egg limitation. The models make three predictions. First, whereas spatially stochastic environments favor increased fecundity, temporally stochastic environments favor increases, decreases, or intermediate maxima in fecundity, depending on egg costs. Second, even when spatially or temporally stochastic environments favor life histories with less‐frequent egg limitation, stochasticity still increases the proportion of all eggs laid in the population that is laid by females destined to become egg limited. This counterintuitive result is explained by noting that stochasticity concentrates reproduction in the hands of a few females that are likely to become egg limited. Third, spatially or temporally stochastic environments amplify the constraints imposed by time and eggs on total reproduction by the population. I conclude that both egg and time constraints are fundamental in shaping insect reproductive behavior and population dynamics in stochastic environments.     

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.     

Energetics of reproduction: consequences of divergent selection on egg size, food limitation, and female age for egg composition and reproductive effort in a butterfly

Using lines artificially selected on egg size and being subjected to a restricted and an unrestricted feeding treatment, we examined the relationships between egg size, egg number, egg composition, and reproductive investment in the butterfly Bicyclus anynana . Despite a successful manipulation of egg size, correlated responses to selection in larval time, pupal mass, pupal time, longevity, fecundity, or the amount of energy allocated to reproduction were virtually absent. Thus, there was no indication for an evolutionary link between offspring size and reproductive investment. Egg composition, in contrast, was affected by selection, with larger eggs containing relatively more lipid and water, but less protein and energy compared to smaller eggs. Hence, females producing large eggs did not have to sacrifice fecundity due to adjustments in egg composition. Food limitation per se caused only minor changes in egg composition, and there was no general reduction in egg provisioning with female age. The latter was restricted to food-limited females, whereas egg quality remained remarkably similar throughout the females' life in control groups. We conclude that neglecting changes in biochemical egg composition, depending on genetic background, food availability, and female age, may introduce substantial error when estimating reproductive effort, and may ultimately lead to invalid conclusions.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 91 , 403–418.     

Interactions leading to persistence in predator-prey systems with group defence

In previous work (Freedman and Wolkowicz, 1986;Bull. math. Biol. 48, 493–508) it was shown that in a predator-prey system where the prey population exhibits group defence, it is possible that enrichment of the environment could lead to extinction of the predator population. In this paper a third population is introduced and criteria are derived under which persistence of all populations will occur. In particular, criteria for a superpredator and for a competitor to stabilize the system in the sense of persistence are analyzed. Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A 4823. This research was carried out while the author was a visiting scholar at the University of Alberta.