A dynamic refuge model and population regulation by insect parasitoids

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

Heterogeneity and density dependence in a field study of a tephritid-parasitoid interaction

Abstract.

• 1 The spatial distributions of two tephritid flies (Urophora stylata (Fabricius) and Terellia serratulae L.) attacking thistle flower heads and the levels of parasitism from their associated parasitoid guilds were studied over a 7-year period.
• 2 Using these data it is possible to seek both temporal, density dependent relationships between average levels of parasitism and host density per generation, and also any spatial patterns of parasitism contributing to stability that may be operating within the same field system.
• 3 Parasitism by the two most important generalist parasitoids of T.serratulae is a direct function of average T.serratulae density per year. There is little evidence of any stabilizing heterogeneity arising from the spatial distribution of parasitism within generations.
• 4 Temporal density dependence of Urophora stylata cannot be confirmed from the 7 years of study but there is evidence of spatial heterogeneity which may have an important effect on the dynamics of the host population.

     

A hierarchical multi‐scale analysis of the spatial relationship between parasitism and host density in urban habitats

Studies on spatial density dependence in parasitism have paid scarce attention to how changes in host density at different hierarchical scales could influence parasitism in an herbivore at a particular scale. Here, we evaluated if rates of parasitism per leaf (by the whole parasitic complex and by dominant species) of the specialist leaf miner Liriomyza commelinae (Diptera: Agromyzidae) respond to variations in host density at the leaf, plant patch and site levels in an urban setting. We used multi‐level Bayesian models that incorporate the spatial hierarchy occurring in this system, as well as habitat factors previously found to have an effect on the L. commelinae parasitoid community in an urban context (patch size, patch isolation and urbanization level). According to the fitted model, overall parasitism rates decreased with increasing number of mines per leaf, being independent of host‐density variations at patch and site level. Patch structure was found to have a strong effect on parasitism rates per leaf. The analysis of parasitism by parasitoid species separately showed consistent results with the response at community level. These results suggest that parasitism of the parasitoid community here studied would be sensitive to hierarchical cues related to the host at the leaf level and to the host habitat at the patch level.     

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.     

Refuge evolution and the population dynamics of coupled host—parasitoid associations

Summary We have investigated the theoretical consequences of character evolution for the population dynamics of a host—parasitoid interaction, assuming a monophagous parasitoid. In the purely ecological model it is assumed that hosts can escape parasitism by being in absolute refuges. A striking property of this model is a threshold effect in control of the host by the parasitoid, when host density dependence is weak. The approximate criteria for the parasitoid to regulate the host to low densities are (1) that the parasitoid's maximum population growth rate should exceed the host's and (2) that the maximum growth rate of the host in the refuge should be less than unity. We then use this ecological framework as a basis for a model which considers evolutionary changes in quantitative characters influencing the size of the absolute refuge. For each species, an increase in its refuge-determining character comes at a cost to maximum population growth rate. We show that refuge evolution can substantially alter the population dynamics of the purely ecological model, resulting in a number of emergent and sometimes counter-intuitive properties. In general, when the host has a high carrying capacity, systems are polarized either with low or minor refuge and top-down control of the host by the parasitoid or with a refuge and bottom-up control of the host by a combination of its own density dependence and the parasitoid. A particularly tantalizing result is that co-evolutionary dynamics can modify ecologically unstable systems into ones which are either stable or quasi-stable (with bouts of unstable dynamics, punctuating long-term periods of quasi-stable behaviour). We present five quantitative criteria which must all be met for the parasitoid to be the agent responsible for control of the host at a co-evolutionary equilibrium. The apparent stringency of this full set of requirements supports the empirically-based suggestion that monophagous parasitoid-driven systems should be less common in nature than those driven by multiple forms of density dependence. Further, we apply our theory to the question of whether exploiters may harvest their victims at maximum sustainable yields and to the evolutionary stability of biological control. Finally, we present a series of testable predictions of our theory and methods useful for testing them.     

Ratio-dependent parasitism with Trissolcus basalis (Wollaston) (Hymenoptera: Scelionidae) on egg rafts of Nezara viridula (Linnaeus) (Hemiptera: Pentatomidae): effect of experimental variables and compatibility of 'ratio' and 'Holling' models

Abstract Egg rafts of Nezara viridula were exposed to the parasitoid wasp Trissolcus basalis in experimental arenas to establish the relationship of the rates of attack and parasitism to various combinations of arena size, parasitoid density, host density and parasitoid-to-host ratio. Arena sizes were varied in the ratio 1:9:63, with the largest having a search area of 1.44 m². Parasitoid and host densities were varied over a 27-fold range. The parasitoid-to-host ratios used were 1:1, 3:1 and 6:1. Finding time was related to a constant factor (flight propensity), rather than to the difficulty of finding (density of hosts). Initial attack rates were therefore related only to parasitoid numbers (or density), even at the lower densities and ratios. Parasitism rates (a function of attack rate per host) were thus also strongly related to parasitoid to host ratio, regardless of densities used and arena sizes. Even reducing host density, while keeping time and parasitoid density constant, increased the parasitism rate. A ratio model for parasitism rate was therefore compatible with the data but the more explicit Holling 'disc' equation was also compatible because handling time was sufficiently large to make it sensitive to the ratio of parasitoids to hosts for the densities used. We conclude that the two models would predict different results if the density of host egg rafts was in a range below one per square metre.     

Adjacent trophic-level effects on spatial density dependence in a herbivore—predator—parasitoid system

Abstract. 1. Spatial density dependence of enemy/victim relationships (predator/prey and host/parasitoid) were examined for the gall-making herbivore Eurosta solidaginis (Diptera: Tephritidae), its predator Mordellistena unicolor (Coleoptera: Mordellidae), and a parasitoid of Mordellistena, Schizoprymnus sp. (Hymenoptera: Braconidae), both before and after experimental perturbation of gall density.
2. Mordellistena predation did not depend on Eurosta density, nor did Schizoprymnus parasitism of Mordellistena depend on Mordellistena density.
3. Schizoprymnus parasitism of Mordellistena depended strongly on the density of Eurosta , the prey of its host.
4. The lack of density dependence in enemy/victim relationships may be explained by effects from adjacent trophic-levels. Ovipositing Schizoprymnus may search for high densities, not of its host Mordellistena , but of its host's prey ( Eurosta galls), and ovipositing Mordellistena may avoid patches of high gall density where the risk of being parasitized is greater.     

Do distances among host patches and host density affect the distribution of a specialist parasitoid?

The effect of spatial habitat structure and patchiness may differ among species within a multi-trophic system. Theoretical models predict that species at higher trophic levels are more negatively affected by fragmentation than are their hosts or preys. The absence or presence of the higher trophic level, in turn, can affect the population dynamics of lower levels and even the stability of the trophic system as a whole. The present study examines different effects of spatial habitat structure with two field experiments, using as model system the parasitoid Cotesia popularis which is a specialist larval parasitoid of the herbivore Tyria jacobaeae. One experiment examines the colonisation rate of the parasitoid and the percentage parasitism at distances occurring on a natural scale; the other experiment examines the dispersal rate and the percentage parasitism in relation to the density of the herbivore and its host plant. C. popularis was able to reach artificial host populations at distances up to the largest distance created (at least 80 m from the nearest source population). Also, the percentage parasitism did not differ among the distances. The density experiment showed that the total number of herbivores parasitised was higher in patches with a high density of hosts, regardless of the density of the host plant. The percentage parasitism, however, was not related to the density of the host. The density of the host plant did have a (marginally) significant effect on the percentage parasitism, probably indicating that the parasitoid uses the host plant of the herbivore as a cue to find the herbivore itself. In conclusion, the parasitoid was not affected by the spatial habitat structure on spatial scales that are typical of local patches.     

Escape from parasitism: spatial and temporal strategies of a sphecid wasp against a specialised cuckoo wasp

Parasites and parasitoids exert an important selection pressure on organisms and, thus, play an important role for both population dynamics and evolutionary responses of host species. We investigated host-parasite interactions in a brood-caring wasp, the European beewolf, Philanthus triangulum (Hymenoptera, Sphecidae), and asked whether females of this species might employ temporal or spatial strategies to reduce the rate of attack by a specialised brood parasitoid, the cuckoo wasp Hedychrum rutilans (Hymenoptera, Chrysididae). Females of the host species might shift their activity to periods of low parasitoid activity both in the course of the season and in the course of the day. On a spatial scale, aggregated or dispersed nesting might be favoured depending on the form of the density dependence of parasitism. The beginning and end of the flight season of host and parasitoid were nearly identical. Activity of chrysidids relative to beewolves did not change significantly during the flight season. However, relative parasitoid activity declined in the course of the day, suggesting the existence of temporal enemy-free space in the evening hours. Shifting the main activity to the evening hours might be a flexible response of beewolves to the presence of chrysidids. Activity of cuckoo wasps per nest was independent of nest density but the actual rate of parasitism as revealed by nest excavations indicated direct density dependence. Total mortality, however, was inversely density dependent. Thus, in the study population aggregated nesting did not reduce parasitism but minimised total mortality.     

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

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

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.     

Inverse density dependent parasitism in a patchy environment: a laboratory system

Abstract. 1. Two species of parasitoids (Anisopteromalus calandrae (Howard) and Heterospilus prosopidis Vier) attacking the bruchid beetle, Callosobruchus chinensis (L.), show marked inverse density dependent relationships between per cent parasitism and host density per patch.
2. These patterns are well described quantitatively using data on the spatial distribution of searching time by the parasitoids and their attack rates on patches of different host density.
3. A model of optimal foraging predicts just the opposite (i.e. density dependent) patterns of parasitism.
4. Both density dependent and inversely density dependent spatial patterns of parasitism can be explained mechanistically in terms of (a) the allocation of searching time in patches of different host density and (b) the maximum attack rate per parasitoid that constrains the extent of host exploitation within a patch.     

A discrete-time host–parasitoid model with an Allee effect

We introduce a discrete-time host–parasitoid model with a strong Allee effect on the host. We adapt the Nicholson–Bailey model to have a positive density dependent factor due to the presence of an Allee effect, and a negative density dependence factor due to intraspecific competition. It is shown that there are two scenarios, the first with no interior fixed points and the second with one interior fixed point. In the first scenario, we show that either both host and parasitoid will go to extinction or there are two regions, an extinction region where both species go to extinction and an exclusion region in which the host survives and tends to its carrying capacity. In the second scenario, we show that either both host and parasitoid will go to extinction or there are two regions, an extinction region where both species go to extinction and a coexistence region where both species survive.     

Delayed feedback and multiple attractors in a host–parasitoid system

 Continuous-time, age structured, host–parasitoid models exhibit three types of cyclic dynamics: Lotka–Volterra-like consumer-resource cycles, discrete generation cycles, and “delayed feedback cycles” that occur if the gain to the parasitoid population (defined by the number of new female parasitoid offspring produced per host attacked) increases with the age of the host attacked. The delayed feedback comes about in the following way: an increase in the instantaneous density of searching female parasitoids increases the mortality rate on younger hosts, which reduces the density of future older and more productive hosts, and hence reduces the future per head recruitment rate of searching female parasitoids. Delayed feedback cycles have previously been found in studies that assume a step-function for the gain function. Here, we formulate a general host–parasitoid model with an arbitrary gain function, and show that stable, delayed feedback cycles are a general phenomenon, occurring with a wide range of gain functions, and strongest when the gain is an accelerating function of host age. We show by examples that locally stable, delayed feedback cycles commonly occur with parameter values that also yield a single, locally stable equilibrium, and hence their occurrence depends on initial conditions. A simplified model reveals that the mechanism responsible for the delayed feedback cycles in our host–parasitoid models is similar to that producing cycles and initial-condition-dependent dynamics in a single species model with age-dependent cannibalism. Received: 24 October 1997 / Revised version: 13 June 1998     

Invertebrate predation of 15N-marked prey in semi-field wheat enclosures

One of the most famous examples of successful, classical biological control in Japan is the introduction of the parasitoids Coccobius fulvus and Aphytis yanonensis against the citrus pest arrowhead scale Unaspis yanonensis. Together, they comprise a host‐parasitoid system that has been demonstrated to be stable. To test the conventional theory that successful biological control of pests occurs through the establishment of a low stable equilibrium, brought about by the density‐dependent responses of natural enemies to the pest species, sampling was carried out at five sites in the field during 2000 and 2001 to examine the relationship between the rate of parasitism by C. fulvus and the density of its host. The data were analysed using three statistical techniques at nine spatial scales. Contrary to conventional theoretical predictions, each method of analysis detected very little density‐dependence at any spatial level in this study. Parasitoid aggregations independent of host density were not sufficient to stabilise host–parasitoid interactions. Our results suggest that neither spatial density‐dependent nor density‐independent parasitism is necessary for successful biological control, or for the stability of the host–parasitoid system. We propose an alternative mechanism: a spatial refuge induced by parasitoid introduction may stabilise a system.     

Spatial patterns of Trybliographa rapae parasitism of Delia radicum larvae in oilseed rape and cauliflower

Trybliographa rapae (Westwood) is an important parasitoid of Delia radicum (L.). Parasitism of D. radicum larvae by T. rapae in relation to host density on canola (oilseed rape) and cauliflower roots was examined at 10 field sites in Germany and Switzerland. For roots with host larvae, the proportion of roots with one or more parasitized hosts increased with increasing host density. However, for these infested roots, the parasitism of individual larvae was not consistently related to host density. When considering only roots on which there were parasitized larvae and the opportunity for multiple attacks, the proportion of larvae that were parasitized decreased with increasing host density in the field locations, and in a cage study under controlled conditions. A model of patch‐finding and number of attacks by female parasitoids suggests that patch‐finding is density‐dependent, but that low attack rate and interference effects limit numbers of attacks to three or less per visit to a host patch; the reduced number of attacks per visit leads to the inverse relationship of larval parasitism with host density in the host patches visited. The interplay of the density‐dependent and inversely density‐dependent processes appears to be responsible for the inconsistency of density dependence of overall larval parasitism in this and previous studies. In the laboratory, adult female T. rapae parasitized hosts at ≤4 cm deep in soil, but not at 6 cm deep. From the depth distribution of larval feeding sites in the field, we infer that between 4% and 20% of Delia larvae may be in a physical refuge from T. rapae parasitism, which may have a stabilizing influence on the host–parasitoid interaction.     

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.     

Population structure of a large blue butterfly and its specialist parasitoid in a fragmented landscape

Habitat fragmentation may interrupt trophic interactions if herbivores and their specific parasitoids respond differently to decreasing connectivity of populations. Theoretical models predict that species at higher trophic levels are more negatively affected by isolation than lower trophic level species. By combining ecological data with genetic information from microsatellite markers we tested this hypothesis on the butterfly Maculinea nausithous and its specialist hymenopteran parasitoid Neotypus melanocephalus. We assessed the susceptibility of both species to habitat fragmentation by measuring population density, rate of parasitism, overall genetic differentiation (theta(ST)) and allelic richness in a large metapopulation. We also simulated the dynamics of genetic differentiation among local populations to asses the relative effects of migration rate, population size, and haplodiploid (parasitoid) and diploid (host) inheritance on metapopulation persistence. We show that parasitism by N. melanocephalus is less frequent at larger distances to the nearest neighbouring population of M. nausithous hosts, but that host density itself is not affected by isolation. Allelic richness was independent of isolation, but the mean genetic differentiation among local parasitoid populations increased with the distance between these populations. Overall, genetic differentiation in the parasitoid wasp was much greater than in the butterfly host and our simulations indicate that this difference is due to a combination of haplodiploidy and small local population sizes. Our results thus support the hypothesis that Neotypus parasitoid wasps are more sensitive to habitat fragmentation than their Maculinea butterfly hosts.     

Consequences for a host–parasitoid interaction of host-plant aggregation, isolation, and phenology

Abstract.  1. Spatial habitat structure can influence the likelihood of patch colonisation by dispersing individuals, and this likelihood may differ according to trophic position, potentially leading to a refuge from parasitism for hosts.
2. Whether habitat patch size, isolation, and host-plant heterogeneity differentially affected host and parasitoid abundance, and parasitism rates was tested using a tri-trophic thistle–herbivore–parasitoid system.
3.  Cirsium palustre thistles ( n = 240) were transplanted in 24 blocks replicated in two sites, creating a range of habitat patch sizes at increasing distance from a pre-existing source population. Plant architecture and phenological stage were measured for each plant and the numbers of the herbivore Tephritis conura and parasitoid Pteromalus elevatus recorded.
4. Mean herbivore numbers per plant increased with host-plant density per patch, but parasitoid numbers and parasitism rates were unaffected. Patch distance from the source population did not influence insect abundance or parasitism rates. Parasitoid abundance was positively correlated with host insect number, and parasitism rates were negatively density dependent. Host-plant phenological stage was positively correlated with herbivore and parasitoid abundance, and parasitism rates at both patch and host-plant scales.
5. The differential response between herbivore and parasitoid to host-plant density did not lead to a spatial refuge but may have contributed to the observed parasitism rates being negatively density dependent. Heterogeneity in patch quality, mediated by variation in host-plant phenology, was more important than spatial habitat structure for both the herbivore and parasitoid populations, and for parasitism rates.     

Ecological drivers of guanaco recruitment: variable carrying capacity and density dependence

Ungulates living in predator-free reserves offer the opportunity to study the influence of food limitation on population dynamics without the potentially confounding effects of top-down regulation or livestock competition. We assessed the influence of relative forage availability and population density on guanaco recruitment in two predator-free reserves in eastern Patagonia, with contrasting scenarios of population density. We also explored the relative contribution of the observed recruitment to population growth using a deterministic linear model to test the assumption that the studied populations were closed units. The observed densities increased twice as fast as our theoretical populations, indicating that marked immigration has taken place during the recovery phase experienced by both populations, thus we rejected the closed-population assumption. Regarding the factors driving variation in recruitment, in the low- to medium-density setting, we found a positive linear relationship between recruitment and surrogates of annual primary production, whereas no density dependence was detected. In contrast, in the high-density scenario, both annual primary production and population density showed marked effects, indicating a positive relationship between recruitment and per capita food availability above a food-limitation threshold. Our results support the idea that environmental carrying capacity fluctuates in response to climatic variation, and that these fluctuations have relevant consequences for herbivore dynamics, such as amplifying density dependence in drier years. We conclude that including the coupling between environmental variability in resources and density dependence is crucial to model ungulate population dynamics; to overlook temporal changes in carrying capacity may even mask density dependence as well as other important processes.