Egg limitation and individual variation in parasitization risk among hosts in host–parasitoid dynamics

Egg limitation is known to destabilize host–parasitoid dynamics. This study reexamines the effect of egg limitation in light of the individual variation in parasitization risk among hosts (e.g., some hosts are more likely to be parasitized than others). Previous studies have considered egg limitation (predicted as a destabilizing factor) and individual variation among hosts (predicted as a stabilizing factor) in isolation; however, their interaction is not known. An individual‐based model was used to examine the effects of each factor and their interaction. The model‐based analysis shows a clear interaction between egg limitation and individual variation in risk among hosts. Egg limitation can both stabilize and destabilize host–parasitioid dynamics depending on the presence and absence of the risk variation. The result suggests that the population‐dynamic consequences of egg limitation are more complex than previously thought and emphasizes the importance of the simultaneous consideration of multiple ecological factors (with individual‐level details) to uncover potential interactions among them.     

Age-dependent clutch size in a koinobiont parasitoid

Abstract.  1. The Lack clutch size theory predicts how many eggs a female should lay to maximise her fitness gain per clutch. However, for parasitoids that lay multiple clutches it can overestimate optimal clutch size because it does not take into account the future reproductive success of the parasitoid.
2. From egg-limitation and time-limitation models, it is theoretically expected that (i) clutch size decreases with age if host encounter rate is constant, and (ii) clutch size should increase with host deprivation and hence with age in host-deprived individuals.
3. Clutch sizes produced by ageing females of the koinobiont gregarious parasitoid Microplitis tristis Nees (Hymenoptera: Braconidae) that were provided daily with hosts, and of females ageing with different periods of host deprivation were measured.
4. Contrary to expectations, during the first 2 weeks, clutch size did not change with the age of the female parasitoid, neither with nor without increasing host-deprivation time.
5. After the age of 2 weeks, clutch size decreased for parasitoids that parasitised hosts daily. The decrease was accompanied by a strong decrease in available eggs. However, a similar decrease occurred in host-deprived parasitoids that did not experience egg depletion, suggesting that egg limitation was not the only factor causing the decrease in clutch size.
6. For koinobiont parasitoids like M. tristis that have low natural host encounter rates and short oviposition times, the costs of reproduction due to egg limitation, time limitation, or other factors are relatively small, if the natural lifespan is relatively short.
7. Koinobiont parasitoid species that in natural situations experience little variation in host density and host quality might not have strongly evolved the ability to adjust clutch size.     

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.     

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.     

Effects of parasitoid fecundity and host resistance on indirect interactions among hosts sharing a parasitoid

We examine the effects of fecundity‐limited attack rates and resistance of hosts to parasitism on the dynamics of two‐host–one‐parasitoid systems. We focus primarily on the situation where one parasitoid species attacks two host species that differ in their suitability for parasitism. While all eggs allocated to suitable hosts develop into adult parasitoids, some of the eggs allocated to marginal host do not develop. Marginal hosts can therefore act as a sink for parasitoid eggs. Three‐species coexistence is favoured by low levels of parasitoid fecundity and by low levels of suitability of the marginal host. Our model also produces an indirect (+, ?) interaction in which the suitable host can benefit from the presence of the marginal host, but the marginal host suffers from the presence of the suitable host. The mechanism driving the indirect (+, ?) interaction is egg limitation of parasitoids incurred by allocating eggs to marginal hosts.     

Adaptive superparasitism in solitary parasitoids: marking of parasitized hosts in relation to the pay-off from superparasitism

Abstract.

• 1 The pay-off from an egg laid in a parasitized host is an important parameter in models on adaptive superparasitism in solitary insect parasitoids.
• 2 For Leptopilina heterotoma, a parasitoid of larval Drosophila, the pay-off from a second egg laid in a host is 0.43 offspring when the interval between the two ovipositions is less than 3h. For longer intervals, this pay-off decreases to almost zero for an interval of 24 h.
• 3 When a female encountering a parasitized host is able to estimate the interval since the first oviposition, it is expected that she will take this into account in her host selection decisions. This is, however, not in the direct interest of the female that lays the first egg, and marks the host.
• 4 We studied whether superparasitism in hosts containing a young egg is more common than in hosts containing an older egg, when searching in a patch containing once-parasitized and unparasitized hosts.
• 5 The acceptance/encounter ratio of parasitized hosts increased for intervals longer than 6h, as predicted when the interests of the marking female and the longevity of the mark are taken into account.
• 6 Superparasitism occurred more often when parasitoids had previously searched a host patch 7 days before the experiment compared to when parasitoids had searched a patch 1 day before, a phenomenon predicted by dynamic optimal diet models.

     

Some dynamical consequences of parasitoid diapause

Parasitoid diapause usually serves to synchronize parasitoids with host populations that are undergoing diapause, to avoid some period of unsuitable conditions. Non-synchronizing diapause can occur, however, in a number of situations. For example, a fraction of the diapausing parasitoids may stay dormant for a number of seasons. Parasitoids attacking each generation of a multivoltine host may enter a "bank" of diapausing individuals that will emerge at the beginning of the next season. Finally, parasitoid diapause initiation may be driven by density-dependent processes. I examine the effect of these three scenarios on the stability of Nicholson – Bailey type models. I show that in general, non-synchronizing parasitoids can potentially have a strong de-stabilizing influence on parasitoid-host dynamics.     

Optimal use of patches by parasitoids with a limited fecundity

1. a mathematical model is presented which predicts the expected optimal-patch-use strategy for solitary parasitoids with a limited fecundity.
2. The model predicts that the quality of the patches is determined by the proportion of unparasitized hosts and not by the density of those hosts, and that throughout the searching period the parasitoids should maintain the level of parasitism equal in all the patches irrespective of the host density per patch.
3. The spatial pattern of parasitism among field patches by a parasitoid with a low fecundity, Praestochrysis shanghaiensis, was in agreement with the prediction of the model, i.e., a similar level of parasitism in different patches was observed when the ratio of female parasitoids to hosts in the whole study area exceeded 0.07. When the ratio was less than 0.05, however, the level of parasitism per patch showed an inverse relation to the host density, and was positively correlated with the female parasitoid-host ratio.
4. The model assumes that the parasitoids move between patches without cost and have perfect information about patch quality. Consideration of the cost of moving and sampling bridges the gap between the observed and predicted rates of parasitism found when the female parasitoid-host ratio in the whole study area was low

     

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.     

Evolutionary constraints on polyembryony in parasitic wasps: a simulation model

Polyembryony involves the production of several genetically identical progeny from a single egg through clonal division. Although polyembryonic development allows highly efficient reproduction, especially in some parasitoid wasps, it is far less common than monoembryony (development of one embryo per egg). To understand what might constrain the evolutionary success of polyembryony in parasitoids, we developed Monte Carlo models that simulate the competition between polyembryonic females and their monoembryonic counterparts. We investigated which simulated life‐history traits of the females allow the monoembryonic mode of development to succeed. Published empirical studies were surveyed to explore whether these traits indeed differ between polyembryonic parasitoids and related monoembryonic species. The simulations predict an advantage to monoembryony in parasitoids whose reproduction is limited by host availability rather than by egg supply, and that parasitize small‐bodied hosts. Comparative data on the parasitoid families Encyrtidae and (to a lesser extent) Braconidae, but not the data from Platygastridae, circumstantially support these predictions. The model also predicts monoembryony to outcompete polyembryony when: 1) hosts vary considerably in quality, 2) polyembryonic development carries high physiological costs, and 3) monoembryonic females make optimal clutch size decisions upon attacking hosts. These multiple constraints may account for the rarity of polyembryony among parasitoid species.     

The combined effect of host and food availability on optimized parasitoid life‐history traits based on a three‐dimensional trade‐off surface

The reproductive success of many insects is considered to be limited by two main factors: the availability of mature eggs to lay (termed egg limitation) and the time to locate suitable hosts (termed time limitation). High host density in the environment is likely to enhance oviposition opportunities, thereby selecting for higher investment in egg supply. In contrast, a shortage of food (e.g. sugar sources) is likely to increase the risk of time limitation, thereby selecting for higher allocation to initial energy reserves. To our knowledge, the combined effect of host and food availability on these optimal life‐history allocations has never been investigated. We thus modelled their simultaneous effects on a three‐dimensional trade‐off between initial investment in energy reserves, egg number and egg size, while focusing on insect parasitoids. The model was based on Monte Carlo simulations coupled with genetic algorithms, in order to identify the optimal life‐history traits of a single simulated parasitoid female in an environment in which both hosts and food are present in varying densities. Our results reproduced the simple predictions described above. However, some novel predictions were also obtained, especially when specific interactions between the different factors were examined and their effects on the three‐dimensional life‐history surface were considered. The work sheds light on long‐lasting debates regarding the relative importance of time versus egg limitation in determining insect life‐history traits and highlights the complexity of life‐history evolution, where several environmental factors act simultaneously on multiple traits.     

Egg distribution of insect parasitoids: a survey of models

A number of (insect) parasitoids have been found to avoid superparasitism, i.e., these parasitoids distribute their eggs more evenly over the available hosts than might be expected from chance only. By doing so each parasitoid individual ensures a greater probability of survival for its offspring as a result of a reduced within-host-competition.Recently a number of mathematical models have been developed, describing the distribution of the parasitoid eggs in the hosts. This paper gives a survey of these models, placing them within one and the same mathematical framework. An essential conceptual distinction, neglected up to now, emerges: parasitoids can either react to the number of previous visits to a particular host, or they can react to the number of eggs already present in that host.For each model the probability-generating function, the mean, the variance, and the probability distribution of the number of eggs are given, as well as a discussion of estimating and testing procedures. A few possibilities for generalizations of these models are discussed too.     

Reproduction now or later: optimal host-handling strategies in the whitefly parasitoid Encarsia formosa

We developed a dynamic state variable model for studying optimal host‐handling strategies in the whitefly parasitoid Encarsia formosa Gahan (Hymenoptera: Aphelinidae). We assumed that (a) the function of host feeding is to gain nutrients that can be matured into eggs, (b) oögenesis is continuous and egg load dependent, (c) parasitoid survival is exponentially distributed and (d) parasitoids encounter hosts randomly, are autogenous and have unlimited access to non‐host food sources to obtain energy for maintenance and activity. The most important prediction of the model is that host feeding is maladaptive under field conditions of low host density (0.015 cm^?2) and short parasitoid life expectancy (maximum reproductive period of 7 d). Nutrients from the immature stage that can be matured into eggs are sufficient to prevent egg limitation. Both host density and parasitoid life expectancy have a positive effect on the optimal host‐feeding ratio. Parasitoids that make random decisions gain on average only 35% (0.015 hosts cm^?2) to 60% (1.5 hosts cm^?2) of the lifetime reproductive success of parasitoids that make optimal decisions, independent of their life expectancy. Parameters that have a large impact on lifetime reproductive success and therefore drive natural selection are parasitoid life expectancy and the survival probability of deposited eggs (independent of host density), the number of host encounters per day (when host density is low) and the egg maturation rate and number of host types (when host density is high). Explaining the evolution of host‐feeding behaviour under field conditions requires field data showing that life expectancy in the field is not as short as we assumed, or may require incorporation of variation in host density. Incorporating variation in walking speed, parasitised host types or egg resorption is not expected to provide an explanation for the evolution of host‐feeding behaviour under field conditions.     

Host-feeding and oviposition strategies of parasitoids in relation to host stage

Until now, mathematical models of parasitoid-host interactions have not incorporated the tendency for destructively host-feeding parasitoids to partition their feeding and oviposition behaviour in relation to different host stages. A literature survey reveals a trend for female parasitoids to feed preferentially or exclusively on earlier host stages and to oviposit preferentially or exclusively in/or later ones. We explore the relative advantages to host-feeding parasitoids of a number of possible host stage selection strategies. We develop hypotheses, formalizing and testing them using modifications to our earlier simulation model of host-feeding strategies (Jervis and Kidd, 1986). We conclude from our modelling that the advantage to be gained from feeding on early host stages and ovipositing in late ones is likely to be associated with: 1) reduced handling times when feeding on early stage hosts; 2) reduced wastage of progeny from mortality factors other than host-feeding by the parent parasitoid, achieved by confining oviposition to late host stages; and 3) reduced probability of progeny mortality resulting from the parent's host-feeding activities.     

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.     

Size-selective oviposition by parasitoids and the evolution of life-history timing in hosts: fixed preferences vs frequency-dependent host selection

The influence of size-selective oviposition behaviour by parasitoids on the evolution of life-history timing in their hosts was examined using an optimization model of a two-stage life history similar to a genetic algorithm. Host populations with varying durations of early-larval development were subjected to selection in scenarios where parasitoids had fixed preferences for oviposition on late-stage larvae, or those where parasitoid attack was dependent on the relative frequencies of the two life stages present in the population. Fixed preference for oviposition on late-stage larvae caused positive directional selection on the duration of early-larval development. Surviving individuals remained for as long as possible in the first stage of development in order to avoid parasitoid attack. Frequency-dependent parasitoid attack, in contrast, caused maintenance of variation in the duration of early-larval development. The influence of the fitness payoffs of different life stages on the plasticity of size-selective oviposition behaviour is discussed, as are possible implications of the model results for parasitoid-host population dynamics.     

An evolutionary interpretation of the “motivation to oviposit”

The ovipositional behavior of parasitoids and other insects is often described by phrases such as “motivation to oviposit” or “ovipositional drive”. This paper shows how an evolutionary (i.e. functional) interpretation can be given to such phrases. A detailed model for the parasitisation of Sycamore aphids by M. pseudoplatani is developed, using experiments by Collins and Dixon (1986). Two models are developed: i) one in which egg complement is the only state variable and ii) one in which egg complement and information concerning host densities are state variables. Comparisons of the behaviour of simulated parasitoids, using the decisions associated with the models, and the experiments suggest that both egg complement and information are important for the parasitoid's decision making. Accepting previously parasitized hosts may be optimal, and not simply an error in parasitoid perception. A number of other detailed predictions are made, such as the relative fitness of first and second eggs in superparasitized hosts and the nature of the memory of the parasitoid.     

Mathematical modelling of host-parasitoid systems: effects of chemically mediated parasitoid foraging strategies on within- and between-generation spatio-temporal dynamics.

In this paper we develop a novel discrete, individual-based mathematical model to investigate the effect of parasitoid foraging strategies on the spatial and temporal dynamics of host-parasitoid systems. The model is used to compare na?ve or random search strategies with search strategies that depend on experience and sensitivity to semiochemicals in the environment. It focuses on simple mechanistic interactions between individual hosts, parasitoids, and an underlying field of a volatile semiochemical (emitted by the hosts during feeding) which acts as a chemoattractant for the parasitoids. The model addresses movement at different spatial scales, where scale of movement also depends on the internal state of an individual. Individual interactions between hosts and parasitoids are modelled at a discrete (micro-scale) level using probabilistic rules. The resulting within-generation dynamics produced by these interactions are then used to generate the population levels for successive generations. The model simulations examine the effect of various key parameters of the model on (i) the spatio-temporal patterns of hosts and parasitoids within generations; (ii) the population levels of the hosts and parasitoids between generations. Key results of the model simulations show that the following model parameters have an important effect on either the development of patchiness within generations or the stability/instability of the population levels between generations: (i) the rate of diffusion of the kairomones; (ii) the specific search strategy adopted by the parasitoids; (iii) the rate of host increase between successive generations. Finally, evolutionary aspects concerning competition between several parasitoid subpopulations adopting different search strategies are also examined.     

Analysis of Foraging Behaviour of the Whitefly Parasitoid Encarsia formosa on a plant: A Simulation Study

The foraging behaviour of Encarsia formosa was analyzed using a stochastic simulation model of the parasitoid's behaviour. Parasitoids were allowed to search during a day on a tomato plant infested with immatures of the greenhouse whitefly, Trialeurodes vaporariorum. The model simulates searching, host selection, host handling and patch leaving behaviour, and the physiological state of the parasitoid. The outputs of the model are the number of visited leaflets and the number of hosts encountered, parasitized or killed by host feeding. The simulation results agreed well with observations of parasitoids foraging on tomato plants. The number of encounters and ovipositions on the plant increased with host density according to a type II functional response. At a clustered host distribution over leaflets and low host densities, the most important parameters affecting the number of ovipositions were the leaf area, the parasitoid's walking speed and walking activity, the probability of oviposition after encountering a host, the initial egg load and the ratio of search times on both leaf sides. At high densities, the maximum egg load and the giving-up time on a leaflet since latest host encounter were the most essential parameters.     

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.