Stage-structured competition and the cyclic dynamics of host-parasitoid populations (original) (raw)

Searching for Food or Hosts: The Influence of Parasitoids Behavior on Host-Parasitoid Dynamics

Theoretical population biology, 1997

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.

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

Researches on Population Ecology, 1996

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 and C. 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, and C. 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) resourceherbivorous 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 densitydependent competition of the host on the host-parasitoid persistence is predicted.

Delayed feedback and multiple attractors in a host-parasitoid system

Journal of Mathematical Biology, 1999

Continuous-time, age structured, host-parasitoid models exhibit three types of cyclic dynamics: Lotka-Volterra-like consumerresource 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.

Evolutionary and population dynamics of host–parasitoid interactions

Researches on Population Ecology, 1999

The role of evolutionary dynamics in understanding host-parasitoid interactions is interlinked with the population dynamics of these interactions. Here, we address the problems in coupling evolutionary and population dynamics of host-parasitoid interactions. We review previous theoretical and empirical studies and show that evolution can alter the ecological dynamics of a host-parasitoid interaction. Whether evolution stabilizes or destabilizes the interaction depends on the direction of evolutionary changes, which are affected by ecological, physiological, and genetic details of the insect biology. We examine the effect of life history correlations on population persistence and stability, embedding two types, one of which is competitively inferior but superior in encapsulation (for parasitoid, virulence), in a Nicholson-Bailey model with intraspecific resource competition for host. If a trade-off exists between intraspecific competitive ability and encapsulation (or virulence, as a countermeasure) in both the host and parasitoid, the trade-off or even positive correlation in the parasitoid is less influential to ecological stability than the trade-off in the host. We comment on the bearing this work has on the broader issues of understanding host-parasitoid interactions, including long-term biological control.

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

Bulletin of Mathematical Biology, 1997

This study examines the influence of various host-feeding patterns on host-parasitoid population dynamics. The following types of host-feeding patterns are considered: concurrent and non-destructive, non-concurrent and non-destrnctive, and non-concurrent and destructive. The host-parasitoid population dynamics is described by the Lotka-Volterra continuous-time model. This study shows that when parasitoids behave optimally, i.e. they maximize their fitness measured by the instantaneous per capita growth rate, the non-destructive type of host feeding stabilizes host-parasitoid dynamics. Other types of host feeding, i.e. destructive, concurrent, or non-concurrent, do not qualitatively change the neutral stability of the Lotka-Volterra model. Moreover, it is shown that the pattern of host feeding which maximizes parasitoid fitness is either non-concurrent and destructive, or concurrent and non-destructive host feeding, depending on the host abundance and parameters of the model. The effects of the adaptive choice of host-feeding patterns on host-parasitoid population dynamics are discussed. 9 1997 Society for Mathematical Biology 9

Variable prey development time suppresses predator-prey cycles and enhances stability

Ecology letters, 2016

Although theoretical models have demonstrated that predator-prey population dynamics can depend critically on age (stage) structure and the duration and variability in development times of different life stages, experimental support for this theory is non-existent. We conducted an experiment with a host-parasitoid system to test the prediction that increased variability in the development time of the vulnerable host stage can promote interaction stability. Host-parasitoid microcosms were subjected to two treatments: Normal and High variance in the duration of the vulnerable host stage. In control and Normal-variance microcosms, hosts and parasitoids exhibited distinct population cycles. In contrast, insect abundances were 18-24% less variable in High- than Normal-variance microcosms. More significantly, periodicity in host-parasitoid population dynamics disappeared in the High-variance microcosms. Simulation models confirmed that stability in High-variance microcosms was sufficient ...

The impact of parasitoid emergence time on host-parasitoid population dynamics

Theoretical population biology

We investigate the effect of parasitoid phenology on host-parasitoid population cycles. Recent experimental research has shown that parasitized hosts can continue to interact with their unparasitized counterparts through competition. Parasitoid phenology, in particular the timing of emergence from the host, determines the duration of this competition. We construct a discrete-time host-parasitoid model in which within-generation dynamics associated with parasitoid timing is explicitly incorporated. We found that late-emerging parasitoids induce less severe, but more frequent, host outbreaks, independent of the choice of competition model. The competition experienced by the parasitized host reduces the parasitoids' numerical response to changes in host numbers, preventing the 'boom-bust' dynamics associated with more efficient parasitoids. We tested our findings against experimental data for the forest tent caterpillar (Malacosoma disstria Hübner) system, where a large num...

Persistent host–parasitoid interaction caused by host maturation variability

Population Ecology, 2008

The heterogeneity of parasitism risk among host individuals is a key factor for stabilizing or sustaining host-parasitoid interactions. Host maturation variability, or the variation in the maturation times among host individuals, is the simplest source of such heterogeneity, but it has often been neglected in previous theoretical studies. We developed a configuration individual-based model (cIBM) of host-parasitoid interaction to investigate to what degree of host maturation variability promotes the persistence of host-parasitoid interactions. We ran simulations with various degrees of host maturation variability for different lengths of unsusceptible period. The result showed that low host maturation variability could sustain host-parasitoid dynamics when the host-unsusceptible period was short. Conversely, high levels of variability could sustain hostparasitoid dynamics when the host-unsusceptible period was about half of the total larval period. This suggests that the balance between variability and unsusceptible period is important for the persistence of host-parasitoid interaction. We conclude that maturation variability is a factor that can contribute to the sustainment of host-parasitoid interactions.

Multiparasitoid-Host Interactions with Egg-Limited Encounter Rates

SIAM Journal on Applied Mathematics, 2009

To address the contentious issue of multiple parasitoid introductions in classical biological control, a discrete-time model of multiparasitoid-host interactions that accounts for host density dependence and egg limitation is introduced and analyzed. For parasitoids that are egg limited but not search limited, the model is proven to exhibit four types of dynamics: host failure in which the host becomes extinct in the presence or absence of the parasitoids; parasitoid-driven extinction in which the parasitoid complex invariably drives the host extinct; host persistence; and conditional host persistence in which, depending on the initial ratios of host to parasitoid densities, the host is either driven extinct or persists. In the case of host persistence, the dynamics of the system are shown to be asymptotic to the dynamics of an appropriately defined one-dimensional difference equation. The results illustrate how the establishment of one or more parasitoids can facilitate the invasion of another parasitoid and how a complex of parasitoids can drive a host extinct despite every species in the complex being unable to do so. The effects of including search limitation are also explored.

Developmental variability and stability in continuous-time host–parasitoid models

Theoretical Population Biology, 2010

Insect host-parasitoid systems are often modeled using delay-differential equations, with a fixed development time for the juvenile host and parasitoid stages. We explore here the effects of distributed development on the stability of these systems, for a random parasitism model incorporating an invulnerable host stage, and a negative binomial model that displays generation cycles. A shifted gamma distribution was used to model the distribution of development time for both host and parasitoid stages, using the range of parameter values suggested by a literature survey. For the random parasitism model, the addition of biologically plausible levels of developmental variability could potentially double the area of stable parameter space beyond that generated by the invulnerable host stage. Only variability in host development time was stabilizing in this model. For the negative binomial model, development variability reduced the likelihood of generation cycles, and variability in host and parasitoid was equally stabilizing. One source of stability in these models may be aggregation of risk, because hosts with varying development times have different vulnerabilities. High levels of variability in development time occur in many insects and so could be a common source of stability in host-parasitoid systems.