Periodicity, persistence, and collapse in host–parasitoid systems with egg limitation

Schreiber, Sebastian J.

doi:10.1080/17513750701450235

Cited by 8 publications

(7 citation statements)

References 30 publications

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“…Provided that F is continuous, and f is a compact map, Proposition 6.1 implies that there is a quasi-stationary distribution µ ε for X ε t with ε > 0. To understand the support of the weak* limit points µ of µ ε , we focus on a generalized Thompson model [Thompson (1924), Getz and Mills (1996), Schreiber (2006aSchreiber ( , 2007]. For this model, f (x 1 ) = exp(r(1 − x 1 /K)) is given by the Ricker equation where r > 0 is the intrinsic rate of growth of the host, and K > 0 is the host's carrying capacity.…”

Section: Metapopulation Dynamicsmentioning

confidence: 99%

Quasi-stationary distributions for randomly perturbed dynamical systems

Faure¹,

Schreiber²

2014

Ann. Appl. Probab.

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ADInternational audienceWe analyze quasi-stationary distributions \μ ε \ ε\textgreater0 of a family of Markov chains \X ε \ ε\textgreater0 that are random perturbations of a bounded, continuous map F:M→M , where M is a closed subset of R k . Consistent with many models in biology, these Markov chains have a closed absorbing set M 0 ⊂M such that F(M 0 )=M 0 and F(M∖M 0 )=M∖M 0 . Under some large deviations assumptions on the random perturbations, we show that, if there exists a positive attractor for F (i.e., an attractor for F in M∖M 0 ), then the weak* limit points of μ ε are supported by the positive attractors of F . To illustrate the broad applicability of these results, we apply them to nonlinear branching process models of metapopulations, competing species, host-parasitoid interactions and evolutionary games

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Section: Metapopulation Dynamicsmentioning

confidence: 99%

Quasi-stationary distributions for randomly perturbed dynamical systems

Faure¹,

Schreiber²

2014

Ann. Appl. Probab.

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“…Such a buffering mechanism may be adaptive in environments with variable host densities (Sevenster et al. ) and this as well as a low risk of starvation may result in greater host suppression (Getz and Mills ; Schreiber ).…”

Section: Discussionmentioning

confidence: 99%

Egg load dynamics and the risk of egg and time limitation experienced by an aphid parasitoid in the field

Dieckhoff

Theobald

Wäckers

et al. 2014

Ecology and Evolution

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Insect parasitoids and herbivores must balance the risk of egg limitation and time limitation in order to maximize reproductive success. Egg and time limitation are mediated by oviposition and egg maturation rates as well as by starvation risk and other determinants of adult lifespan. Here, we assessed egg load and nutritional state in the soybean aphid parasitoid Binodoxys communis under field conditions to estimate its risk of becoming either egg- or time-limited. The majority of female B. communis showed no signs of egg limitation. Experimental field manipulations of B. communis females suggested that an average of 4–8 eggs were matured per hour over the course of a day. Regardless, egg loads remained constant over the course of the day at approximately 80 eggs, suggesting that egg maturation compensates for oviposition. This is the first case of such “egg load buffering” documented for a parasitoid in the field. Despite this buffering, egg loads dropped slightly with increasing host (aphid) density. This suggests that egg limitation could occur at very high host densities as experienced in outbreak years in some locations in the Midwestern USA. Biochemical analyses of sugar profiles showed that parasitoids fed upon sugar in the field at a remarkably high rate. Time limitation through starvation thus seems to be very low and aphid honeydew is most likely a source of dietary sugar for these parasitoids. This latter supposition is supported by the fact that body sugar levels increase with host (aphid) density. Together, these results suggest that fecundity of B. communis benefits from both dynamic egg maturation strategies and sugar-feeding.

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“…They found 18% of the dissected individuals had an egg load of zero and, consequently, were extremely egg limited. Several theoretical studies have examined the combined effects of egg limitation and search limitation on host-parasitoid dynamics [6,10,26,30,27,28]. If one takes a broad view that egg limitation is a form of predator saturation, then it can be said that Rogers [26] was the first to consider egg limitation by translating Holling's type II functional response to a host encounter rate.…”

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confidence: 99%

“…Studying models without host self-regulation, Getz and Mills [6] found that stability of the host-parasitoid equilibrium requires parasitic attacks to be sufficiently aggregated and the intrinsic fitness of the parasitoid to exceed the intrinsic fitness of the host. Including host regulation, Schreiber found that parasitoids with aggregated attacks and sufficiently weak search limitation can suppress their hosts to extremely low densities and even drive them to extinction [27,28]. None of these studies, however, considered how egg limitation influences multiparasitoid-host interactions.…”

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Multiparasitoid-Host Interactions with Egg-Limited Encounter Rates

Kon¹,

Schreiber²

2009

SIAM J. Appl. Math.

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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. parasitoid species takes too much time and money and, consequently, have advocated releasing all available natural enemies [33,15]. Theoretical studies have shown that whether multiple species introductions are advisable depends on the details of the biology [21,18,2,29]. For instance, May and Hassell [21] argued that, in general, multiple parasitoid introductions result in greater suppression of the host than single parasitoid introductions. This conclusion, however, relied on the assumption that the parasitoid species aggregate independently of one another and independently of host density. Indeed, Kakehashi, Suzuki, and Iwasa [18] showed that single parasitoid introductions are more effective when both parasitoid species aggregate to the same regions of space. These theoretical studies assume that the parasitoids are search limited and not egg limited. Moreover, their analysis is typically limited to numerical simulations and, occasionally, equilibrium stability analysis. In contrast to these earlier studies, we analyze the global dynamics for multiparasitoid-host interactions when the parasitoids are egg limited but not search limited.All parasitoids experience egg limitation to some degree [6,12,17,19]. For instance, synovigenic parasitoids, which continuously produce eggs over their lifetime, experience egg limitation whenever the number of hosts they encounter in a day exceeds their daily production of eggs. In a field study, Heimpel and Rosenheim [12] caught and dissected 270 synovigenic parasitoids of the species Aphelinidae aonidiae. They found 18% of the dissected individuals had an egg load of zero and, consequently, were extremely egg limited. Several theoretical studies have examined the combined effects of egg limitation and search limitation on host-parasitoid dynamics [6,10,26,30,27,28]. If one takes a broad view that ...

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Periodicity, persistence, and collapse in host–parasitoid systems with egg limitation

Cited by 8 publications

References 30 publications

Quasi-stationary distributions for randomly perturbed dynamical systems

Quasi-stationary distributions for randomly perturbed dynamical systems

Egg load dynamics and the risk of egg and time limitation experienced by an aphid parasitoid in the field

Multiparasitoid-Host Interactions with Egg-Limited Encounter Rates

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