Multiparasitoid-Host Interactions with Egg-Limited Encounter Rates

Abstract

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 ...

Stochasticity in Reproductive Opportunity and the Evolution of Egg Limitation in Insects

“…For over 80 years, different researchers have answered this question differently. The result has been the creation of competing families of models for host–parasitoid population dynamics, one emphasizing time limitation (Lotka 1925; Nicholson and Bailey 1935; Hassell 1978, 2000; Murdoch et al 2003) and another emphasizing egg limitation (Thompson 1924, Getz and Mills 1996; Shea et al 1996; Heimpel et al 2003; Schreiber 2006, 2007; Schreiber and Vejdani 2006; Kon and Schreiber 2009), and competing families of models of insect reproductive behavior, again one emphasizing time limitation (Charnov and Skinner 1985; Visser et al 1992; Godfray 1994) and another emphasizing egg limitation (Iwasa et al 1984; Mangel 1987; Mangel and Heimpel 1998). These different classes of models often make very different predictions (e.g., Mangel 1989), underscoring the importance of resolving the relative importance of time and egg limitation.…”

Effect of egg production dynamics on the functional response of two parasitoids

“…For more than 80 years, researchers have put forth various models to assess whether the realized lifetime reproductive success of adult female parasitoids is constrained by the limited time available for finding oviposition sites [38][39][40][41][42], or by the finite supply of mature eggs [43,44]. Rosenheim [45] employed models to investigate how stochastic factors affect the evolution of egg limitation among insects.…”

Effect of egg production dynamics on the functional response of parasitoids

“…For over 80 years, researchers have proposed different models to determine if the realized lifetime reproductive success of adult female parasitoids was limited by the finite amount of time available to locate hosts that serve as oviposition sites [33][34][35][36][37], or by the finite supply of mature eggs [38,39]. Rosenheim [40], using models to explore how stochasticity influences the evolution of egg limitation in insects, found that both egg and time limitations are fundamental in shaping insect reproductive behavior and population dynamics.…”