Density Dependence in Host-Parasitoid Models

May, Robert M.; Hassell, M. P.; Anderson, Roy M.; Tonkyn, David W.

doi:10.2307/4142

Cited by 188 publications

(126 citation statements)

References 13 publications

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“…A well-known example of f is given by Nicholson and Bailey [20], f (p) = e −dp , where parameter d > 0 represents the per capita searching efficiency of the parasitoids. May et al [16] discussed the effects of timing of density dependence in host-parasitoid interactions with f given by f (p) = (1 + αp/k) −k , where parameter α > 0 is also the parasitoid's searching efficiency and k > 0 is termed the 'clumping' parameter. May et al [16] noticed that the limit of their f as k goes to infinity is the f used by Nicholson and Bailey [20], lim k→∞ (1 + αp/k) −k = e −αp .…”

Section: A Predator-prey Model With Cannibalism In the Preymentioning

confidence: 99%

“…May et al [16] discussed the effects of timing of density dependence in host-parasitoid interactions with f given by f (p) = (1 + αp/k) −k , where parameter α > 0 is also the parasitoid's searching efficiency and k > 0 is termed the 'clumping' parameter. May et al [16] noticed that the limit of their f as k goes to infinity is the f used by Nicholson and Bailey [20], lim k→∞ (1 + αp/k) −k = e −αp . In both of these examples, f is strictly decreasing, concave up, and satisfies (H2).…”

Section: A Predator-prey Model With Cannibalism In the Preymentioning

confidence: 99%

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Cannibalism in discrete-time predator–prey systems

Chow

Jang

2012

Journal of Biological Dynamics

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In this study, we propose and investigate a two-stage population model with cannibalism. It is shown that cannibalism can destabilize and lower the magnitude of the interior steady state. However, it is proved that cannibalism has no effect on the persistence of the population. Based on this model, we study two systems of predator-prey interactions where the prey population is cannibalistic. A sufficient condition based on the nontrivial boundary steady state for which both populations can coexist is derived. It is found via numerical simulations that introduction of the predator population may either stabilize or destabilize the prey dynamics, depending on cannibalism coefficients and other vital parameters.

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Section: A Predator-prey Model With Cannibalism In the Preymentioning

confidence: 99%

Section: A Predator-prey Model With Cannibalism In the Preymentioning

confidence: 99%

Cannibalism in discrete-time predator–prey systems

Chow

Jang

2012

Journal of Biological Dynamics

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“…Intraspecific density-dependent mortality is assumed to precede mortality due to parasitism (see, e.g. [5,19,20]). One interpretation of this assumption is that the parasitoids are koinobionts.…”

Section: The Modelmentioning

confidence: 99%

“…Traditionally, these models have assumed that the parasitoids are limited primarily by their ability to locate hosts [1][2][3][4][5][6][7][8]. This assumption, however, neglects the fact that parasitoids may be limited by the number of eggs available for oviposition.…”

Section: Introductionmentioning

confidence: 99%

“…An important component of these difference equation is the host encounter rate E, which describes the average number of attacks or parasitic encounters per host. Based on the foundational work of Nicholson and Bailey [17], studies of host-parasitoid models traditionally assume that the encounter rate only depends on the density of the parasitoid [1][2][3][4][5][6][7][8]18]. This assumption, however, neglects the fact that at higher host densities, parasitoids are more likely to be egg-limited and, consequently, less likely to attack hosts.…”

Section: Introductionmentioning

confidence: 99%

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

Schreiber

2007

Journal of Biological Dynamics

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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 hostparasitoid 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 hostparasitoid 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.

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Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

Din¹,

Hussain²

2018

Asian Journal of Control

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In this paper, a new density-dependent host-parasitoid model is proposed. The modification is based on density-dependent factor by introducing Hassell growth function in host population. Moreover, the permanence of solutions, existence and uniqueness of positive equilibrium, local asymptotic stability and global behavior of the positive equilibrium point are also investigated. It is demonstrated that system endures Neimark-Sacker bifurcation for wide range of bifurcation parameter. In order to control chaos due to emergence of Neimark-Sacker bifurcation, two feedback control strategies, that is, OGY and hybrid control methods are implemented. Finally, all mathematical analysis, particularly, Neimark-Sacker bifurcation, chaos control strategies, and global asymptotic stability of unique positive point are verified with the help of numerical simulations.

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Density Dependence in Host-Parasitoid Models

Cited by 188 publications

References 13 publications

Cannibalism in discrete-time predator–prey systems

Cannibalism in discrete-time predator–prey systems

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

Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

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