Discrete-time host–parasitoid models with pest control

Jang, Sophia R.‐J.; Yu, Jui‐Ling

doi:10.1080/17513758.2012.700074

Cited by 24 publications

(11 citation statements)

References 27 publications

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“…A traditional approach to describe parasitoid-host dynamics is to use discrete time models, such as the Nicholson-Bailey model [9] and others considered more recently [10,11,12,13,14]. Discrete models can monitor the change in population density for distinct points in time, such as each year or each generation, which agrees with typical life-cycle themes of insects in temperate climates [15].…”

Section: Introductionmentioning

confidence: 99%

The effects of host-feeding on stability of discrete-time host–parasitoid population dynamic models

Emerick

Singh

2016

Mathematical Biosciences

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Discrete-time models are the traditional approach for capturing population dynamics of a host-parasitoid system. Recent work has introduced a semi-discrete framework for obtaining model update functions that connect host-parasitoid population levels from year-to-year. In particular, this framework uses differential equations to describe the host-parasitoid interaction during the time of year when they come in contact, allowing specific behaviors to be mechanistically incorporated. We use the semi-discrete approach to study the effects of host-feeding, which occurs when a parasitoid consumes a potential host larva without ovipositing. We find that host-feeding by itself cannot stabilize the system, and both populations exhibit behavior similar to the Nicholson-Bailey model. However, when combined with stabilizing mechanisms such as density-dependent host mortality, host-feeding contracts the region of parameter space that allows for a stable host-parasitoid equilibrium. In contrast, when combined with a density-dependent parasitoid attack rate, host-feeding expands the non-zero equilibrium stability region. Our results show that host-feeding causes inefficiency in the parasitoid population, which yields a higher population of hosts per generation. This suggests that host-feeding may have limited long-term impact in terms of suppressing host levels for biological control applications.

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Section: Introductionmentioning

confidence: 99%

The effects of host-feeding on stability of discrete-time host–parasitoid population dynamic models

Emerick

Singh

2016

Mathematical Biosciences

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“…Although the existence and stability of equilibria of subsystem 1 have been investigated [15], we also prove the existence of the equilibria of two subsystems briefly, which are useful for discussing the types of the equilibria of the whole switching system (3).…”

Section: Equilibria Of Two Subsystemsmentioning

confidence: 99%

Dynamic Complexity of a Switched Host-Parasitoid Model with Beverton-Holt Growth Concerning Integrated Pest Management

Xiang

Yang

2014

Journal of Applied Mathematics

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The switched discrete host-parasitoid model with Beverton-Holt growth concerning integrated pest management has been proposed, and the switches are guided by the economic threshold (ET). The integrated pest management (IPM) tactics are applied to prevent the economic injury if the density of host population exceeds the ET, and the IPM tactics are called off once the density of host population descends below ET. To begin with, the regular and virtual equilibria of switched system has been discussed by two or three parameter-bifurcation diagrams, which reveal the regions of different types of equilibria. Besides, numerical bifurcation analyses about inherent growth rates show that the switched discrete system may have complicated dynamics behavior including chaos and the coexistence of multiple attractors. Finally, numerical bifurcation analyses about killing rates indicate that the system comply with the Volterra principle, and initial values of both host and parasitoid populations affect the host outbreaks times.

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“…Numerous investigators [3,7,8,11,13,17,18,21] have nevertheless cited Beddington et al [5] and use the structure of model (2). These authors often derive their models from previous work, without a careful explanation of the underlying biology.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Analysis of Host--Parasitoid Models with Density Dependence Preceding Parasitism

Marcinko¹,

Kot²

2020

Preprint

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We present a systematic comparison and analysis of four discrete-time, hostparasitoid models. For each model, we specify that density-dependent effects occur prior to parasitism in the life cycle of the host. We compare density-dependent growth functions arising from the Beverton-Holt and Ricker maps, as well as parasitism functions assuming either a Poisson or negative binomial distribution for parasitoid attacks. We show that overcompensatory density-dependence leads to period-doubling bifurcations, which may be supercritical or subcritical. Stronger parasitism from the Poisson distribution leads to loss of stability of the coexistence equilibrium through a Neimark-Sacker bifurcation, resulting in population cycles. Our analytic results also revealed dynamics for one of our models that were previously undetected by authors who conducted a numerical investigation. Finally, we emphasize the importance of clearly presenting biological assumptions that are inherent to the structure of a discrete-time model in order to promote communication and broader understanding.

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Discrete-time host–parasitoid models with pest control

Cited by 24 publications

References 27 publications

The effects of host-feeding on stability of discrete-time host–parasitoid population dynamic models

The effects of host-feeding on stability of discrete-time host–parasitoid population dynamic models

Dynamic Complexity of a Switched Host-Parasitoid Model with Beverton-Holt Growth Concerning Integrated Pest Management

A Comparative Analysis of Host--Parasitoid Models with Density Dependence Preceding Parasitism

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