The Effect of Partial Crop Harvest on Biological Pest Control

Nundloll, Sapna; Mailleret, Ludovic; Grognard, Frédéric

doi:10.1216/rmj-2008-38-5-1633

Cited by 14 publications

(15 citation statements)

References 22 publications

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“…This proof does not depart very much from the one of Theorem 4, and is given in detail in [Nundloll et al, 2007].…”

Section: G(x((n + 1)tmentioning

confidence: 78%

“…This function is increasing in S and r because the sign of the partial derivatives is determined by the sign of factor Γ, which is positive [Nundloll et al, 2007]. Theorem 4.…”

Section: Stability Analysis In the Presence Of Pestsmentioning

confidence: 96%

“…The proof is constructed in the same manner as for Proposition 2, and is detailed in [Nundloll et al, 2007].…”

Section: Pest-free Stability Analysismentioning

confidence: 99%

See 2 more Smart Citations

Global Stability in a General Impulsive Biological Control Model with Harvest

Nundloll

Mailleret²,

Grognard

2008

IFAC Proceedings Volumes

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In this paper, the effects of periodic partial harvesting of a continuously grown crop on augmentative biological control are analysed. Partial harvesting can remove a proportion of both pests and biological control agents, so its influence on the control efficiency cannot be a priori neglected. An impulsive model consisting of a general predator-prey model in ode is used. It is augmented by a discrete component to depict releases of biological control agents and the periodic partial harvesting. A stability condition for pest eradication is expressed as the minimal value of the budget per unit time to spend on predators. We consider the partial harvesting period to be fixed so that the only manipulated variable is the release period. One period is taken as the integer multiple of the other. We show that when the releases are carried out more often than the harvests, the release period influences the minimal budget. Conversely, there is no effect on this budget when releases take place as often as or less frequently than harvests.

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“…This proof does not depart very much from the one of Theorem 4, and is given in detail in [Nundloll et al, 2007].…”

Section: G(x((n + 1)tmentioning

confidence: 78%

“…This function is increasing in S and r because the sign of the partial derivatives is determined by the sign of factor Γ, which is positive [Nundloll et al, 2007]. Theorem 4.…”

Section: Stability Analysis In the Presence Of Pestsmentioning

confidence: 96%

See 1 more Smart Citation

Global Stability in a General Impulsive Biological Control Model with Harvest

Nundloll

Mailleret²,

Grognard

2008

IFAC Proceedings Volumes

Self Cite

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show abstract

“…Moreover, in most of the studied cases, (τ k+1 − τ k ) is a constant for all k, but once again there are examples where it is not (e.g. Lakmeche & Arino 2001;Liu et al 2005;Nundloll et al 2008).…”

Section: Semi-discrete Modelling: a General Formalism And Two Illustrmentioning

confidence: 93%

A note on semi-discrete modelling in the life sciences

Mailleret

Lemesle

2009

Phil. Trans. R. Soc. A.

100

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Semi-discrete models are a particular class of hybrid dynamical systems that undergo continuous dynamics most of the time but repeatedly experience discrete changes at some given moments. In the life sciences, since the first semi-discrete model was derived to describe population dynamics by Beverton & Holt (Beverton & Holt 1957 In Fisheries investigations , series 2, vol. 19), a large body of literature has been concerned with such modelling approaches. The aim of the present contribution is twofold. On the one hand, it provides a comprehensive introduction to semi-discrete modelling through two illustrative examples: the classical work by Beverton and Holt is recalled and an original example on immigration in a population model affected by a strong Allee effect is worked out. On the other hand, a short overview of the different applications of semi-discrete models in the life sciences is proposed.

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“…We seek to answer two questions: firstly, what conditions are required for the pest population to be eliminated and secondly, what release strategy is to be employed for this eradication be as quick as possible. In our work, the size of a release is defined explicitly as the product of the rate of predator release per unit time and the release period (see also Mailleret and Grognard, 2006;Nundloll et al, 2008). By doing so, we are able to compare different biological control strategies in terms of the release size and release frequency that involve the same overall number of predators.…”

Section: Introductionmentioning

confidence: 99%

Influence of Intrapredatory Interferences on Impulsive Biological Control Efficiency

2010

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International audienceIn this paper, a model is proposed for the biological control of a pest by its natural predator. The model incorporates a qualitative description of intrapredatory interference whereby predator density decreases the per capita predation efficiency and generalises the classical Beddington-DeAngelis formulation. A pair of coupled ordinary differential equations are used, augmented by a discrete component to depict the periodic release of a fixed number of predators into the system. This number is defined in terms of the rate of predator release and the frequency at which the releases are to be carried out. This formulation allows us to compare different biological control strategies in terms of release size and frequency that involve the same overall number of predators. The stability properties of the zero-pest solution are analysed. We obtain an upper bound on the interference strength (the biological condition) and a minimal bound on the predator release rate (the managerial condition) required to eradicate a pest population. We demonstrate that increasing the frequency of releases reduces this minimal rate and also increases the rate of convergence of the system to the zero-pest solution for a given release rate. Additionally, we show that other conclusions are to be expected if the interferences between predators have weaker or stronger effects than the generalised Beddington-DeAngelis formulation proposed in this paper

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The Effect of Partial Crop Harvest on Biological Pest Control

Cited by 14 publications

References 22 publications

Global Stability in a General Impulsive Biological Control Model with Harvest

Global Stability in a General Impulsive Biological Control Model with Harvest

A note on semi-discrete modelling in the life sciences

Influence of Intrapredatory Interferences on Impulsive Biological Control Efficiency

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