Natural enemies deployment in patchy environments for augmentative biological control

Ghosh, Bapan; Grognard, Frédéric; Mailleret, Ludovic

doi:10.1016/j.amc.2015.06.021

Cited by 10 publications

(4 citation statements)

References 22 publications

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“…However, these programs are most of the time carried out in large culture fields and this requires to know where and how to introduce predators in the space to achieve pest eradication. A study of a patchy environment in which individuals could interact between patches could be considered in future works, as it has been done in (Ghosh et al, 2015). In another direction, considering recent biological control projects, it appears that the quantities of released predators are not exactly the same at each introduction for different reasons: acclimatization, environmental variations, quality of breeding before introduction and so on.…”

Section: Discussionmentioning

confidence: 99%

Augmentative biocontrol when natural enemies are subject to Allee effects

2016

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Intraspecific interactions such as Allee effects are key properties that can guide population management. This contribution considers component Allee effects that are elementary mechanisms leading to declines of fitness at the population scale, i.e. demographic Allee effects. It especially focuses on the consequences of such properties in predator populations, and investigates their repercussions in a biological control context. A modelling framework able to account for reproductive and/or foraging component Allee effects is proposed. From this, four models of augmentative biological control, corresponding to the periodic introduction of natural enemies, have been investigated. This is done using semi-discrete models: ordinary differential equations are used to depict predator-prey dynamics and a discrete equation describes the abrupt augmentation of predators at periodic intervals. In that context, stability of a prey-free solution corresponding to pest eradication has been analyzed. It has been found that rare but large introductions should be preferred over frequent and small ones, when Allee effects influence predator populations. In particular, the occurrence of foraging, rather than reproducing, Allee effects significantly hinders pest eradication. Cases where the pest-free solution is locally, but not globally, stable were also observed and were shown to be favored by the occurrence of reproductive Allee effects among predators.

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Section: Discussionmentioning

confidence: 99%

Augmentative biocontrol when natural enemies are subject to Allee effects

2016

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“…We analyse the spectral radius R c of this matrix and check that it is smaller than one for the local stability of the cPDFS Y T (t) of system (23). We term this method "semi-numerical" as it requires numerical computations, but not extensive simulations of the system [42].…”

Section: Semi-numerical Analysis Of the Controlled Modelmentioning

confidence: 99%

Impulsive modelling of rust dynamics and predator releases for biocontrol

Djuikem

Grognard

Touzeau

2023

Mathematical Biosciences

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“…In recent years, impulsive differential equations are widely used in practical issues [12][13][14][15][16][17] such as the pulses vaccination in diseases [18][19][20][21][22], pulse injection nutrient in the medium [23][24][25][26] and population dynamics [27][28][29][30][31]. Results suggest that the predator-prey system can be constructed by using impulsive differential equations to simulate the pest control and get some positive theoretical results [32][33][34][35][36][37][38][39], as exemplified in the release of predators periodically [40][41][42], the periodic release of pests that are infected with disease [43][44][45] and periodically release of predators combined with periodic sprayed pesticides [46,47]. However, scholars find that the impulsive control strategy on the basis of the density of insect pests population has more practical significance.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay

Shi

Cheng

2019

Mathematics

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In our paper, we propose a single population Smith model with continuous delay and impulsive state feedback control. The application in pest management of this model is investigated. First, the singularity of this model is qualitatively analyzed; then, we consider the existence and uniqueness of order-one periodic orbit in order to determine the frequency of the implementation of chemical control. Moreover, based on the limit method of the sequences of subsequent points, we verify the stability of periodic orbit to ensure a certain robustness of this control; at last, we carry out the numerical simulations to verify the correctness of the theoretical results.

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Natural enemies deployment in patchy environments for augmentative biological control

Cited by 10 publications

References 22 publications

Augmentative biocontrol when natural enemies are subject to Allee effects

Augmentative biocontrol when natural enemies are subject to Allee effects

Impulsive modelling of rust dynamics and predator releases for biocontrol

Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay

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