Economic Thresholds

Stern, Vernon M.

doi:10.1146/annurev.en.18.010173.001355

Cited by 159 publications

(76 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We therefore obtain that u D (x, t) and u N (x, t) satisfy the same diffusion equation, the same initial condition u 0 (x) and the same left-hand side boundary condition u D (0, t) = u N (0, t) = 0 but have different value of the gradient at the right-hand side boundary as given by (38). Then, by virtue of the comparison theorem, u D (x, t) ≥ u N (x, t) for any t > 0 and all 0 ≤ x ≤ L. Similarly to the above, let us assume that there exist x * ∈ (0, L) and t * such as u D (x * , t * ) = u N (x * , t * ).…”

Section: Theorem 1 Consider the Diffusion Equation In The Domain 0 <mentioning

confidence: 89%

See 1 more Smart Citation

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Bearup

Petrovskaya

Petrovskii

2015

Mathematical Biosciences

View full text Add to dashboard Cite

Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. Firstly, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called "activity-density" problem). Secondly, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a mean-field mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a well-studied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth.

show abstract

Section: Theorem 1 Consider the Diffusion Equation In The Domain 0 <mentioning

confidence: 89%

“…A reliable estimate is required in order to help the IPM specialists to make an informed decision about control measures, e.g. application of chemical pesticides when the pest density exceeds a certain threshold (Stern, 1973;Higley and Pedigo, 1996) and yet to avoid their unjustified use.…”

Section: Introductionmentioning

confidence: 99%

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Bearup

Petrovskaya

Petrovskii

2015

Mathematical Biosciences

View full text Add to dashboard Cite

show abstract

“…Ecological monitoring programs require estimates of pest species abundance. Important information about population numbers (or trap counts) can be translated and used to make decisions with regards to pest control, costs and pesticide application [67]. Chemical pesticides have their obvious drawbacks in additional operator costs, wheeling damage to the crop and general agricultural produce damage.…”

Section: Introductionmentioning

confidence: 99%

Time Dependent Diffusion as a Mean Field Counterpart of Lévy Type Random Walk

Ahmed

Petrovskii

2015

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

Abstract. Insect trapping is commonly used in various pest insect monitoring programs as well as in many ecological field studies. An individual is said to be trapped if it falls within a well defined capturing zone, which it cannot escape. The accumulation of trapped individuals over time forms trap counts or alternatively, the flux of the population density into the trap. In this paper, we study the movement of insects whose dynamics are governed by time dependent diffusion and Lévy walks. We demonstrate that the diffusion model provides an alternative framework for the Cauchy type random walk (Lévy walk with Cauchy distributed steps). Furthermore, by calculating the trap counts using these two conceptually different movement models, we propose that trap counts for pests whose dynamics may be Lévy by nature can effectively be predicted by diffusive flux curves with time-dependent diffusivity.

show abstract

“…The following indicators can be used: the Economic Threshold (ET) and the Economic Injury Level (EIL). According to Stern [7], the Economic Threshold is "the density at which control measures should be determined to prevent an increasing pest population from reaching the economic injury level". According to Pedigo et al [8], the Economic Injury Level is defined as "the lowest population density that will cause economic damage".…”

Section: Introductionmentioning

confidence: 99%

“…For several decades, the Economic Injury Level has been estimated and used as a fundamental principle in assessing integrated pest management [7,8,13,14]. Concerning Tephritidae, a study on Ceratitis capitata and C. rosa was carried out by Vincenot and Quilici for citrus fruits in Reunion Island [12].…”

Section: Introductionmentioning

confidence: 99%

The mango tree in central and northern Benin: damage caused by fruit flies (Diptera Tephritidae) and computation of economic injury level

Vayssières¹,

Korie²,

Coulibaly³

et al. 2009

Fruits

View full text Add to dashboard Cite

The mango tree in central and northern Benin: damage caused by fruit flies (Diptera Tephritidae) and computation of economic injury level.Abstract --Introduction. In the southern Sudanian zone of Benin, fruit flies are major pests and responsible for considerable yield losses in mango production. The two main species of economic importance affecting mango trees in Benin are Ceratitis cosyra and Bactrocera invadens. During the 2006 crop year and across seven main cultivars, losses stood at 17% in early April and exceeded 70% in mid-June. By the middle of the crop year, over 50% of losses occurred in mango orchards. Materials and methods. The Stone and Pedigo method was used to compute the economic injury level, using variables such as pest control costs, level of losses and mango prices. Results and discussion. The Economic Injury Level (EIL) was highly variable. For the cultivar Kent, for example, it varies from (30 to 75) fruit flies captured per ha and per week, whereas for Keitt the level ranges from (24 to 57) fruit flies·ha -1 ·week -1 . EIL variability depends among other things on market price fluctuation. This method is based on the early introduction of detection traps in mango orchards. A weekly monitoring of trapped fruit flies is used to compute the EIL and make a decision about pest control. Pest control (GF-120 in this case) is recommended if the gross returns exceed production costs. If the number of trapped fruit flies is below the EIL, a treatment is not recommended because pest control will not be profitable. Conclusion. The EIL is an accurate tool to set the optimal (economic) timing of pest control treatment in mango orchards. These preliminary results should lead to the introduction of integrated pest management (IPM) activities to deal with the fruit fly species that are threatening the profitability of mango production in central and northern Benin. Résumé --Introduction. Dans la zone soudanienne méridionale du Bénin les mouches des fruits constituent la contrainte phytosanitaire majeure pour le manguier et sont responsables de pertes de production considérables. Les deux principales espèces de mouches des fruits d'intérêt économique sont Ceratitis cosyra et Bactrocera invadens. Durant la campagne 2006, les pertes moyennes enregistrées au niveau de sept cultivars étaient de 17 % en début avril et dépassèrent 70 % à partir de mi juin. Le seuil de 50 % de pertes a été enregistré et dépassé en milieu de la campagne. Matériel et méthodes. La formule de Stone et Pedigo a été utilisée pour calculer le seuil économique de nuisibilité en utilisant des variables clés telles les coûts des traitements phytosanitaires, les pertes de rendement et les différents prix du marché pour les mangues. Résultats et discussion. Le seuil économique de nuisibilité a été très variable. Pour le cultivar Kent par exemple, ce seuil a fluctué entre (30 et 75) mouches des fruits par hectare et par semaine, alors qu'il a varié de (24 à 57) mouches pour le cultivar Keitt. Un facteur important affectant le seuil économique...

show abstract

Economic Thresholds

Cited by 159 publications

References 0 publications

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Time Dependent Diffusion as a Mean Field Counterpart of Lévy Type Random Walk

The mango tree in central and northern Benin: damage caused by fruit flies (Diptera Tephritidae) and computation of economic injury level

Contact Info

Product

Resources

About