Kaushik Chakraborty and Debes Chandra Deb. Department of Zoology, Alipurduar College, Alipurduar, Jalpaiguri, West Bengal, India

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1 World Applied Sciences Journal 17 (10): , 01 ISSN IDOSI Publications, 01 A Mathematical Model for Pesticide Recommendations in Contemplation of Alternative and Variable Threshold Combinations of Insect Pests in the Paddy Field 1 Kaushik Chakraborty and Debes Chandra Deb 1 Department of Zoology, Alipurduar College, Alipurduar, Jalpaiguri, 7361 West Bengal, India Department of Zoology, University of North Bengal, Raja Rammohanpur, Darjeeling, West Bengal, India Abstract: Pesticides though have ecological adverse effects are still the prime way for pest control. Selection of the pesticide formulation is based upon mostly on a single pest economic threshold level (ETL). But field insect pests represent a more complex and heterogeneous association as it characterizes an admixture of different species of variable life-stages. As, pesticide of a single brand is not equally effective to all insect pests, a broadly defined insecticide application strategy based on a single pesticide application cannot not be taken in toto for paddy insect pest control. Side by side re-validation of the presently running ETL system in consideration of threshold limit is required. Brown plant hopper (BPH), yellow stem borer (YSB), gall midge (GM) and paddy bug (PB) are four major paddy insect pests in the northern parts of West Bengal, India. A mathematical model of pest occurrence was proposed after conducting the field experiment for five consecutive years ( ) at three blocks of the district Uttar Dinajpur, West Bengal. In the present model four incidence grades of YSB, BPH and GM and three grades of PB was considered. Gradation was done either depending on the incidence of the individual species or the damage symptoms. During gradation, the nationally advocated economic threshold level (ETL) of each of the pest species was considered as the maximum indices for all the pests. Multiple mutual combination between the grades of all the four pests showed that the pests could occur in 19 combinations. But at a given growth stage of paddy only one pest combination occurs. Depending on the key insect pest in a combination, 19 combinations were again grouped in 1 cultivation modules (CMs) for practical applicability. Each CM was named in consideration of key insect pest species of that group and accordingly application strategy of pesticides for particular CM was recommended. Key words: Threshold levels Cultivation module Pesticide formulations Action pathway INTRODUCTION suppression using effective, least toxic methods which is practical to apply and cost effective to operate [6-8]. A pest management system, its consistency and As pest management is a complicated process, it is not honesty in decision-making and hence the output simply a matter of substituting good pesticides for bad accruing from management actions and approach, depend pesticides. It is rather an improved way to select and to a large extent on threshold values for action decisions apply the pesticide in judicious mode in consideration of [1, ]. The use of chemical pesticides in Indian agriculture the incidence of insect pest population [9, 10]. has seen a sharp increase in recent years and in some Out of the 1 important paddy insect pests, 7 are areas has reached alarming levels [3, 4]. Inspite of that, economically more injurious in the northern parts of West pesticides as prime pest control input are still used by a Bengal, India [11]. These are yellow stem borer (YSB), number of farmers [5]. Modern IPM s focus on pest brown plant hopper (BPH), gall midge (GM) and paddy Corresponding Auhtor: Kaushik Chakraborty, Department of Zoology, Alipurduar College, Alipurduar, Jalpaiguri, 7361 West Bengal, India. 1370

2 bug (PB). Considerable differences of bio-ecology, Underlying Principle of Categorization: Let us consider numerical abundance, extent of infestation and nature of a set of n groups X 1, X, X 3,.., X n. Any ordered damage by these four pests were noted [1]. Accordingly arrangement (X i1, X i, X i3,, X ir), 1 i n of r the pesticide application strategy should be befitted [13]. symbols is called an ordered sample of size r. If groups are Incidence of YSB was noted throughout the paddy selected one by one and repetitions are permitted then growth stages [14]. Abundance of BPH increases as the r clearly there are n samples of size r. Gradation were done growth stage of paddy advances and attains the maximum depending on the field incidence of the four insect at early grain maturation stage [13]. Activity of gall midge species. Again, if X 1, X, X 3,., X ngroups having n 1, n, was mostly restricted to the tillering stage [15]. PB is n 3,.., nr represents the incidence of insect pests mainly injurious to the developing grains [16]. Selection respectively, then there are ordered sequences or samples of a single pesticide brand is not equally effective to all (permutation with repetition ) are n 1 x n x n 3 x.. x nr. these four pests in relation to the particular paddy growth In our case, We have considered four grades (1,,3,4) for stage [17]. Systemic pesticide is effective for YSB, BPH YSB, BPH, GM and three grades (1,,3) for PB and GM while both contact and systemic pesticide is respectively, then the total number of different ordered favoured for PB. However Further in a field peak arrangements of the groups is 4(YSB) x 4(BPH) x 4(GM) x abundance of all the four insect pests differs 3(PB) = 19. considerably. So a more reliable method of pesticide application which is based on based on multiple pest Categorization of Insect Damage Depending on National threshold level instead of single pest assessment is Protocol: Economic threshold level (ETL) as described in urgently required [18]. the national protocol for these four pests was taken as the Presently, the terms economic threshold (ETL), uppermost limit during gradation (..). A limit of 0 damage threshold level (DTL), injury threshold level (ITL) individuals/hill, 1 egg mass/m, 1 silver shoot/m and 1 and action threshold (ATL) were used to explain the individual/hill were recognized as the national ETL limit of insect pest status of the field. DTL are more realistic [19] BPH, YSB, GM and PB respectively. Depending on these and can easily be used in examination of varying level of values, the pests or the damage symptoms are divided pest infestation [0]. Sogawa et al. [1] have commented into four (for YSB, BPH and GM) or three (for PB) tolerant that most economic thresholds for insects are numerical grades. Collective contemplation of the four grades for and not based on damage functions. So selection of YSB, BPH and GM and three grades for each of PB pesticides in consideration of single pest threshold level reflected that in relation to the four growth stages of is less applicable to check the crop damage since the paddy the pests could occur in a total of 19 matrix pests occur at multiple threshold combination [8]. combination matrices (Table 1). Each combination Prophylactic application of single pesticide formulation is indicated its relative occurrence and the potential of still widely practiced in the southern parts of Asia. damage. Combinations which were supposed to require Experiment on the relative superiority of the pesticide the same pattern of prophylactic or corrective measures formulation on a particular pest species was carried out by were taken in one group, regarded as Cultivation Module various authors [-4]. But hardly any author advocates (CM). the application of pesticide in consideration of variable grades of pest occurrence. Under this situation the RESULTS AND DISCUSSION presently available ETL limit should be graded in to sub-etl levels and accordingly should be redefined. Redefining the Pest Action Threshold Level: ETL value This paper quantifies the nature of pesticide application described in the national protocol is more or less fixed. in relation to action threshold of four major insect pest It explains the incidence either of insect individuals or the populations. damage symptoms numerically. Decisions to apply pesticide are taken only when the pest indices crosses the MATERIALS AND METHODS limit. But such pest management strategy disregards the heterogeneity of the pest complexes. Most of the Selection of Pests: Only four major insect pests were pesticide based paddy insect pest control module is considered in the present mathematical model. These are prepared in consideration of the economic injury level yellow stem borer (YSB), brown plat hopper (BPH), gall (EIL) of a single pest. But dynamics of insect pest is more midge (GM) and paddy bug (PB). complex and heterogeneous as it represents an 1371

3 Table 1: Categorization of the major pests into different grades depending on the observable field threshold Gradation of ETL limit with threshold value Pests with unit of ETL limit given Threshold level(s) observations Symbol in national protocol Nomenclature Grade(s) Individuals/damage symptoms Brown plant hopper Individual(s)/hill A 0 individuals/hill PT A FT A AT A BT A4 0.1< Yellow stem borer Egg mass(s)/m B 1 egg mass/m PT B FT B AT B BT B4.0< Gall midge Individual(s)/m C 1 silver shoot /m PT C FT C AT C BT C4 >1.5 Paddy bug Individual(s)/hill D 1 individual/m PT D FT D AT D3 1.6< 1: Permissible threshold (PT), : Functional threshold (FT), 3: Action threshold (AC), 4: battle threshold (BT) admixture of different pest population of variable life- Each CM was named in consideration key insect pest stages. The objective of the modern IPM is to suppress species and accordingly pesticides for particular CM were the pest rather than its abolition. When the individual recommended. A total of 1 CMs were formed of which 6 number of a pest approaches the ETL limit, control of were found to be economically and ecologically more population by pesticides is more crucial. So gradation of important (indicated by * in the Table ) in the northern abundance of insect individuals or the damage symptoms parts of West Bengal. Probability of occurrence of each were done taking the nationally defined ETL level as CM was determined after observation on 50 plots in each working limit. Naming of each grade was done according block for five consecutive years. After assessing the pest to the necessity of management procedure. There were status in the field, farmers would be able to follow the four grades for YSB, BPH and GM and three grades for appropriate group combination and adopt suitable PB. No special attention to the field is required in case of prophylactic or corrective measures. Each of the 1 permissible threshold (PT) as the pest status is far domains has its individuality and is characterized by the below ETL. At functional threshold (FT) the pest status presence or absence of the activity of pest(s) (indicated approached to the limit of ETL and the situation could be in the Table 1). Threshold combinations under the same managed only after taking special attention to some domain have nearly same pest intensity and accordingly cultural practices including pesticide application. Action require more or less same pesticidal treatment. threshold (AT) required the steady prophylactic alteration of the cropping practices while in battle Application Protocol of Different Pesticides in threshold (BT) (absent in case of PB) immediate Consideration of Single Pest Attack: CMs have shown pesticidal input together with the adoption of the that some pesticides were equally effective to more than corrective measures at local level for future crop one insect pest (Table 3). Pest combinations under CM, cultivation was given priority. CM4, CM5, CM6, CM7 and CM8 were more common in the northern parts of Bengal. Farmers may select a single Naming of the CM Domain: Multiple mutual combination pesticide among the batches in consideration of particular between all the grades (four grades of YSB, BPH and GM CM. But mode of application of single pesticide under and three grades of PB) of all the four pests showed that different CM may differ. the pests could occur in 19 combinations. But only one Generic name of the pesticides was recommended combination can occur at a time. Depending on the key depending on only the gazette of Government of India insect pest, 19 pest-combinations were again grouped in Ministry of Agriculture Department of Agriculture and 1 cultivation modules (CMs) for practical applicability. Cooperation, Directorate of Plant Protection, Quarantine 137

4 Table : Multiple threshold combinations of the four major pests from the paddy fields and their categorization into cultivation modules (CMs). CMs and probability of its occurrence Threshold Combinations (TC) CM1 (Nil) A1B1C1D1, A1BC1D, A1B1CD1 *CM (BPH+YSB) ABC1D1, ABC1D, ABC1D3, ABCD1, ABCD, ABCD3, ABC3D1, ABC3D, ABC3D3, AB3C1D1, AB3C1D, AB3C1D3, ABCD1, AB3CD1, AB3CD, AB3CD3, AB3C3D1, AB3C3D, AB3C3D3, A3BC1D1, A3BC1D, A3BC1D3, A3BCD1, A3BCD, A3BCD3, A3BC3D1, A3BC3D, A3BC3D3, A3B3C1D1, A3B3C1D, A3B3C1D3, A3B3CD1, A3B3CD, A3B3CD3, A3B3C3D1, A3B3C3D, A3B3C3D3, A4B1CD, A4BC1D1, A4BC1D, A4BC1D3, A4BCD1, A4BCD, A4BCD3, A4BC3D1, A4BC3D, A4BC3D3, A4B3C1D1, A4B3C1D, A4B3C1D3, A4B3CD1, A4B3CD, A4B3CD3, A4B3C3D1, A4B3C3D, A4B3C3D3 CM3 (BPH+GM) A3B1CD1, A3B1CD, A3B1CD3, A3B1C3D1, A3B1C3D, A3B1C3D3, A3BCD1, A3BCD, A3BCD3, A3BC3D1, A3BC3D, A3BC3D3, A3B3C3D1, A3B3C3D, A4B1CD3, A4B1C3D, A4B1C3D3, *CM4 (GM+PB) A1B1CD, A1B1CD3, A1B1C3D, A1B1C3D3, A1BCD, A1BCD3, A1BC3D, A1BC3D3, A1B3CD, A1B3CD3, A1B3C3D, A1B3C3D3, AB1CD3, AB1C3D, AB1C3D3, ABCD3, AB3CD, AB3CD3, A3B3C3D3, A4B1CD3, A4B1C3D1, A4B1C3D, A4B1C3D3, A4B3C3D3 *CM5 (YSB+PB) A1BC1D, A1BC1D3, A1B3C1D, A1B3C1D3, ABC1D, ABC1D3, A3B3C1D, A3B3C1D3, A3B3CD, A3B3CD3, A4BC1D, A4B3C1D, A4B3C1D3 *CM6 (BPH+PB) AB1C1D, AB1C1D3, AB1CD, AB3C1D, AB3C1D3, A3B1C1D3, A3B1CD, A3B1CD3, A3B1C3D, A3B1C3D3, A3BC1D, A3BC1D3, A3BCD, A3BCD3, A3BC3D, A3BC3D3, A4B1C1D, A4B1C1D3, A4B1CD3, A4BC1D3, A4BC3D3, A4B3CD, A4B3CD3 *CM7 (BPH+GM+PB) AB1CD1, AB1CD, AB1CD3, AB1C3D1, AB1C3D, AB1C3D3, AB3C3D1, AB3C3D, AB3C3D3, A3B3C3D3, A4B1C1D1, A4B1CD, A4B3C3D, A4B3C3D3 *CM8 (YSB+GM+PB) A1BCD1, A1BCD, A1DCD3, A1BC3D1, A1BC3D, A1BC3D3, A1B3CD1, A1B3CD, A1B3CD3, A1B3C3D1, A1B3C3D, A1B3C3D3, ABCD1, ABCD, ABC3D, ABC3D3, AB3CD1, AB3CD, AB3CD3, A3B3CD1, A3B3CD, A3B3CD3, A4B1CD, A4BCD1, A4BCD, A4BCD3, A4BC3D1, A4BC3D, A4BC3D3, A4B3CD1, A4B3CD, A4B3CD3, A4B3C3D1 CM9 (YSB) A1BC1D1, A1B3C1D1, AB3C1D CM10 (BPH) AB1C1D1, A3B1C1D1, A3B1C1D, A4B1C1D1 CM11 (GM+PB) A1B1CD1, A1B1C3D1, A1BC3D1 CM1 (PB) A1B1C1D, A1B1C1D3, A1BCD3 * Major insect pest domains in the northern parts of Bengal Table 3: Multiple threshold combinations of the four major pests from the paddy fields and their categorization into cultivation modules (CMs) CMs Recommended pesticides CM1 (Nil) lindane, monocrotophos, phosalone, phorate, quinalphos, etofenprox, fipronil *CM (BPH+YSB) carbaryl, carbofuran, diazinon, endosulfan, ethion, fenthion, lindane, methamidophos, monocrotophos, phorate, phosphalone, phosphamidon CM3 (BPH+GM) carbaryl, carbofuran, chlopyriphos, cypermethrin, decamethrin, diazinon, fenitrothion, monocrotophos, phosphamidon, fenthion, phorate, etofenprox *CM4 (GM+PB) carbofuran, chlopyriphos, diazinon, fenthion, mephosfolan, phorate phosphamidon, quinalphos *CM5 (YSB+PB) aldrin,carbaryl, chlopyriphos, dichlorvos, endosulfan, fenthion, malathion, methyl parathion, phosphamidon,quinalphos,trichlorphon *CM6 (BPH+PB) acephate, bromophos, carbaryl, carbofuran, cartap, chlorpyriphos, endosulfan, ethion, fenitrothion, etofenprox *CM7 (BPH+GM+PB) acephate, carbaryl, carbofuran, cartap, chlopyriphos, fenthion, fenvalerate, monocrotophos, permethrin, phosphamidon, quinalphos, triazophos *CM8 (YSB+GM+PB) carbaryl, carbofuran, chlopyriphos, cypermethrin, decamethrin, diazinon, fenitrothion, monocrotophos, phosphamidon, fenthion, phorate CM9 (YSB) carbofuran, chlopyriphos, diazinon, Fenthion, mephosfolan, phorate phosphamidon, quinalphos, phosphamidon CM10 (BPH) carbaryl, carbofuran, chlopyriphos, cypermethrin, carbofuran decamethrin, diazinon, fenitrothion, monocrotophos, phosphamidon, fenthion, phorate, etofenprox, cartap hydrochloride CM11 (GM+PB) carbofuran, chlopyriphos, diazinon, fenthion, mephosfolan, phorate phosphamidon, quinalphos, imidacloprid CM1 (PB) fenthion, malathion, phosphamidon, carbaryl *major domains and Storage, Central Insecticide Board and Registration Application of etofenprox, moncrotophos, Committee, Faridabad [5]. Application strategies of some phosalone or 0.5 kg a.i./ha or lindane selected pesticides in consideration of four important 0 EC at 1 liter/ha in the early stages of the crop pests are delineated below: growth. Application of granular insecticides such as For brown plant hopper (BPH): phorate or cartap hydrochloride or carbofuran at 1 kg a.i./ha. Spraying of 0.75 kg a.i./ha during early Application of fipronil 0.3% G at 5 kg/ha during mid growth stage of paddy. growth stage. 1373

5 Application of granules of carbofuran at 0.75 kg For gall midge (GM): a.i./ha or phorate at 1.5 kg a.i./ha at maximum vegetative growth stage. Seed treatment with chlorpyriphos 0.% solution for 1 Spray application of phosalone or etofenprox or / hours or seed mixing with either chlorpyriphos chlorpyriphos or carbaryl, at 0.5 kg a.i./ha or fipronil (0.75 kg a.i./100 kg seeds) or imidacloprid (0.5 kg at 50 g a.i./ha. a.i./100 kg seeds) provide protection for 35-day in the Application of resurgence causing insecticides like nursery. quinalphos, chlorpyriphos, methyl parathion, Seedling root dip in 0.0% chlorpyriphos emulsion deltamethrin and cypermethrin should be restricted in before transplanting for 10-1 hours gives protection application. for 35 days. Sprouted seed soaked with imidacloprid 1 For yellow stem borer (YSB): 0.05% (.5ml/lit) for / hours then shade dried and broadcasted on raised nursery bed give protection Application of fipronil 5% SC at 1 liter/ha if the against gall midge. incidence of dead heart crosses 10% limit at early vegetative stage. For paddy bug (PB): Spraying of fenthion or fenitrothion or endosulfan or phosalone or monocrotophos or etofenprox or Dusting carbaryl 10% and repeat it depending upon cartap hydrochloride or chlorpyriphos at 0.5 kg the extent of infestation. a.i./ha. Seedlings root dip treatment for 10-1 hours before Carbaryl kg/ha/ abamectin 500ml/ha/ transplanting in 0.0% chlorpyriphos gives phosphamidon 40SP 1 lit/ha or dusting with protection up to 35 days against stem borer. malathion 5kg/ha. Seed treatment with 5g/kg seed. Determination of Action Pathway: Decision to follow a If the pest crosses economic threshold level (ETL) particular CM mostly comes from a serial observation in then apply cartap hydrochloride 0kg/ha or fipronil an area on a particular pest species in relation to the 0.3G 5kg/ha growth stage of paddy. After extensive observation for five consecutive years ( ) on the relative Phorate 10kg/ha or 33 kg/ha or occurrence of the four major pests in the three carbosulfan 16kg/ha in the main field. administrative blocks of Raiganj, Uttar Dinajpur, West Alternately spray with cartap hydrochloride 50 SP - Bengal a comprehensive pest incidence table (Table 4) for 500g/ha. the farmers was prepared. Fipronil 5 SP 1 lit/ha/ monocrotophos/ quinalphos/ Utility of modern IPM in rice cropping system has chlorpyriphos/ phosphamidon / triazophos / emerged as a multi-factorial cropping system approach profenophos 1 lit/ha. known as component technology of rice production Table 4: Relative threshold level of four insect pests in relation to the paddy growth stages in the three blocks of the district Uttar Dinajpur, West Bengal, India Threshold level of pest species* Growth stage of paddy crop Raiganj Hemtabad Itahar Major stage Sub stages YSB BPH GM PB YSB BPH GM PB YSB BPH GM PB Nursery - PT PT PT PT PT PT PT PT PT PT PT PT Seedling early FT PT PT PT PT FT PT PT PT PT PT PT late FT FT PT PT FT AT PT PT PT FT PT FT Vegetative early FT FT PT PT FT AT PT PT FT AT FT FT middle AT FT FT PT FT AT FT PT FT AT FT FT late AT AT FT FT AT AT FT FT FT AT AT AT Reproductive early AT AT FT FT AT AT FT FT FT BT AT AT late FT AT FT FT AT AT FT FT AT BT AT AT Ripening early FT BT PT FT AT BT AT FT AT BT AT PT late FT BT PT PT AT BT PT FT PT BT AT PT *Permissible threshold (PT), Functional threshold (FT), Action threshold (AC), battle threshold (BT) 1374

6 [6, 7]. No mathematical model is presently available pest management operations on large, medium and small which suggests the pesticide application based on the acreage rice fields. However, it is admitted that the method probable multiple combinations of pest occurrence. In the of determination of action threshold used here does not present study, only four major insect pests were include pertinent variables such as damage, plant considered simultaneously. But more than seven species compensation, yield potential, economic and marketing was economically significant in the northern parts of considerations.. Present site-specific village level farming Bengal. Further predators and parasitoids play significant involves the measurement and analysis of within-field suppressive role for pest control [8, 9]. So during the yield variability only to the variety Swarna mashuri formulation of the final pest management decision-making (MTU 709) and targetting the four major insect pests. system based on pesticide application, the population Based on this future mathematical model may focus on status of natural enemies should also be considered multiple pest constraints on all the cultivars by computer separately and pesticide application strategy should based monitoring system that will help the decision be constructed depending on only pest: defender value makers to evolve the appropriate cultivation strategy. [30, 31]. The success of the present model lies on the extensive field survey, enlisting the pests and natural REFERENCES enemy population at regional level, assessing the maximum probable combinations of pest occurrence and 1. Rola, A.C. and P.L. Pingali, 199. Choice of crop finally to adopt the action taken path way [6]. So any protection technologies under risk: An expected bias involved in management action/no-action decisions utility maximization framework. Philipp. J. Crop Sc., based on the superficial field observation of both pests 17(1): and natural enemies will underscore the practical utility of. Pedigo, L.P., S.H. Hutchins and L.G. Higley, the model. Economic injury levels in theory and practice. Anul. The design of IPM programs is influenced by Rev. Entomol., 31: researcher/policymaker perceptions of pest-related yield 3. Pingali, P.L., M. Hossain and R.V. Gerpacio, losses [6, 1]. Where perceived and actual yield losses Asian Rice Bowls: The Returning Crisis? diverge widely, recommended economic thresholds for Wallingford, UK:CAB International. spraying are too low, thus reducing the usefulness of IPM 4. Oerke, E.C., H.W. Dehne, E. Schtinbeck and [, 5, 9]. Necessity of multiple threshold definitions like A. Weber, Crop Production and Crop permissible threshold, functional threshold, action Protection: Estimated Losses in Major Food and threshold and battle threshold could have described the Cash Crops. Elsevier, Amsterdam. field pest situation in better way. So, uncorrected 5. Knipling, E.F., The basic principles of insect application dosages may exacerbate the post application population suppression and management. problem. Farmer normally either tends to under-dose or Washington, DC: USDA, Agricultural Handbook, over-dose, using low or high than the recommended pp: amount of chemicals per application. Upon complete 6. Andow, D.A. and K. Kiritani, The economic implementation of the present application module, most injury level and the control threshold. Japan Pesticide of them adjust their dosages. An ill-conceived IPM Inform., 43: 3-9. program could thus lead farmers to spray more often and 7. Dhwan, A.K., A.S. Sidhu and J. Sing, Testing of with heavier concentrations than before.national IPM new insecticides with different sprayers against recommendations, unless adapted to local conditions with cotton jassid, Amrasca devastans (Distant). fine tuning, could overstate the case for applying Pestology, 3: pesticides and could cause amplify in pesticide 8. Foster, V. and S. Mourato, 000. Valuing the multiple applications in cases where a natural control strategy impacts of pesticide use in the UK: A contingent would be more effective. ranking approach, J. Agric. Econ., 51: 1-1. The present recommended area-specific cultivation 9. Ecobichon, D.J., 000. Pesticide use in the developing management or precision farming compensates the countries. J. Tox., 160(1-3): shortcomings of the broadly defined national protocols 10. Graham, H.M., P.D. Lingren, C. Lincoln and P.L. and protect environment by rationalizing of the chemical Adkisson, 197. The economic threshold of inputs. Undoubtedly the level of usefulness of these infestation for Heliothis spp. on cotton. Southern action thresholds lies in actual testing when implementing Cooperative Series Bull., 169:

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