An Intraseasonal Bioeconomic Model of PLRV Net Necrosis

Transcription

1 An Intraseasonal Bioeconomic Model of PLRV Net Necrosis Thomas L. Marsh 1, Ray G. Huffaker 2, Raymond J. Folwell 2, Gary Long 3 Selected Paper 1998 AAEA Annual Meeting Salt Lake City 1 Assistant Professor, Department of Agricultural Economics, Kansas State U., Manhattan Kansas; 2 Department of Agricultural Economics, Washington State U., Pullman, Washington;. 3 Department of Entomology, Washington State U., Pullman, Washington.

2 Abstract (AAEA): A bioeconomic model is developed as an IPM planning tool to combat PLRV net necrosis in the PNW potato industry. Environmental/biological and production processes are linked to marketing activities using discrete time control. We find that pesticides can be optimally timed to reduce applications and still protect against net necrosis.

3 Introduction The pest management literature has traditionally focused on insect control, treating insects as agents that cause crop damage by direct activities such as feeding on plants. Examples include, studies of economic thresholds (Headley; Hall and Norgaard), predator-insect relationships and pesticide residue (Feder and Regev), insects as common property resources (Regev, Gutierrez, and Feder; Lazarus and Dixon), insect resistance (Regev, Shalit, and Gutierrez), and timing insecticides (Talpaz and Borosh; Hueth and Regev). In these studies the damage function typically has been specified to reflect yield loss due to insect density. The purpose of this study is to develop an empirical intertemporal planning model for an integrated pest management (IPM) problem characterized by vector-virus-plant interactions. The objective is to optimally time insecticide applications. Talpaz and Borosh, and also Hueth and Regev, previously investigated the frequency of insecticide applications for a single insect population with no predation. In our case the pest is a virus, which has the characteristics that it can not reproduce outside a host organism and it is transmitted by a single vector. The primary role of the insect is to vector the virus from plant-to-plant. We assume that the insect faces predation and is initially virus free; it must acquire the virus by feeding on an infected host plant before being able to vector and is then infected for life; and insect feeding does not effect plant productivity. The vector-virus-plant problem alters traditional pest models in two ways, by changing the damage function and by introducing quality constraints. First, vector-virus-plant interactions considerably complicate the underlying structure of the damage function. Damage functions resulting from these interactions involve multiple processes, which account for the vector-virus process governing plant infection and virus-plant 1

4 processes causing crop damage after infection. The event that plants become infected depends not only upon insect density, but also upon the presence of a virus source and the period over which plants are exposed to insect populations. For example if no source of the virus (e.g., reservoir in seed stock, volunteer plants, native plants, or weeds) is available with which to infect insect populations, or no insects are present to vector the virus, then pest control is often not necessary. In contrast if a significant source of the virus is present in a field, even small numbers of insects can over time disseminate the virus throughout the field. Once plants are infected the virus can induce crop damage in different ways, each of which respond to different factors. For instance, current season damage of infected plants can come either in the form of decreased yield or quality degradation due to the virus expressing itself in the plant. Yield loss due to virus infection depends upon, among other factors, climatic conditions and the growth stage of the plant at infection. Quality degradation due to virus expression in the plant or its raw product (e.g., fruit, tuber) may depend upon the developmental stage at infection and other characteristics (e.g., storage temperature or length). The second alteration to the traditional pest model is that in many crops viruses can significantly reduce desirable quality characteristics in the plant or its raw product. Strict quality standards for key characteristics of agricultural output are often pre-specified in marketing arrangements between growers and buyers or at times stipulated by government regulators (Lichtenberg; Starbird; Babcock, Lichtenberg, and Zilberman). To reflect the impacts of standards on pest control decisions, we integrate into the model a quality assurance constraint that forms an upper bound on the level of acceptable damage. An important implication of vector-virus-plant interactions becomes evident when defining 2

5 economic thresholds, or pest levels at which controls should be initiated. Economic thresholds exist for both insect infestation levels and for the fraction of infected plants in a field over the growing season. In general the thresholds can vary according to different insect vectors, the particular virus, and the type or variety of plant infected. As an empirical application we optimize an intraseasonal bioeconomic control for an important pest management problem in the potato industry, potato leafroll virus expressed as net necrosis in tubers. Potato leafroll virus (PLRV) is responsible for yield and quality losses wherever potatoes (Solanum tuberosum L.) are grown. The most efficient vector of PLRV to potato plants in commercial fields is the green peach aphid (Myzus persicae (Sulzer)). In the state of Washington, Folwell et al. has identified PLRV as one of the most important forms of production risk faced by the potato industry. Over the past decade use of a controversial systemic pesticide - aldicarb - to control aphid infestations in commercial potato fields has brought the industry s pesticide practices under extreme scrutiny by the public, as well as state and federal regulators (Seattle Post-Intelligencer, Capital Press). The IPM approach discussed in this paper focuses on reducing pesticide use by timing pesticide applications to control aphids, while still guarding against PLRV net necrosis in tubers stored over a given period. For empirical purposes the traditional predator-insect dynamics (e.g., Feder and Regev) is respecified in favor of the insect and its predator complex. The predator complex is an index of an insects predators, which is based on the predator s potential effectiveness to prey at different stages in an insect s life cycle. In a theoretical model the predator complex acts as an idealized predator species in the control of the insect. In an empirical model it is useful in establishing quantitative models that are more reliable predictors of predator-insect dynamics (Tamaki). 3

6 Empirical Bioeconomic Model PLRV is expressed as net necrosis in tubers, which is a netting of discolored tissue that develops first in the stem-end of the tuber and then spreads further toward the apical-end. Not all tubers from an infected plant of a susceptible cultivar develop net necrosis, and those that do need not develop necrosis at the same time or to the same degree. Infected potatoes that are not necrotic at harvest may become so in storage. Necrotic tubers are not suitable for the fresh market or processing, and thus are diverted to lower market value alternatives 1. Nearly twothirds of Washington s commercial potato crop consists of Russet Burbank tubers, which are mostly contracted for processing - but are highly susceptible to net necrosis. In value of production, this translates to.$300 mill/yr at risk to PLRV net necrosis (USDA-ERS; WSDA). In Washington, potato growers typically bargain with processors to establish preseason production and storage contracts (henceforth contracts). Contracts reduce price risk by establishing the base price of potatoes paid to growers, while providing processors with an increase in average tuber quality. In addition, contract terms set quality constraints that define the maximum allowable incidence of net necrosis per shipment. Potato shipments from commercial operations are generally of mixed quality because quality characteristics are often not readily apparent to visual inspection, while inspection and sorting have high cost. After harvest a grower may choose to store potatoes for increased marketing flexibility, or may be required to do so for an undetermined period by contractual agreement with the processor. Contracts often contain terms allowing processors to determine storage period, and to 1 For example, actual 1995 production contracts between growers and processors in the Columbia Basin region of Washington specified P H =$4.50/cwt for acceptable processing tubers and P L =$.005/cwt for processing culls. 4

7 reject shipments of tubers with incidences of net necrosis over a predetermined level. As a rule of thumb the rejection level specified in a contract is 5%, which is in accordance with the USDA Standards for Grades of Potatoes, but it may vary slightly across contracts depending upon the present technology at the processor s plant or the final product (e.g., fries, chips, or dehydration). Under these terms the grower faces the brunt of the production or storage risk, and must turn to in-field chemical control of aphids to protect themselves against net necrosis. The empirical model represents a grower producing a fall crop of Russet Burbank potatoes in Washington s Columbia Basin. It is assumed the potatoes are grown under center pivot irrigation that follows an alfalfa rotation and, except for pest management strategies, under standard production conditions. Yields, costs, and production scheduling are taken from Hinman et al., where planting occurs in April and is followed by harvest 150 days later. Storage costs and parameters are taken from Guenthner and Sparks. The grower s intraseasonal planning problem is specified to maximize the present value of a stream of net returns subject to natural processes and a quality assurance constraint. The state variables are the stocks of green peach aphids per.5 m 2, or g t, and predators per.5 m 2, or p t. The control variable is the timing and rate of pesticide applied, a t. Hence the grower is anticipating a pesticide application decision on each of the t days (t=1,...,t) over the growing season to optimally control aphids and guard against PLRV net necrosis, with the expectation of storing output for an exogenously determined storage period S. Let ß (1%d) &1 be the discount factor with discount rate d. Then following Pindyck and Holmes an optimal planning problem can be specified as a discrete time model with objective function 5

8 (1) max a t $0 ß (T%S) P H [y T (1&D(T)&L(S))]& j T&1 t 0 [ß t c a a t ]&ß (T%S) c s S[y T (1&D(T)] subject to the equations of motion, other empirical relationships, and a quality constraint that are defined as follows. In (1) it is assumed that a grower agrees to a contract with a processor, receives a predetermined price P H ($/cwt) for high quality potatoes, and collects revenue for potatoes upon delivery to the processor at day T+S. The variable y T is the yield at harvest time T (570 cwt/acre), while L(S) (.0004)S reflects potato shrinkage after S days in storage. The fraction of yield loss due to PLRV infection, D(T), is discussed below. The constant marginal cost function highlights expenditures on pesticide applications a t and storage period S, where c a is the $/acre for an insecticide application and c s is the $/cwt/day to store tubers. Predator-Aphid Dynamics. In aphids and its predators, climate plays a major role in development of populations. For example, developmental times of the aphid are commonly measured on a physiological time scale of degree-days or d t. The number of degree-days on a given day is obtained by cumulating the excess of the temperature over a minimum temperature for aphid development which is 4EC. Ro and Long (1997) and Ro (1995) developed a degreeday model of the population dynamics of the aphid and its predator complex in the Columbia Basin region of the state of Washington. The model can precisely predict not only egg hatches and peak departure of the aphids from its overwintering host the peach tree, but also the arrival to potato fields and predator-aphid population levels throughout the growing season. The aphid and predator equations of motion in (2) and (3) are a discrete version of the Larkin (1966) predator-prey model based on Ro (1995). The aphid model is given by 6

9 (2) g t%1 g t %g t 1& g t g max r g t &µg t p t &K(a t,g t ), g 0 g 0 Net growth in aphid stocks is the difference between a logistic function representing aphid growth, an interaction term representing predation, and a kill function. Here g max is the aphid s environmental carrying capacity, its degree-day dependent intrinsic growth rate is defined by r g t, and µ is a predation constant. The effectiveness of spraying pesticides is assumed to be proportional to the application rate a t and the current population level, or K(a t, g t )=k 1 a t g t with constants k 1. For k 1 =1 the spray rate a t, or the pesticide effectiveness, can be expressed as the fraction of aphids killed so that 0# a t #1. Predator complex dynamics are represented by (3) p t%1 p t %p t 1& p t p max r p t, p 0 p 0 where p max is the predator s environmental carrying capacity and its degree-day dependent intrinsic growth rate is defined by dependent and are functions of degree-days. r p t. The parameter values for (2) and (3) are weather Vector-Virus Interaction. The vector-virus interaction identifies the apterous (wingless) aphids ability to transmit PLRV to plants in the potato field. While alate (winged) aphids can introduce the virus into the field from outside sources, it is their offspring the apterous aphids that colonize the potato field and are the efficient vectors of PLRV to potato plants in the field. Following Hanafi et al. (1989) and Flander et al. (1991) we specified an empirical relationship between the discrete event that potato plant was infected with PLRV and the number of apterous-days measured in the field. Apterous-days are the cumulative sum of apterous aphids 7

10 per.5 m 2 measured in the potato field over the growing season. The empirical relationship was estimated as a logit model using field experiment data and is given by (4) v t 1/(1%exp(&(&19.37%( & 3)ad t ))) where ad t denotes the apterous-days by day t. The outcome of the empirical relationship predicts the fraction of the potato field infected with PLRV. It ranges from no infection in the field (v t =0) to infection of the entire field (v t =1), while infection from day t to t+1. v t%1 v t%1 &v t represents the increase in PLRV Virus-Yield Loss Process. The virus-yield loss process represents the decrease in yield due to PLRV inoculation at a particular plant growth stage. The percent of yield loss due to virus infection over the growing season is highest during the early season, ranging from 0 to 15% over the growing season. The damage function due to PLRV infection by aphids in [t,t+1] is d t &4 %( &3 )t&( &5 )t 2, if 0<t<85 &3.67%( &2 )t&( &4 )t 2, if 105<t<150 0, otherwise The cumulative percent of yield loss through period t is then (5) D(t) j t j 1 ( v j )(d j ) Virus-Net Necrosis Relationship. This relationship links the discrete event that a tuber will become necrotic in storage, given it is from a plant infected with PLRV, to the plant age at inoculation t (days), storage length S (days), and tuber weight w (grams). Its specification is based on earlier work by Roosen et al. (1997) and Marsh et al. (1998). The empirical relationship is estimated as a logistic regression model corrected for spatial correlation by geographic region, 8

11 which is described in Marsh (1998). Final model results are given below (6) q(s,t,w) 1/(1%exp(&(&10.70%.24t&( &2 )t 2 %( &6 )t 3 %( &2 )h&( &5 )h 2 &(3.82e&3)w%( &5 )w 2 &( &8 )w 3 %( &5 )(h( t)&( &10 )(h( w) 2 ))) Here h(s,t,w) S if S<s(t,w) s(t,w) if S$s(t,w) and s(t,w) 1 2 ( &2 )%( &5 )t ( &5 )%( &10 )w 2 necrosis relationship to be monotonic over the storage period., which restrict the net Quality Constraint. The deterministic constraint ensuring the contractual level of net necrosis Q * =5% is satisfied appears in (7). The anticipated level of tuber net necrosis per period is Q t ( v t )(q t ), while the cumulative amount over the growing and storage season is given by (7) T j t 1 Q t j T t 1 Q(g t,p t,a t ;S,t,w)<Q ( Results and Discussion The completed system is comprised of equations (1)-(7). For the actual optimization process the problem was formulated as a nonlinear programming model (Canon, Cullum, and Polak) and solved on a personal computer using GAMS/MINOS5 (Brooke, Kendrick, and Meeraus). The planning scenario investigated in this paper assumes a contract price of P H =$5/cwt and grower storage for 6 months. Consistent with the concept of IPM the chemical used to spray is a selective aphicide (e.g., pirmicarb at $15/acre/application 2 ), which targets aphids but is relatively nontoxic to predators. Furthermore, a degree-day sequence was used that generated high aphid infestations. Tuber weight is set at 500 grams. 2 Personal communication with sales representative. Pirmicarb is currently being used for potatoes in Europe and Canada and is in the processes of being introduced for potatoes in the US. 9

12 For the base case scenario with no pest control the uncontrolled aphid population rapidly disseminated PLRV throughout the potato field and resulted in an expected incidence of net necrosis of around 50%. These results are consistent with observations in commercial fields reported by Powell and Mondor (1973) and others. The optimal spray pattern resulting from the IPM planning scenario concentrated spraying at two times during the growing season (Figure 1), ensuring the incidence of net necrosis was less than 5%. The first applications occur on days 52 and 53 after planting at a rate of 1 and.1 and the second spraying occurred on day 78 at a rate of.6 for a total cost of $25/acre. This result is starkly different from the current prophylactic scenarios used by growers to control pest populations, which generally include early season applications of a systemic insecticide (April) and later season multiple applications of foliar insecticides (June, July, and August) at around $180/acre (Hinman et al.). The controlled aphid population (Figure 2) is obtained by spraying on days 52 and 53 after planting to slow colonization, then the population is allowed to increase at its natural rate until the second spray application on day 78. The second period spray is applied at an optimal time and rate to slow the aphid growth, which is near its peak flight, enabling the predator complex populations to overtake the aphid population. After day 78 the veracious feeding of the predator complex rapidly dominates and crashes the aphid population for the remainder of the growing season. Alternatively interpreted, Figure 2 presents empirical economic thresholds for both aphids and PLRV infection that are dynamic over the potato growing season. 10

13 Conclusions We find evidence that an optimal bioeconomic control - timing selective aphicide applications in conjunction with natural predation of the aphid - can sharply reduce pesticide use relative to traditional prophylactic practices, while still ensuring the quality assurance constraint was satisfied. This IPM strategy has the potential to directly reduce a growers insecticide costs for aphids (.$100/acre), as well as reduce costs from pest resurgence or secondary pest problems, and yet provide the marketing flexibility to store tubers after harvest for a predetermined storage period. By reducing the number of applications, it also has the potential to decreases adverse effects of pesticide residue on the environment and human health. For the Columbia Basin region, precise predictions of aphid flights are provided over various public communication systems and are also available on the Washington State University IPM home page. The IPM program we endorse to combat PLRV net necrosis should include roguing fields for volunteers and weeds and continued use of certified seed stock to keep sources of PLRV at a minimum in the field. Furthermore the pest management program should include monitoring for green peach aphid activity, timing pesticide applications with forecasted aphid flights, and strategic management of storage to prevent incidences of tuber net necrosis. 11

14 FIGURE 1. Optimal Timing and Rate of Selective Aphicide Applications Over Growing Season. FIGURE 2. Dynamic Economic Thresholds for Controlled Aphids and PLRV Infection. (Net Necrosis#5%, Max aphid population =333 aphids/.5m 2. Max PLRV infection=9.5%) 12

15 References Babcock, B.A., E. Lichtenberg, and D. Zilberman. The Impacts of Damage Control on the Quantity and Quality of Output: Estimating Pest Control Effectiveness. Am. J. Agr. Econ. 74(February 1992): Brooke, A., D. Kendrick, and A. Meeraus. GAMS: A User's Guide. The Scientific Press, Redwood City, CA, Canon, M.D., C.D. Cullum, and E. Polak. Theory of Optimal Control and Mathematical Programming. McGraw-Hill Book Company, New York, Capital Press. Friday, Sept. 29, Temik officially back for use by NW potato growers. Salem, Oregon. Feder, G. and U. Regev. Biological Interactions and Environmental Effects in the Economics of Pest Control. J. Environ. Econ. Manag. 2(1975): Flanders, K. L., E. B. Radcliffe, and D. W. Ragsdale. Potato Leafroll Virus Spread in Relation to Densities of Green Peach Aphid (Homoptera: Aphididae): Implications for Management Thresholds for Minnesota Seed Potatoes. J. Econ. Entomol. 84:(1991) Folwell, R.J., D.L. Fagerlie, G. Tamaki, A.G. Ogg, R. Comes, and J.L. Baritelle. "Economic evaluation of selected cultural methods for suppressing the green peach aphid as a vector of virus diseases of potatoes and sugarbeets." Coll. Agr. Res. Ctr. Bull. 0900, Wash. State U., Pullman, Guenthner, J. F. Economics of Potato Storage. Amer. Pot. J. 72:(1995) Hall, D. C. and R. B. Norgaard. On the Timing and Application of Pesticides. Am. J. Agr. Econ. 55 (1973): Hanafi, A., E. B. Radcliffe and D. W. Ragsdale.. Spread and control of potato leafroll virus in Minnesota. J. Econ. Entomol. 82(1989): Headley, J. C. Defining the Economic Threshold. In Pest Control Strategies for the Future. Washington, DC: National Academy of Sciences., Hinman, H., G. Pelter, E. Kulp, E. Sorensen and W. Ford Enterprise Budgets for Alfalfa Hay, Potatoes, Winter Wheat, Grain Corn, Silage Corn, and Sweet Corn Under Center Pivot Irrigation, Columbia Basin, Washington. EB Washington State University Cooperative Extension. Pullman, WA,

16 Holmes, W. L. Derivation and Application of a Discrete Maximum Principle. Western Economic Journal December Hueth D. and Regev, U. Optimal Agricultural Pest Management with Increasong Pest Resistance. Am. J. Agr. Econ. 56 (August 1974): Larkin, P. A.. Interspecific Competition and Exploitation. Journal of the Fisheries Research Board of Canada 20(1963): Lazarus, W. F. and B.L. Dixon. Agricultural Pests as Common Property: Control of the Corn Rootworm. Am. J. Agr. Econ. 56 (November 1984): Lichtenberg, E. The Economics of Cosmetic Pesticide Use. Am. J. Agr. Econ. 79 (February 1997): Marsh, T. L Linking Natural Processes to Marketing Flexibility: Potato Leafroll Virus Net Necrosis. Ph.D. Dissertation, Washington State University. Marsh, T. L., R. G. Huffaker, R. C. Mittelhammer, R. J. Folwell, G. E. Long, D. R. Horton, and H. H. Toba. Potato Leafroll VirusNet Necrosis: Identifying Pest Management Tradeoffs Between the Inoculation Interval, Storage Length, and Tuber Weight." J. Econ. Entomol (in press), Pindyck, R. S. Optimal Planning for Economic Stabilization: The Application of Control Theory to Stabilization Theory. North-Holland, London Powell, D. M. & T.W. Mondor. Control of the Green Peach Aphid and Suppression of Leafroll on Potatoes by Systemic Soil Insecticides and Multiple Foliar Sprays. J. Econ. Entomol. 66(February1973): Regev, U., Gutierrez, A. P., and Feder, G. Pests As a Common Property Resource: A Case Study of Alfalfa Weevil Control. Amer. J. Agr. Econ. 58(1976): Regev, U., Shalit, H. and Gutierrez, A. P. On the Optimal Allocation of Pesticides with Increasing Resistance: The Case of Alfalfa Weevil. J. Environ. Econ. Manag. 10(1983): Ro, T. H. "Analysis and Simulation of the Dynamics of a Myzus Persicae (Homoptera: Aphididae) - Predator Complex Community in the Central Basin of Washington." Ph.D. Dissertation, Washington State University, Ro, T. H. and G.E. Long. Development of Aphelinus asychis (Hymenoptera: Aphelinidae) and Its Susceptibility to Insecticides Applied to Mummies of Its Hosts, the Green Peach Aphid. J. Entomol. Soc. Brit. Columbia. 1997(in press). 14

17 Roosen, J., R. G. Huffaker, R. J. Folwell, T. L. Marsh and R. C. Mittelhammer. The Relation of Potato Leafroll Virus Net Necrosis in Potato Tubers to the Interval Between Planting and Inoculation. Crop Prot. 16 (1997): Sparks, W. C Potato Storage Factors of Economic Importance. Am Potato J 52: Starbird, S. A. The Effect of Quality Assurance Policies for Processing Tomatoes on the Demand for Pesticides. J. Agr. and Res. Econ. 19(July 1994): Seattle Post-Intelligencer. Tuesday, March 21, Alarm sounded over insecticide used on potatoes. Seattle, Washington. Tamaki, G. Biological Control of Potato Pests. Advances in Pest Management, eds. J. H. Lashomb and Richard Casagrande, Pennsylvania: Hutchinson Ross, Talpaz H. and I. Borosh. Strategy for Pesticide Use: Frequency and Applications. Amer. J. Agr. Econ. 56 (November 1974): USDA (U.S. Dept. of Agric.). United States Standards for Grades of Potatoes. Agricultural Marketing Service, WSDA (Washington State Dept. of Agric.). Washington Agricultural Statistics. Olympia, Washington, Zacharias, T. P. and A. H. Grube. Integrated Pest Management Strategies for Approximately Optimal Control of Corn Rootworm and Soybean Cyst Nematode. Amer. J. Agr. Econ. 68 (August 1986):