Population dynamics and the economics of invasive species management: The greenhouse whitefly in California-grown strawberries

Journal of Environmental Management 90 (2009) 561e570 www.elsevier.com/locate/jenvman

Population dynamics and the economics of invasive species management: The greenhouse whitefly in California-grown strawberries Gregory J. McKee a,*, Rachael E. Goodhue b, Frank G. Zalom c, Colin A. Carter b, James A. Chalfant b a b

Department of Agribusiness and Applied Economics, North Dakota State University, 205 A Morrill Hall, Fargo, ND 58102, USA Department of Agricultural and Resource Economics, University of California, Davis, 1 Shields Avenue, Davis, CA 95616, USA c Department of Entomology, University of California, Davis, 1 Shields Avenue, Davis, CA 95616, USA Received 27 April 2007; received in revised form 15 November 2007; accepted 8 December 2007 Available online 22 January 2008

Abstract In agriculture, relatively few efficacious control measures may be available for an invasive pest. In the case of a new insect pest, insecticide use decisions are affected by regulations associated with its registration, insect population dynamics, and seasonal market price cycles. We assess the costs and benefits of environmental regulations designed to regulate insecticide applications on an invasive species. We construct a bioeconomic model, based on detailed scientific data, of management decisions for a specific invasion: greenhouse whiteflies in California-grown strawberries. The empirical model integrates whitefly population dynamics, the effect of whitefly feeding on strawberry yields, and weekly strawberry price. We use the model to assess the optimality of alternative treatment programs on a simulated greenhouse whitefly population. Our results show that regulations may lead growers to ‘‘under-spray’’ when placed in an economic context, and provide some general lessons about the design of optimal invasive species control policies.  2007 Elsevier Ltd. All rights reserved. Keywords: Greenhouse whitefly; Strawberry; Bioeconomic model; Insecticide

1. Introduction Heightened awareness of the impacts of economic activities on the establishment and spread of invasive species has generated concern over the potentially catastrophic effects on agriculture (Perrings et al., 2000; Sumner, 2003; Zhao et al., 2005). Increased international agricultural trade, with its potential to transport foreign organisms worldwide, better understanding of ecosystems, and increased ability to identify and control organism pathways, such as ports of entry, have all redirected policy focus on the connection between economic activity and the spread of invasive species (USDA, Animal * Corresponding author. Tel.: þ1 701 231 8521; fax: þ1 701 231 7400. E-mail addresses: [email protected] (G.J. McKee), goodhue@ primal.ucdavis.edu (R.E. Goodhue), [email protected] (F.G. Zalom), [email protected] (C.A. Carter), [email protected] (J.A. Chalfant). 0301-4797/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jenvman.2007.12.011

and Plant Health Inspection Service, 2000). Understanding the characteristics of pest populations and their impacts on agriculture, which in turn prescribe management thresholds, is critical for policy purposes (Harper et al., 1994; McKee, 2006; Wu, 2001). Government agencies are paying greater attention to developing effective tools with which to manage invasive species. The California State Senate, for example, passed a bill (S. 497) in August 2006, which requires shipping vessels to treat their ballast water to prevent the introduction of invasive species into state waters before dumping it in ports or coastal waters. Given the fundamentally new relationship between the invader and the agricultural system, understanding the dynamics of the pest population and the cumulative effect of the population size are important (Eiswerth and Johnson, 2002; Knowler and Barbier, 2000; Wu, 2001; Harper et al., 1994). Previous studies, however, do not consider the associated difficulty of incorporating new types of chemical control in

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the management of invasive pests when prior registered chemicals are ineffective due to insect resistance or other reasons. Economic models can be useful to policymakers to aid in evaluating the benefits and costs of chemical registrations. In some cases, such as the one analyzed here, a registration may include use restrictions in order to reduce the rate of the development of target pest resistance to the new chemical control. The objective of this paper is to assess how insecticide use restrictions e made with little information about interaction between invasive pests and agricultural production decisions e interact with invasive pest biology and agricultural production decisions to affect the optimal timing of insecticide applications and resulting profits. This is done by calculating the optimal management strategy given the biological, economic, and selected regulatory constraints. This analysis illustrates a more general approach to evaluation of invasive species management questions. 1.1. Unique attributes of the greenhouse whitefly invasion The greenhouse whitefly (Trialeurodes vaporariorum) is common to the coastal region and had not previously used strawberries as a host. As such we might term it a ‘‘resident invader’’ of strawberries (Fragaria ananassa). Large populations on strawberry plants were observed for the first time in the Oxnard, California strawberry growing region in 1999e 2001. A smaller outbreak occurred in the Watsonville, California region in 2002e2003. The addition of a summer strawberry crop, the practice of leaving plantings in the ground for more than a season, and perhaps, as some experts suggest, genetic changes in the greenhouse whitefly have contributed to whitefly infestations in these regions. The recent greenhouse whitefly invasion of strawberries in California has particular economic and biological characteristics that make it an interesting case. First, restrictions associated with insecticides registered for use against the whitefly create a complex management problem. Due to resistance or inefficacy, chemicals previously registered for use against other insect species on strawberries proved ineffective upon its establishment. Two insecticides with different modes of action received registrations for use against greenhouse whiteflies on strawberries in 2003: imidacloprid and pyriproxyfen. Second, the greenhouse whitefly’s life cycle can be modeled plausibly with a single season of data. Since four to five generations occur in a season, it is possible to estimate important biological parameters using data from a relatively short time period. The estimated model can then be used for sensitivity analysis, and to guide data collection efforts. Finally, since some growers in the study area leave their strawberry fields in the ground for more than one season and the whitefly can migrate across fields, whitefly management decisions made in the current season affect those in subsequent seasons. 1.2. The California strawberry industry Strawberries are an economically important crop in California. Total revenue from all varieties of strawberries grown in

California currently exceeds $1.2 billion per year (California Department of Food and Agriculture, 2005). California accounts for nearly 90% of U.S. fresh strawberry production (USDA, National Agricultural Statistics Service, 2005). This is due to both greater acreage and greater per-hectare yield than other states. Florida, the next largest producing state, accounts for less than 10% of production. Strawberries are produced at various rates during the life of the plant. Strawberry plants begin by producing relatively slowly. Production in a commercial field in the Watsonville region was observed to peak in June, with observed average yield per plant 241% larger on June 19 (average yield of 1800 g per plant) than May 29 (average yield of 746 g per plant). The rate of production decreases thereafter. The harvest on July 10 (average yield of 249 g per plant), for example, was 16% of that on June 19. Strawberries are grown commercially in five geographically distinct regions along the California coast. From south to north, these are the San Diego area, Orange County, the Oxnard plains in Ventura County, the Santa Maria Valley, and the Watsonville/Salinas area. The market price for fresh strawberries within and across growing regions varies over the course of the year. Using data described in Section 2, we observed that during the period when there are fewer strawberries harvested (between October and January), a kilogram of fresh strawberries has historically sold at wholesale for more than $1.10 and occasionally more than $4.40 (USDA, Agricultural Marketing Service). Simple average wholesale prices for processed strawberries over the same period range from $1.65 per kg, when few are sold to the processed market, to $0.55 per kg by the end of the season. 1.3. The greenhouse whitefly The greenhouse whitefly is a pest of greenhouse crops and ornamentals. It damages plants by feeding on nutrients in a plant’s sap, which may result in yield loss (Byrne et al., 1990; McKee et al., 2007a). It was first observed on strawberry plants, which had not previously been reported as a host, at Oxnard and Watsonville, California, in the late 1990s. More widespread outbreaks were observed on field grown strawberries in the Watsonville region in 2002e2003. The whitefly uses strawberry plants as the dominant host in the Watsonville area. 1.4. Chemical management of the greenhouse whitefly When favorable host crops are grown in neighboring fields, cultural and biological control techniques alone have not been effective against outdoor infestations of the greenhouse whitefly in strawberries (Philips et al., 1999; Bi et al., 2002a; Toscano and Zalom, 2003). Chemical insecticides, therefore, are an important part of an effective whitefly control program. The greenhouse whitefly reproduces rapidly and tends to live on the underside of leaves, making it a difficult pest to manage effectively with chemicals. Heavy use of older insecticides, such as organophosphates, on greenhouse whitefly populations

G.J. McKee et al. / Journal of Environmental Management 90 (2009) 561e570

on other crops, including greenhouse and ornamental plants, has fostered their resistance to those chemicals. This has increased the need for and value of innovations in chemical control. In 2003, when our data were collected, two chemicals were registered for use on whiteflies on strawberries and were relatively effective at controlling them. Pyriproxyfen, an insect growth regulator marketed by the Valent Corporation as Esteem, is relatively effective on whiteflies. The chemical works principally by killing the eggs and nymph whiteflies (Bi et al., 2002b,c; Ishaaya and Horowitz, 1989), has a limited direct effect on the adults (Ishaaya et al., 1994), and the effect of a single application can last from 4e9 weeks on whiteflies on strawberry plants (Bi et al., 2002b,c). Conversations with anonymous pest control applicators indicate that a typical foliar application costs $162.50 per hectare at the application rate of 730 mL per hectare used in the field trial. The second chemical, imidacloprid, a systemic neonicotinoid insecticide marketed by Bayer Crop Protection as Admire, is also relatively effective on whiteflies, and has a different mode of action than pyriproxyfen. It is effective against nymph and adult greenhouse whiteflies (Ishaaya and Horowitz, 1989; Bi et al., 2002b), and the effect of a single application can last up to 8 weeks (Bi et al., 2002b). In contrast to pyriproxyfen, imidacloprid has a 14-day withdrawal period, which makes it economically infeasible for strawberries during the period when harvests occur, typically once in every 3e7 days production begins. Conversations with anonymous pest control applicators indicate that a typical drip line application costs $523.64 per hectare at the application rate of 2338 mL per hectare used in the field trial. The California Department of Pesticide Regulation issued regulations to manage the use of pyriproxyfen in order to encourage development of alternatives to it and to delay development of greenhouse whitefly resistance to it. The registration (California Department of Pesticide Regulation, 2004) restricts growers to a limit of two applications per unit area per year, the same as other plants and crops Esteem is registered for use on. Growers are required to apply pyriproxyfen as soon as whiteflies appear. In addition, the registration requires that, if whiteflies were present in the field the previous year, use of pyriproxyfen be accompanied by use of imidacloprid at planting. Hence, the number and timing of pyriproxyfen applications is a management decision. We analyze the costs and benefits of these restrictions to growers in the Watsonville area within a single season. Although thorough evaluation of how these restrictions prevent resistance is beyond the scope of this paper, we also briefly discuss possible resistance prevention benefits provided by these restrictions based on our analysis. 2. Materials and methods 2.1. Data description Data used in this paper are from several sources. Strawberry prices and quantities were obtained from daily average

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regional wholesale price reports for growers in the fresh strawberry market. Daily fresh market price data between 1988 and 2003 were obtained from the ‘‘National Berry Report’’ published by the Agricultural Market News Service of the USDA. Weekly processed strawberry price and quantity data for the same period were obtained from the California Processing Strawberry Advisory Board. Costs for imidacloprid and pyriproxyfen treatments were obtained from discussions with growers and pest control advisors. Prices were deflated using the Consumer Price Index, a price index representing a bundle of items purchased by typical urban consumers. These average prices should be reasonably good measures of the price expected by growers, since none of the 5 years had particular or unusual price patterns that would have a misleading influence on the calculation of an average or expected price. The deflated prices were then averaged to calculate a weekly average real price so as to smooth out any yearspecific market conditions, leaving a representative price for the analysis. Watsonville is on California’s Central Coast, approximately 120 km south of San Francisco. Weather information for the area, including temperature and precipitation, was obtained online from observations made at a National Weather Service weather station located in Watsonville. Average low temperatures range from just above 0  C to just below 10  C between January and March to about 12  C between July and September. Average high temperatures range from 16  C between January and March to 25  C between July and October. Data on the effects of whiteflies feeding on strawberries were measured by University of California entomologists between November 2002 and July 2003 near Watsonville, in Santa Cruz County, CA, USA. The experimental site was a commercial strawberry field located west of Watsonville. Strawberries (var. Camarosa) were transplanted into the field on 12 November 2002. This site was located across a paved road and, based on prevailing winds, upwind from infested strawberry plants transplanted in fall 2001 which had not yet been removed. The new planting was immediately infested by adult whiteflies present in the area. Three replicates each of nine whitefly management treatments and six replicates of untreated controls were established in a completely randomized design. Each experimental plot was three rows wide, with each row 142.2 cm wide from center to center, and 50 m long. We observed the size of the whitefly population, associated strawberry yields, and the efficacy of various chemical treatments against the whitefly.

2.2. Bioeconomic model description Different dates for insecticide applications may affect the development of the whitefly population, and hence profits, differently. One way to evaluate the effect of alternative treatment dates is to conduct controlled scientific experiments of insecticide efficacy for all possible application dates. Unfortunately, this would require a substantial amount of costly data collection.

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A less costly alternative is to use a mathematical simulation. Simulations have an important advantage over field research in that they allow evaluation of the effects of changes in key variables, such as chemical application dates, without additional field trials. If such a model can be calibrated for the interaction between the greenhouse whitefly and strawberries, gaps in our understanding can be filled. We created a parameterized model of the development of a greenhouse whitefly population on a typical strawberry plant leaf. Selection of parameters affecting the rate of whitefly population development was influenced by the work of Hulspas-Jordaan and van Lenteren (1989), who modeled the population dynamics of the greenhouse whitefly on tomatoes in controlled conditions. However, strawberry plants are a new host plant for the greenhouse whitefly and little is known about their relationship. The main function of this model is to simulate the timing and size of whitefly population growth by replicating the observed life cycle of the greenhouse whitefly in the commercial strawberry field described above. An overview of the model is presented below, and a complete description of the model is found in McKee et al. (2007b). The rate of whitefly physiological development is based on observed degree-days (measured in degrees celsius). Daily calculations are made to predict the flow of whiteflies from the egg to nymph and then adult life stages. These were assumed to occur after 122.9 and 257.8 degree-days, respectively (Osborne, 1982). A minimum temperature of 8.9  C was used with no upper limit. The size of whitefly egg, nymph, and adult populations in the model is calibrated to the observed sample by adjusting the parameters controlling reproduction (oviposition), mortality, adult lifespan, and pesticide efficacy. Parameter values compare with those in the entomology literature for observed interactions between the whitefly and strawberry plants (Bi et al., 2002b,c). The relationship among the egg, nymph, and adult whitefly populations can be represented symbolically as follows: T X

eggst ¼

T X

t¼1

! adultst ðovipositionT Þ

t¼1 T1 X

þ

! eggst ð1  mort eT Þ

t¼1



T1 X

ð1Þ

nymphsðdegreedaysÞt

t¼1 T X

nymphst ¼nymphsðdegreedaysÞT

t¼1

þ

T1 X

! nymphst ð1  mort nT Þ

t¼1



T1 X t¼1

adultst 

T1 X

! nymphst

t¼1

 ð1  mort pyriproxyfenÞ

ð2Þ

T X

adultst ¼adultsðdegreedaysÞT

t¼1

þ

T1 X

! adultst ð1  mort aT Þ

t¼1



T1 X t¼T30



T1 X

! adultst !

adultst ð1  mort imidaclopridT Þ

ð3Þ

t¼1

where T is the current simulated day, t refers to any prior day, and mort_eT, mort_nT, and mort_aT are daily mortality rates for whitefly egg, nymph or adult populations, respectively. The parameter ovipositionT refers to the daily average oviposition rate of the adult population. Eq. (1) calculates the cumulative size of the egg population on day T as the sum of eggs oviposited by the population of adults on day T, the cumulative number of eggs surviving from any previous day, as determined by the daily mortality rate, less the number of eggs that have matured into nymphs by day T. Eq. (2) calculates the size of the nymph population on day T as the sum of eggs maturing into nymphs on day T, as a function of accumulated degree-days, the cumulative number of nymphs surviving from the previous day, less nymphs that matured into adults before day T, and less nymphs mortality from applications of pyriproxyfen, mort_pyriproxyfen. Eq. (3) calculates the size of the adult population on day T as the sum of nymphs maturing into adults on day T, as a function of accumulated degree-days, and the cumulative number of adults surviving from the previous day, less the number of adults achieving a maximum lifespan of 30 days, and less the number of adults killed by an imidacloprid application, mort_imidacloprid. The population model is combined with a statistically estimated relationship between the whitefly population size and strawberry yield and an economic model of grower profit-maximizing behavior. While the precise mechanics of the interaction between whitefly feeding and strawberry yield are unknown, it is apparent that strawberry yield is adversely affected by the whitefly (Toscano and Zalom, 2003; Udayagiri et al., 2000). We hypothesize that an appropriate way to model the yield as a function of pest abundance is to assume that feeding in week t affects yield potential the next week. This is observed through a reduction in the incremental contribution from total yield each harvest. We regress weekly strawberry yield as a linear function of treatment dummy variables, time since planting, the cumulative number of adult whitefly-days since the last harvest, an interaction between the aggregate number of whitefly-days since the last harvest and the number of weeks since planting, a dummy for the sudden yield surge in June, and an error term. The estimated yield loss equation is (McKee et al., 2007a).

G.J. McKee et al. / Journal of Environmental Management 90 (2009) 561e570

Yt ¼

11 X

t X

di þ t þ t2 þ b1

t¼1 t X

þ b2

!

WFj

0

j¼j1

WFj t þ dJune þ 3

ð4Þ

where yt is weekly strawberry harvest, dummy variables ðdi Þ represent each treatment, t denotes the number P of weeks since planting, t2 is the square of this number, tj¼j1 WFj represents the cumulative number of adult whitefly-days since the P last harvest, ð tj¼j1 WFj Þt represents an interaction between the aggregate number of whitefly-days since the last harvest and the number of weeks since planting, dJune is a dummy for any observation in June, and 3t is an error term. Estimated coefficients are reported in Table 1. We make several assumptions in order to simplify the behavioral model. First, we assume that the grower maximizes profits from a representative field infested with greenhouse whiteflies at planting. We scale up the biological model from the plant level to the hectare level, and we assume that the field is uniformly infested with whiteflies. We assume that there are constant returns to scale and analyze returns for each treatment scenario on a per-hectare basis. Finally, changes in average harvest costs as a function of insecticide use (average costs decrease when the number of higher-quality berries harvested per unit of time increases) are ignored due to a lack of data. The grower chooses the timing of pyriproxyfen treatments to maximize !! T T t X X X pt ¼ ðpt ÞYt WFt Ei;k Ce Ce;t ; t ˛½1;T ð5Þ t¼1

k¼1

subject to 0  Yt WFt

t X

!! Ei;k

Ei;k  2; ck; k ˛½1; T

ð7Þ

k¼1

j¼j1

t¼1

T X

565

 g; i ˛f0; 1; 2g; t ˛½1; T

ð6Þ

k¼1

WFt  0; ct

ð8Þ

where pt refers to profits net of treatment and other expenses in week t, T is the last week the plants remain in the ground, and pt is the weighted average weekly regional wholesale fresh and processed strawberry price. The total number and the timing of pyriproxyfen treatments in week t is expressed in Ei;t , which is the ith pyriproxyfen P application in the season in week t at the label rate and tk¼1 Ei;k is the cumulative number of applications within week t. Finally, Ce is the per-hectare cost of pyriproxyfen and Ce;t refers to other all expenses in week t, which are assumed to be unaffected by the application of pyriproxyfen. The model constraints are the following: the weekly yield of the infested field cannot exceed that of a field that is not infested, g (Eq. (6)) (McKee et al., 2007a); at most, two pyriproxyfen applications can be made on the same unit of land per season (Eq. (7)); and the number of whitefly-days can never be negative (Eq. (8)). Eqs. (6) and (8) represent the biological features of the model. Eq. (7) represents the constraints imposed by the restrictions on pyriproxyfen use. To determine the optimal timing for a one-treatment control program, for example, we used the numerical simulation model of the greenhouse whitefly population to compute the effect of a single application of pyriproxyfen on the whitefly population and profit for every week in the season. We limit the set of application dates for the Watsonville model to February 1 and beyond, because prevailing cold temperatures in the area reduce the efficacy of pyriproxyfen prior to that date. Profit is determined by the magnitude and timing of the strawberry yield increase resulting from an application of pyriproxyfen, which reduces the whitefly population. We identified the optimal timing of the application by combining results of the population, yield, and economic model to

Table 1 Parameter estimates for the empirical model of the effect of incremental adult whitefly feeding on incremental strawberry harvests, Watsonville, CA, 2002e2003 Dependent variable: ln(Incremental harvest, g/plant)

Coefficienta

Weeks since planting

t S.E. t2 S.E. WFt S.E. (WFt)t S.E. d1 S.E. d2 S.E. d3 S.E. d4 S.E.

(Weeks since planting)2 ln(Incremental whitefly-days) [ln(Incremental whitefly-days)  (weeks since planting)] Dummy: untreated control Dummy: imidacloprid (Admire) and pyriproxyfen (Esteem) treatment Dummy: imidacloprid (Admire) at planting Dummy: second untreated control

Coefficienta 4.854 (1.148) 0.051 (0.090) 52.016 (16.480) 52.070 (16.480) 84.183 (30.510) 84.267 (30.500) 84.260 (30.490) 84.361 (30.510)

Dummy: pyriproxyfen (Esteem) 3/19/03 Dummy: malathion and fenpropathrin (Danitol) 3/19/03 Dummy: imidacloprid (Admire) (drip) 12/2/02 Dummy: imidacloprid (Admire) 12/13/02 Dummy: malathion 3/19/03 Dummy: imidacloprid (Admire) 2/27/03 Dummy: mineral oil (Omni Supreme) 1/30/03 & 3/19/03 June dummy

All coefficients are significant at P < 0.05. N ¼ 182, adjusted R2 ¼ 0.8736. The hypothesis of autocorrelation is rejected. a Standard errors appear in parentheses.

d5 S.E. d6 S.E. d7 S.E. d8 S.E. d9 S.E. d10 S.E. d11 S.E. dJune S.E.

84.200 (30.500) 84.161 (30.510) 84.016 (30.510) 84.264 (30.510) 84.346 (30.490) 84.364 (30.500) 84.220 (30.510) 1.203 (0.067)

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determine the week when the estimated return to the simulated pyriproxyfen application is greatest. Using this method, we evaluate the cost and benefits of the three selected pyriproxyfen use restrictions: the limit to two applications per year, the requirement to use imidacloprid with pyriproxyfen, and the requirement to make an application as soon as adult whiteflies appear. 3. Results To determine the effect of the pyriproxyfen use restrictions on strawberry production behavior (optimal insecticide quantity and optimal insecticide application timing) and profits, we compute the optimal constrained and unconstrained treatment control programs. We report our results in terms of the increase in profits relative to an untreated hectare. The results are then used to estimate the annual cost of the regulations to strawberry growers and their effects on insecticide use. We also discuss the effect of these regulations on whitefly management choices in future production seasons. 3.1. The optimal unconstrained treatment program We first use the simulation model to identify the timing of a set of three pyriproxyfen treatments that provides the highest estimated contribution to total strawberry profits. The optimally timed program includes applications during the weeks of February 4, March 12, and May 5. This treatment program adds a total of nearly $10,100 per hectare in profit relative to untreated plants, or about 11% of gross returns to strawberry production in the Watsonville area (Bolda et al., 2004). The estimated incremental profit of the third treatment is approximately $2200 relative to an optimally timed two-treatment program, which includes applications during the weeks of February 1 and March 5, indicating that a third application is economically justified. Given that additional profits could be obtained from additional applications, we conclude the restriction to two or fewer treatments, when examined alone, is a binding constraint on strawberry producer behavior. We also found that the requirement to apply pyriproxyfen when adult whiteflies first appear is not a binding constraint on the profit-maximizing two-treatment application program. Our simulation indicates that adult whiteflies would emerge on February 1. Growers are not constrained by this requirement when two applications are made e the first profit-maximizing application is done February 1. Consequently, given the restriction to two or fewer applications, the requirement to apply pyriproxyfen when adult whiteflies first appear does not further reduce profits. We now discuss the combined effect of the use restrictions limiting producers to two pyriproxyfen applications and the requirement to use pyriproxyfen in combination with an application of imidacloprid within 10 days of planting. In addition to having a different mode of action, imidacloprid is effective on adult whiteflies (Bi et al., 2002b) while pyriproxyfen may be effective against whitefly nymphs in outdoor conditions (Bi et al., 2002b; Ishaaya and Horowitz, 1989).

Analyzing the joint effect of the imidacloprid/pyriproxyfen requirement and the restriction to two applications of pyriproxyfen is important for two reasons. First, we will be able to determine whether the imidacloprid use requirement itself reduces profits. Second, it allows us to determine whether the restriction to two applications of pyriproxyfen is still inefficient given the imidacloprid/pyriproxyfen requirement. To study whether the requirement to use imidacloprid with pyriproxyfen is economically justified, we measure the profit first from an application of imidacloprid alone. We then calculate the joint effect of the restrictions by measuring the profit from three applications of pyriproxyfen after an application of imidacloprid. We conduct a simulation of the effect that an application of imidacloprid has on the whitefly’s population dynamics and its associated profits. In the simulation, an application of imidacloprid is made at planting. The increase in profit from this application, relative to an untreated hectare, is about $6700 per hectare, or about 8% of gross returns to strawberry production in the Watsonville area (Bolda et al., 2004). Hence, using imidacloprid is economically justified in the absence of using pyriproxyfen and provides an economic benefit to growers. A program with imidacloprid and three optimally timed applications of pyriproxyfen calls for the pyriproxyfen treatments to occur during the weeks of February 4, March 12, and May 5 e dates identical to those for the three-treatment, pyriproxyfen-only program. We interpret this result to mean that, despite the delay in whitefly population development caused by the application of imidacloprid at planting, the value of waiting to make any of the three pyriproxyfen applications, relative to the pyriproxyfen-only program, is zero. This program increased total profits by $23,500, or about 26% of average gross returns net of application costs (Bolda et al., 2004) The results of this simulation show that the limit to two or fewer applications of pyriproxyfen per hectare per season combined with requiring the use of imidacloprid imposes a short-term economic cost, just as it did in the case without an imidacloprid treatment. Hence, requiring use of imidacloprid at planting does not mitigate the cost of this restriction. In fact, because the complementarity between imidacloprid and pyriproxyfen increases the incremental profit of a third pyriproxyfen application, these costs are increased. 3.2. The optimal constrained treatment program In this section, we explore the benefits and costs associated with the imposing the combination of all three pyriproxyfen use restrictions on whitefly population management within a single season and single field. We compare the profits from when the grower complies with all three use restrictions to those obtained when choosing the optimal imidacloprid/ three-pyriproxyfen treatment program described in Section 3.1. The results show that greater profits are available from strawberry production when the optimal imidacloprid/threepyriproxyfen treatment program is used than when a program complying with all three use restrictions is employed.

G.J. McKee et al. / Journal of Environmental Management 90 (2009) 561e570

The ‘‘fully regulated’’ treatment program is defined as an application of imidacloprid at planting, an application of pyriproxyfen on February 1 (to comply with the timing requirement), and a second application of pyriproxyfen on March 8 (the optimal date, given February 1 as the date of the first application). This program results in increased profits of about $18,300 relative to an untreated hectare, or about 21% of average gross returns from strawberry production in the Watsonville area (Bolda et al., 2004). In comparison, the optimal three-treatment program comprised of an application of imidacloprid at planting and applications of pyriproxyfen during the weeks of February 4, March 12, and May 5, increased total profits by $23,500, or about 26% of average gross returns net of application costs (Bolda et al., 2004). These results show that the combination of the three-pyriproxyfen use restrictions impose a short-term cost on strawberry production. The restriction to two applications per season results in a smaller increase in profits as compared to allowing a third application. This causes profits to decrease from $23,500 to $18,300. When this is combined with the restriction to make the first application when adult whiteflies appear, increased profits remain at $18,300 and $23,500 for the constrained and unconstrained programs, respectively. The requirement to use imidacloprid, however, imposes no additional economic cost given the existence of the other two use restrictions. These results quantify the costs of the use restrictions. The difference in increased profits between the optimal imidacloprid/three-pyriproxyfen treatment program, $23,500, and the fully regulated program, $18,300, is $5200 per hectare of infested strawberries. Since the scientific and economic information used to perform this analysis is already available to policymakers, $5200 represents a lower bound on the shortterm cost the use restrictions impose on strawberry production. The costs could be greater because of the effect of suboptimal timing of treatment applications on whitefly population size at the end of the season, discussed below. To the extent the adult whitefly population is larger than the one that would result from the imidacloprid/three-pyriproxyfen treatment program, the costs of control and foregone yields will be greater in subsequent seasons due to larger migrating adult whitefly populations. These results also characterize the effects of the use regulations on optimal insecticide use. The timing of the pyriproxyfen applications changes, with the second application being made about 3 days earlier in the optimal constrained program than in the optimal unconstrained program. The frequency of applications is also affected, with one fewer application being made during a single season under the optimal constrained program than in the optimal unconstrained program. This implies that the total volume of insecticide used is lower during a single season under the optimal constrained program than in the optimal unconstrained program. 3.3. Sensitivity analysis In order to assess the robustness of our results, we analyze the sensitivity of the effect of the pyriproxyfen use restrictions

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on strawberry production behavior (optimal insecticide quantity and optimal insecticide application timing) and profits to changes in four parameters in our bioeconomic model. The biological parameters we examine include the size of the whitefly effect on strawberry yields, the efficacy of imidacloprid and pyriproxyfen against the greenhouse whitefly, and the timing of the imidacloprid application. We first measure the sensitivity of these three results to the size of the whitefly’s effect on strawberry yields.P We increase t the yield effect, as estimated in the variables ð j¼j1 WFj Þ Pt and ð j¼j1 WFj Þt in Eq. (4). We find that if the yield effect is increased by 1%, use restriction costs are reduced from about $5200 per hectare to about $3500 per hectare. Increases of 5%, 10%, and 20% in the yield effect also lead to decreases in use restriction costs to $3200, $3000, and $3000 per hectare, respectively. These results indicate that as the yield effect becomes more severe the economic benefit of the optimal unconstrained program is reduced. This is most likely P due to the increased yield loss over time, measured by the ð tj¼j1 WFj Þt variable. Our results also indicate that use restriction costs are relatively sensitive when small changes occur in the yield effect but the rate of change in estimated use restriction costs declines for larger percentage changes in the yield effect. For example, the estimated difference in increased profits between the optimal unconstrained and fully regulated treatment programs, $5200 per hectare, is reduced by 33% when the yield effect changes by 1%. When the yield effect changes 20%, a change 20 times larger, the difference in increased profits between the optimal unconstrained and fully regulated treatments programs is reduced by 42%, only 1.3 times the change at 1%. The volume of insecticide use and the optimal application timing remain unaffected. We next measure the sensitivity of the three results to changes in maximum mortality rates from applications of imidacloprid and pyriproxyfen. Our analysis in Sections 3.1 and 3.2 assumes 70% mortality for adult greenhouse whiteflies (Bi et al., 2002b). Adult whitefly mortality from applications of imidacloprid has been observed to be between 58% and 90% in commercial strawberry plantings (Bi et al., 2002b). When mortality from imidacloprid is assumed to be 58%, the difference in increased profits between the optimal imidacloprid/threepyriproxyfen treatment program, now $22,500 per hectare, and the fully regulated program, $17,500 per hectare, is reduced to $5000 per hectare of infested strawberries, a change of $200. When mortality from imidacloprid is assumed to be 90%, the difference in increased profits between the optimal imidacloprid/three-pyriproxyfen treatment program, now $25,200 per hectare, and the fully regulated program, $19,800 per hectare, is increased to $5400 per hectare of infested strawberries, a change of $200. These results indicate that use restriction costs are relatively unresponsive to changes in imidacloprid mortality rates. The optimal volume or insecticide applied and the optimal application timing remained unchanged. Our analysis in Sections 3.1 and 3.2 assumes 85% mortality for the single pyriproxyfen instar mortality parameter used, mort_pyriproxyfen. Applications of pyriproxyfen in commercial strawberries led to reductions of first and second instars

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by 51e100%, and 37e87% of third and fourth instars relative to an untreated field (Bi et al., 2002b). Note that the mode of mortality is to prevent whitefly eggs from maturing into instars. We evaluate the sensitivity of use restriction costs, total volume of insecticide applied, and optimal timing of applications to changes in pyriproxyfen efficacy rates. When mortality is assumed to be 37%, the difference in increased profits between the optimal imidacloprid/three-pyriproxyfen treatment program, now $11,900, and the fully regulated program, $10,100, is reduced to $1800 per hectare of infested strawberries, a change of $3400. The optimal amount of insecticide applied and optimal timing of the applications remain unchanged. When mortality is assumed to increase to 99%, the difference in increased profits between the optimal imidacloprid/three-pyriproxyfen treatment program, now $42,000, and the fully regulated program, $32,600, is increased to $9400 per hectare of infested strawberries, a change of $4200. These results suggest that the use restriction costs are relatively sensitive to changes in pyriproxyfen efficacy rate, and more generally to assumptions of mortality rates in the model. We found that the total volume of insecticide and optimal timing remain unchanged as the pyriproxyfen efficacy was changed. Finally, we measure the sensitivity of our results to changes in the timing of the imidacloprid application. The use restrictions indicate that this application should be done at planting. However, if adult whiteflies persist over time and the producer waits to make an application for several days, then the exposure of the plants to adult whiteflies will increase and allow a larger number of eggs to be oviposited. We assessed the effect of waiting 2 weeks to make an imidacloprid application on our results in both the constrained and unconstrained cases, under the assumption that the adult whiteflies that initially enter the field only remain for the first few days of the plant’s life. This scenario assumes that the requirement to make the application ‘‘at planting’’ is only loosely interpreted. In this case, the difference in increased profits between the optimal imidacloprid/three-pyriproxyfen treatment program, now $23,500 per hectare, and the fully regulated program, $18,300 per hectare, is unchanged from $5200 per hectare of infested strawberries. This result indicates that the use restriction costs are insensitive to small changes in imidacloprid application timing. We also found that the optimal amount of insecticide used and the optimal timing of the applications remained unchanged. 3.4. Effect of current whitefly management on future plantings and insecticide resistance To this point, our analysis has focused on the impacts of biological, economic, and selected use restrictions on grower behavior and returns within a single season. Because in many cases invasive species persist for more than a single growing season, it is important to analyze the effect of the pyriproxyfen use restrictions over time. Several authors have studied the dynamics of agricultural system management when controlling factors, such as resistance, which last for

several growing seasons. These include Hurley et al. (2001, 2002), Laxminarayan and Simpson (2002), and McKee (2006). One way to account for the impact of the use restrictions over multiple seasons is to consider the effect of various pyriproxyfen treatment programs on the size of the whitefly population near the time of the next strawberry planting. This is important for two reasons. First, the single-season analysis calculates that optimal application dates occur relatively early in the season. Growers may hypothesize that better inter-seasonal control could be achieved by making treatments near the end of the season. If that were the case, a grower’s privately optimal decisions might change depending on the time horizon considered. Second, the spatial and temporal organization of strawberry production in the Watsonville area is conducive to cross-season effects as adult whiteflies migrate to newly planted fields from adjacent old plantings that are still in the ground. We conduct a simulation for the Watsonville area that compares the date on which the adult whitefly population reaches an assigned carrying capacity of 50 adult whiteflies per leaf when zero, one, two, or three optimally timed pyriproxyfen applications are used during the season. An untreated field reaches carrying capacity around September 20, which is near the period when fields are traditionally removed. Waiting to make the first pyriproxyfen application at this date would require reducing a larger population than that found in a field that has already received one or more applications. The whitefly population on the untreated plants reached carrying capacity first because of the larger population in August relative to the treated plants. In contrast, a field that receives three optimally timed, simulated, treatments reaches carrying capacity on October 16, 24 days later than the untreated field. The simulation also indicates that the adult whitefly population grows more rapidly on untreated plants at this time than on treated plants because the population for this generation on the untreated plants begins at a higher initial density and assuming that the plants remain a suitable host. For example, the adult whitefly population doubles in early September, the earliest point at which a grower would consider removing plants, from about 10 to about 20 adult whiteflies in 6 days. In contrast, the population doubles in about 10 days for plants that receive one, two, or three optimally timed treatments. These differences in population growth rates can affect profitability in the current season because the interval of 24 days allows for additional harvests prior to removing the plants from the field while generating a whitefly population no larger than the one found in an untreated hectare. This presents a tradeoff for the grower. On one hand the grower can obtain more marketable fruit and the associated profits from additional harvests. On the other hand, the grower could remove the old plants before the start of the 24-day period, reducing whitefly management costs and foregone yields in subsequent seasons for adjacent fields associated with the larger adult whitefly population which will migrate to a newly planted field. Consequently, by incurring plant removal costs in the current season, a grower can reduce control costs for

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future plantings. However, due to the migration by adult whiteflies, the reduced control costs will benefit the operator of adjacent fields, who may or may not be the grower making the plant removal decision. This result suggests that incentives exist for growers to abuse the public-good nature of the pool of pyriproxyfensusceptible whiteflies. In this case, growers have incentives to inefficiently reduce the susceptible population of whiteflies by making too many pyriproxyfen applications. Hence, conditions may exist for which these regulations are beneficial over several seasons, but cause a loss in any single season. This would comprise a portion of any long-term benefit created by the insecticide use regulations studied here.

4. Discussion and conclusion The analysis in this paper demonstrates that the essential biological, economic, and regulatory features of the grower’s profit-maximizing problem must be modeled in order to create regulations that best respond to biological invasions. Designing the appropriate policy for managing invasive species is difficult given growers’ profit-maximizing responses to a biological invasion. In this paper, such an approach required information on the factors affecting greenhouse whitefly population development, a measure of its damage to yields, a model of grower decision making, and a way to illustrate the feedback among these components over time. We found that the dynamics of the whitefly population cycle in the Watsonville, California region are important in selecting optimal management timing, and that the role of prices is to change the absolute level of profits from applications made on the optimal date, not the date itself. The results of the analysis in this paper also show that invasive pest management decisions, and resulting profits, are affected by laws designed to prevent the development of insecticide resistance. For example, in Section 3 we found that the combined restrictions on pyriproxyfen applications constrain grower decisions, causing growers in the Watsonville to lose an estimated $5200 in profits per hectare per season. The requirement to use imidacloprid generates benefits to the grower, but when combined with the other two, losses increase. To accurately determine the costs and benefits of policies that regulate invasive species management, these effects on grower behavior must be identified. As shown, accurately modeling the interaction between production decisions and biological changes associated with invasive species can identify sources of these effects. The estimated costs of the combined restrictions is relatively sensitive, however, to assumptions about the efficacy of pyriproxyfen and the size of the effect of whiteflies on strawberry yields, and relatively insensitive to assumptions on the efficacy of imidacloprid or the timing of its application e if done early in the first 2 weeks of the strawberry plant’s life. The optimal amount of insecticide used, three applications of pyriproxyfen and one application of imidacloprid, and the optimal timing of the applications, for both the constrained and unconstrained program, are insensitive to these model assumptions.

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Finally, the costs and benefits of regulation over time must also be considered. Biological invasions, and hence the effects of regulation, can persist for more than one growing season. The analysis in Section 3.4 demonstrated the use of a bioeconomic model for estimating the multi-season effect of the pyriproxyfen use restrictions by simulating their effect on the likely size of migrating adult whitefly populations. This demonstrated that since a tradeoff exists between current harvests and reduced future harvests and increased future control costs, that a multi-season model may be appropriate under various conditions. Another important direction for additional research is examining the effect the use regulations have on the development of insecticide resistance in the target pest population. Again, this research question requires a multi-year model in order to address the tradeoff between the cost of reduced control now and the benefit of better control in future periods. Based on the public-good nature of the pyriproxyfen-susceptible population, an extension of this research would examine not only the expected cost of repeated applications and the benefits of slower resistance development due to use regulations, but would also analyze the benefit of creating policies to manage insecticide susceptibility over several seasons, both in conjunction with the use regulations and as a substitute. Acknowledgements This research was conducted as part of the dissertation submitted by McKee in the Department of Agricultural and Resource Economics at the University of California, Davis, and was supervised by Rachael Goodhue, Colin Carter, James Chalfant, and Frank Zalom. Goodhue, Carter, and Chalfant are members of the Giannini Foundation of Agricultural Economics. This research was supported by the Program of Research on the Economics of Invasive Species Management (PREISM), Economic Research Service of the USDA, under Cooperative Agreement 43-3AEM-3-80081. The authors thank Pat Thompson for invaluable research support. We also thank Alison R. Gill and two anonymous referees. References Bi, J., Toscano, N., Ballmer, G., 2002a. Seasonal population dynamics of the greenhouse whitefly Trialeurodes vaporariorum (Homoptera: Aleyrodidae) on strawberries in southern California. J. Econ. Entomol. 95, 1179e1184. Bi, J., Toscano, N., Ballmer, G., 2002b. Field evaluations of novel chloronicotinyls and insect growth regulators against the greenhouse whitefly on strawberry. HortScience 37, 914e918. Bi, J., Toscano, N., Ballmer, G., 2002c. Greenhouse and field evaluation of six novel insecticides against the greenhouse whitefly Trialeurodes vaporariorum on strawberries. Crop Prot. 21, 49e55. Bolda, M.P., Tourte, L.J., Klonsky, K.M., De Moura, R.L., 2004. Sample Costs to Produce Strawberries: Central Coast Region, Monterey and Santa Cruz Counties. University of California Cooperative Extension Report ST-CC-04. Available from:. http://www.agecon.ucdavis.edu/uploads/ cost_return_articles/strawcc2004.pdf (accessed November 2004). Byrne, D., Bellows, T., Parrella, M., 1990. Whiteflies in agricultural systems. In: Whiteflies: Their Bionomics, Pest Status and Management. Intercept Ltd., Andover, Hants, UK, pp. 227e261.

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