Bioeconomic Modeling of Greenhouse Whiteflies in California Strawberries

Second, the whitefly's life cycle can be modeled plausibly based on data from a single season. The resultant model can be used to study management alternatives and to guide data collection efforts for other invasive species by revealing key parameters associated with population development and interactions with economic activities. Third, the whitefly is a significant economic problem in two geographically separate California regions. The climate and other differences across these regions create different host cycles and whitefly population dynamics, which then lead to differences in decisions concerning whitefly management.

The biological, economic, and regulatory features of the invasion cause grower incentives for whitefly control to vary by region and by week. Therefore, in order to create economically and environmentally efficient whitefly management policies, an understanding is needed of a grower's profit-maximizing response to pest damages. Empirical "bioeconomic" models, which unify information on biological relationships, economic relationships, and interactions between them, are useful in developing such policies (McKee, 2006; McKee, Goodhue, Chalfant, & Carter, 2006; Eiswerth & Johnson, 2002; Knowler & Barbier, 2000).

Also, when doing invasive species modeling it is often the case that limited information is available. In this study, we examine the value of adding information first using only data arising soon after the establishment of the whitefly population and then adding other information about the whitefly's life cycle from the scientific literature.

Models of Whitefly Population Development in California Strawberries

Strawberries are grown along the California coast almost year-round. A plant is typically in the ground for approximately nine months, usually starting in the fall. Weekly yields are relatively small in the early spring, increase very rapidly in mid- to late-spring, and then taper off during the summer. The population growth rate of the greenhouse whitefly on strawberries changes throughout the season since temperature regulates maturity rate. Whitefly reproduction and population development are slowest during the coolest parts of the growing season and more rapid during the hotter, spring and summer months.

Alternative Approaches to Modeling

Thus, two models are used. The first estimates a daily adult population series using egg count data from the invasion. The second uses invasion egg, nymph (juvenile whitefly), and adult whitefly data, along with observations from other whitefly studies (Hulspas-Jordaan & van Lenteren, 1989) to inform the model about how variations in environmental conditions affect whitefly population development. The additional population data were acquired at little additional cost.

Results

Model Replication of Population

The solid line in Figure 1 represents the estimated adult whitefly population series from the first model; the dashed line represents the second. The 13 large dots represent the observed sample. As the figure shows, both models reasonably predict the timing of peaks and troughs in the whitefly population.

One way to more precisely compare the results of these two models is to measure the area under each curve. This area measures the size of the population and the length of time it persists, stated in units we call "whitefly-days." There were 505 cumulative whitefly-days observed in the sample. The first model (case-specific data only) predicts 430 whitefly-days (15% error), while the second predicts 564 cumulative whitefly-days (10% error). Based on this criterion, the second model generates a superior prediction.

Information and Costs of Esteem Limits

We first examine the difference in the model results regarding the development of the whitefly population for the case of a single Esteem treatment, illustrated in Figure 2. When using the first model, the optimal date for a single Esteem application is March 29, just after the largest observed adult whitefly population peak. In contrast, the additional information used in the second model changes the optimal pesticide application date to March 5^th, just before the adult whitefly population begins to build. Prior to March 5, the populations are identical. The population generated by the March 5 application generates smaller population peaks than the March 29 application, and higher net revenues. Collectively, the more accurate model results in a difference of approximately 3% of net revenue per untreated acre.

To provide further perspective, we examine the cost of the Esteem regulation limiting growers to two or fewer applications per season. Using the second model, under two applications we get about $7,800 per acre, as opposed to about $9,500 per acre for three, a regulation cost of about $1,700 per acre. In contrast, under the simpler model the net revenues from the restricted case are about $4,700 per acre, compared to about $7,000 per acre for the relaxed case, which is a difference of about $2,300 per acre.

The added information suggests the cost of the regulations is smaller under more informed pest management, amounting to 18% versus 33% of net revenue. The benefit is partially due to the difference in the optimal spraying time, and partially due to the more accurate representation of post-treatment population development. Based on about 1,000 infested acres in 2003, the value of relaxing the application limit would have been $1.7 million, in net revenue, per year. However, additional applications would have increased the likelihood of resistance, and if complete resistance arose we estimate losses relative to the two-application case would be about $7.8 million per year. While this is obviously a very simplistic view of the implications of resistance, it illustrates how large the benefits from preventing or delaying the development of resistance can be in this specific case.

The weaknesses of the first model suggest that for decisionmaking support it would be valuable to merge experimental data on pest life cycle stages with other known information. Of course, if unlimited data were available, the performance of the first model would be augmented including other relevant variables. However, our model comparison was motivated by the often limited data available for policymakers examining invasive species policy options, as existed in the case study we examined.

What Types of Models should Policymakers and Growers use for Decisionmaking?

We found that the difference in the population models substantially affected the estimates of the per-acre cost of the Esteem application limit for growers. Using only data from the invasion, the cost was $2,300 per acre, or $2.3 million in the infested area. Using the augmented model, the cost was $1,700 per acre, or $1.7 million in the infested area.

Our analysis of this specific case illustrates that information on the life cycle of the pest, when available, can improve decision making. Namely, the model with more information is better able to describe the feedback between grower management decisions and the invader/host plant environment. Policymakers need to determine whether or not they need to intervene in the system. In our case, regulators were concerned about the possibility of the whitefly developing resistance to the only effective control treatment prior to the development of alternative treatments. Using the augmented model resulted in a 26% lower estimated per-acre cost of complying with the requirement of two or fewer Esteem applications in order to obtain the benefit of a decreased likelihood of resistance development. Of course, the off-setting caveat is that the modeler must make careful decisions regarding which outside information is sufficiently relevant.

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