ECONOMIC THRESHOLD DECISION RULES AS AN INTEGRATED PEST MANAGEMENT TOOL IN FLORIDA CITRUS PRODUCTION

Transcription

1 ECONOMIC THRESHOLD DECISION RULES AS AN INTEGRATED PEST MANAGEMENT TOOL IN FLORIDA CITRUS PRODUCTION By ARTHUR THOMAS TOMERLIN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

2 Copyright 2005 by Arthur Thomas Tomerlin

3 TABLE OF CONTENTS page LIST OF TABLES... v LIST OF FIGURES...vi ABSTRACT...vii CHAPTER 1 INTRODUCTION LITERATURE REVIEW... 8 Pesticide Regulation... 8 Benefit-Cost Framework of Pesticide Use Florida Citrus Culture Citrus Rust Mite Pest Thresholds Derivation of Economic Thresholds Action Threshold (AT) and Economic Injury Level (EIL) Economist s Economic Threshold (ET econ ) Entomologist s Economic Threshold (ET entom ) Summary CITRUS RUST MITE MANAGEMENT MODEL PARAMETERS Citrus Rust Mite Scouting and Monitoring Citrus Rust Mite Damage to Orange Fruit Percent Damage Per Mite Per Day Threshold Biological Parameters Threshold Economic Parameters Price Costs THRESHOLD DECISION RULE CONSTRUCT Mite Day Accumulation Threshold Models Decision Tree Model Model iii

4 5 RESULTS Results Treatment Timing Threshold Models M1-M5 Economic Performance CONCLUSIONS, LIMITATIONS, AND RECOMMEDATIONS APPENDIX OPTIMAL PATHS FOR M5 BDT LIST OF REFERENCES BIOGRAPHICAL SKETCH iv

5 LIST OF TABLES Table page 2-1 Economic threshold definitions by discipline Estimated % fruit surface area damage per mite day by month a m (t) Florida orange on-tree price per box for 20 seasons Sigmoid mite day curves CRM threshold models Mite day functions A-E: incremental and cumulative mite days First application day Model rank according to first treatment date Economic performance of models M1, M2, M3 and M5 utilizing baseline parameters (Ye= 400, P=$1.78, and Spray Costs = $65/acre) v

6 LIST OF FIGURES Figure page 2-1 Socially optimal pesticide use (Q*) and price (P*) Action thresholds under three alternate management tactics Stylized population density of CRM with hypothetical ET and EIL Damage rate vs. time of year for Valencia oranges. (Allen 1976 p. 1087) Grower fruit allocation decision tree Cumulative mite day functions Daily mite day functions CRM treatment binary decision tree M First application date and cumulative mite day functions A-E for threshold M2, M3, and M First application date and cumulative mite day functions A-E for threshold M2, M3, and M4 (Zoomed for detail) Optimal scouting effort vi

7 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ECONOMIC THRESHOLD DECISION RULES AS AN INTEGRATED PEST MANAGEMENT TOOL IN FLORIDA CITRUS PRODUCTION By Arthur Thomas Tomerlin May 2005 Chair: Thomas H. Spreen Major Department: Food and Resource Economics The decision to pursue management action against an economic pest is a keystone decision in any integrated pest management program. For any particular pest, farm-level decision rules have been developed to judge when management action is economically justified. These economic threshold decision rules have been adopted by producers with varying degrees of practicable success. Both qualitative and quantitative threshold decision rules have been developed and applied. While model rigor and performance are important considerations, a producer will also consider implementation costs when deciding to adopt any decision rule framework. Through investigation of the plant-host relationship between citrus and the Citrus Rust Mite (Phyllocoptruta oleivora Ashmead), our study examined the benefits and costs associated with different decision rules from the perspective of the producer. Prescription-based decision rules in managing Citrus Rust Mite are justified in vii

8 typical mite growth situations that occur at predictable times. Comparison of an action threshold with a binary decision tree demonstrated that treatment timing can have both positive and negative profit implications. These differences are largely a function of how and when the pest population increases. Simpler threshold decision rules will likely perform comparably with the more complex models if the residual control of pesticides is high. The additional scout and information costs associated with more-complex decision rules become warranted when uncertainties exist regarding the target market outlet (i.e., fresh versus processed fruit markets) and in cases where mite populations are exceptional with respect to intensity, timing, and/or pace. viii

9 CHAPTER 1 INTRODUCTION Integrated approaches to pest management have evolved over some time. As the forerunner of Integrated Pest Management (IPM), the field of Economic Entomology included many elements of IPM as practiced today. Integrated Pest Management (IPM) was borne out of concern over the control of agricultural pests. Before adopting IPM methods, the standard farm operating procedure was to eliminate (i.e., control) economically significant pests. As an objective function, control of economic pests may not be consistent with farm-level profit maximization. In practice, the costs of control may exceed the associated increases in yield value. The distinction is that control implies elimination of the pest, whereas management refers to more judicious use of resources, recognizing the benefits and costs of the practice. Pedigo and Higley (1996) detailed the evolution of management and control with respect to pest management. Until the 1960s, pesticides were used liberally in conjunction with farm level objectives to control pests. Indeed, the development of IPM was promulgated by the recognition of human health and environmental effects associated with liberal use of pesticides. Today, IPM is the preferred approach, and its implementation is strongly supported by State Agricultural Extension and other agencies involved with agricultural enterprises. Public agency support and a legal definition of IPM were given in the Food Quality Protection Act of 1996 (7 U.S.C. 136r ): 1

10 2 The Secretary of Agriculture, in cooperation with the Administrator, shall implement research, demonstration, and education programs to support adoption of Integrated Pest Management. Integrated Pest Management is a sustainable approach to managing pests by combining biological, cultural, physical, and chemical tools in a way that minimizes economic, health, and environmental risks. Integrated pest management has far-reaching implications because it favors using a variety of methods to manage a pest based on a consideration of costs and benefits. t unexpectedly, the role of economics in pest management increased with the advent of IPM. The drive for more efficient farm level pest management has been pervasive. This is well evidenced by the development of decision rules, which relate the level of pest infestation with available pest management tactics (Pedigo and Higley, 1996). An underlying assumption of these decision rules is that the cost of an input should, at minimum, be matched by the increased return gained by its use. The focus of our study was to examine the use of such decision rules in Florida citrus culture. Under current conditions surrounding the U.S. Environmental Protection Agency s implementation of the Food Quality Protection Act (FQPA), pest management in citrus must be under meticulous husbandry. Applied pesticides are under intense scrutiny. The orderly removal of Ethion from the market place is an example of recent regulation directly affecting citrus production. The exposure of farm workers and adulteration of food with pesticide residues are focal points in the regulation process. In addition, environmental and non target organism impacts have likewise become critical points in the regulatory review process. Given this climate, the significance of IPM is heightened and pest

11 3 management must be implemented so as to preserve the production of an adequate, wholesome, and economical food supply. On the surface, IPM seems a rather innocuous concept considering it simply refers to using multiple tactics to meet economic ends. Although simple in concept, IPM is the umbrella under which many other complex pest management concepts reside. Biological, cultural, physical, and chemical management tactics are all appropriate in an IPM program. A common misunderstanding in IPM is that chemical control is averted. Rather, IPM seeks the most efficient set of tactics based on a consideration of risks and benefits. Indeed, chemical control agents (pesticides) are efficient pest management tools when used prudently. As such, a body of research has evolved that develops decision rules to address optimal pesticide application(s). The idea of tolerating pests in numbers that cause minimal economic damage is central to these decision rules. The principle of pest threshold decision rules is perhaps the most basic, yet misunderstood IPM concept. Many have argued that the fundamental basis of IPM is rooted in pest threshold decision rules (Higley and Pedigo, 1996; Pedigo et al. 1996). Decision rules based on pest thresholds broadly refers to the concept of treating a pest only when benefits (i.e., damages avoided) exceed treatment costs. More specifically, most agricultural pests can be tolerated in numbers up to a threshold level (beyond which the value of yield losses exceed control costs). In other words, a pest threshold decision rule refers to the pest population level above which economic damage, in excess of treatment costs, would occur. The earliest definition of a pest threshold decision rule came from

12 4 Stern et al. (1959) where an Economic Injury Level (EIL) was defined as the lowest population density that will cause economic damage. The threshold concept has since evolved, with varying degrees of complexity added. The application of economic principles to farm-level pest management is central to IPM. The continual development and refinement of pest threshold decision rules is testimony to the importance of economic considerations in an IPM program. Throughout the literature, varying degrees of complexity have been added to the original threshold concept to account for dynamic and stochastic elements of the pest management problem. netheless, the simpler static and deterministic threshold decision rules, or no use at all, remain widely practiced pest management strategies at the farm level. The high commodity value and pest susceptibility of Florida citrus necessitates the development and use of a well-balanced IPM program. While Florida s humid subtropical climate is well suited to citrus production, it is likewise conducive to immense pest pressure. Knapp et al. (1996 p. 317) summarized the current arsenal of IPM techniques currently used in Florida citrus production: Today, the Florida citrus IPM program utilizes host-plant resistance, natural enemies, horticultural practices, and selective chemicals to maintain pest populations below economic levels. Maintaining pests below economic levels is the core of pest threshold decision rules. Accordingly, pest threshold decision rules are key elements in the Florida citrus IPM program. Development and use of pest threshold decision rules in Florida citrus has taken many forms. Where threshold decision rules have been developed, a great deal of variance exists with regard to model

13 5 efficiency and practicality of use. When adopting decision rules, producers are often faced with a presumed trade-off between simplicity of use and precision. Economists have criticized simpler threshold decision rules as being too abstract and oversimplified. Some entomologists have countered that more complex rules are not amenable to practical application. Moreover, entomologists have argued that decision rules are dynamic by nature because the parameters that determine thresholds change over time. Our study developed and comparatively examined the performance of different decision rules for a particular pest management scenario in Florida citrus. Decision rules were developed with varying degrees of complexity, and then compared in accord with various performance measures (such as treatment timing and expected net returns). More specifically, we developed decision rules for management of Florida Citrus Rust Mite (CRM) Phyllocoptruta oleivora (Ashmead). Total economic loss due to CRM related damage to Florida citrus is almost impossible to estimate with precision. netheless, the Florida Citrus Integrated Pest and Crop Management Handbook (Knapp, 1987) distinguishes the CRM as the most economic arthropod pest of Florida citrus, based on incurred damage and annual cost of control (Knapp, 1987). The CRM feeds on the surface (epidermal) layer of fruit, creating a rust discoloration on fruit. Damage from CRM is generally associated with a loss in fruit quality, although more serious yield effects are associated with heavy infestations. Loss in fruit quality and appearance is a serious concern for fresh market fruit.

14 6 Growers of fresh market citrus must routinely answer an important question: when are CRM numbers high enough to justify management action (e.g., a pesticide application)? The general problem area is that this question has been answered many times, resulting in different decision rule advice. Our objective was to comparatively examine competing threshold decision rules for managing CRM in Florida citrus. Decision rules developed for CRM in Florida citrus were comparatively examined across several factors. Expected net returns and other performance measures for yearly/routine set-time applications, use of static decision rules, and use of a more complex dynamic model were simulated for citrus rust mite control in Florida citrus. The specific objectives are the following: 1. Describe and further refine pest threshold relationships developed for Citrus Rust Mite (Phyllocoptruta oleivora Ash.) 2. Incorporate these relationships into decision rule models for managing citrus rust mites in Florida fresh market citrus 3. Compare and contrast the performance of the developed models 4. Briefly examine each model s economic implications at a coarse level and investigate the presumed trade-off between decision rule efficiency and ease of use. This study is organized into five remaining chapters. A general discussion of pesticide regulation, Florida citrus culture, the Citrus Rust Mite, and pest threshold decision rule theory and analysis techniques is presented in Chapter 2. In Chapter 3, the plant-host relationships between citrus and the Citrus Rust Mite are presented relative to model components presented in Chapter 2. Necessary threshold decision rule parameters are also developed in Chapter 3. In Chapter

15 7 4, these decision rule components are assimilated into select decision models for management of citrus rust mite in Florida citrus. In Chapter 5, these select decision rules are compared and contrasted utilizing different pest growth scenarios. Concluding comments and analysis are provided in Chapter 6.

16 CHAPTER 2 LITERATURE REVIEW Necessary entomological and economic concepts that dominate decision rule research are presented in this chapter. This chapter addresses three topic areas. Because pesticides are the most prevalent tool available in pest management, the first section outlines the state of pesticide regulation in the United States. The second topic area is a brief introduction to Florida citrus culture and the Citrus Rust Mite (CRM) and its life cycle. The third topic area examines pest management decision rule concepts from both an entomological and economic standpoint. The model construct presented in this chapter will be used to benchmark and compare the competing decision rules developed in subsequent chapters. Pesticide Regulation Despite routine adjustment and revision, pesticide regulation continues to focus on direct control. Moreover, pesticide regulation is conducted primarily at the national (federal government) level under the auspices of the U.S. Environmental Protection Agency (EPA). Direct control in pesticide regulation consists of either banning or limiting the permissible level of pesticides through label restrictions or other mechanisms. Direct control also involves requiring the use of specialized procedures and methods in applying pesticides. The Food Quality Protection Act of 1996 (FQPA) amends both the Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) and the Federal Food, Drug, and 8

17 9 Cosmetic Act (FFDCA). Pesticides are regulated under these three policies (EPA 1996). Pesticide regulation is complicated by public perception of pesticide risks. Much of the research on public attitudes toward pesticide use has centered on issues of food safety (for example: Kramer 1990, Jussaume and Judson 1992, Misra et al. 1991, Dunlap and Beus 1992, Buzby et al. 1998). In general, the public sees government intervention as necessary in regulating pesticide use. Through response to a public survey, Dunlap and Beus (1992 p. 429) determined the following: Clearly a majority of the public sees government as having the responsibility of protecting them from pesticides, a position that is consistent with their fear of pesticides and their skepticism about farmers insuring food safety. Direct-control pesticide regulation lacks economic incentives and a clear benefitcost analysis structure. The ban-or-limit regulatory approach, however, may help alleviate the intense public concern over pesticides. In other words, perceived public perception of pesticide effects may help drive the current direct control approach. Zilberman and Millock (1997) provided a thorough economic critique of U.S. pesticide use and regulation. Economists do not generally support the existing direct control approach in pesticide regulation. Policies that use market mechanisms in a benefit-cost analysis framework are considered more efficient. Zilberman and Millock (1997 p. 330) discussed this point: Current pesticide regulations are significantly inefficient, even acknowledging the difficulties associated with determining pesticide policies. They can be greatly improved by incorporating economic considerations into the policy process. Moving from bans toward financial

18 10 incentives and flexible policies that will allow chemical use where the benefit-cost ratios are high will improve resource allocation. Economically sound incentives to increase precision of chemical application and reduce chemical residues may also reduce environmental side effects of pesticide use in a cost effective manner. The FQPA continues to limit economic considerations in granting tolerances and also requires periodic re-evaluation of pesticide registrations with respect to these tolerance levels. Re-evaluation of pesticides for compliance with tolerance levels may accelerate the ban, restriction, or voluntary withdrawal of pesticides (EPA 1996). Benefit-Cost Framework of Pesticide Use Pesticide policy is difficult to design because of the private versus social costs associated with their use (Zilberman and Millock 1997, Zilberman et al. 1991). Much insight can be derived by viewing the regulatory challenge in this private versus social costs framework. A simple depiction of this framework is provided in Figure 2-1. The curve labeled MPC is the private marginal cost of pesticide use. It is the cost that the producer pays; it includes the purchase price of pesticides, application costs, storage costs, and so on. The curve labeled MSC is the marginal cost to society. Marginal social cost (MSC) includes both the private cost of pesticide use and the costs to non-producers. Pesticide policy is designed around these external costs to non-producers. Social optimum is given at the intersection of marginal social cost (MSC) and marginal benefit (MB), which occurs at Q*. Marginal benefits (MB) consist of increased yield values, associated with incremental increases in pesticide use. Marginal private costs (MPC) consist of all private (producer) costs associated with incremental increases in pesticide use (e.g., pesticide costs, labor and

19 11 machinery costs). Marginal private costs (MPC) are typically captured within market exchanges. On the other hand, marginal social costs (MSC) also include external costs not explicitly traded within a market. Hence, the difference between MSC and MPC gives the marginal externality cost (MEC) associated with the pesticide's use. P MSC = MPC + MEC P* MPC P MB Q* Q Q (Pesticide Use) Figure 2-1. Socially optimal pesticide use (Q*) and price (P*) Theory states that the producer considers only private costs (MPC) and will therefore seek to use pesticide quantity Q by equating MPC with MB. The MEC associated with the pesticide's use (the difference between MSC and MPC), causes overuse and under-pricing of the pesticide. Direct control in pesticide regulation seeks to directly fix the socially optimum quantity (Q*). Although not addressed in this research, this construct can be extended to illustrate the case of pesticide bans. A regulatory ban on a pesticide implies that MSC is significantly high to lie above MB at all points. Indeed pesticide regulation is

20 12 almost entirely focused on measurement of MECs. A singular focus on externality costs can be myopic in some cases. The externality cost associated with pesticide use (MEC) consists of a variety of different cost elements. Federal pesticide regulations prioritize healthbased safety standards for pesticide residues in food. As such, food safety externalities associated with pesticide use receive much regulatory attention. To a lesser extent, pesticide regulations address other externality costs, including water quality and non-target organism impacts. Outside of food safety, most of the social costs of pesticide use are more localized in nature. In other words, the social costs accrue to the immediate area surrounding the treated field/grove. Common examples include well and groundwater contamination, mortality of beneficial predator organisms, and other aquatic/land animal poisoning. Although these environmental costs are fairly localized, their regulatory management remains primarily at the national level. Internalizing these more localized pesticide impacts into marginal private cost (MPC) would provide a market based approach in eventually determining socially optimum pesticide usage (Q*). It is important to recognize that MSC consists of both MEC and MPC as given by the relationship MSC = MPC + MEC. As shown in Figure 2-1, a social optimum (Q*) is reached when MSC = MB, or when (MPC + MEC) = MB. Farmlevel decision rules serve to better quantify MPC and MB at the producer level. The social optimum (Q*) implies that MPC and MB are known with a high degree of certainty and that the private optimum Q can be realized. The ability to

21 13 effectively fix optimal pesticide quantities (Q*) necessarily assumes that farm-level pest management decisions are efficient, from a private cost standpoint. In other words, the producer will make decisions consistent with his MPC and MB framework. Unfortunately, this is often not the case at the farm level. Producers are often faced with too little information on the MPCs and MBs associated with their pest management decisions. It is common for producers to rely on routine rule-of-thumb decision rules to dictate when a pesticide treatment is warranted. These practices may not be consistent with a level of optimization at which marginal private benefits equal marginal private costs (MB = MPC). Using pest threshold decision rules provides a way to consider this at the farm level. A primary goal of our study was to develop pest management decision rules that operationalize this behavior for a particular plant-host scenario. Our study examined the use of pest threshold decision rules for managing Citrus Rust Mite in Florida citrus culture. We did not address externality costs associated with pesticide use. Before, reviewing pest threshold research and decision rule modeling, a brief overview of the Florida citrus industry and the CRM is provided Florida Citrus Culture Citrus is Florida s leading agricultural commodity in terms of both production value and acreage. Florida produced more than 298 million boxes of citrus fruit during the 1999/2000 growing season on 762,400 bearing acres (Florida Agricultural Statistics: Citrus Summary, ). While the production value of citrus totaled approximately $1.73 billon for the 1999/2000 growing season, this number does not reflect the industry s full economic impact on the state. Using

22 14 input-output modeling, Hodges et al. (2001) estimated the total economic impact of the Florida citrus industry in as follows: $9.13 billion in industry output $4.18 billion in value added 89,700 jobs The Florida citrus industry has experienced many industry wide hurdles over the past 2 decades. Severe freezes in the 1980s destroyed large areas of citrus production in central regions of Florida. These freezes resulted in wide-scale replanting of citrus to the south. Hallmarks of this geographic shift in production were moving citrus to poorly drained flatwoods soils that require drainage improvement and an increase in tree density to maintain production. This increase in per-acre tree density was in response to limits on root growth caused by the shift of citrus production to more poorly drained soils (Knapp et al. 1992). This geographic shift in citrus production had very little effect on the pest management costs facing a grower. Results of an informal survey conducted by Knapp et al. (1992) found that among all production costs, the spray program represents the largest share of production costs in both the Central Florida Region (26% of costs) and the Indian River (29% of costs) Region. Weed control costs (23% of costs) exceeded spray program costs (18% of costs) in the Southwest Florida production region (Knapp et al. 1992). The CRM is the top ranked pest in terms of annual control costs (Knapp, 1987). Citrus Rust Mite The humid subtropical climate of Florida has enabled the establishment of a multibillion-dollar citrus industry. This same climate also manifests intense pest

23 15 pressure on Florida citrus culture. The Citrus Rust Mite (Phyllocoptruta oleivora Ashmead) is considered the most damaging economic arthropod pest of Florida citrus based on management costs (Knapp, 1987). Hubbard (1885) reported damage to fruit and leaves caused by the citrus rust mite (CRM), indicating a recognized 120-year history of the pest in Florida. The CRM feeds on the fruit, twigs, and leaves of citrus plants. The CRM feeds using its piercing mouthparts to rupture the epidermal cells of fruit. This feeding results in visible injury on the fruit peel. Symptoms of peel injury differ by variety and maturity of fruit. Injury to orange fruit is often referred to as russeting or bronzing depending on whether the feeding damage occurred in early or late season, respectively. The CRMs overwinter on all parts of the citrus tree. In the spring, mites appear on the spring flush and begin to reproduce on the leaves. As young fruit reach a growth stage having sufficient moisture, CRMs begin to inhabit and feed on the fruit. CRM populations begin to increase in April and May, reaching the highest population levels from June to August. In the months of May, June, and July, a life cycle takes 7 to 10 days. A secondary population peak occurs between vember and December. This second winter peak rarely reaches mid-summer population levels. The lower temperatures in the winter months might increase the life cycle to 14 days (Knapp, 1994). CRM damage to the surface area of fruit that is less than or equal to 5% is usually acceptable for the fresh fruit market. CRM damage to the surface area of fruit that is less than or equal to 75% is usually acceptable for the processed fruit

24 16 market (Knapp et al. 1996). These general damage standards play an important role in determining packout rates. Packout refers to the share (rate) of fruit that is deemed acceptable for a particular market outlet (i.e., fresh use or processed). Fruit targeted for the fresh market will be graded at the packinghouse and then diverted into either fresh use or eliminations. Although not acceptable for the fresh market, eliminations can nonetheless be processed. Eliminations are hauled to the processing plant and an elimination charge is levied. CRM damage plays a critical role in how fruit is graded, and therefore has a direct influence on fresh market packout rates. Processed fruit, however, is only modestly affected by CRM surface area damage. Pest Thresholds Pest threshold decision rule research is beset with confused terminology. Entomologists and economists have defined thresholds differently. Moreover, a great deal of terminology variation exists even within these respective professions. Up to this point, the generic term "pest threshold decision rule" has been used to characterize all such terms. Specific terms used by practitioners include economic threshold, economic injury level, and action threshold. To complicate things further, these same terms have different meanings across disciplines. A general definition for economic thresholds could be a pest population level above which economic damage to the crop would occur without management action (adapted from USDA-ERS 1997). This definition implies that economic damage occurs when yield value losses exceed treatment costs. The entomologic terms used in our study are consistent with those first introduced by Stern et al. (1959) and later standardized by Higley and Pedigo (1996). While

25 17 the economic terminology coincides with that of Headley (1972), it was later addressed by Moffitt et al. (1984), Hall and Moffitt (1985), and others. The major threshold terms used by economists and entomologists are given in Table 2-1. Table 2-1. Economic threshold definitions by discipline Threshold term Definition Entomologist: Economic Injury Level (EIL) Entomologist: Economic Threshold (ET entom ) Economist: Action Threshold (AT) Economist: Economic Threshold (ET econ ) Lowest pest population density that will cause economic damage (Stern et al. 1959) Pest population density at which control measures should be initiated to prevent an increasing pest population from reaching the EIL (Stern et al. 1959) Pest population large enough to cause damages valued at the cost of practical control (Edwards and Heath 1964) The population that produces incremental damage equal to the cost of preventing that damage (Headley 1972) As shown in Table 2-1, threshold definitions can be confounding. At the risk of falling into this trap, two points are worth mention. First, the entomologist s economic threshold (ET entom ) represents the time for taking management action for the entomologist, whereas the economist s ET econ is a marginalist concept representing a pest population at which the marginal cost of management action equals the marginal revenue of control. Second, the action threshold (AT) of economists roughly coincides with the entomologist s economic injury level (EIL) (i.e., AT EIL). Rather than getting bogged down in clarifying these distinctions, the derivation of economic thresholds from profit maximizing behavior provides a unified foundation from which these concepts originate. Derivation of Economic Thresholds The definitions used by economists for the AT and ET econ is derived from profit, production, and kill functions. The three equation model presented below is adapted from Moffitt et al. (1984) and later adapted and used by others (Moffitt

26 18 et al. 1984, Hall and Moffitt 1985, Moffitt 1986, Moffitt and Farnsworth 1987, Carlson and Wetzstein 1993): π = PY VM F (2.1) Y = Ye - αn (2.2) n = Ne -BM (2.3) Equation (2.1) is a profit function depicting total revenue as the product of unit price (P) and final yield (Y), and total cost as the product of variable cost (V) and management tactic (M) minus fixed costs (F). All other production costs are considered constant and not addressed herein, ceteris paribus. The profit function (2.1) is total revenue (PY) minus total variable and fixed pest management costs (VM+F). The yield equation (2.2) is expected yield (Y e ) minus yield loss due to pest damage (α n), which is given by the product of yield loss per pest (α) and post application pest density (n). Yield function (2.2) denotes yield as expected non-pest yield less damage incurred from pests surviving a pesticide (management) application. A negative exponential kill function is assumed in (2.3) to relate pre and post application pest populations. The kill function (2.3) defines post-application pest density (n) as pre-application pest density (N) exponentially declining with pesticide efficacy (B) and pest management tactic (M): n M = BNe BM < 0 (2.4) Action Threshold (AT) and Economic Injury Level (EIL) The action threshold is a break-even concept that only requires calculation of N, and management action M is only available in a given fixed

27 19 dosage/application (M^). This fixed application (M^) is usually associated with the legally permissible label rate for a pesticide. Hence, the decision is to consider profits under a no treatment scenario, M = 0, and profits under the fixed treatment scenario, M = M^, then selection of the highest profit action at varying N. With no treatment (M = 0), we see that pre and post application pest numbers are the same (N = n) and no fixed costs (F = 0) are incurred since no management action takes place. Making the appropriate substitutions in (2.1) - (2.3) the decision maker will choose to treat with M^ when profit (π) is: π(treatment) > π(no treatment) (2.5) or if P[Ye - αne -BM ] VM F > P(Ye - αn) (2.6) Rearranging this inequality, the break even point for the dichotomous treat or no treat decision is where: (TC treatment) = (Benefit of treatment - Value of Yield Saved by Treating) VM + F = PαN[1 - e -BM ] (2.7) Solving this expression for N, we derive the AT decision rule: Apply fixed dosage M^ if: N VM + * > BMˆ Pα [1 e and apply 0 at pest levels below N*. F ] (2.8) As mentioned, the AT is equivalent to the entomologist s EIL with one exception. Entomologists generally break out yield loss per pest (α) into yield loss per unit injury multiplied by injury units per pest. netheless, the AT/EIL

28 20 decision rule is basically one of applying a fixed specified management tactic when the total benefits of doing so outweigh the total costs. In practice, the AT has been the decision rule of choice since it only requires determination of existing pest numbers which in turn determine whether to apply a fixed dosage rate or postpone treatment. Economist s Economic Threshold (ET econ ) The ET econ is likewise derived from equations (2.1) - (2.3), yet allows management tactic M to vary. Hence, use of the ET econ decision rule requires field estimation of N and then calculation of an optimal management dosage M* which is then applied to the field to reach the ET econ. This is consistent with the Headley (1972) ET econ definition (Table 2-1) which is the pest population at which marginal benefits equal marginal costs. In short, the ET econ is a marginal benefitcost analysis concept whereas the AT is a total benefit-cost analysis. The ET econ is derived by making appropriate substitutions in functions (2.1) - (2.3) and maximizing with respect to management tactic M: Max π = P[Ye - αne -BM ] VM F wrt M s.t. M 0 Assuming an interior solution, first order conditions for this problem: π M = BPαNe BM V = 0 Solving for the profit maximizing management tactic M* e BM = V BPαN taking the logarithm of both sides

29 21 BM = ln V BP αn and solving, yields the profit maximizing dosage/application rate M*: ln( BPαN) lnv M* = B Solving the profit function s first order conditions yields M* which is the factor demand function for M. The decision maker calculates M* and the ET econ is the pest population remaining after applying M*. Inserting M* into kill function (2.3): n * = Ne B ln( BP α N B ) ln V = Ne ln V ln( BP α N ) = Ne ln V BP α N = = N V BP BP α V α N The ET econ is given by n* and is expressed as a post application pest population. The profit maximizing dosage rate (M*) depends on initial pest densities (N) and must be computed for each N encountered in the field. Hence, M* varies continuously with N. Given the ET econ 's n*, the operational preference for the AT decision rule (N*), or EIL, becomes clear. Under the AT or EIL, the decision maker need only calculate N and apply a fixed given pesticide/management tactic M^ if N > N*. Mumford and rton (1984), Mi (1998), and Carlson and Wetzstein (1993) have presented the AT/EIL concept in graph form. Figure 2-2 shows expected profits across pest populations under differing management tactics. The fundamental threshold

30 22 concept of tolerating some pests is very evident in Figures 2-2 and 2-3. In Figure 2-2, profits are higher under a no action scenario up to pest density N1, if pests are present in densities between N1 and N2 management tactic 1 is preferred, and densities beyond N2 would favor using tactic 2. The decision maker would obviously choose the highest net return tactic for the particular pest density encountered. Higher returns of one tactic over another at any particular pest density can be the result of differences in costs or other threshold parameters. For both N* (AT) and n* (ET econ ), thresholds invariably vary according to the following parameters: Increases with costs (VM + F) Decreases with yield price (P) Decreases with yield loss per pest (α) Decreases with pesticide efficacy (B) Profit Action Tactic 1 Tactic 2 N1 N2 Pest Numbers Figure 2-2. Action thresholds under three alternate management tactics.

31 23 Figure 2-3. Stylized population density of CRM with hypothetical ET and EIL Basing a decision rule on fixed values for these parameters can result in relatively rigid threshold measures. A more resilient procedure is to calculate thresholds under varying parameter values. Presentation of thresholds under differing parameter values (e.g., in table format) can provide the farmer greater freedom in adjusting thresholds according to anticipated market and grove conditions. Entomologist s Economic Threshold (ET entom ) The derivation framework based on Equations 2.1 to 2.3 provides a unified approach in contrasting the major threshold concepts, namely the AT/EIL and ET econ. The ET entom, however, is not embedded in this model. The ET entom used by entomologists as defined in Table 2-1, is a time safeguard to prevent a rising pest population from reaching the EIL (or AT). The ET entom is typically set below

32 24 the EIL accounting for time delays in management implementation and effectiveness. For lack of a better criterion, oftentimes the ET entom is set as a percentage (e.g., 80%) of the EIL (see Pedigo 1996, Pedigo et al. 1986). How the ET entom might lie in relation to the AT/EIL is presented in Figure 2-3. Figure 2-3 is a stylized graph of citrus rust mite population growth throughout time (adapted from Knapp 1987). The hypothetical EIL is set in accordance with total costs and benefits as defined above. The entomologist ET entom is set at a level below the EIL, perhaps 80%, and represents the time at which management action should be taken to avoid reaching the EIL. As conventionally described, the ET entom indexes the time in which to take management action. Summary This chapter emphasized three major points: (1) a description of U.S. pesticide regulation in economic terms, (2) review of CRM and Florida citrus, and (3) an examination of pest management decision rule concepts from both an entomological and economic standpoint. Despite terminology confusion and the disconnect between economists and entomologists, economic thresholds are a simple merger of economic concepts with biology. This chapter discusses how decision rules can help producers manage pests in a manner consistent with marginal private cost (MPC) and marginal benefits (MB). At the farm level, models that successfully incorporate elements of economics with biology can result in powerful decision tools. The Moffitt (1984) model presented in this chapter does a good job of associating the mainstream threshold concepts defined in Table 2-1. Given this, development and analysis of threshold decision rules in our research generally comply with the theory and methodology

33 25 presented in this chapter. More specifically, threshold parameter values are developed in Chapter 3 consistent with the AT/EIL model just outlined. Then, these parameters are assembled to formulate select CRM decision rule models in Chapter 4. Chapter 5 compares and contrasts specific model outcomes in the context of the theory presented in Chapter 2.

34 CHAPTER 3 CITRUS RUST MITE MANAGEMENT MODEL PARAMETERS The biological and plant-host relationships needed to formulate the profit, yield, and kill relationships outlined in the previous chapter are well documented in prior research. Research on CRM damage has come from Allen (1976), Allen (1978), Allen and Stamper (1979), Allen (1981), Yang et al. (1994), and Allen et al. (1994). The model presented herein relies heavily on these research works. Threshold component relationships for percent surface damage by CRM, resultant pack out (yield) losses, and mite day accumulations are taken from existing research findings. The purpose of this chapter is to present these threshold model components. These components are assembled into profit, production and kill functions in accordance with the model construct presented in Chapter 2. In the next two chapters, these model parameters are tied together to formulate various CRM decision rules and model results are presented. In the concluding chapter these threshold decision rules are compared and contrasted. Before presenting these threshold model parameters, however, it is necessary to outline CRM scouting, monitoring, and count techniques. Citrus Rust Mite Scouting and Monitoring Knapp et al. (1987) outlines proper CRM scouting techniques in the Citrus IPM manual. Scouting for mites requires the use of a hand lens with a typical magnification of at least 10X. A lens field of 1cm 2 is used to standardize the measuring surface. The Florida Citrus and Integrated Pest and Crop 26

35 27 Management Handbook (1987) should be consulted for a detailed explanation of field technique. CRM s mode of damage is time sensitive. In determining how to unitize and measure CRM damage, time must be considered for two reasons. A few mites feeding on fruit for a long period of time can produce the same amount of damage as many mites feeding for a short time. As citrus fruit matures its sensitivity to CRM damage increases. The first consideration is addressed by measuring CRM damage according to mite days one mite day is equivalent to 1 mite per cm 2 x 1 day, or 2 mites per cm 2 x ½ day, or 100 mites per cm 2 x 1/100 day From this, accumulated mite days can be calculated from the number of mites observed on two monitoring dates (M1 and M2): MD = (M1 + M2) / 2 x D where D represents the number of days between the two dates. The nature of the relationship between rust mite and citrus necessitates a metric of pest numbers across time. Albeit a labor intensive practice, the use of mite days is the most accurate CRM metric. Citrus Rust Mite Damage to Orange Fruit Citrus Rust Mite damage to fruit is unique in several ways. For instance, given the rust mite s puncture of individual cells accumulates over time; important features of proper management include consideration of mite days with respect to monitoring, which accounts for a fruit s increased sensitivity to mite damage as it matures. Allen (1976) demonstrated a relationship between rust mite

36 28 population density and percent surface damage on Valencia orange fruit. In later research, Allen et al. (1994) compiles and discusses all the necessary relationships for developing the CRM s damage parameter. Allen et al. (1994) outlines how these relationships come together to define the CRM s damage parameter in the following sequence: 1. Define the time varying relationship between percent (%) surface area damage per mite per day, (a(t) = % damage/mite/day), 2. Utilize the a(t) relationship to determine mean surface area damage by applying it to observed mite numbers over time (p(t) = percent surface damage), and 3. Define the relationship between mean surface area damage, p(t), to the share of fruit deemed acceptable for the fresh market (P o = packout). Armed with the ability to approximate CRM s effect on packout, it is possible to derive yield loss per mite day. Taken together, these relationships can be used to determine yield loss associated with accumulated mite days, which is essentially the α (damage) threshold parameter discussed in Chapter 2. Percent Damage Per Mite Per Day Allen et al. (1994) indicates that percent damage per mite day (% per mite per day) is an increasing function of fruit age. In other words, the damage rate on mature fruit in winter is higher than on young fruit in spring by about a factor of 10 (Allen et al. 1994). In plotting percent damage per mite per day against Julian time (t), Allen (1976) found a time-dependent relationship (as hypothesized) with a sigmoid curve offering the best fit against other tested functional forms (Allen, 1976):.0115 a( t) = (1 + exp( t)). (3.1)

37 alpha(t) = % damage/mite day alpha(t) = % damage/mite day julian day Figure 3-1. Damage rate vs. time of year for Valencia oranges. (Allen 1976 p. 1087) Data points used in Figure 3-1 were derived from the individual slope coefficients of estimated linear functions between mite days and percent surface damage with R-square values ranging between.90 to.99 (Allen, 1976). It is important to note that Equation (3.1) gives percent fruit surface area damaged per mite day as a function of Julian calendar day (January 1 = 1 December 31 = 365). This relationship provides the foundation on which to calculate the mean percent surface area damage (i.e., p(t)) associated with accumulated mite days. Allen et al. (1994) writes this in differential equation form as dp( t) = a( t) N( t) (3.2) dt

38 30 Where p(t) and N(t) are the mean percent surface area damage and numbers of mites feeding at time t, and a(t) is the time-varying damage rate per mite given by Equation (3.1). Inserting the a(t) relationship estimated in Equation (3.1) and writing this in integrated form we have t N( t) p( t) = dt (3.3) (1 + exp( t)) 0 as an expression for the accumulated surface area damage at time t from a time varying mite population (Allen et al., 1994, Allen, 1976). Equation (3.3) relates CRM population density to percent surface damage on Valencia orange fruit (Allen, 1976). As shown in Figure 3-1, percent russet damage per mite day increases as the season progresses. Integration of Equation 3.1 with respect to the Julian day (t) interval corresponding to each month produces the percent fruit surface damaged per mite day by month, given by: t 2 1 a m ( t) = a( t) dt. (3.4) t2 t1 t1 where a m (t) represents the percent surface russet (damage) per mite day integrated over each month. The results of carrying out this operation for each monthly interval are presented in Table 3-1 (Knapp, 1987). Instead of allowing a(t) to vary across each julian day, these values represent an operational compromise by integrating damage per mite per day over a monthly time period. This results in 12 different mite day damage coefficients for each month. Percent russet (damage) accumulates as the season progresses. These accumulating damage levels are then used to estimate fresh market pack-out

39 31 assuming a minimum acceptable level of russet. The use of discrete (monthly) damage coefficients, as presented in Table 3-1, will be compared with the use of continuous damage coefficients (Equation 3.1). The increased sensitivity of citrus to CRM damage, as the growing season progresses, is clearly evidenced in Table 3-1. As with the continuous (julian day) a(t) specification, the mean surface area damage, by month, p m (t) can be written as dp m dt ( t) = a ( t) N ( t) (3.5) m m This greatly simplifies calculation of accumulated damage by limiting the number of time periods to 12 months instead of each julian day. The third needed relationship linking mean percent surface area damage p(t) to fresh market packout loss is discussed in the next section. Table 3-1. Estimated % fruit surface area damage per mite day by month a m (t) Month Percent Fruit Surface Damage/Mite Day April May June July August September October vember December January February March Threshold Biological Parameters The CRM s primary mode of damage is to the surface layer of the fruit (peel). Consequently, reductions in the proportion of fruit acceptable for the fresh market make up the lion s share of economic loss associated with CRM.

40 32 Although the CRM has been found to affect both fruit growth and fruit drop, much of the fruit deemed unsuitable for the fresh market can nonetheless be processed. Allen and Stamper (1979) developed an approximating formula relating mean fraction of surface damage p(t) to the proportion of fruit acceptable for fresh market packout. Allen and Stamper (1979) found the distribution of mean percent surface damage to follow a modified Beta frequency distribution: P o r p( t) /1 p( t) = (3.6) where P o is pack-out and r represents some percentage level of damage deemed acceptable for the fresh market (e.g.,.05), and p(t) is the on-tree mean damage at harvest. Allen and Stamper (1979) found Equation (3.6) to approximate the proportion of fruit acceptable for fresh market packout. Expected packout loss from accumulated mite days can be calculated from the plant-host relationships presented above. More particularly, the a(t) p(t), a m (t) p m (t), and P o relationships allow calculation of yield loss per mite day, or α(t). Percent surface damage per mite day (Table 3-1) and pack-out equation 3.6 can be used to calculate percent packout loss per accumulated mite days for each month t (L m( t)): L m = (1 Po ) = 1 r pm ( t) /1 pm ( t) ( t) (3.7) Equation 3.7 relates CRM surface damage with a corresponding loss in fresh market pack-out. Armed with expected yield figures (e.g., Ye = boxes/acre), equation 3.7 can be applied directly to estimate yield loss associated with accumulated mite days for each month t:

41 33 pm ( t) /1 pm ( t) α ( t) = (1 P ) Ye = ( Lt)( Ye) = (1 r )( Y ) (3.8) m o where Ye is expected yield, α m (t) represents fresh market yield loss associated with an accumulated mite days in month t, and p m (t) represents the mean percent surface russet (damage) per mite day in month t. Equation 3.8 simply applies pack-out loss (L m( t)) to expected yield (Ye) to derive fresh market yield loss. Yield loss per unit of pest damage (α(t)) represents the core biological parameter in constructing a pest threshold model for CRM damage to fresh market citrus fruit. The model construct presented in Chapter 2 was developed from profit, production and kill functions. Given α(t), the production function becomes: Y = Y e α m (t)n(t) (3.9) The state average fruit yield (Y e ) is reported in the Budgeting Costs and Returns for Citrus Production conducted by Muraro and Oswalt on a periodic basis. A statewide yield of roughly 400 boxes (90 lbs. per box) per acre was used as a starting point for the analysis. It should be noted that the decision rule s economic parameters (price and cost) will vary across the various production regions within the state (i.e., Central Florida, Indian River, and Southwest). These data are readily available through the Budgeting Costs and Returns for e Citrus Production Series. Given α m (t) and the production function, derivation of remaining threshold parameters is straightforward. Prior to introducing economic parameters, management tactic (i.e., pesticide) efficacy must be introduced in order to specify a kill function in accordance with the theory outlined in the previous chapter. Often 100%

42 34 mortality (B) is considered a desirable property when developing management tactics (M). Data on pesticide efficacy can be obtained from field trial data in which different treatments and treatment concentrations are tested. Experiments of this sort are routinely sponsored and conducted by University of Florida researchers, pesticide manufacturers, and independent researchers. Pesticide efficacy is consistently high for most compounds registered for use on CRM. There is, however, noticeable variance in a miticide s persistence/residual kill. For instance, an insect growth regulator (IGR) such as Micromite (25wp UniRoyal) will persist longer than a more broad spectrum pesticide such as Agri-Mek. A broad spectrum pesticide s initial kill, however, is typically higher than that of an IGR. In any case, the question of efficacy becomes substantially more complex should environmental factors be considered (e.g., weather). Each model developed in Chapter 4 are tested against a set of kill assumptions. As with any forecasting effort, threshold decision rules are a hybrid between art and science. The common mantra of forecasting early and often is also true with respect to farm level pest management. Obviously, routine scouting for CRM is needed in order to assess pest numbers. The routine nature of pest scouting coupled with environmental factors affecting mite blooms support the use of a simple kill function specification. At its most basic level, a kill function of the form n(t) = (1 - B)N(t) (3.10)

43 35 shows post application pest numbers (n(t)) as pre application pest numbers (N(t)) decreasing by kill B. CRM damage must be measured in mite days. Hence fruit damage is a cumulative phenomenon and the benefits of a treatment application (B) are actually realized in the reduction of future mite days. In other words, a treatment will reduce the number of mite days that would have accumulated, which will be evident at the next scouting event. The spray decision must be made in order to limit mite days from accumulating to a level that causes economic loss to fresh packout yield returns. This inter-temporal linkage between management action and resultant pest reduction is the primary justification for more sophisticated dynamic decision models. It is important to note, however, that the decision to treat for CRM can be made in discrete decision periods. A discrete decision rule would seek to prevent the value of yield losses from exceeding control costs for the current monitoring period. Threshold Economic Parameters Data needed for empirical estimation of CRM threshold decision rules come from a variety of sources. Utilizing the nomenclature presented in Chapter 2, threshold decision rules consist of economic parameters (P, V, F) and biological parameters (α, B). The core biological relationships were developed above with the derivation of α(t). The production (3.9) and kill functions (3.10) introduced above will be incorporated into a profit function after developing the economic parameters of treatment cost and price. Price The future price of citrus is the best early season barometer for the producer when calculating thresholds. Future price is uncertain to the grower,

44 36 but any determination of economic thresholds also depends on estimation of yield value. Consistent with objectives, thresholds will be calculated and reported for varying P levels. An appropriate gauge for selecting a suitable range is past years averages plus/minus some deviation. Accordingly, Table 3-2 shows 20 seasons of on-tree prices for Florida Oranges. Orange prices are used since the biological relationships based on Allen s work were derived utilizing oranges. Table 3-2. Florida orange on-tree price per box for 20 seasons Dollars per 90 lb. box ($) Season Early and Midseason Valencia Total Fresh Processed Fresh Processed Fresh Processed Mean (20 Seasons) Standard Deviation (20 Seasons) Mean (Last 10 Seasons) Standard Deviation (Last 10 Seasons) Last 10 Season Fresh Premium (Pf-Pp) Season Fresh Premium (Pf-Pp) Output prices for both processed and fresh markets are presented in Table 3-2. Since the focus of this research is on CRM s damage to the surface (rind) layer of the orange, a critical assumption of this research is that the grower is

45 37 pursuing cultural practices for the fresh market, but the processed market remains an alternative. Browning (1992) offers an assessment of critical factors in determining fruit marketability. Browning (1992) said Success in a fresh fruit grove is to maximize the packout and minimize the fruit going to juice (Browning 1992). This functional definition of success for a fresh fruit grove represents the underlying objective of the decision rules developed in this research. A thorough discussion of the grower s decision on a spray/cultural program is outlined by Muraro (1992). Figure 3-2 is adapted from Muraro (1992) and summarizes the grower s decision sequence for fruit allocation. Two sequential decisions must be made regarding production objectives. The first decision (decision node 1), is made at the beginning of the production season. It is at this point where a grower establishes production targets for either the fresh or processed markets and this pre-season decision will influence cultural costs. From a pest management perspective, the fresh market requires more attention given the concern for external fruit quality. It is for this reason, that this research assumes the grower has decided to pursue the fresh market at decision node 1. The anticipated path through the Figure 3-1 decision tree has been bolded. The second critical decision (decision node 2) occurs at harvest when the grower must evaluate the effectiveness of his first decision. Given the assumption to pursue the fresh market at node 1, it is now necessary to assess whether to continue with the fresh market or send fruit into the processed market. Muraro (1992 p. 29) summarized:

46 38 Fresh Fresh Process (eliminations) Fresh Process Process Process Process Process Decision de 1 Begin Cultural Program Decision de 2 Harvest Packing or Processing Time Figure 3-2. Grower fruit allocation decision tree At this time, the fruit characteristics, yield, prices, and costs are less uncertain. The objective now is to maximize returns by comparing the fresh and processed returns. Indeed, the variables mentioned by Muraro (1992) represent the components of an economic threshold decision rule. In essence, the CRM is treated as a pest of fresh market citrus in this research. Should CRM damage exceed acceptable levels for the fresh market, the grower can then decide at harvest (decision node 2) to divert fruit into the processed market. The goal of developing CRM thresholds is to effectively avoid this diversion and to continue along the fresh fruit path beyond decision node 2. For this reason, the differential between fresh and processed market price is

47 39 used to determine economic thresholds. More specifically, the price parameter for CRM thresholds is given by P = (P f P p ) - E c (3.11) Expression 3.11 is the fresh market price premium (P f P p ) less an elimination charge (E c ) associated with pursuit of the bolded path through the (Figure 3-1) decision tree. Hence the decision to treat for CRM is based around the real per unit return associated with the fresh market. Costs Spray costs for CRM vary according to product, dosage and whether additional treatments are included in the spray. Economic thresholds developed in Chapter 2 require determination of an optimal dosage rate, which is then applied in the field. This profit maximizing dosage rate yields a post-application pest threshold below a level that causes economic damage. There are several problems with this method when applied to CRM management. First, there is little opportunity to vary dosage rates to match pest infestation levels. Set dosage rates are mandated through label restrictions, except for the flexibility to use a dose lower than the label rate. Management tactic costs consist of application and material costs. Per acre costs of alternate miticide spray programs are readily available. The Budgeting Costs and Returns for Citrus Production reports published annually by the Institute of Food and Agricultural Sciences (IFAS) are the source of these data.

48 40 Given these decision rule components, it is now possible to more explicitly assemble the profit, production and mortality functions from which CRM economic thresholds can be derived: π = PY VM F (3.12) Y = Y e α(t) N(t) (3.13) n(t) = (1 - B)N(t) (3.14) Where pm ( t) /1 pm ( t) α ( t) = (1 P ) Ye = ( L( t))( Ye) = (1 r )( Y ) (3.15) m o P = (P f P p ) - E c (3.16) Consistent with theory outlined in Chapter 2, these relationships underlie the construct of the decision rules developed in Chapter 4. More particularly, these relationships are used to develop both static and dynamic decision rules in the next chapter. Decision rule performance and results are compared to prescriptive non-empirical decision rules already in practice in Chapter 5. e

49 CHAPTER 4 THRESHOLD DECISION RULE CONSTRUCT Threshold decision rules for the management of CRM in Florida Citrus are presented in this chapter. Five different decision rule models are assembled in this chapter. The models utilize the relationships and parameters outlined in the preceding chapter consistent with the profit, production, and mortality functions introduced in Chapter 2 and calibrated in Chapter 3. Prior to introducing the decision rules, it is necessary to model how mite days typically accumulate throughout a growing season. The pest threshold decision rules developed in this chapter will be examined and compared against this set of typical mite day bloom scenarios in Chapter 5. Mite Day Accumulation Damage to the surface layer of fruit accumulates with mite days during the growing season. Citrus fruit targeted for the fresh market is most vulnerable to CRM damage. A long growing season (10 or even 12 months), which culminates at harvest, produces a great deal of uncertainty for the grower. The decision to treat CRM is driven by anticipated revenues and costs. As is the case with many farm level decisions, the grower is faced with imperfect information in determining the benefits (i.e., increased revenues) of a spray decision. There does exist, however, some uniformity in the timing of CRM population cycles. As depicted in Figure 2-3, CRM populations typically peak in June-July with a less severe secondary peak occurring in vember-december. 41

50 42 Allen (1976) found that a sigmoid curve accurately approximates mite day accumulations based on empirical field data. Five sigmoid curves estimated by Allen (1976) are used to test the threshold models developed here. More precisely, a sigmoid curve is given by CRM k = a bt (4.1) (1 + e ) where t represents Julian day (January 1 = 1 December 31 = 365). The constants for these sigmoid curves are presented in Table 4-1. Table 4-1. Sigmoid mite day curves Curve ID k a b Peak A Mid June B Late July C Mid December D Early July E Early July Together, these functions provide a range of typical mite bloom scenarios. These functions are mapped and presented in Figure 4-1. The proliferation of mite numbers on a daily basis is depicted in Figure 4-2. The population peaks outlined in Table 4-1 become apparent in Figure 4-2. This figure helps illustrate the important fact that CRM populations bloom, but then naturally subside within a seasonal cycle.

51 43 Cumulative Mite Day Functions C um u lative M ite D ay s Calender Day 14-Jan 28-Jan 11-Feb 25-Feb 11-M ar 25-M ar 8-Apr 22-Apr 6-M ay 20-May 3-Jun 17-Jun 1-Jul 15-Jul 29-Jul 12-Aug 26-Aug 9-Sep 23-Sep 7-Oct 21-Oct 4-v 18-v 2-Dec 16-Dec 30-Dec Date Figure 4-1. Cumulative mite day functions B E D A C A B C D E Mites Per Day E A B C D E C 0 Calender Day 15-Jan 30-Jan 14-Feb 1-Mar 16-Mar 31-Mar 15-Apr 30-Apr 15-May 30-May 14-Jun 29-Jun 14-Jul 29-Jul 13-Aug 28-Aug 12-Sep 27-Sep 12-Oct 27-Oct 11-v 26-v 11-Dec 26-Dec Date Figure 4-2. Daily mite day functions

52 44 In general, CRM populations bloom in May-July and then declines in late summer (around August). There is a smaller secondary bloom which occurs later in the year (Function C) that is typically less dense than the summer bloom. Threshold Models Various decision rules can be constructed utilizing the profit, production and mortality/kill functions presented in Chapter 3. Five models are developed and/or tested against one another: 1. Prescriptive threshold measure. This decision rule is from the IFAS Citrus Rust Mite Fact Sheet (ENY-619) by Knapp (1994). The following excerpt is taken from this bulletin: Fruit grown for the fresh fruit market should not exceed five percent average surface area damage by citrus rust mites. If fruit is to be grown for the fresh market, the following monitoring and spray application guidelines should be followed: a. The post bloom Melanose spray can be delayed, in most years, until late April or early May. A material for controlling citrus rust mites should be added at this time in addition to foliar nutritional if necessary. b. A treatment to control greasy spot is applied in June or July. A material to control citrus rust mite is added at this time. c. Grove monitoring for citrus rust mites should begin as soon as fruit is evident in the grove. This monitoring should be repeated every two weeks (From J.L. Knapp Citrus Rust Mite, IFAS Fact Sheet ENY- 619). Although this recommendation is not an explicit decision rule, it nonetheless provides guidance on when to treat for CRM. This recommendation calls for a treatment to occur in late April - early May, and then in June or July. Subsequent spray decisions are based on findings from bi-weekly monitoring and the recommendation to keep surface damage below 5%. Although this Fact Sheet has been updated on the IFAS Extension s Electronic Data Information Source

53 45 (EDIS) website (accessed in Dec. 2004) ( it still remains a viable treatment alternative for purposes of comparison. 2. Action threshold based on observed mite numbers. This decision rule is from the 2004 Florida Citrus Pest Management Guide (Childers et al. 2004). The following excerpt is taken from the 2004 Florida Citrus Pest Management Guide: Rust Mites, Spider Mites, and Other Phytophagous Mites (Childers et al. 2004): Processed fruit: Initiate rust mite monitoring for PCRM in early April on leaves and fruit through casual observations and continue every 2-3 weeks throughout the fruit season. CRM will tend to develop later in the spring or summer. Select trees at random and within uniformly distributed areas throughout a acre block representing a single variety with uniform horticultural practices. Avoid sampling adjacent trees. Fruit should be sampled at random representing the four quadrants of the tree and taken midway in the canopy (between interior and exterior). One fruit surface area should be examined midway between the sun and shade areas. The number of rust mites per cm 2 should be recorded and averaged for the 10 acres, represented by 20 trees with four fruit per tree or 80 readings per 10 acres. Six rust mites/cm 2 would be a planning threshold where pesticide intervention may be required within days. Ten rust mites/ cm 2 would be an action threshold where treatment would be required as soon as possible. Fresh fruit: Similar to above except monitor every days with an average of 2 CRM/cm 2 as an action threshold (From 2004 Florida Citrus Pest Management Guide, 2004). The above represents the most recent management advice from IFAS regarding CRM management. The most notable attribute of this advice concerns metrics. More specifically, the action threshold for fresh fruit is considered 2 CRM/cm 2. This represents an evident break from the more complex practice of considering mite days. Hence, a grower need only keep track of average number of CRMs observed per cm 2, without needing to calculate mite days that have accrued since the last monitoring date. 3. Action Threshold with Discrete (Monthly) Damage Coefficients. This decision rule utilizes the discrete damage coefficients presented in Table 3-1. This rule is an action threshold in accordance with the theory

54 46 outlined in Chapter 2. Using monthly damage coefficients does simplify the decision rule since a grove manager need not calculate yield loss per mite day (α(t)) for every julian calendar date. Fruit surface area damage per mite day (a(t)) is integrated over each monthly period to yield a m (t) as presented in Chapter 3. In other words, α(t) (yield loss per a single mite day) remains constant over a monthly interval. Where.0115 a( t) = (1 + exp( t)) and a m 1 ( t) = t2 t1 More precisely, the decision rule is given by: t 2 t1 a( t) dt SprayCost N = = Pα t B [( Pf m( ) VM+ F pm ( t)/(1 pm ( t) P ) E ][( 1 r ) Y ] B p c e (4.2) α m (t) is held constant each month consistent with Table 3-1 values and integrating over a single mite day for that month. Unlike the prescriptive threshold and mite number thresholds introduced above, this threshold requires a grove manager to calculate mite days. 4. Action Threshold with Continuous Damage Coefficients. This decision rule utilizes a continuous damage coefficient (α(t)). The specification for this rule is identical to above, except α(t) is treated as a continuous function: SprayCost VM + F N = = (4.3) p( t) /(1 p( t) Pα( t) B [( Pf Pp ) Ec ][(1 r ) Ye ] B This threshold more accurately represents the time sensitivity of CRM damage. The mean surface damage per mite day (p(t)), however, is considered a continuous variable that is not as readily applied as the Table 3-1 monthly values. 5. Decision Tree (Dynamic) Threshold. A complete decision tree model was developed for deciding when to treat CRMs throughout a growing season. A binary decision tree (BDT) model is developed which expresses the alternative actions (i.e., treatment or no treatment) available to a grower

55 47 during periods of CRM population growth. A thorough discussion of BDT analysis can be found in most Operations Research textbooks, such as Hillier and Lieberman (1986). A BDT diagram consists of nodes and branches. A node rectangle represents the decision to be made at each time interval. Typically, a BDT is read from left to right with nodes classified as either interior or leaf nodes, depending on whether they produce a child node or terminate the tree. At each terminal leaf node, the BDT s objective function value is derived according to the decision path followed through the tree. The basic building block decision in the model is whether or not to treat for CRM. A series of tolls are paid along each branch of the tree. More specifically, each dichotomous yes/no decision incurs the following tolls or costs: If Yes (Spray): Pay spray costs plus lost revenues associated with fresh fruit packout losses due to incurred CRM damage. If (Don t Spray): Pay lost revenues associated with fresh fruit packout losses due to incurred CRM damage. Of course, fresh fruit packout losses decline with spray treatments. More precisely, the optimal path through the BDT is a cost minimization problem given by: Min 5 t= 1 { Sx t + [(1 4 t= 1 B x t t 1 ) N ] PA } where t t (4.4) x t = 0 Treatment (Don t Spray), and x t = 1 Treatment (Spray) S represents treatment costs and X t represents the dichotomous (i.e., 0, 1) decision variable for the yes/no spray decision. A more elaborate kill function that considers residual kill effects across time is specified by the B parameters. Packout losses usually become smaller when spray(s) occur. Consequently, the decision rule is based on whether or not the value of salvaged fresh yield exceeds the additional cost of spraying. A decision to treat reduces the accrual of mite days and results in a reduction of packout losses. At the

56 48 onset, the apparent strength of this approach is recognition of the temporal linkages between decisions throughout a growing season. Another benefit associated with BDT analysis is that it provides a diagram (visual) representation of choices. While a BDT can be specified mathematically, the diagram representation is arguably more intuitive to field practitioners (i.e., growers). The five decision rules: 1. Prescriptive Threshold Measure, 2. Action Threshold Based on Observed Mite Numbers, 3. Action Threshold with Discrete Damage Coefficients, 4. Action Threshold with Continuous Damage Coefficients, and 5. Decision Tree Threshold introduced above were carefully selected consistent with study objectives. It is recognized, however, that many other sampling and treatment methods are used in the field. It is common for growers to settle into seasonal management routines after observing reoccurring trends throughout the years. The five rules presented above are listed in order of their relative application difficulty. The first rule is general treatment advice recommending the first CRM spray to occur in late April or early May. This was an IFAS Extension recommendation throughout the 1990s (Citrus Rust Mite Fact Sheet (ENY-619) 1994). The second decision rule is from the 2004 Citrus Pest Management Guide. This rule is an action threshold based on the average number of mites observed pursuant to a random sampling method. This threshold s measurement of pest damage units according to pest numbers, rather than days, is an apparent break from the previous work of Allen (1976, 1978, 1979, and 1981). An action threshold of 2 CRM/cm 2 can be converted to mite days with the conversion

57 49 formula presented in Chapter 3. Assuming the two week period begins with no mite activity (M1 = 0) and culminates at the action threshold of 2 CRM/ cm 2 (M2 = 2), mite days are given by the following: M1+ M MD = ( )# Days = ( )14 = Although other derivations could be produced, 14 mite days is the most plausible given bi-weekly monitoring and the fact the first monitoring day observed no mites. The third and fourth thresholds are action thresholds derived from the Moffitt model presented in Chapter 2. The distinction between threshold models M3 and M4 is in their treatment of pest damage units, where model 3 uses a monthly table value and model 4 treats damage units continuously. Finally, threshold. 5 is a binary decision tree model that utilizes the relationships derived in the previous chapter within a diagrammed decision tree framework. Each model is generally outlined in Table 4-2. Models 1 through 4 represent general treatment advice (M1), a direct action threshold (M2), and action thresholds based on theory outlined in Chapter 2 (M3 and M4). Before comparing model outcomes, the binary decision tree model (M5) needs to be explained in greater detail.

58 50 Table 4-2. CRM threshold models Threshold Model. Specification M1 First Treatment - late April or early May Prescriptive Threshold Measure A treatment to control greasy spot is applied in June or July. A material to control citrus rust mite is added at this time. M2 Action threshold Based on Observed Mite Numbers M3 Action Threshold with Discrete (Monthly) Damage Coefficients M4 Action Threshold with Continuous Damage Coefficients M5 Binary Decision Tree (Dynamic) Threshold Action Threshold = Treat when average of 2 CRM/cm 2 SprayCost VM+ F N= = P α p ( t) B [( P P) E][( 1 r m f p c ) Y B m ( t)/( 1 pm( t)) e] SprayCost VM+ F N= = p( t)/(1 p( t)) Pα ( t) B [( Pf Pp ) Ec ][( 1 r ) Ye ] B Cost minimization BDT problem given by: Min 5 t= 1 { Sx t + [(1 4 t= 1 B x t t 1 ) N ] PA } where t t x t = 0 Treatment (Don t Spray), and x t = 1 Treatment (Spray) A series of interconnected Yes/ spray decisions. Each dichotomous yes/no decision incurs the following tolls or costs: If Yes (Spray): Pay spray costs plus lost revenues associated with fresh fruit packout losses due to incurred CRM damage. If (Don t Spray): Pay lost revenues associated with fresh fruit packout losses due to incurred CRM damage. Decision Tree Model Model 5 A binary decision tree model was constructed utilizing DPL 4.0 software by Applied Decision Analysis LLC. The decision tree has five stages consistent with recommendations for bi-weekly monitoring and the likelihood of fresh programmed fruit to receive up to five sprays (Browning, 1992). The decision tree is diagrammed in Figure 4-3.

59 51 The optimal paths through the Figure 4-3 decision tree are provided in the Appendix. Each stage (decision node) represents a Yes/ spray decision. The decision tree reads from left to right as the growing season progresses. Each branch of the tree is assigned a pay expression. As depicted, the pay expression is shown on each branch. It is important to note that a one stage lag exists between a yes decision and the spray s effect on successive mite day counts. Hence a yes decision results in an immediate toll of spray costs, but the resultant reduction in mites is not realized until the next stage. The objective function is to find the least cost path through the tree. Mite days accumulate at each stage in accord with mite day functions A - E. After a spray occurs, mite days that would have accumulated are reduced over a 6-week period, as follows: 90% reduction after two weeks, 80% reduction after four weeks, 60% reduction after six weeks, and 4 This mortality function is given by B x t t t= 1 1 within the BDT s model specification, equation 4.3. This more explicit treatment of pesticide persistence is an obvious strength of the decision tree model. Each pay expression is dependent on whether a spray treatment occurs. The central trade-off within the tree is whether the value of salvaged fresh packout yield from a spray treatment warrants its associated costs. The optimal path through the tree is a cost minimization problem with tolls being exacted for fresh packout yield losses and spray costs.

60 52 stage1 stage2 PS2 Yes SC+(1-PO_stage1)*P*Y stage2 (1-PO_stage1)*P*Y stage3 PS2 PS4 Yes SC+(1-PO_stage2_PS2)*P*Y stage3 PS4 (1-PO_stage2_PS2)*P*Y Yes stage3 PS2 Yes SC+(1-PO_stage2)*P*Y Yes stage5 PS2 PS4 PS6 PS8 Yes Yes SC+(1-PO_stage5_PS2_PS4_PS6_PS8)*P*Y stage4 PS2 PS4 PS6 SC+(1-PO_stage4_PS2_PS4_PS6)*P*Y Yes (1-PO_stage5_PS2_PS4_PS6_PS8)*P*Y stage5 PS4 PS6 PS8 Yes SC+(1-PO_stage3_PS2_PS4)*P*Y SC+(1-PO_stage5_PS4_PS6_PS8)*P*Y (1-PO_stage4_PS2_PS4_PS6)*P*Y (1-PO_stage5_PS4_PS6_PS8)*P*Y stage5 PS2 PS6 PS8 Yes Yes SC+(1-PO_stage5_PS2_PS6_PS8)*P*Y stage4 PS4 PS6 SC+(1-PO_stage4_PS4_PS6)*P*Y (1-PO_stage5_PS2_PS6_PS8)*P*Y (1-PO_stage3_PS2_PS4)*P*Y stage5 PS6 PS8 Yes SC+(1-PO_stage5_PS6_PS8)*P*Y (1-PO_stage4_PS4_PS6)*P*Y stage5 PS2 PS4 PS8 Yes (1-PO_stage5_PS6_PS8)*P*Y Yes SC+(1-PO_stage5_PS2_PS4_PS8)*P*Y stage4 PS2 PS6 SC+(1-PO_stage4_PS2_PS6)*P*Y Yes (1-PO_stage5_PS2_PS4_PS8)*P*Y stage5 PS4 PS8 Yes SC+(1-PO_stage3_PS4)*P*Y SC+(1-PO_stage5_PS4_PS8)*P*Y (1-PO_stage4_PS2_PS6)*P*Y (1-PO_stage5_PS4_PS8)*P*Y stage5 PS2 PS8 Yes Yes SC+(1-PO_stage5_PS2_PS8)*P*Y SC+(1-PO_stage4_PS6)*P*Y stage4 PS6 (1-PO_stage5_PS2_PS8)*P*Y stage5 PS8 Yes (1-PO_stage3_PS4)*P*Y SC+(1-PO_stage5_PS8)*P*Y (1-PO_stage4_PS6)*P*Y (1-PO_stage5_PS8)*P*Y stage5 PS2 PS4 PS6 Yes Yes SC+(1-PO_stage5_PS2_PS4_PS6)*P*Y SC+(1-PO_stage4_PS2_PS4)*P*Y stage4 PS2 PS4 (1-PO_stage5_PS2_PS4_PS6)*P*Y stage5 PS4 PS6 Yes SC+(1-PO_stage5_PS4_PS6)*P*Y SC+(1-PO_stage3_PS2)*P*Y (1-PO_stage4_PS2_PS4)*P*Y (1-PO_stage5_PS4_PS6)*P*Y stage5 PS2 PS6 Yes stage4 PS4 Yes SC+(1-PO_stage4_PS4)*P*Y SC+(1-PO_stage5_PS2_PS6)*P*Y (1-PO_stage5_PS2_PS6)*P*Y stage5 PS6 Yes (1-PO_stage3_PS2)*P*Y (1-PO_stage4_PS4)*P*Y SC+(1-PO_stage5_PS6)*P*Y stage5 PS2 PS4 Yes (1-PO_stage5_PS6)*P*Y Yes SC+(1-PO_stage4_PS2)*P*Y SC+(1-PO_stage5_PS2_PS4)*P*Y (1-PO_stage5_PS2_PS4)*P*Y stage4 PS2 stage5 PS4 Yes SC+(1-PO_stage3)*P*Y (1-PO_stage4_PS2)*P*Y SC+(1-PO_stage5_PS4)*P*Y (1-PO_stage5_PS4)*P*Y stage3 (1-PO_stage2)*P*Y stage4 (1-PO_stage3)*P*Y Yes stage5 PS2 SC+(1-PO_stage4)*P*Y stage5 (1-PO_stage4)*P*Y Yes Yes SC+(1-PO_stage5_PS2)*P*Y (1-PO_stage5_PS2)*P*Y SC+(1-PO_stage5)*P*Y (1-PO_stage5)*P*Y Figure 4-3. CRM treatment binary decision tree M5

61 53 The decision of timing (i.e., stage length) is dictated by extension recommendations on monitoring frequency. In short, bi-weekly monitoring is recommended for fresh programmed fruit. Given this, a stage is set to begin on either the 1 st or 15 th of each month. Since each stage actually represents when the treatment decision is made, accumulated mite days are assessed the day prior. At least one mite day must be accumulated before the cycle is allowed to begin and the cycle is set to include the peak period of mite growth. The five stage decision tree model is run one time for the summer bloom (Curves A, B, D & E) and one time for the secondary winter bloom (Curve C). This chapter focused on the introduction and construction of five decision rule models dealing with management of Citrus Rust Mite on Florida citrus. The relative performance of these models is discussed in the next chapter.

62 CHAPTER 5 RESULTS The economic management of citrus rust mite (CRM) requires explicit consideration of plant-host relationships. Prior chapters discussed both entomological and economic aspects of the Florida citrus CRM relationship. These relationships are introduced and incorporated into five (5) different decision rules in Chapter 4. The focus of this chapter is to test the hypothesized trade off between model rigor and ease of use by comparing these select decision rules. This comparative analysis is made within the context of the unique attributes of the CRM s plant-host relationship. In this comparative analysis, the central performance measure is treatment timing and its effect on grove level returns. Results The five threshold models described in Chapter 4 vary a great deal from an operational perspective. At this juncture, it is important to stress that models M1-M5, as developed, are deterministic models with no stochastic considerations. Furthermore, each of these models is tested against a set of mite day functions that are also deterministic (i.e., mite day functions A-E). Although field level pest management decisions have stochastic elements, these considerations do not detract from the objectives of this research to develop CRM treatment decision rules. 54

63 55 Prior to assessing each model, it is helpful to reintroduce the mite day functions presented in Chapter 4. Mite day functions A-E are presented in tabular form in Table 5-1. Table 5-1 values commence in April consistent with a typical growing season. As generally discussed in the previous chapter, there is utility in viewing mite day accumulation both incrementally and in a cumulative fashion. Table 5-1. Mite day functions A-E: incremental and cumulative mite days Curve A A B B C C D D E E Month Increm Cumul Increm Cumul Increm Cumul Increm Cumul Increm Cumul 1-Apr Apr May May Jun Jun Jul Jul Aug Aug Sep Sep Oct Oct v v Dec Dec Jan Jan Feb Feb Mar Mar Totals (k values) tes: 1. Highlighting indicates date range tested with M5. 2. Increm = Incremental MDs up to specified date 3. Cumul = Cumulative MDs up to specified date. Source: Allen, 1976.

64 56 Table 5-1 s presentation of mite day accumulation on the 1 st and 15 th of each month is consistent with extension recommendations on monitoring frequency, the use of a monthly damage parameter α m (t), and model M5 s decision stages. This chapter will comparatively analyze decision rules against Table 5-1 mite day functions A-E. Specifically, decision rule models are comparatively analyzed with respect to treatment timing and returns associated with minimization of packout losses (i.e., profit maximization). Treatment Timing For purposes of comparing models M1-M5, it becomes necessary to identify suitable metrics. Timing of the first spray decision represents a direct and low biased metric for comparing model outcomes. This is so given the first spray decision is not influenced by what has gone on before. In other words, the influence of previous spray decisions and the resultant kill/residual effects are not present in the first decision period. Hence, advice for the season s first treatment date is not affected by spray treatments that may have occurred earlier. Using the baseline set of parameter values developed in Chapter 3, first application date results for the five threshold models are presented in Table 5-2. The baseline parameter values utilized in the analysis are: Ye=400, P=$1.78, B=.90, Spray costs=$65/acre. Expected yield (Ye=400 boxes/acre) is the statewide bearing acreage yield from the Florida Agricultural Statistics, Citrus Summary, Price (P=$1.78) is the average premium for fresh utilization over processed utilization for all Florida oranges over the 20-year period extending from to Spray costs ($65/acre) is derived from the University of Florida s Budgeting and Returns for Citrus Production report data

65 57 for miticide treatments. These values are outlined in the second column, and are from the sources outlined in the previous chapter. In accordance with the threshold decision rule models developed in Chapters 2 and 3, application date is directly dependent on parameter values for expected yield, price, kill, and spray costs. For purposes of a comparative analysis, these deterministic values serve little value other than providing each model a baseline set of parameters based on experience. The relative application timing of each model is the focus of Table 5-2. Table 5-2. First application day Modeled Mite Day Function A* Relative Peak Early Summer B* Relative Peak Late Summer C* Relative Peak Late Season D* Relative Peak Mid-Summer E* Relative Peak Mid-Summer Model s First Application Date (Ye= 400, P=$1.78, B=.90, (M1-M4) Spray Costs = $65/acre) Model 1 - late April, early May Model 2 - May 14 Model 3 - June 9 Model 4 - June 8 Model 5 - June 1 Model 1 - late April, early May Model 2 - July 1 Model 3 - July 24 Model 4 - July 21 Model 5 - July 1 Model 1 - NA Model 2 - v. 2 Model 3 - v. 27 Model 4 - v 24 Model 5 - v 15 Model 1 - late April, early May Model 2 - May 7 Model 3 - June 30 Model 4 - June 25 Model 5 - June 15 Model 1 - late April, early May Model 2 - April 20 Model 3 - June 18 Model 4 - June 15 Model 5 - June 1 * Source: Allen, 1976

66 58 In terms of first application date, the non-specific time bracket of the prescriptive threshold M1 coincides with M2 results for mite day functions A, D and E. M1 s recommendation to treat in late April or early May is premature when a mite bloom occurs in late summer (mite function B). In short, the prescriptive threshold (M1) is more closely aligned with M2 results than the remaining three models in that it dictates early treatment recommendations. For all five mite bloom scenarios A - E, the action threshold of M2 results in the earliest specific application date. M3 and M4 treatment dates all lie within one week of one another for all five mite day functions. Figures 5-1 and 5-2 provide a graphical treatment of M2, M3 and M4. The discrete monthly damage coefficients of M3 result in a step function with close correspondence to M4 s continuous damage parameter. M2 s very low threshold is better depicted in Figure 5-1 where the graph is magnified to show detail. First Treatment Date 5000 E 4000 A M4 A Cumulative Mite Days D B C D E M3 M Jan 8-Jan 15-Jan 22-Jan 29-Jan 5-Feb 12-Feb 19-Feb 26-Feb 5-Mar 12-Mar 19-Mar 26-Mar 2-Apr 9-Apr 16-Apr 23-Apr 30-Apr 7-May 14-May 21-May 28-May 4-Jun 11-Jun 18-Jun 25-Jun 2-Jul 9-Jul 16-Jul 23-Jul 30-Jul 6-Aug 13-Aug 20-Aug 27-Aug 3-Sep 10-Sep 17-Sep 24-Sep 1-Oct 8-Oct 15-Oct 22-Oct 29-Oct 5-v 12-v 19-v 26-v 3-Dec 10-Dec 17-Dec 24-Dec 31-Dec B C Date Figure 5-1. First application date and cumulative mite day functions A-E for threshold M2, M3, and M4.

67 59 First Treatment Date A E D Jan 8-Jan 15-Jan 22-Jan 29-Jan 5-Feb 12-Feb 19-Feb 26-Feb 5-Mar 12-Mar 19-Mar 26-Mar 2-Apr 9-Apr 16-Apr 23-Apr 30-Apr 7-May 14-May 21-May 28-May 4-Jun 11-Jun 18-Jun 25-Jun 2-Jul 9-Jul 16-Jul 23-Jul 30-Jul 6-Aug 13-Aug 20-Aug 27-Aug 3-Sep 10-Sep 17-Sep 24-Sep 1-Oct 8-Oct 15-Oct 22-Oct 29-Oct 5-v 12-v 19-v 26-v 3-Dec 10-Dec 17-Dec 24-Dec 31-Dec Cumulative Mite Days B M4 A B C D E M3 M2 C Date Figure 5-2. First application date and cumulative mite day functions A-E for threshold M2, M3, and M4 (Zoomed for detail) It is important to note that Figures 5-1 and 5-2 do not depict any resultant reduction in mite days subsequent to the first spray. It is interesting to note that the decision tree model M5 produced earlier treatment date recommendations than M3 and M4, yet later than M2. More specifically, the five threshold decision models performed in the same rank order across all five mite day functions A-E (Table 5-1) for first application date, except for mite day function B where M2 and M5 both recommend treatment on July 1. Table 5-3. Model rank according to first treatment date Rank 1- Earliest treatment date M2 Action threshold based on observed mite numbers Rank 2 M5 Decision Tree (Dynamic) Threshold Rank 3 M4 Action Threshold with Continuous Damage Coefficients Rank 4 - Latest treatment date M3 Action Threshold with Discrete (Monthly) Damage Coefficients

68 60 With the exception of M2 s simple construct, Table 5-3 reveals that the more complex threshold models produced earlier treatment recommendations. Before assigning any weight to this assertion, it is prudent to question whether this observation has any economic significance. In regard to comparing model outcomes, what are the benefits and costs of delaying or expediting a spray/treatment decision? It is apparent that spray/treatment decisions are economical within the context of the five mite day functions (A-E) used herein. As mentioned earlier, these mite day functions do represent typical mite bloom scenarios. Moreover, in all cases, we see that each model requires spray treatments. Threshold Models M1-M5 Economic Performance The economic performance of the respective models reduces to questions of treatment timing and frequency. Additionally, scouting (informational) costs of the respective models must also be considered. From this perspective, CRM decision rules should consider the following points: Whether application timing has the effect of influencing the total number of spray applications throughout the entire growing season - thereby affecting total management costs, Whether the decision rules result in any significant differences in fresh market packout - thereby affecting total revenue, Consideration of atypical mite bloom scenarios that may warrant much earlier or later treatments compared to the typical seasonal cycle, and Full consideration of the scouting (informational) costs associated with the decision rule. With the exception of M4, each of the models is analyzed with respect to total number of applications and total fruit revenue. Particular attention is given

69 61 to comparing the action threshold of M3 to the binary decision tree model of M5. The prescription-based threshold of M1 and the static mite number action threshold of M2 do not fully consider the range of parameters developed in Chapters 2 and 3. There are several reasons for isolating M3 and M5 for comparison. First, as described in Chapter 4, M5 s stage length is dictated by extension recommendations based upon bi-weekly monitoring. Given this, a stage is set to begin on either the 1 st or 15 th of each month, as shown in Table 5-1. Second, considering this practical decision stage length, plus the close correspondence between M3 and M4, it is not practical to field examine mite day accumulation on a daily basis consistent with M4. Finally, the goal of the comparison is to identify differences at a coarse level in effort to identify substantial differences. Given this objective, the less specific advice of M1 and M2 is also compared against the full decision rule models of M3 and M5. M1, M2, M3 and M5 are tested against mite day curves A-E as assembled in Table 5-1. Results from this comparison are shown in Table 5-4. The decision to spray for CRM is depicted by a table entry within Table 5-4. M1 s general treatment advice was assigned to May 1 and June 15. When M3 recommends a spray treatment that falls in between the 1 st and 15 th of the month, the spray was assigned to the earlier date for purposes of depicting results. For instance, as shown in Table 5-2, M3 s first spray date of June 9 was assigned to June 1 for curve A in Table 5-4.

70 Table 5-4. Economic performance of models M1, M2, M3 and M5 utilizing baseline parameters (Ye= 400, P=$1.78, and Spray Costs = $65/acre) Curve A (summer) B (summer) C (winter) D (summer) E (summer) Date M1 M2 M3 M5 M1 M2 M3 M5 M1 M2 M3 M5 M1 M2 M3 M5 M1 M2 M3 M5 1-Apr 15-Apr 1-May M1 M1 M1 M1 15-May M2 1-Jun M2 M3 M5 M2 M5 15-Jun M1 M2 M3 M5 M1 M1 M2 M3 M5 M1 M2 M3 M5 1-Jul M2 M2 M5 M2 M3 M5 M2 M3 M5 15-Jul M2 M2 M3 M2 M3 M5 M2 M3 1-Aug M2 M5 M2 M2 15-Aug M2 1-Sep 15-Sep 1-Oct 15-Oct 1-v 15-v M2 M3 M5 1-Dec M2 M3 M5 15-Dec M2 M3 M5 1-Jan M2 15-Jan M2 1-Feb 15-Feb 1-Mar 15-Mar Per Acre Costs & Revenues Total Costs (Packout Losses plus Spray Costs) $355 $367 $213 $215 $324 $218 $131 $188 NA $385 $269 $256 $362 $375 $265 $258 $579 $401 $306 $242 Net Return $357 $345 $499 $497 $388 $494 $581 $524 NA $327 $443 $456 $350 $337 $447 $454 $133 $311 $406 $470 Best Performer M3 M5 M3 M5 M5 M5 Source: Allen,

71 63 At the outset, it is necessary to qualify the results presented in Table 5-4. Typically, 2 to 4 miticide treatments are sufficient to achieve CRM control in a growing season. The seemingly excessive number of treatments presented in Table 5-4 (i.e., 4 to 6 treatments) seems out-of-line with common practice. The reason for this is that the models tested herein do not account for the exceptional residual control of today s miticides. In addition, it is important to recognize that our models were constructed with an underlying goal of maximizing fresh market packout by maintaining surface area damage levels below 5%. This goal necessarily assures a maximum level of protection against CRM damage. netheless, given the objective of examining each model s economic performance in a comparative manner, these considerations detract little from the analysis. By design, M1 and M2 perform in an identical manner for all tested mite growth curves. M1 s recommendation to treat in late April or early May appears to be premature for all mite curves. The early treatment advice of M1, however, may be prudent should a pesticide s residual control be exceptional (e.g., 90- days). The back-to-back spray recommendations proffered by M2 for all mite curves is based around preventing mite days from surpassing 14 days in any given period as developed in Chapter 4. For all tested mite curves A-E, a posttreatment kill of 90% is not sufficient to keep 14 mite days from accumulating, which leads to M2 s recommendations. Once again, exceptional residual control of a pesticide may substantially increase the efficiency of M2 by eliminating the

72 64 need for back-to-back treatments. For these reasons, M1 and M2 are not focal points in the comparative analysis. As tested, M3 and M5 recommend the same treatment regime for mite curves A, C and D. The difference in net returns associated with curves C and D are largely driven by the precise date of spray and how each model addresses CRM mortality after a spray treatment. The most noteworthy result occurs with mite curve B and E. In each of these cases, M5 recommends a much earlier treatment date. In the case of curve B, this earlier treatment advice results in less return. The highest differential in net returns, however, occurs with the large CRM bloom of curve E. Here, M5 s earlier treatment advice yields a much higher net return than M3. The profit differential between M3 and M5 almost meets the $65 spray costs for mite curve E. At each stage, M5 levies costs for spray applications and packout losses. CRM population blooms lend themselves to examining the spray decision in a discrete manner. A spray should not occur in any one decision period if it is not economic. Under the baseline assumptions presented in Table 5-2, M2-M5 each recommend one to five spray applications during the summer season blooms represented by curves A, B, D and E. These results are not inconsistent with the prescriptive threshold advice proffered by M1. M3 and M5 recommend two spay applications for mite curve A and three spray applications for mite curve D. As discussed previously, the increased sensitivity of fruit in the later season leads to three spray applications for winter bloom function C pursuant to M3 and M5. The results for M3 and M5 suggest, however, that in certain summer CRM blooms

73 65 there may exist benefits in postponing a spray (curve B), or costs in postponing a spray (curve E). These results need further research but do contradict M1 s recommendation to apply a first application in late April/early May and a second spray in June or July (in combination with a greasy spot treatment). In mite bloom curves A, C, and D similar treatment advice suggests that cost differences are not extreme. Furthermore, M3 and M5 recommend three spray applications in response to the secondary late season bloom (mite function C) largely due to the increased sensitivity of fruit in late season. Given the tested scenarios, the most likely cost difference between the models exists where a mite bloom is very large (Curve E) and when a prescriptive threshold (M1) or pest number threshold (M2) is used in cases where a bloom occurs later in the summer. In a late summer bloom scenario, it may be possible to delay the first spray application recommended by M1 and M2 so as to reduce the total number of applications in a growing season. This difference is especially prevalent for M1 s prescriptive treatment advice. The question of an earlier than expected bloom is not fully vetted here, recognizing the five mite bloom scenarios used to test the models. A full comparative examination of revenue impacts is complicated due to limitations in modeling pest kill. As mentioned, one strength of the decision tree model (M5) is a fuller specification of the kill function since linkages between decision stages are explicitly considered. As mentioned, exceptional residual control will likely reduce the profit differential between the models. Nevertheless, yield loss per mite day, parameter α m (t), implicitly accounts for a minimum

74 66 acceptable level of russet in its construct. It was demonstrated in Chapter 3 that packout (P o ) was defined according to a modified beta distribution (see equation 3.4). While M2-M4 do not lend themselves to direct examination of end season packout, the damage parameter construct of M3 and M4 insures that surface layer damage will be kept below aesthetic damage levels. Regarding model sensitivity to various pest bloom scenarios, atypical mite bloom scenarios can also be examined as a question of timing. Atypical timing may occur in at least two different ways. The first case is when an anticipated bloom occurs later or earlier than expected (Curve B). Although curve B is less intense than the other tested summer blooms, the increased sensitivity of fruit in later summer influenced M5 s two spray recommendation. It is also interesting to note that both M3 and M5 recommend two spray treatments for curve A despite being an early season bloom. This can be explained by curve A s rapid rate of growth which requires two treatments despite its occurrence when fruit is less susceptible. The effect of a seasonal bloom that occurs later than expected is addressed elsewhere. Unfortunately, the mite day curves utilized in this research did not allow for testing of earlier than expected mite bloom scenarios. The second atypical scenario can occur when mite days accumulate at an aberrant rate. For instance, we see that curves D and E accumulate mite days at a much slower pace in the initial months than curves A, B and C. When the rate of growth is slow in early season, M2 will likely lead to earlier than warranted treatment given it is based around observed mite numbers (2 CRM/cm 2 ). The economic significance of this possibility is ultimately dependent on whether this

75 67 earlier than expected treatment leads to additional application(s) throughout the course of the season. This is indeed the case given the simple kill specification used to produce Table 5-4 results. Should the residual kill of a pesticide be exceptional, early treatment advice will likely prove economical. In all cases, it is important to be cognizant of the natural decline in CRM populations. It is important to emphasize that only one late season bloom was tested (Curve C) and that the increased sensitivity of fruit was the primary reason for M3 and M5 recommending three spray applications. Of course, these observations are directly influenced by the baseline parameter set used to test the models. netheless, the fully specified decision rules of M3 and M5 performed in a relatively close range of one another in most cases. Moreover, the direct cost of spray treatment would necessarily be equivalent when the same numbers of applications are applied. Hence, the loss differential between M3 and M5 for curves A, C, D and E are due solely to packout differences. The economies of scale associated with piggy-backing treatments onto one another (e.g., combine with greasy spot spray) are an important consideration, but are not addressed in this study. Moreover, the simple kill specification is also recognized as a shortcoming of the decision models developed herein. Given the close margin between M3 and M5 model performance in most cases, some good insight can be gained in assessing the use of each model with respect to information costs. Grove management and pest scouting are costly activities. As with any other economic activity, pest scouting should occur as long as its marginal benefit MB exceeds its marginal costs MC. The familiar

76 68 graph presented in Figure 5-3 suggests the grove manager will continue to scout up to point S*. $/Scouting Unit MC information MB information Scouting Units S* Figure 5-3. Optimal scouting effort Figure 5-3 indicates that a grove manager should scout and manage for pests until marginal benefits equal marginal cost. In the grove, additional management is costly and there is little certainty that each increment of scouting will prove economic. The rational grove manager should increase scouting efforts when the fresh market premium is high and when the opportunity costs of scouting are relatively low. Recognizing the proximity of each model s outcome, grower preference for simpler threshold decision rules may be explainable from an information cost perspective. Moreover, should residual control of a pesticide span the typical length of a CRM bloom (i.e., 90-days+), early treatment advice may be prudent.

77 69 The purpose of this chapter is to assemble, present and offer comment on select decision models designed to help a grower determine if and when a treatment for citrus rust mites should occur. Two decision models, (M1 and M2), are obtained directly from extension recommendations. The three remaining models are derived from the three equations (i.e., profit, production, mortality) framework introduced in Chapters 2 and 3. The next chapter provides major observations, implications and recommendations from this research.

78 CHAPTER 6 CONCLUSIONS, LIMITATIONS, AND RECOMMEDATIONS Data and findings presented in the preceding chapters dealt with development of economic threshold decision rules for grove level management of CRM in Florida citrus. A theoretical construct was introduced and used as a benchmark for the development and comparison of five different decision rules. As with most pest management scenarios, CRM management advice varies in many respects. This variance in management advice is reflected in the range of decision rules tested within this research. Threshold decision rules in the form of general prescriptive advice (M1), action thresholds based on pest numbers (M2) and mite days (M3, M4), as well as a binary decision tree model (M5) were all developed within this research. Perhaps the most important application of this research is its assimilation of data regarding CRM management. The biological relationships needed for the decision models came primarily from Allen (1976), Allen (1978), Allen and Stamper (1979), Allen (1981), Yang et al. (1994), and Allen et al. (1994). The greatest contribution of this research was incorporation of these biological relationships into a decision model framework. The hallmark characteristic of the threshold concept is the merging of biological relationships into an actionable model for use on the front-line by producers. This research demonstrates that the relatively complex plant-host relationships between citrus and the citrus rust 70

79 71 mite can be integrated into decision rules (e.g., M3, M4 and M5) for use by producers. In many respects, this research reinforces previous IPM research concerning the use of decision rules in determining when a pesticide application is warranted. That is, it recognizes that management input should be gauged and applied in a manner than maximizes profits subject to constraints. Furthermore, the nature of CRM s mode of economic damage and its particular effects on fresh market produce are unique attributes addressed in this analysis. The aesthetic nature of CRM damage and the time sensitivity of fruit damage were addressed in three of the decision rules (i.e., M3, M4, and M5) through incorporating Allen s (1976) russet damage relationships. In addressing these characteristics, this research illustrated the importance of the plant-host relationship when formulating decision rules to guide pest management. An intricate physiological relationship between plant and host implies that a sophisticated decision rule is needed. This logic is only reinforced by the IPM goal of making simultaneous decisions for many pests. A primary objective of this research was to examine this assertion for a particular plant pest scenario. Before summarizing findings regarding the presumed trade-off between decision rule efficiency and ease of use, it is helpful to re-state the general context under which decision rules are currently developed. As noted in Chapter 2, entomologists and economists often have different starting point goals when constructing pest management decision rules. As described by Moffitt (1984), the economist strives for a theoretically correct rule based on marginal analysis.

80 72 Within the Moffitt (1984) framework, the economist s economic threshold requires a simultaneous determination of pesticide dosage level depending on pest density. This approach necessarily assumes pesticide dosage can be incremented to a profit maximizing rate depending on pest infestation levels. The practicality of incrementing pesticide dosage is restricted by pesticide regulation except for lower than label doses. For this reason, this research assumed that a fixed label-rate dosage was the only avenue available to the grower. This assumption translates into a constant spray cost per treatment. On the other hand, the entomologist typically stresses operational aspects of a decision rule. As presented in Chapter 2, the entomologist defines an economic threshold as the pest population density at which control measures should be initiated to prevent an increasing pest population from reaching the Economic Injury Level - EIL (Stern et al. 1959, & others). Action thresholds (M3, M4) developed herein roughly coincides with the entomologist s economic injury level (EIL). Given this, it is recognized that the treatment recommendations of Models 3-5 (i.e., M3-M5) do not include a safeguard planning time period consistent with the entomologist economic threshold (ET entom ) introduced in Chapter 2 (Pedigo 1996). In other words, treatment time recommendations of M3-M5 assume that a spray treatment can be applied immediately, and that kill will occur upon application. Recognizing this will take time, the operational utility of the entomologist paradigm becomes apparent. Further refinement and research is needed to incorporate this planning time period in a decision rule s theoretical construct. This research developed various decision rule models for

81 73 management of citrus rust mites in Florida fresh market citrus. Models 3-5 are consistent with the model construct for the action threshold (AT) and Economic Injury Level (EIL) discussed in Chapter 2. The treatment recommendations developed herein are evaluated against the sigmoid mite day functions developed by Allen (1976). These five sigmoid curves (Table 4-1) possess unique characteristics that can provide insight into decision rule performance. A sigmoid curve depicts mite populations as increasing exponentially, but instead of continuing unchecked, the growth rate reaches a maximum and then decreases to zero. The point at which the growth rate changes from increasing to decreasing is the inflection point. The point of inflection is localized approximately at half the cumulative total number of mite days or at k/2. The inflection point and rate of change are immediately observable in the graphs of daily mite day propagation for functions A-E (Figure 4-2). The cumulative and daily depictions of mite day functions A-E are analogous to a cumulative distribution function (CDF) and probability density function (PDF), respectively. In summary, threshold decision rules are built around the acknowledgement that when pest numbers are low, management costs will exceed benefits. As pest numbers increase beyond some threshold level, benefits will exceed costs. The mite day functions used in this research all followed a typical seasonal pattern where CRM numbers increase in the summer and winter. The seasonal certainty of CRM population blooms supports the utilization of prescriptive thresholds (e.g., M1), especially if the residual control of pesticides is high. The

82 74 simple prescriptive decision rule of M1 will not perform grossly out of line with the more complex models of M3, M4, and M5 if the summer CRM bloom begins in late April to early May. M1 may result in non-optimal treatments, however, when mite days accumulate more slowly or rapidly since the advice is static. Hence, the additional scout and information costs associated with more complex decision rules are certainly warranted when uncertainties exist regarding the target market outlet (i.e., fresh versus processed) and in cases where mite blooms may be more unpredictable. CRM management is further complicated by the pest s natural life cycle. Pest management decisions should recognize the natural decline in population that occurs with a pest bloom. Treatment decisions that fully account for pest life cycle should help conserve management resources, yet also results in additional informational costs. Life cycle issues and temporal carryover effects have both been used in support of developing dynamic thresholds that account for future effects. The decision tree model (M5) fulfills these requirements. The decision models provide interesting insight into the comparison of mite day rates of growth versus levels of growth. Mite day function A stands out among the other functions due to its high rate of change (i.e., steepness) in mite days. Mite curve A required two back-to-back summer treatments pursuant to both M3 and M5 despite being an early season bloom. Mite curve E produced the most divergent results with M5 outperforming M3, with increased profits of $64 an acre (over M3). This differential is due to the earlier treatment advice proffered by M5. However, mite curve B shows that earlier treatment advice is

83 75 not always optimal. For curve B, M3 outperformed M5 through postponing the spray one decision period. While mite curve C required three treatments, this is largely due to the increased sensitivity of later season fruit (i.e., a higher α m (t)), rather than the steepness of the growth curve. Given mite curve E actually possesses a higher cumulative number of mite days (i.e., higher k value) than mite curve A suggests that rate of growth is an important factor when making a treatment decision. This observation is important, however, field use of thresholds is made ex ante by trying to predict future values. netheless, this finding underscores the importance of recognizing both the level and rate of mite growth when scouting. The use of a decision tree model (M5) was a unique characteristic of this study. A decision tree modeling framework is able to capture dynamic aspects of pest management decisions while at the same time retaining some level of intuitive appeal to growers. The ability to diagram optimal policy trees depending on infestation levels is appealing. The model presented herein, however, needs further refinement and calibration before reaching a level of practical field use. netheless, this research is a starting point for extending this method. The focus of this research on the fresh market can be critiqued on many levels. The margin between fresh and processed fruit prices is used in the models to assess premium losses. The CRM s damage to the surface layer of fruit seldom affects suitability to process fruit. Hence the models were developed around the price differential (i.e., premium) associated with the fresh market outlet. Browning (1992) outlines the potential need for five sprays in a fresh

84 76 cultural program. Under the baseline assumptions and mite curves utilized in this research, the decision tree model (M5) found five CRM spray treatments were warranted for Mite Curve combinations A+C and B+C. Six spray treatments were found to be needed for all other summer-winter Mite Curve combinations (i.e., D+C, E+C). table differences between M3 and M5 recommendations came primarily from the relatively large mite bloom situation of curve E. Considering these results, the utilization of more sophisticated decision rules can be evaluated with respect to grower risk preference and information costs. This investigation demonstrated that the most powerful tool in pest management is a thorough understanding of pest populations. For CRM management, a firm understanding of seasonal pest dynamics lays a general foundation in support of developing a routine prescriptive treatment regime. This research suggests that within a prescribed seasonal CRM treatment program, a modest scouting program that can adjust prescribed treatments in recognition of mite levels and rates of growth may perform in-line with more complex rules. Further research is needed to more thoroughly delineate an economically defensible CRM decision rule. A fuller specification of pesticide efficacy, especially residual control, is a critical first need in extending our research. Findings of this research also reinforce the conclusion that future analysis should better focus on predicting pest population dynamics, prices, and biological control effects. A more thorough treatment of these factors will enable the grove manager to more precisely answer the question of when to spray? Moreover, remote sensing technology has progressed to a level that may allow the addition

85 77 of a spatial dimension to the problem. Further research and development into adding this spatial element to the decision rule framework may enable the grove manager to more precisely answer the question of Where to spray? While additional research is warranted, producer adoption of decision rules will largely depend on implementation costs and practicality of use. The many economic and biological factors involved in the management of pests render empirical modeling intricate and complex. One outcome of such modeling attempts is the recognition that farm experience (i.e., standard operating procedure) possesses informational value. Indeed, the informational value of collective solutions have been shown to be optimal, especially in cases where individual agents may find the problem difficult (Suroweicki 2004). Efforts to better assimilate and share farm level pest management experience is a continued need that underscores the importance of basic extension work.

86 APPENDIX OPTIMAL PATHS FOR M5 BDT

87 Curve A Stage 1 = May 15 Stage 2 = June 1 Stage 3 = June 15 Stage 4 = July 1 Stage 5 = July 15 Yes stage2_ps2 [ ] stage1 [ ] stage2 [ ] Yes stage3_ps2 [ ] Yes stage4_ps2_ps4 [ ] stage4_ps4 [ ] stage5_ps2_ps4_ps6 Yes [ ] stage5_ps4_ps6 [ ] Yes [ ] [ ] stage3 [ ] Curve B Stage 1 = July 1 Stage 2 = July 15 Stage 3 = August 1 Stage 4 = August 15 Stage 5 = September 1 stage1 [ ] Yes stage2_ps2 [ ] stage2 [ ] Yes stage3_ps2_ps4 [ ] stage3_ps4 [ ] Yes stage4_ps2_ps6 [ ] stage4_ps6 [ ] stage5_ps2_ps4_ps8 Yes [ ] stage5_ps4_ps8 [ ] Yes [ ] [ ]

88 80 Curve C Stage 1 = vember 15 Stage 2 = December 1 Stage 3 = December 15 Stage 4 = January 1 Stage 5 = January 15 stage1 [ ] Yes stage2_ps2 [ ] stage2 [ ] Yes stage3_ps2_ps4 [ ] stage3_ps4 [ ] stage4_ps2_ps4_ps6 Yes [ ] stage4_ps4_ps6 [ ] stage5_ps2_ps4_ps6_ps8 Yes [ ] stage5_ps4_ps6_ps8 [ ] Yes [ ] [ ] Curve D Stage 1 = June 15 Stage 2 = July 1 Stage 3 = July 15 Stage 4 = August 1 Stage 5 = August 15 stage1 [ ] Yes stage2_ps2 [ ] stage2 [ ] Yes stage3_ps2_ps4 [ ] stage3_ps4 [ ] stage4_ps2_ps4_ps6 Yes [ ] stage4_ps4_ps6 [ ] stage5_ps2_ps4_ps6_ps8 Yes [ ] stage5_ps4_ps6_ps8 [ ] Yes [ ] [ ]

89 81 Curve E Stage 1 = June 1 Stage 2 = June 15 Stage 3 = July 1 Stage 4 = July 15 Stage 5 = August 1 stage1 [ ] Yes stage2_ps2 [ ] stage2 [ ] Yes stage3_ps2_ps4 [ ] stage3_ps4 [ ] stage4_ps2_ps4_ps6 Yes [ ] stage4_ps4_ps6 [ ] stage5_ps2_ps4_ps6_ps8 Yes [ ] stage5_ps4_ps6_ps8 [ ] Yes [ ] [ ]

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94 BIOGRAPHICAL SKETCH Tom Tomerlin is a Florida Native. He holds a bachelor's degree from the University of Florida (in food and resource economics) and a Master of Science degree from Clemson University (Clemson, S.C) in agricultural and applied economics. He has held a number of positions throughout the state of Florida in the fields of economics, urban planning, environmental sciences, and biology. Recently, he has been involved with the economic study of sustainable land development in Florida. 86