ECONOMICALLY OPTIMAL MANAGEMENT OF HUANGLONGBING...

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ECONOMICALLY OPTIMAL MANAGEMENT OF HUANGLONGBING IN FLORIDA CITRUS

By

ABDUL WAHAB SALIFU

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

2013

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© 2013 Abdul Wahab Salifu

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To Mma Memunatu, M’pa’a Abiba, M’bihi Nasara mini Tehsuma

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ACKNOWLEDGMENTS

All thanks and praises are due to God. On this note I would like to first

acknowledge that this research was supported by the Citrus Initiative Grant.

I wish to express my heart-felt appreciation and gratitude to the chair of my

committee, Dr. Thomas Spreen, for his role as a professional father throughout my

career as a Ph.D. student. I especially want to thank him for offering me this research

opportunity in spite of my shortcomings in recognizing his generosity from the onset of

my Ph.D. career.

I also wish to extend my deepest gratitude to my advisory committee: Dr. Jerome

Hogsette, Dr. Kelly Grogan, Dr. Fritz Roka, and Dr. Diego Valderrama. I have been very

fortunate to have their expertise available to me. Their kindness is very much

appreciated. Dr. Grogan has been especially instrumental in the model development for

this research, and I am so grateful to her and Dr. Roka for the timely intervention in

sourcing for the much needed funding for the completion of this research and degree.

I would like to acknowledge Drs. Eunice Bonsi, Conrad Bonsi, and Robert

Zabawa for providing me the opportunity to pursue my master’s degree at Tuskegee

University in 2007. I would also like to acknowledge Dr. Nii Tackie for his guidance at

some point in my master’s student career.

The collective and individual contributions and support of all my class mates,

FRED and UF staff and faculty, and the entire gator nation towards this noble

achievement is herein acknowledged and much appreciated. Long live the spirit of the

gator nation. I especially wish to thank Jessica Herman for all the administrative support

and encouragement I got from her at FRED.

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I am also very blessed to have a superb family. To my wife, Abiba Wumbei, who

is selfless in supporting me and our two equally gracious daughters, Thalma and Thaida

Wahab. I am most gracious to my mom, Memunatu Sumani, whom, in spite of her

illiteracy insisted and ensured that I get circular education. May God bless her for me.

My late dad, Salifu Alidu has also been equally inspirational and supportive to me

throughout his life, may God have mercy on his soul.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF TABLES ............................................................................................................ 8

LIST OF FIGURES ........................................................................................................ 10

ABSTRACT ................................................................................................................... 11

CHAPTER

1 INTRODUCTION .................................................................................................... 13

Background ............................................................................................................. 13 Problem Statement ................................................................................................. 14

Strategies of Control ............................................................................................... 16 Objectives ............................................................................................................... 20 Scope of Research ................................................................................................. 20

2 LITERATURE REVIEW .......................................................................................... 22

HLB Disease Incidence, Latency, and Spread ........................................................ 22

The Impact of HLB .................................................................................................. 25

HLB Control ............................................................................................................ 26

Social Consequences of HLB Persistence .............................................................. 29 Effects of HLB on Yield and Cost of Production ...................................................... 30 Economics of Disease Control Strategies ............................................................... 33

Bioeconomic Models of Disease Control (with Incorporated Discount Rates) ........ 36

3 BIOECONOMIC ESTIMATION ............................................................................... 38

Optimal Investment Theory ..................................................................................... 38 Overview .......................................................................................................... 38 Optimal Capital Investment Model .................................................................... 39

The Economic Model .............................................................................................. 40

The Biological Model............................................................................................... 40

4 MODEL RESULTS ................................................................................................. 44

Model Estimation Assumptions ............................................................................... 44

Empirical Results of Model ............................................................................... 45 Conclusions ...................................................................................................... 49

5 SENSITIVITY ANALYSIS ....................................................................................... 63

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The Effects of a Price Decline ................................................................................. 63

The Effects of a Price Increase ............................................................................... 64 The Effects of a Lower Annual Rate of Spread ....................................................... 65

The Effects of an Increased Annual Rate of Spread ............................................... 66 The Effects of a Lowered Latency Period ............................................................... 67

6 CONCLUSIONS, RECOMMENDATIONS AND LIMITATIONS .............................. 86

LIST OF REFERENCES ............................................................................................... 90

BIOGRAPHICAL SKETCH ............................................................................................ 99

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LIST OF TABLES

Table page 4-1 Baseline Parameter Values ................................................................................ 50

4-2 Non-Valencia Orange Yield Estimated Boxes per Tree, by Age Group in Florida, 2004-2005 through 2008-2009 .............................................................. 51

4-3 NPV1 for Strategy 1 (Do Nothing) ....................................................................... 52

4-4 NPV1 for Strategy 2 (Symptomatic Tree Removal) ............................................. 53

4-5 NPV1 for Strategy 3 (Enhanced Foliar Nutritional Program) ............................... 54

4-6 NPV1 for the Three Strategies for Age Classes 0 and 3 ..................................... 55

4-7 NPV1 for the Three Strategies for Age Classes 6 and 10 ................................... 56

4-8 NPV1 for the Three Strategies for Age Classes 14 and 17 ................................. 57

4-9 NPV1 for the Three Strategies for Age Classes 0 and 3 at Different Yield Penalty2 Levels for Strategy 3 ............................................................................ 58



5-1 NPV1 for the Three Strategies for Age Classes 0 and 3 from a Price Decline2 ... 69

5-2 NPV1 for the Three Strategies for Age Classes 6 and 10 from a Price Decline2 .............................................................................................................. 70

5-3 NPV1 for the Three Strategies for Age Classes 14 and 17 from a Price Decline2 .............................................................................................................. 71

5-4 NPV1 for the Three Strategies for Age Classes 0 and 3 from a Price Increase2 ............................................................................................................ 72



5-7 NPV1 for the Three Strategies for Age Classes 0 and 3 from a Decline in Beta2 ................................................................................................................... 75

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5-10 NPV1 for the Three Strategies for Age Classes 0 and 3 from an Increase in Beta2 ................................................................................................................... 78



5-13 NPV1 for the Three Strategies for Age Classes 0 and 3 from a Lowered Latency Period2 .................................................................................................. 81

5-14 NPV1 for the Three Strategies for Age Classes 6 and 10 from a Lowered Latency Period2 .................................................................................................. 82

5-15 NPV1 for the Three Strategies for Age Classes 14 and 17 from a Shortened Latency Period2 .................................................................................................. 83

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LIST OF FIGURES

Figure page 4-1 Net Present Value per Acre as a Function of Disease Incidence and Average

Age (Years) of Trees at First Detection with Contour Lines for the Do Nothing Strategy .............................................................................................................. 61

4-2 Net Present Value per Acre as a Function of Disease Incidence and Average Age (Years) of Trees at First Detection with Contour Lines for Strategy 2 ......... 61

4-3 Net Present Value per Acre as a Function of Disease Incidence and Average Age (Years) of Trees at First Detection with Contour Lines for Strategy 3 (30% Yield Penalty) ............................................................................................ 62

4-4 Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age (Price = $1.50/pound solid, 30% yield penalty for strategy 3) ........... 62

5-1 Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age from a Change in Price: Top Subplot is Baseline, Middle and Bottom Subplots Shows Price Decline (from $1.50 to $1.20) and Increase (from $1.50 to $1.80), respectively ..................................................................... 84

5-2 Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age from a Change in Beta: Top Subplot is Baseline, Middle and Bottom Subplots Shows Beta Decline and Increase, respectively ...................... 84

5-3 Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age from a Change in Latency: Top Subplot is Baseline, Bottom Subplot Shows Decline in Latency from 1 year to 6 Months for Groves with Average Age of 0 and 3 while the Latency for Groves 6 Years or Larger Remain at 2 Years .............................................................................................. 85

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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

ECONOMICALLY OPTIMAL MANAGEMENT OF HUANGLONGBING IN FLORIDA

CITRUS

By

Abdul Wahab Salifu

May 2013

Chair: Thomas H. Spreen Major: Food and Resource Economics

Following the declaration of the endemic status of Huanglongbing (HLB) in

Florida in 2005 with no formal control policy for the disease, it is natural that an

empirical examination and justification of the management protocols implemented at the

farm-level to control HLB be made. We develop farm level decision rules to judge when

it is economically justified to implement a particular control strategy. Models are

developed that allow economic assessment of each strategy and determine the

scenarios for which each strategy is optimal or yield a positive net present value,

considering average grove age at first detection, and rates of infection at first detection.

Our results justify the heterogeneous decisions of growers regarding their choice among

control strategies, in a way that optimizes each grower’s utility. As hypothesized, the

superiority of either strategy depends upon the level of infection at the time when the

disease is first found in a particular block, the rate of spread of the disease, the average

age of the grove at first infection, expectations of future fruit prices, and the latency

period. Our research identifies important efficacy targets that must be achieved for the

long-term economic viability of a citrus grove. Our results provide a recommendation of

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the optimal control strategy for a given set of conditions such as the age of the planting

and initial rate of infection.

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CHAPTER 1 INTRODUCTION

Background

Huanglongbing (HLB) is a bacterial disease that affects all varieties of citrus. It is

commonly referred to as citrus greening. HLB was first discovered in Florida in 2005

and is now found in all counties where commercial citrus is produced (Manjunath et al.

2008). It is spread by a small leaf-feeding insect, the Asiatic citrus psyllid (ACP). The

ACP was first found in June 1998 in Delray Beach, and it is noted for its short-range

maneuverability and long range drift by wind, which facilitates its ability to spread HLB

far and wide. HLB acts to disrupt the phloem of the tree thereby limiting its ability to

uptake nutrients. Initially this leads to yellowing of leaves, promotion of premature fruit

drop, and production of small, misshapen fruit that contain bitter juice with no economic

value. As the disease spreads through the tree, the amount of usable fruit produced

diminishes until eventually the tree is of no economic value (Brlansky et al. 2011).

Worldwide, three different bacteria are known to cause HLB: Candidatus

Liberibacter asiaticus (LAS), Candidatus Liberibacter africanus (LAF), and Candidatus

Liberibacter americanus (LAM). The most prevalent of these is LAS, which is found

worldwide, including the United States. Asiatic HLB is caused by LAS, and it is

transmitted by the Asian citrus psyllid (ACP), Diaphorina citri. While LAM is found to be

prevalent in Brazil and China, the African HLB caused by LAF, can be found in Africa,

Saudi Arabia, and the South Asia, and is spread by its vector, the African citrus psyllid

(Trioza erytreae) (Gottwald 2010).

HLB is the single most vicious and debilitating citrus disease responsible for the

destruction of almost 100 million trees in major citrus growing areas of the world where

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the disease has become endemic (Aubert et al. 1985, Bové 1986). This is partly due to

its elusiveness to various regionally specific management prescriptions. At the present

time, the only known way to effectively combat the disease is through early detection

and a strict eradication program of infected trees. The standard control strategy adopted

by HLB affected regions of the world is an integrated control program that involves

psyllid control, symptomatic tree removal, restricted movement of citrus propagation

materials, and distribution of disease-free seedlings and budwood (Gottwald et al. 2012,

Aubert 1990).

Problem Statement

Florida is the leading citrus-producing state in the United States, with nearly

600,000 acres devoted to commercial production. HLB poses as the most serious

obstacle faced by the state’s $9.3 billion citrus industry (National Research Council

2010), which supports almost 80,000 jobs. In its eight-year presence in Florida, it is

estimated that over 10 million of the 60 million orange trees are currently infected with

HLB (Irey et al. 2011), and $1.3 billion in citrus revenue have been lost (Hodges and

Spreen 2012; Bolton 2012). To appreciate the devastating impact of HLB on Florida

citrus, it is said to cause far worse tree damage than citrus canker, which was

responsible for the destruction of over 4 million trees. Tree removal due to HLB infection

has resulted in the reduction of approximately 10 percent of Florida’s commercial citrus

production, and a 40 percent increase in production costs (Irey et al. 2008). HLB has

already been implicated for loss in land acres allocated to citrus in the state since 2006,

and soaring grower costs in terms of tree eradication, psyllid control, inspections, and

replanting costs (TBO 2008). Hodges and Spreen (2012) estimated that within the last

five years, Florida has lost 8,257 jobs, total revenue of $4.541 billion comprised of

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indirect revenue of $2.717 billion, due to HLB. A more important longer-term

consequence has been the fact that HLB has created huge uncertainty among Florida

citrus growers with respect to future investment/planting.

HLB is a disease with two important characteristics. First, the rate of spread is

strongly affected by tree age because psyllids prefer new growth (Brlansky et al. 2008).

Young trees, which are more vigorous as compared to mature trees, produce more

flushes and thereby are more susceptible to psyllid feeding and disease transmission. In

the case of mature trees, the disease spreads more slowly (Gottwald 2010).

Consequently, an infected mature tree is capable of producing usable fruit for several

years while at the same time serving as a source of infection for other healthy trees.

Other factors that affect the rate of spread of HLB are the ACP population and initial

level of infection at first find of the disease. The density of the ACP population is the

single most important factor because theoretically, if the ACP population is reduced to

zero, spread of HLB will stop with immediate effect. Second, control through tree

eradication is complicated by a latency period between the time a tree first becomes

infected and when it expresses visual symptoms. Once a mature tree is infected, it may

not begin to exhibit symptoms of the disease for up to two years (Gottwald 2010). If the

rate of infection in a particular grove is relatively high at the time the disease is first

discovered, a policy of eradication of symptomatic trees may result in destruction of the

entire grove.

Just a few months after the discovery of HLB in Florida, the citrus canker

eradication program was terminated following the sweeping spread of canker over most

southern Florida groves by a series of hurricanes that blew over the citrus belt in 2004

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and 2005. Later in 2005, an interdisciplinary team of USDA HLB experts declared HLB

endemic to Florida, with no chances of eradication (Gottwald and Dixon, 2006). So far, it

is even more troubling to note that neither the citrus industry nor the state or USDA has

put in place a clear cut and decisive procedure for control of HLB, unlike in the case of

the aborted citrus canker control program.

Strategies of Control

At this time, there are three distinct strategies being employed to deal with

greening. Strategy 1, referred to as “do nothing”, allows the disease to spread and takes

no measures to slow its spread including controlling psyllid populations or mitigating

HLB’s impact on tree health. Strategy 1 has no effect on per acre costs as management

tactics are not modified. Per acre revenues, however, are gradually affected as the

disease spreads and the number of healthy fruit that can be harvested and utilized

gradually declines. At some point, per acre revenues will not cover per acre grove

maintenance costs and at that point, the grove is no longer economically viable. The

disease spreads faster in younger groves, so younger groves cease to be economically

viable at a faster rate compared to an older grove with the same initial level of infection.

Strategy 2 follows the standard plant pathology disease control model and is the

only internationally accepted control strategy for HLB (Aubert 1990). Under Strategy 2,

an aggressive psyllid control program is also put into place to suppress psyllid

populations. In addition, between four and twelve inspections are conducted annually to

identify symptomatic trees. Once found, symptomatic trees are immediately eradicated

(Brlansky et al. 2008). The logic behind Strategy 2 is that by eradicating symptomatic

trees, the level of inoculum in a particular citrus grove gradually will be reduced.

Eventually the incidence of the disease will be reduced to a point where it can be

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economically tolerated. Muraro (2010) has estimated that in Florida, Strategy 2

increased pesticides costs by about $450 per acre. Overall production cost have

increased from $800 (2004, pre HLB) to $1,500 (2009, post HLB + canker). There are

five problems associated with Strategy 2. First, plant pathologists have yet to

characterize the key parameters that would significantly define the timeline by which to

control HLB through eradication of symptomatic trees. These parameters include a

controllable base level of HLB infection, the number of years it would take to achieve

that base level, and the probability that young tree resets will survive to productive

maturity. Second, the latency period of the disease implies that not all diseased trees

will be removed in a timely manner, and these asymptomatic trees will serve as a

reservoir of the disease inoculum. Third, if a grove is already at a high level of known

infection and given that more trees are infected but not yet symptomatic, it may not be

possible to effectively reduce inoculum levels in a particular grove without eradicating

the entire grove. The probability of this outcome is related to the age of the grove and

the level of infection when the first positive tree is found. Fourth, eradication or

suppression of the disease to a tolerable level in one grove may not be possible if

neighboring growers are not adequately suppressing the disease in their groves.

Neighboring groves will serve as sources of the inoculum, and the disease may be

continually re-introduced into the groves of the grower following Strategy 2. Fifth, relying

on visual detection of HLB-infected trees by scouting is estimated to be about 50%–

60% effective in finding all the symptomatic trees in a single survey (Futch et al. 2009;

Spann et al. 2010). One other factor that also impacts the effectiveness of this strategy

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is the neighbor’s HLB management behavior. If psyllid control or tree removal is not

coordinated with neighbors of a grove, inoculum builds up in the local vicinity.

Strategy 3 is an approach first developed in southwest Florida and is, in part, a

response to the Achilles heel of Strategy 2, namely if Strategy 2 is initiated too late, the

entire grove may be eradicated before the disease can be suppressed. While an initial

high rate of disease incidence is one possible motivation to adopt Strategy 3, it is also

possible that under some conditions, Strategy 3 may yield a higher return than Strategy

2 even though Strategy 2 could successfully reduce HLB inoculums to a manageable

level. Strategy 3 proposes to treat the symptoms of HLB through foliar application of

micro and macro nutrients. The tree’s defense response to an HLB infection is to

produce compounds that block phloem vessels of the tree’s vascular system. This

resulting damage to the root system inhibits the ability of the tree to uptake nutrients

from the ground. In the foliar feeding method, a portion of the nutritional needs of the

tree is applied through foliar sprays including both macro and micro nutrients (Spann et

al. 2010). Formulation of the enhanced nutritional program depends on the program, but

generally the active ingredients include standard essential micronutrients, and

phosphite, and salicylate salts (Gottwald et al. 2012). Symptomatic trees are not

removed and scouting for the disease is discontinued. As with Strategy 2, a strong

psyllid control program is practiced. Roka, et al. (2010) have estimated that the

additional nutrient applications increase production costs between $200 to $600 per

acre, depending on the type and amount of foliar nutritionals a grower decides to apply.

The primary concern among plant pathologists with Strategy 3 is that HLB

inoculum is left unchecked. The economic implications of Strategy 3 include whether it

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is feasible for young trees (ages 3-8) to reach their productive maturity, whether planting

the next generation of citrus trees is economically viable, and whether the presence of a

grove following Strategy 3 while other growers follow Strategy 2 will cause increased

damage on the latter growers’ fields. Spatial analysis of disease spread in south Florida

suggests that spread between citrus blocks is a more significant portion of disease

spread than the spread of the disease within a citrus block (Gottwald et al. 2008). This

suggests that heterogeneous control methods may reduce the viability of Strategy 2.

This study addresses the economic consequences of the three strategies. In

other words, how does a grower determine which strategy is in her/his best interests

(given average grove age and initial infection rate)? Strategy 1 needs to be considered

as a baseline to reference Strategies 2 and 3. Growers make heterogeneous decisions

regarding their choice among control strategies. Models are developed that allow

economic assessment of each strategy and determine the scenarios for which each

strategy is optimal or yield a positive net present value, considering tree age at first

detection, and rates of infection at first detection. Since the optimal strategy may vary

due to tree age at first detection and the rate of infection at first detection, the optimal

strategy may vary across growers located nearby. Currently, the long term net present

value of the control strategies is unknown because of uncertainty in the efficacy of the

strategies. Our research identifies important efficacy targets that must be achieved for

the long-term economic viability of a citrus grove.

Our results provide a recommendation of the optimal control strategy for a given

set of conditions. It is hypothesized that the superiority of any one strategy depends

upon the level of infection at the time when the disease is first found in a particular

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block, the rate of spread of the disease, the average age of the grove at first infection,

expectations of future fruit prices, and the latency period. The rate of spread is a

function of psyllid populations and the efficacy of psyllid control measures.

Objectives

The primary objective of this study is to determine the optimal economic

management strategies of citrus greening in Florida. This is accomplished through the

following specific objectives:

1. Identify grove age and level of initial disease incidence at which each strategy yields positive economic returns.

2. Determine the ranges of initial grove age and initial disease incidence for which a given control method is economically preferred over other available methods.

Scope of Research

The study implements a net present value analysis of the control strategies

adapted by Florida citrus growers following the advent of HLB in the state. This is

essential to the determination of which strategy is economically superior, from the

grower’s point of view. It is of more importance to consider the private benefits/cost of

the tree eradication policy to the grower, as no compensation is paid for removed trees.

The impact of HLB on citrus yield is first modeled through a disease spread function; a

discrete logistic function approximated from a Gompertz function. Since the spread rate

of HLB is dependent on the average grove age, the logistic function is approximated for

three average age classes of 0, 3, and 6 or older. Due to lack of available data for the

estimation of model parameters for Florida, we obtain parameter estimates from a

corresponding region of HLB spread. Given this logistic function, disease spread in an

infected grove with a tree density of 150 per acre is simulated for given parameter

values for each age class, while varying the initial level of infection. The logistic curves

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thus incorporate both asymptomatic and symptomatic trees expressed in a ratio

involving total diseased trees. Total diseased is the sum of the asymptomatic (latently

infected trees without visual symptoms) and symptomatic tree categories. From this, a

spread function is generated and fed into HLB tree and grove severity functions for the

calculation of the relative yield due to HLB presence in the affected grove. The net

present value is then estimated from the corresponding relative yield estimates given

the yield from a healthy grove unaffected by HLB, obtained as estimated boxes of fruit

per tree by age group for non-Valencia oranges from the Florida agricultural statistics

service (Florida citrus statistics 2008-2009). Fruit prices are expressed as delivered-in

(to the processing plant) $/pound solids ($1.50/pound solid is the baseline price) with

pound solids per box values dependent on tree age. The model described above is the

baseline model for the ‘do-nothing’ policy. Hence two other models are developed: the

infected tree eradication model and the enhanced foliar nutrition model. These models

are unique in the sense that they include a latency period of HLB infection, as well as

take into account the average grove age, the natural variation in disease incidence at

first detection across groves in a region, and periodic removal of symptomatic trees

(specific to the tree eradication model). The robustness of each model is tested by a

sensitivity analysis conducted for the main model parameters.

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CHAPTER 2 LITERATURE REVIEW

Responses to stem the devastating effects of HLB or plant diseases in general

especially in academia have been enormous. This chapter reviews relevant literature in

all aspects of related disciplines including HLB epidemiology, the variety of control

methods experimented to date, the impact of HLB across the globe and in Florida as

well as its social ramifications if left unchecked. In addition, the review includes work on

HLB effects on production and yield costs, and general economic and bio-economic

models of disease control.

HLB Disease Incidence, Latency, and Spread

Disease incidence has been estimated using a variety of approaches. Gottwald

et al. (2010) determined disease incidence via a logistic spread rate per year calculated

by linear regression of transformed1 disease incidence in Florida. HLB incidence in

Florida has also been found in similar studies to increase within 10 months from 0.2 %

to as much as 39 % (Gottwald et al. 2007b, 2008; Irey et al. 2008). Spatiotemporal

spread models have also been used to characterize HLB in Florida where simultaneous

within and across grove spread were common (Gottwald et al. 2008). Other studies

have been conducted such as in Vietnam where HLB incidence is found to vary

depending on the management strategy employed (Gatineau et al. 2006) or in Brazil

where incidence has been shown to depend on proximity to HLB-infected citrus groves

and/or on neighbors’ behavior (Bassanezi et al. 2006; 2005, Gatineau et al. 2006;

1 The disease incidence data was first transformed via a logistic linear function given

by )1/ln()(logit yyy .

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Gottwald et al. 2007a; 2007b). Albrecht et al. (2012) showed in a Florida study that

HLB disease incidence is unaffected by the type of rootstock used in propagation.

Disease latency refers to the time between when infection by a pathogen occurs

and the onset of symptoms. HLB latency has also been demonstrated in some studies

where for every symptomatic tree in a given grove, 13 (range 2 to 56) HLB-positive but

asymptomatic trees existed in its neighborhood, which expressed symptoms in

subsequent assessments (Bassanezi et al. 2006). Irey et al. (2006) use PCR

techniques to test for the presence of the bacteria that causes HLB (Candidatus

Liberibacter asiaticus) in plots of about 190 trees and found that 60 percent more

asymptomatic trees existed in addition to the symptomatic trees that were found (Irey et

al. 2006). High correlation (R2 = 0.89) between infected trees and total number of

infected trees among the plots suggests natural disease transition from asymptomatic

trees to symptomatic trees. In some instances, high bacteria titer was found with PCR in

some asymptomatic trees, suggesting the need for roguing asymptomatic trees as well

(National Research Council 2010; Irey et al. 2006). The presence of a high percent

(80%) of infected trees within 25 m of a symptomatic tree also signifies short distance

spread of HLB (Irey et al. 2006).

HLB progression in a grove has also been determined to depend on the vector

population and inoculum levels as well as average grove age at first detection. HLB

progression in Reunion Island, China, and the Philippines is reported to follow a sigmoid

curve, with clustering of diseased trees (Gottwald and Aubert 1991; Gottwald et al.

1989, 1991). In Reunion Island more aggregation towards the direction of prevailing

wind was observed, suggesting that psyllids are dispersed by the wind. Aggregation in

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China was facilitated by closer tree spacing. Logistic growth rates are more plausible for

both growth of an infested area in space and population density growth than constant

growth rates (Kompas and Che 2009). This suggests that an infected area initially

grows exponentially, slows down and finally stops as the potential range of the species

is attained. Disease progression can reach asymptotic levels faster in young groves

than older groves (Gottwald et al. 2007, 2007a). The dispersal distance for HLB-infected

psyllids have been estimated to range from 0.88 to 1.61 km with a median of 1.58,

which may imply that groves more than 2km apart are unlikely to directly affect each

other with HLB (Gottwald et al. 2007b, Gottwald et al. 2008). Thus HLB spread is

spatially continuous and simultaneous, primarily via psyllid feeding behavior between

groves and secondarily through within grove feeding of the psyllids, necessitating the

need for landscape management practices (neighbors HLB management practices

should be compatible) for effective control. Manjunath et al. (2008) in a study to detect

HLB bacteria from a sample of over 1,200 psyllid adults and nymphs in Florida found

that the bacteria spread in an area may be detected one to several years before

symptom development in plants. Raphael et al. (2012) developed a deterministic

mathematical model that involve susceptible citrus, infectious but asymptomatic citrus,

symptomatic citrus, non-infective adult ACP, and infective adult ACP that acquired HLB

in the adult and nymph stages to study the dynamics of HLB in a citrus grove. Results

show that all trees in the grove are infected after 5 years even after removal of

symptomatic trees with 47% detection efficiency. They concluded that the best control

strategy is the reduction of the vector populations. Chiyaka et al. (2012) used a

mathematical model of HLB transmission to indicate the importance of ACP for initial

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HLB infection. Their work also underscores the importance of flush production and

latency period in influencing HLB development.

The Impact of HLB

HLB, which in Chinese means “yellow dragon disease”, was first described in

southern China in 1919 and spread widely and devastated citrus establishments in the

Philippines, Indonesia, Thailand, and South Africa between 1960 – 1980. Until recently

(2004/5), symptoms of HLB were found in two countries in the Americas; specifically in

São Paulo State in Brazil, in which nearly three million HLB infected trees were

removed in subsequent years, and in Florida, USA (Bové 2006; National Research

Council, 2010). HLB now occur in other North American areas, such as Cuba, Georgia,

Louisiana, South Carolina, Nayarit (Mexico), California, Texas, Costa Rica, and Belize.

HLB is a very serious, debilitating disease that affects all varieties of citrus. HLB’s

destructive abilities are unwavering no matter the mode of propagation; reducing yield

significantly through fruit drop, dieback and stunted growth, in addition to causing poor

quality of un-harvested fruits (National Research Council, 2010). Depending on the

psyllid vector population, bacteria titer, and age cohort of the grove at first detection,

HLB can take over an entire grove in 3 – 13 years following the expression of first

symptoms (Catling and Atkinson 1974; Aubert et al. 1984; Gottwald et al. 1991;

Gatineau et al. 2006; Gottwald et al. 2007a; Gottwald et al. 2009). Symptoms can

become very severe within one to five years from onset of the disease, depending upon

tree age at time of infection and the range of infection (Lin 1963; Schwarz et al. 1973;

Aubert 1992). The progression of HLB severity in a grove results in yield reduction,

rendering the grove uneconomical within 7 – 10 years after planting. (Aubert et al. 1984;

Aubert 1990; Gottwald et al. 1991; Roistacher 1996).

26

Worldwide, nearly 100 million trees are estimated to be affected by HLB. In some

parts of Thailand in 1981, close to 100 percent of trees were affected. Between 1961

and 1970 in the Philippines, citrus acreage was reduced by 60 percent, which

represents the fallout from the infection of an estimated seven million trees in 1962

(Altamirano et al. 1976; Martinez and Wallace 1969). Three million trees were removed

in Java and Sumatra within that same period, and a loss of 3.6 million trees were

reported in Bali within four years from 1984 to 1987. The HLB havoc extended to

southwestern Saudi Arabia, where most sweet orange and mandarin trees were killed

by 1983. In the 1960s, the entire citrus industry in Reunion Island was devoured by HLB

(Altamirano et al. 1976; Martinez and Wallace 1969).

Since its arrival in São Paul State, Brazil in early 2004, three million HLB affected

sweet orange trees have been removed as part of measures taken to control HLB

(National Research Council 2010). In the wake of the panic from the first reports of HLB

in Florida citrus in 2005, no public policy has emerged to handle HLB, as a result of

which growers evolved their own private stop-gap management strategies, rendering

the citrus industry to be labeled as an endangered industry. Before effective control of

the African psyllid with systemic insecticides was discovered in the late 1980s, HLB

devastated the South African citrus industry across the length and breadth of the

country, affecting four million out of the 11 million trees in South Africa, during the mid-

1970s (National Research Council 2010).

HLB Control

This section outlines the various recommended control measures for a pre- and

post-HLB presence in a given region. These include quarantine, roguing, psyllid control,

27

and use of healthy nursery propagation materials. The effectiveness of some of these

measures as gleaned from the literature is also presented.

So far, the first line of control of HLB is by adoption of quarantine measures to

prevent disease introduction. If however HLB is found in a hitherto HLB-free region, a

series of coordinated actions known as preventative control measures could be taken to

control the disease. Affected areas are mapped through surveys to identify infected

trees, which are later removed to prevent re-infection. A rigorous psyllid control program

should also be put in place. To avoid infection through plant propagation practices,

production of healthy citrus seedlings should be ensured especially if resetting is

required after symptomatic trees are removed. This is because without control, it takes

on average eight years for a grove to reach 100% infection (Bové 2006).

Control by roguing is effective through well-timed and carefully repeated surveys

to identify all affected trees as much as possible. The latency period of HLB, which can

be up to two or more years (Gottwald 2010), reduces the effectiveness of roguing as a

control measure; hence the need for repeated surveys. The quality of roguing is also

affected by the presence of uncontrolled psyllids in the grove in which infected tree

removal is practiced. Roguing must therefore be accompanied with a rigorous psyllid

control regime. Detection of HLB in Florida and São Paulo is done by mounting

platforms that allow for inspection of the tops of mature trees as it is reported that many

affected trees start showing symptoms first on the upper part of the canopy (National

Research Council 2010). Brlansky et al. (2009) recommend four inspections per year,

even though some growers carry out two to three inspections per year. Futch et al.

(2009) indicated that no scouting method is 100% accurate in detecting HLB

28

symptomatic trees. This re-emphasizes the need for multiple inspections within the

year. Irrespective of age or severity of infection, all symptomatic trees should be

removed (Ayres et al. 2005), and prior to removal these symptomatic trees should be

sprayed with a contact insecticide (Rogers et al. 2010). Unlike citrus canker in which

infected trees as well as all surrounding trees at 15 m radii are removed, this practice is

not feasible for HLB (Bassanezi 2005), as the psyllid vector feeds randomly across a

given grove, and can disperse farther to other groves by wind, hurricanes or storms.

The proportion of the infected trees removed depends on the initial disease incidence

and hence the entire grove can be eradicated at very high rates of initial disease

incidence. For instance, a grove with 10% symptomatic trees implies 20% infected

trees, and groves with 20%, 30% and 50% symptomatic trees give rise to 36%, 50%

and 70% infected trees respectively, due to latency and hence the presence of

asymptomatic trees (Bové 2006). Recently, Bové (2012) has been discounting the

latency period saying that it is just incomplete inspections, while Futch et al. (2009)

indicates that the latency period of HLB is unknown within a tree. Resetting can be done

with healthy seedlings, after infected trees are removed.

Application of contact and systemic insecticides as well as use of biological

agents reduces psyllid populations and HLB spread, depending on the species of the

psyllid. Biological control is reported to have been successful in Reunion Island (Aubert

and Bové 1980; Aubert et al. 1980), mainly due to the fact that there were no

hyperparasitoids on the introduced Tamarixia radiata and T. dryi parasitoids to hamper

their effectiveness (Aubert and Quilici 1984). Predators such as spiders, lacewings,

ladybugs, minute pirate bugs, and some wasp parasitoids attack the Asian citrus psyllid.

29

However, the most effective natural enemy is reported to be the coccinellid lady beetles

Olla v-nigram, and Harmonia axyridis (Michaud, 2004). In Florida, attempts have been

made to establish the biological agent T. radiata to control psyllids (Bové 2006) with

little effect on the citrus psyllid population. Major reasons for this failure include

presence of hyperparasites and inadequate number of alternative hosts for the

parasitoids (Halbert and Manjunath 2004, National Research Council, 2010).

In Brazil, encouraging results were obtained in the use of tree removal and

insecticides against psyllids to control HLB. HLB incidence decreased from 7% to

0.03% in the 10th survey of a grove with 71,000 trees (Ayres et al. 2005). The African

version of HLB in South Africa was effectively managed for some period by the adoption

of disease-free nursery stock, intensive psyllid control coupled with rouging of

symptomatic trees. In China, however, the Asian HLB has proven more difficult to

handle with preventative control measures. Aggressive implementation of similar

measures brought some success in Brazil, and gave rise to the identification of factors

that affect HLB preventative control effectiveness. These factors include farm size, age

cohort of grove, HLB incidence frequency in the area of the grove, neighbors HLB

management behavior, HLB incidence at first inspection, date of first scouting, number

of scouting for affected trees, and frequency of insecticide application (Belasque, Jr. et

al. 2009). In Florida, it is also been observed that large grove size with well-maintained

groves in the same area that have low bacteria titer lowers HLB incidence by reducing

the spread across groves.

Social Consequences of HLB Persistence

The $9.3 billion citrus industry in Florida supports almost 80,000 jobs (grove

employees, seasonal pickers, haulers, processors, and packers). With total annual

30

wages of $2.7 billion, these workers earn roughly 1.5 percent of Florida’s wage income

(Norberg 2008). Inefficiency in managing HLB in the state will affect not only these full-

time equivalent job employees of the industry, but also the general public will be

deprived of health benefits derived from citrus products, albeit still enjoyed at a higher

cost from imported juice and fruit. Growers who cherish citrus production as a way of life

will be affected. The worldwide recognition of Florida as a citrus producing state whose

brand name has contributed to the state’s attractiveness to tourists, retirees, and

consumers will also be compromised. To augment shortfalls in both fresh and

processed citrus demand domestically, imports have to rise, putting further strains on

the economy.

Effects of HLB on Yield and Cost of Production

Effective management of HLB implies a dramatic increase in production costs

through adoption of various control measures such as use of disease-free nursery

stock, scouting and roguing symptomatic trees, and psyllid vector control. Other

reasons for reduced profit include declining yield and fruit quality of affected trees,

production of healthy nursery trees, costs of tree replacement and care, and value of

income/production losses from replaced trees. Yield effects of HLB depend on

tree/grove age and severity of infection. Young trees/groves become unproductive

faster than mature trees/groves. Mature trees/groves remain productive for several

years with less severe infection, and productive life could be reduced to as low as two

years with severe infections on a tree/grove (National Research Council 2010).Yield

reduction is high (19%) for younger infected groves (1-5 years olds) 2-4 years after the

onset of infection compared to older groves (over 5 years olds) where high yield

reduction occurs only after 5-10 years of first symptomatic tree onset (Bassanezi et al.

31

2011; Bassanezi and Bassanezi 2008). Optimal control policy for a pest has been

shown to depend significantly on the costs of pest damage per unit of infected area

(Carrasco et al. 2009; Sharov 2004).

Stringent requirements for raising disease free nursery trees in screened houses

have resulted in an increase from $4.50 to $9.00 in the cost per nursery tree. Given the

recommended four inspections per year for symptomatic trees and an estimated cost of

between $25–30/acre per inspection, annual inspection costs could add as much as

$100 to $120 to production costs (Morris et al. 2008). Assuming six trees are detected

for removal each year, tree removal costs add another $34 per acre per year to

production expenses (Muraro 2008b). Morris et al. (2008) suggested little economic

difference between controlling HLB with roguing and doing nothing to ameliorate the

impact of the disease until the grove becomes economically useless.

Psyllid control is accomplished either with soil application of recommended

insecticides or application of foliar insecticides such as zeta-cypermethrin , carbaryl,

dimethoate, imidacloprid, chlorpyrifos, malathion, phosmet, spinetoram, spirotetramat,

fenpropathrin, and petroleum oil. A combination of soil insecticide and three foliar

insecticide applications is required for psyllid control of a mature grove at an estimated

cost of $288/acre/year (Morris et al. 2008).

Citrus production costs and returns depend on the variety, intended use (fresh

fruit market or processed juice market), and yield quantities. Fruits for the processed

juice market are sold on pounds-solids basis in Florida, which relates to the juice

content of the fruit. This is estimated to be about 6.5 pounds of solids/90-pound box of

fruit, on average. Given production costs for Valencia oranges without HLB or citrus

32

canker at $1,657 per acre, harvesting, delivery and assessment costs at $1,226 per

acre, yield of between 300 to 600 90-lb boxes per acre, and assuming no resetting of

removed trees, the break-even price has been calculated to range from $0.80 to $1.19

per pound solids and with HLB or canker, the break-even price would be $0.89 to $1.38

(Muraro 2008a).

Fresh fruit is sold on a per box basis and for white grapefruit in the Indian River

area; total production cost is estimated at $3,195 per acre without canker or HLB and

$3,600 when both canker and HLB are present. This results in break-even prices of

between $8.37 to $5.82 per box for yields of between 350 to 650 boxes per acre without

HLB and canker and $10.03 to $6.71 with both HLB and canker (Muraro 2008a).

Assuming prices of pound solids range from $1.25 to $1.50, Morris et al. (2008) deduce

that processed citrus production will remain profitable in spite of the 41% increase in

production cost due to the presence of HLB, which can even be offset with a suggested

increase in planting densities.

Growers have been shown to benefit significantly in terms of the yield increase,

improved quality of produce and labor productivity, as well as the reduced control costs,

following their participation in a landscape management program against fruit flies in

Hawaii (Mau et al. 2007). Expected expenses needed for the control of an established

invasion of pests such as pesticides, labor, and equipment have been shown to depend

on the distribution, numbers, and rate of spread of the pests (Stohlgren and Schnase

2006). Likewise, a credible economic assessment of pest control requires an

understanding of the biology of the pest, the region of invasion, and temporal data of the

pest in the region under investigation (Stohlgren and Schnase 2006). Further, grower

33

losses must include not only reduced yield following a pest infestation, but also the

adjusted price effects if the infestation has the potential of affecting the supply/demand

mechanisms for the commodity in the locality, depending on its price elasticity (Myers et

al., 1998).

Economics of Disease Control Strategies

Economic models have been developed to determine the optimal control

strategies for some plant diseases. Such models range from barrier effectiveness

(Brown et al. 2002; Sharov 2004; Huffaker et al. 1992), infection risk and insurance

premium rates assessments (Goodwin and Piggott 2009) to models of optimal control of

invasive species such as effects of the environment, discount rate, marginal damages of

invasion and marginal costs of control on optimal control choices (Olson and Roy 2002).

Some models study the effects of imperfect information about the degree of infestation

from an invasive species on optimal control policy (Haight and Polasky 2010). Models

on optimal control of invasive species management using a logistic growth function to

express the growth of the invasive species have also been demonstrated (Eiswerth and

Johnson 2002). It has been shown that the optimal control strategy involving pest

eradication, reducing pest spread rate or doing nothing is a function of the size of the

area infested, the pest damage per unit area and the rate of discount used in the net

benefit calculation (Sharov and Liebhold 1998; Sharov 2004). Yet, others have

demonstrated the effectiveness of using disease-free plants and biological control of

psyllid vectors in survey studies (Aubert et al. 1996). Chan and Jeger (1994) developed

a dynamic mathematical model to assess among other things, the effects of disease

control by tree removal and planting resets. They found that at low infection rates,

symptomatic tree removal alone is sufficient to eradicate the disease. At high infection

34

rates, removal of asymptomatic but infected as well as symptomatic plants is advisable.

Jeger and Chan (1995) examined the relevance of theoretical models to strategic

disease management decisions and concluded that it is the interplay of theory, relevant

epidemiological data and predicting the likely effects of control that offers a useful

means of refining tactical disease control decisions.

Fishman et al. (1983) developed bioeconomic models for citrus tristeza virus

(CTV) infection and spread to assess the cost-effectiveness of roguing as a disease

eradication policy in Israel. They simulated the model to estimate the net present values

to reflect private and social gains from the two policies of eradication or do nothing and

found that roguing is more cost effective than do nothing. Kobori et al. (2011) developed

an Individual-Based Model (IBM) that simulated the disease spread dynamics of HLB

and suggested that delaying the latency period and roguing are two effective ways of

reducing the spread of HLB in a grove. Their preliminary results showed that regional

control may be effective in reducing HLB bacteria titer in the field.

Fishman and Marcus (1984) provide a deterministic model of infectious disease

spread within and across rows of plants with periodic roguing. Improving the detection

method with other parameters and conditions held constant results in time of infection

reduced in some rows, or the number of infected plants increases initially, attains a

maximum and declines afterwards. Pierre et al. (2006) considers the optimal

combination of monitoring (minimum cost of establishing, maintaining and monitoring

traps for fruit flies) and the cost of control once fruit flies are detected. They applied a

Bayesian decision process to solve the optimization problem of choosing between

detection expenses (cost of traps set around entry points) and eradication expenses

35

(cost of spraying with insecticides, release of sterile male flies, or quarantine measures).

They found optimal trapping density for two entry locations (Miami and Tampa) to be

higher than the actual number of traps deployed in practice, suggesting the need for

additional modifications to the model. Batabyal and Nijkamp (2008) use renewal theory

to construct and analyze a dynamic and stochastic model of optimal control for invasive

species in an orchard. They also derive the long run expected cost (LREC) for the

orchard per unit time and show that the optimal roguing and resetting densities solves

the derived LREC minimization problem. Their model treated commercial orchards as

entities whose growth and output are by nature dynamic and stochastic under constant

threats from a variety of invasive plant or animal species. Lominac and Batabyal (2009)

focused on a representative tree in a grove and used discrete time Markov chains to

model the tree’s management under attack of an invasive species. The specified model

is used to define the trees one step transition probabilities, determine the time the tree

is affected in the long run and the long run schedule of replacements for the

representative tree when it dies.

Morris and Muraro (2008) perform an economic analysis of greening

management of tree removal with/without different densities of resetting, versus do

nothing. They concluded that resetting is preferable to do nothing if resets reach

maturity in a mature grove. Replanting at higher density is best for a grove that is

unproductive due to HLB. Oleś et al. (2012) present a bioeconomic model for

optimization of disease control with latency, using the network/individual – based

methodology. Depending on total cost of disease incidence (consisting of costs of

treating infected individuals and prevention of infection), three optimal strategies are

36

identified. These include total population preventive treatment, local treatment within a

neighborhood of certain size, and only treatment of diagnosed cases with no prevention.

Some epidemiological factors do affect the optimal strategy of local treatment.

Bioeconomic Models of Disease Control (with Incorporated Discount Rates)

Bioeconomic approaches to optimal management of perennial biological

resources involving complex patterns or transitioning processes such as pests/disease

incidence require economic assessment that incorporates discount rates into cost–

benefit estimates involving present value analysis. The net present value of an asset is

the weighted exponential function of the time at which net expected revenues of the

asset are obtained; T

r tetN0

)( ,)( where N(t) is the net revenue at time t, r is the discount

rate, and T is the time period (Clark 1976). Only Sharov and Liebhold (1998) use

present value for optimization of long-term pest management options involving barrier

zones. Their theoretical model shows that pest control mechanisms that slow pest

population spread is a feasible strategy unlike strategies that stop population spread,

which require natural barriers to be optimal. Enkerlin and Mumford (1997) estimated the

net present value for three improved management options to control the Mediterranean

fruit fly across three countries (Israel, Palestinian Territories, and Jordan). Given the

nine-year analysis, the predominant control method is the sterile male suppression

option whereas over a longer time period, the sterile male eradication option

predominates. Odom et al. (2003) developed and applied a deterministic dynamic

programming model in a case study to derive optimal control rules for the management

of an environmental weed (scotch broom) in a national park. Model results show the

need for biological control as a viable option. In a similar study, Chalak‐Haghighi et al.

37

(2008) utilized ecological and economic information to construct a dynamic bio-

economic optimization model to evaluate the net benefits of a range of possible control

options for Californian thistle (Cirsium arvense) weed in New Zealand pasture. Factors

considered in the maximization of the net benefit include the costs and effectiveness of

control options, and the revenue from animal production. Their results suggest that the

optimal strategy is a mix of a bio-control agent with one or more integrated weed

management strategy, especially when the initial density of the thistle population

exceeds 1.0 shoot m-2.

38

CHAPTER 3 BIOECONOMIC ESTIMATION

This chapter contains an overview of optimal investment theory, which provides

the theoretical framework for the use of net present value analysis in the study. Next is

an expatiation on the income method for asset valuation and its appropriateness for this

type of study, herein known as our economic model. Finally, a biological model is

presented, and it spans the Gompertz and logistic functions, the tree and grove severity

functions, and the negative exponential function for relative yield.

Optimal Investment Theory

Overview

Two possibilities exist in designing a framework for the theory of optimal

investment, namely the neoclassical theory of optimal capital accumulation and utility

maximization theory. We will adopt the neoclassical theory of the firm for our theoretical

framework since it is a more powerful theory than the utility-maximizing theory

(Jorgenson 1967). Neoclassical theory assumes that capital growth depends on utility

maximization of a consumption stream. Essentially, a given firm maximizes

consumption utility subject to a given production function at fixed current and future

prices and interest rates for both input and output flows. A production plan is then

chosen to maximize the present value of the returns from the investment. Maximizing

the present value of the firm is the only criterion consistent with utility maximization

theory. The resulting theory of optimal capital accumulation broadly includes special

cases of econometric models of investment actions (Jorgenson 1967).

When an investment involves expense and income flows into the future, such as

investments in perennial crop production, it is necessary to estimate the present value

39

of the series of cash flows projected from the proposed investment. Net present value

(NPV) calculation attempts to do just that, and gives a measure of how much the

investor gains today for investing in the project. In NPV calculation, future cash flows

are discounted at a specified discount rate that depends on the time value of money,

the interest from an alternative guaranteed investment, and the degree of risk

compensation that is being accepted in the project.

Optimal Capital Investment Model

The present value of a firm that is assumed to produce a single output from a

single variable and capital input is given by the expression:

)()()( ,)(0 tRtqtw(t)Cp(t)Q(t)I(t) dttIrteNPV

0),,F ),()((t)K :Subject to KC(QtKtR

where r is the discount rate, I is net income, Q, C, and R represent output, variable input

and fixed inputs respectively, and p, w, and q are their corresponding prices

(Jorgenson, 1967). Net present value (NPV) is maximized subject to the constraints that

the rate of change of the flow of capital services ( (t)K ) is related to the flow of net

investment ( )()( tKtR ), where is a constant of proportionality and denotes

depreciation of capital and K is capital services. The second constraint states that the

production function is constrained by output (Q) and input (C, K) levels. The

maximization problem is solved for the optimal variable input (C*), output (Q*), and

capital services (R*) and the marginal productivity for variable input and capital as well

as the shadow price for capital services. Thus the complete optimal capital

accumulation model consists of the production function, the two marginal productivity

conditions, and the function for the shadow price for capital services (Jorgenson 1967).

40

The Economic Model

A citrus grove is an asset. We estimate the economic impact of HLB through its

effect on the value of a particular citrus grove. There are a variety of approaches in

asset valuation, but the most appropriate approach in this application is the income

method. In the income method, future costs and revenues are estimated to give per

annum net revenue. Future net revenue is discounted to the present to give net present

value (NPV) using the formula,

T

ttr

tQ

tC

tQ

tP

NPV

11)1(

))((

where tP is price in time period t, tQ is yield in time period t, tC are costs in time period t,

and r is the discount rate. HLB affects the NPV of an infected grove by increasing costs

if control is implemented, and decreasing future fruit production, thereby reducing future

revenues. Since the rate of spread depends in part upon the tree age at first infection,

we compute NPV as a function of tree age as well as the level of infection at first

detection. Since the NPV of a particular grove depends upon several factors, which are

subject to random variation, stochastic dominance is an appropriate method to identify

the superior strategy. At this time, however, knowledge of the underlying probability

distributions of those random factors is not available, so our economic assessment is

done in a deterministic framework.

The Biological Model

Our original idea to depict HLB spread was motivated by a Gompertz function as

proposed by Bassanezi and Bassanezi (2008). This function specifies that the disease

incidence, y, at time t is:

41

1)-(3 )

0ln(

tey

eGt

y

where y0 is the disease incidence at first detection and is the annual rate of spread of

the disease. However, the Gompertz function always converges to 100% infection,

which does not allow us to analyze control strategies that prevent 100% disease

infection. A logistic function has the advantage of being more flexible and allows for a

steady state level of disease infection that is less than 100%. In this case we estimate

the parameters of the logistic function that approximate the Gompertz function, and use

those parameters to estimate the impact of Strategies 2 and 3. To do this, we use

parameter values for y0 and for each age class from Bassanezi and Bassanezi

(2008) to simulate Gompertz spread from low to high incidence until field incidence

reaches 100%. Using nonlinear regression, the simulated Gompertz data for each age

class are used to estimate the corresponding logistic . Our logistic function is derived

from the deterministic differential equation:

2)-(3 1

),1( Gt

yY,Gt

yGt

yYYYYt

Y

where Y is the proportion of diseased trees at time t, Y is the change in the proportion of

diseased trees and is the annual rate of spread of the disease. The result of this

procedure yielded our logistic estimates to be 1.5148125, 0.8450625, and 0.4440625

of their Gompertz counterparts of 1.3, 0.65, and 0.325 obtained from Bassanezi and

Bassanezi (2008), for each corresponding age class consisting of average grove age of

0, 3, and 6 (Table 4-1). The logistic curves are then generated according to Equation 3-

3:

42

3)-(3 )1

1(1

ˆ1

t

Yt

Yt

Yt

Y

For strategy 1, tY includes both symptomatic disease incidence, s

tY as well as

asymptomatic disease incidence, a

tY . The assumption on latency period in the baseline

model (Strategy 1) is 1 year for groves of average age of 0 and 3, and 2 years for

groves with average age of 6 or larger (Gottwald 2010). In the sensitivity analysis,

latency period is one of the parameters we alter to check model robustness. For

Strategy 2, if the assumption on latency is 1 year for instance, then trees remain

asymptomatic for one year, implying that a

t

s

t YY 1 . Further, we assume that all

symptomatic trees are immediately removed once the tree exhibits symptoms, implying

that 1tY in Equation 3-3 equals a

tY 1 . Since the disease moves both across trees in the

grove and across canopy in a given infected tree, we need to model the spread of the

disease in canopy area as well to determine the yield effect of HLB for Strategies 1 and

3. It is worthwhile to mention here that HLB is spread only by psyllids hence vector

control will have significant effects on disease spread. As a result, one of the factors for

sensitivity analysis addressed in Chapter 5 is latency period, which we assume to be

the proxy for psyllid control. We estimate the yield impact of HLB ( tr ) as a function of

symptomatic grove canopy area or disease severity tX and yield of a healthy grove (Rt,

average boxes per tree) for Strategy 1 using the negative exponential model:

4)-(3 1,2,....t;i ,)1

ˆ

1

ˆ( ),(1

it

xLt

yt

t

Li

yt

XtbX

et

Rt

r

)))()1)

0/1(1/(1

texx

43

where Rt equals 1, denotes the full yield of a healthy grove (average boxes per tree), 1

tr

is the percent of healthy yield obtained for a given level of disease severity for strategy

1, b is the rate of yield reduction as a function of HLB severity, Xt is total grove severity

at time t, x is the fraction of HLB symptomatic tree canopy area at time t, x0 is the

fraction of HLB symptomatic tree canopy area at first detection, and θ is the annual rate

of disease severity progress in an affected tree. For Strategy 2, all symptomatic trees

are removed, so the spread of yield losses through the canopy does not occur.

For Strategy 3, the yield effect is assumed to be in-between the yield effect for

strategy 1 and a healthy grove. Since the reduction in yield relative to a healthy grove is

unknown, we use averages between healthy yield and strategy 1’s yield given by:

5)-(3 ..3,........0.1,0.2,0. where ),1(13 t

rt

r

With all three strategies modeled, we determine the scenarios for which each

strategy would be optimal, considering all possible strategy efficacies and tree age and

rates of infection at first detection.

44

CHAPTER 4 MODEL RESULTS

In this chapter, the baseline model results are presented. Key parameters such

as the annual rate of spread of HLB ( ), price per pound solids, length of latency, and

yield penalties are fixed at specified values according to relevant literature and

secondary data sources (Table 4-1). The chapter begins with an exposition of the

assumptions of the model, after which empirical results of the model are presented

followed with some concluding remarks.

Model Estimation Assumptions

We create disease spread curves using β values described in Chapter 3 and use

those parameters to estimate the NPV of Strategies 1, 2, and 3. Historical data on

boxes of fruit per tree by age group for non-Valencia oranges from the Florida

Agricultural Statistics Service (Florida Citrus Statistics 2008-2009) are used to establish

yield curves by variety. Next logistic curves of disease spread are interacted with the

investment or NPV model as specified above to estimate the impact of HLB on grower

earnings based on tree age and first detection of the disease. Fruit prices are expressed

in $/pound solids delivered-in ($1.50/pound solid) with pound solids per box values

dependent on tree age. The estimates are made on a per acre basis for a grower with

150 trees per acre and 100% original tree acreage remaining. We use a 10% discount

rate for calculation of net present values. Operating and production costs for a mature

grove include herbicide, pesticide, and fertilizer applications, irrigation, and pruning, but

do not include HLB foliar nutritional sprays or pesticide applications in the baseline

calculations. Since we assume no resetting (replacing trees lost in the citrus grove), the

45

adjusted reset grove costs by tree age are assumed to be zero2, as well as the

establishment costs/acre for new solid set, the cost of tree removal and planting reset-

replacement trees, reset frequency, and reset yield adjustments. Yield loss due to

freeze or other diseases is assumed to be zero.

We calculate net present value of a stylized citrus grove using a 15-year time

horizon. Beyond 15 years, the net present value per year approaches zero. We

calculate the net present value for groves with an initial average age ranging from 0 to

17. Beyond 17 years of age, tree yields no longer increase, so calculations for groves

of this age represent our net present value upper bound.

Empirical Results of Model

Under Strategy 1 (do nothing) all groves with an average tree age of 0 and 3

years yield a negative net present value at any initial disease incidence rate. Groves

that contain younger trees at first detection also experience a faster spread of the

disease. Consequently, young groves that become infected with HLB are unable to

produce a sufficient volume of fruit to recover investment costs. Irrespective of the

disease incidence rate at first detection, all groves with an average age of 6 years and

over yield a positive net present value under Strategy 1. In Table 4-3 the net present

values for groves with initial rates of disease incidence varying from 0.1% to 50% and

for average initial grove ages of 0, 3, 6, 10, 14, and 17 years are reported under

Strategy 1. A plot of the net present values as a function of disease incidence and

average age at first detection is shown in Figure 4-1. Also shown are contour lines, with

2 The assumption of no resetting greatly simplifies the calculation of disease spread and the

accompanying reduction in fruit production per acre. The assumption clearly is a limitation on the derived results.

46

the green contour line marking the ages and disease rates at which the net present

value is $0.00.

Under tree removal (Strategy 2), groves with average age of 0 display negative

net present values whereas groves with an average age of 3 years show negative net

present value when the initial disease incidence is 20% and larger. Groves with an

average age of 6 show positive net present value for initial disease incidence ranging

from 0.1% to 30%, but shows negative net present value for initial disease incidence of

40% and 50%. All other age categories show a positive net present value, no matter the

initial rate of disease incidence (Table 4-4). In Figure 4-2, the green contour line marks

the ages and disease rates at which the net present value is $0.00 for strategy 2.

An enhanced foliar nutritional program (Strategy 3) is expected to boost yield of

an HLB affected grove, but will be lower compared to a disease free grove. This

analysis assumes a yield penalty of 30% compared to a healthy grove under Strategy 3.

The estimated NPVs associated Strategy 3 is presented in Table 4-5. As before,

groves with average age of 0 show negative net present value at all levels of initial

disease incidence. For this strategy, the ages and disease rates at which the net

present value is $0.00 are indicated by the green contour line of Figure 4-3.

For ease of comparison, Tables 4-6 through 4-8 juxtapose the net present value

for the three strategies for each age class. Bolded values indicate the superior strategy

at a particular age of first detection and initial rate of infection. For groves whose

average age is 0 at first detection, the net present values are all negative. For trees with

average age of 3 years, Strategy 2 is better than Strategies 1 and 3 when disease

incidence ranges from 0.1% to 7.0%, and thereafter (incidence of 8.0% to 50%),

47

Strategy 3 is better than both Strategies 1 and 2. For trees with average age of 6 and

10, Strategy 1 is better than Strategies 2 and 3 at lower rates of initial disease incidence

(0.1% to 2.0%), after which Strategy 2 becomes superior to Strategies 1 and 3 when the

disease incidence ranges between 3.0% and 10.0%. At the highest initial disease

incidence of between 20% and 50%, Strategy 3 is superior to Strategy 2 and 1 in net

present value. For trees with average age of 14 and 17, Strategy 1 outperforms the

other two strategies at the low rates of disease incidence (0.1% to 2.0%), and for the

middle rates of disease incidence of between 3.0% and 8.0%, Strategy 2 is better than

the other two strategies. At the highest rates of initial disease incidence (10% to 50%),

Strategy 3 becomes superior to Strategies 1 and 2.

The results presented in Table 4-6 through 4-8 provide several interesting

implications. While it may be surprising that Strategy 1 is ever identified as the superior

strategy, the results suggest that at very low levels of initial infection, the costs

associated with both Strategy 2 and Strategy 3 exceed gains to be realized in the future

by mitigating the effects of the disease. One could describe this result as the

“temptation of waiting.” At higher levels of initial infection, Strategy 3 emerges as the

superior strategy because of the large number of trees that must be removed if Strategy

2 is followed. The results herein support that argument that once the disease becomes

well-established, the economic rational approach is to attempt to “live with the disease”

via Strategy 3.

These results also point out a major limitation of the methodology employed

here. The neighbor effects are ignored. Adoption of any of the three strategies implies

neighbor effects. Since both Strategy 1 and 3 entail non-removal of symptomatic trees,

48

the level of disease inoculum in a particular grove is not being diminished. Strategy 2

calls for the removal of symptomatic trees and its primary intent is to reduce the level of

inoculum. If one grower pursues Strategy 2 and his/her neighbor pursues Strategy 3,

the actions of the second neighbor will adversely affect the first neighbor because the

neighboring grove will continue to serve as a source of inoculum.

Figure 4-4 delineates the ranges of initial grove age and initial disease incidence

for which each strategy maximizes net present value, after adjusting for age classes in

which all strategies post negative net present values (age class of 0 and sometimes 3).

Strategy 3 dominates at incidence levels of 8% - 50% for groves of almost all ages.

Strategy 2 dominates for groves with average age of 0 and 3 years at low initial disease

incidence of 0.1% to 2% and also at disease incidence levels of 3% to 8% for all groves

with average age of 6, 10, 14, and 17. Strategy 1 dominates for all groves with average

age of 6, 10, 14, and 17 only when disease incidence is 0.1% to 2%. Therefore, for

almost all groves at almost all initial HLB disease incidence, there is the likelihood that

the enhanced nutritional program will generate a higher NPV for the grower than if one

were to follow a do nothing or tree eradication management strategy. For groves with

average age of 6 - 17 years at initial HLB disease incidence of 3% to 8%, tree

eradication program management strategy will yield higher returns to the grower than

do nothing or implementation of the enhanced nutritional program. For groves at 6 - 17

years at very low HLB incidence (0.1% to 2%), the grower will be better off by doing

nothing than either implementing the tree eradication or enhanced nutritional program.

For a new solid set grove at any level of initial disease incidence, the enhanced

nutritional program is likely to give the grower the best earnings on his/her investment

49

than any other strategy. No matter how high the initial rate of disease incidence, each

strategy remains positive in net present value for mature groves (groves with average

age of 6 or larger). Strategy 3 performs even better especially for mature trees at almost

all rates of disease incidence when the assumption on yield penalty of a healthy grove

is 5%, 10%, or even 20% instead of the 30% yield penalty (Tables 4-9 to 4-11) used in

the comparison. For all age classes, cost eventually exceeds revenue, especially for

mature groves at high rates of initial disease incidence.

Conclusions

Which strategy is superior to the other(s) depends on the age of trees at first

detection and the initial rate of disease incidence at first detection. Each strategy has its

range of relevance region within which it maximizes a grower’s net returns given the

initial level of infection and the average age of the grove. Growers with groves of all

ages at 20% or more initial incidence may be better off implementing the enhanced

nutritional program (Strategy 3). For growers whose groves are three years or older in

average age with initial HLB infection rate at 3% to 8%, (or growers with newly

established groves at 0.1% - 2% HLB incidence), the best strategy is Strategy 2

(infected tree removal). Strategy 1 is the least optimal strategy and it is only optimal

when incidence is very low (0.1% to 2%) for groves with average age of 6 or larger.

50

Table 4-1. Baseline Parameter Values

Parameter Trees Age Class

0 3 6

Annual HLB Spread Rate Gompertz (β) 1.3000000 0.65000000 0.32500000

Annual HLB Spread Rate Logistic (β) 1.5148125 0.84506250 0.44406250

Price/pound solid ($) 1.5000000 1.50000000 1.50000000

Latency Period (years) 1.0000000 1.00000000 2.00000000

Tree Severity Rate of HLB (θ) 3.6800000 1.84000000 0.92000000

Yield Reduction Rate of HLB (b) 1.8000000 1.80000000 1.80000000

Initial Severity (x0) 0.2000000 0.10000000 0.05000000

Source: Bassanezi and Bassanezi (2008); Bassanezi et al. (2011)

51

Table 4-2. Non-Valencia Orange Yield Estimated Boxes per Tree, by Age Group in Florida, 2004-2005 through 2008-2009

Tree Age Average1 Yield (2004/5 - 2008/9)

Yield2 (boxes/tree)

1

1.2

0

2 0

3 1

4 1.2

5 1.4

6

1.8

1.7

7 1.8

8 1.9

9

2.26

2

10 2.1

11 2.3

12 2.4

13 2.5

14

3.05

2.6

15 2.7

16 2.8

17 2.9

18 3

19 3.1

20 3.2

21 3.3

22 3.4

23 3.5

Sources: Florida Citrus Statistics 2008-2009. FASS 1Average yields of 1.2, 1.8, 1.26, and 3.05 boxes/tree are for groves of ages 3 – 5, 6 – 8, 9 -13, and 14 – 23 years respectively 2 Yield for each tree age is derived from the 5-year average yield in column two

52

Table 4-3. NPV1 for Strategy 1 (Do Nothing)

Disease Incidence at First Detection

Average Age (Years) of Trees at First Detection

0 3 6 10 14 17

0.001 -2,614 3,843 11,463 14,551 16,487 17,101

0.010 -4,142 927 9,539 12,562 14,488 15,102

0.020 -4,532 -17 8,442 11,407 13,322 13,935

0.030 -4,696 -662 7,686 10,601 12,505 13,118

0.040 -4,779 -961 7,213 10,084 11,978 12,591

0.050 -4,942 -1,182 6,673 9,505 11,389 12,002

0.060 -5,004 -1,599 6,360 9,157 11,032 11,644

0.070 -5,052 -1,754 5,893 8,656 10,521 11,133

0.080 -5,089 -1,886 5,659 8,393 10,250 10,861

0.100 -5,140 -2,097 5,265 7,947 9,786 10,396

0.200 -5,338 -2,960 3,555 6,032 7,799 8,405

0.300 -5,369 -3,531 2,563 4,897 6,604 7,207

0.400 -5,462 -3,988 1,463 3,634 5,278 5,877

0.500 -5,482 -4,164 1,077 3,176 4,779 5,375 1 Cumulative 15-year NPV ($/ac).

Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

53

Table 4-4. NPV1 for Strategy 2 (Symptomatic Tree Removal)



0 3 6 10 14 17

0.001 -645 4,830 8,441 11,534 13,470 14,084

0.010 -4,050 4,322 8,207 11,276 13,204 13,818

0.020 -5,478 3,790 7,949 10,993 12,910 13,525

0.030 -6,302 3,287 7,694 10,712 12,620 13,235

0.040 -6,871 2,813 7,442 10,435 12,333 12,947

0.050 -7,297 2,363 7,193 10,160 12,049 12,663

0.060 -7,639 1,936 6,946 9,888 11,768 12,382

0.070 -7,916 1,531 6,701 9,619 11,489 12,103

0.080 -8,152 1,144 6,460 9,353 11,213 11,828

0.100 -8,529 423 5,983 8,828 10,670 11,284

0.200 -9,569 -2,411 3,745 6,359 8,111 8,725

0.300 -10,043 -4,421 1,721 4,124 5,790 6,404

0.400 -10,295 -5,937 -106 2,101 3,686 4,300

0.500 -10,433 -7,114 -1,752 276 1,784 2,399 1 Cumulative 15-year NPV ($/ac).

Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

54

Table 4-5. NPV1 for Strategy 3 (Enhanced Foliar Nutritional Program)



0 3 6 10 14 17

0.001 -2,170 3,030 7,822 10,915 12,852 13,466

0.010 -2,610 2,211 7,245 10,318 12,252 12,866

0.020 -2,727 1,872 6,916 9,972 11,902 12,516

0.030 -2,776 1,679 6,689 9,730 11,657 12,271

0.040 -2,826 1,589 6,547 9,575 11,499 12,113

0.050 -2,850 1,523 6,385 9,401 11,322 11,936

0.060 -2,868 1,398 6,291 9,297 11,215 11,829

0.070 -2,883 1,351 6,151 9,146 11,062 11,675

0.080 -2,894 1,312 6,081 9,067 10,981 11,594

0.100 -2,909 1,248 5,962 8,933 10,841 11,454

0.200 -2,968 989 5,449 8,359 10,245 10,857

0.300 -2,978 818 5,152 8,019 9,887 10,498

0.400 -3,006 681 4,822 7,640 9,489 10,099

0.500 -3,011 628 4,706 7,502 9,339 9,948 1 Cumulative 15-year NPV ($/ac).

Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

55

Table 4-6. NPV1 for the Three Strategies for Age Classes 0 and 3



0 3

Strategy Strategy

1 2 3 1 2 3

0.001 -2,614 -645 -2,170 3,843 4,830 3,030

0.010 -4,142 -4,050 -2,610 927 4,322 2,211

0.020 -4,532 -5,478 -2,727 -17 3,790 1,872

0.030 -4,696 -6,302 -2,776 -662 3,287 1,679

0.040 -4,779 -6,871 -2,826 -961 2,813 1,589

0.050 -4,942 -7,297 -2,850 -1,182 2,363 1,523

0.060 -5,004 -7,639 -2,868 -1,599 1,936 1,398

0.070 -5,052 -7,916 -2,883 -1,754 1,531 1,351

0.080 -5,089 -8,152 -2,894 -1,886 1,144 1,312

0.100 -5,140 -8,529 -2,909 -2,097 423 1,248

0.200 -5,338 -9,569 -2,968 -2,960 -2,411 989

0.300 -5,369 -10,043 -2,978 -3,531 -4,421 818

0.400 -5,462 -10,295 -3,006 -3,988 -5,937 681

0.500 -5,482 -10,433 -3,011 -4,164 -7,114 628 1 Cumulative 15-year NPV ($/ac).


56




6 10

Strategy Strategy

1 2 3 1 2 3

0.001 11,463 8,441 7,822 14,551 11,534 10,915

0.010 9,539 8,207 7,245 12,562 11,276 10,318

0.020 8,442 7,949 6,916 11,407 10,993 9,972

0.030 7,686 7,694 6,689 10,601 10,712 9,730

0.040 7,213 7,442 6,547 10,084 10,435 9,575

0.050 6,673 7,193 6,385 9,505 10,160 9,401

0.060 6,360 6,946 6,291 9,157 9,888 9,297

0.070 5,893 6,701 6,151 8,656 9,619 9,146

0.080 5,659 6,460 6,081 8,393 9,353 9,067

0.100 5,265 5,983 5,962 7,947 8,828 8,933

0.200 3,555 3,745 5,449 6,032 6,359 8,359

0.300 2,563 1,721 5,152 4,897 4,124 8,019

0.400 1,463 -106 4,822 3,634 2,101 7,640

0.500 1,077 -1,752 4,706 3,176 276 7,502 1 Cumulative 15-year NPV ($/ac).


57




14 17

Strategy Strategy

1 2 3 1 2 3

0.001 16,487 13,470 12,852 17,101 14,084 13,466

0.010 14,488 13,204 12,252 15,102 13,818 12,866

0.020 13,322 12,910 11,902 13,935 13,525 12,516

0.030 12,505 12,620 11,657 13,118 13,235 12,271

0.040 11,978 12,333 11,499 12,591 12,947 12,113

0.050 11,389 12,049 11,322 12,002 12,663 11,936

0.060 11,032 11,768 11,215 11,644 12,382 11,829

0.070 10,521 11,489 11,062 11,133 12,103 11,675

0.080 10,250 11,213 10,981 10,861 11,828 11,594

0.100 9,786 10,670 10,841 10,396 11,284 11,454

0.200 7,799 8,111 10,245 8,405 8,725 10,857

0.300 6,604 5,790 9,887 7,207 6,404 10,498

0.400 5,278 3,686 9,489 5,877 4,300 10,099

0.500 4,779 1,784 9,339 5,375 2,399 9,948 1 Cumulative 15-year NPV ($/ac).


58

Table 4-9. NPV1 for the Three Strategies for Age Classes 0 and 3 at Different Yield Penalty2 Levels for Strategy 3



0 3

Strategy Strategy

1 2 3 1 2 3

20% 10% 5% 20% 10% 5%

0.001 -2,614 -645 -1,535 -900 -582 3,843 4,830 3,477 3,924 4,147

0.010 -4,142 -4,050 -1,828 -1,046 -655 927 4,322 2,894 3,632 4,002

0.020 -4,532 -5,478 -1,906 -1,085 -675 -17 3,790 2,705 3,538 3,954

0.030 -4,696 -6,302 -1,939 -1,101 -683 -662 3,287 2,576 3,473 3,922

0.040 -4,779 -6,871 -1,955 -1,110 -687 -961 2,813 2,516 3,444 3,907

0.050 -4,942 -7,297 -1,988 -1,126 -695 -1,182 2,363 2,513 3,421 3,896

0.060 -5,004 -7,639 -2,000 -1,132 -698 -1,599 1,936 2,389 3,380 3,875

0.070 -5,052 -7,916 -2,010 -1,137 -701 -1,754 1,531 2,358 3,364 3,868

0.080 -5,089 -8,152 -2,017 -1,141 -702 -1,886 1,144 2,331 3,351 3,861

0.100 -5,140 -8,529 -2,027 -1,146 -705 -2,097 423 2,289 3,330 3,850

0.200 -5,338 -9,569 -2,067 -1,160 -715 -2,960 -2,411 2,117 3,244 3,807

0.300 -5,369 -10,043 -2,073 -1,169 -716 -3,531 -4,421 2,002 3,187 3,779

0.400 -5,462 -10,295 -2,092 -1,178 -721 -3,988 -5,937 1,911 3,141 3,756

0.500 -5,482 -10,433 -2,096 -1,180 -722 -4,164 -7,114 1,876 3,123 3,747 1 Cumulative 15-year NPV ($/ac). 2Yield from HLB infected trees reduced 20%, 10% and 5% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

59




6 10

Strategy Strategy

1 2 3 1 2 3

20% 10% 5% 20% 10% 5%

0.001 11,463 8,441 7,865 7,907 7,929 14,551 11,534 10,958 11,002 11,023

0.010 9,539 8,207 7,480 7,715 7,832 12,562 11,276 10,560 10,803 10,924

0.020 8,442 7,949 7,260 7,605 7,778 11,407 10,993 10,329 10,687 10,866

0.030 7,686 7,694 7,109 7,529 7,740 10,601 10,712 10,168 10,607 10,826

0.040 7,213 7,442 7,036 7,482 7,716 10,084 10,435 10,087 10,555 10,800

0.050 6,673 7,193 6,906 7,428 7,689 9,505 10,160 9,949 10,497 10,771

0.060 6,360 6,946 6,844 7,397 7,673 9,157 9,888 9,879 10,462 10,754

0.070 5,893 6,701 6,750 7,350 7,660 8,656 9,619 9,779 10,412 10,739

0.080 5,659 6,460 6,704 7,327 7,638 8,393 9,353 9,727 10,386 10,715

0.100 5,265 5,983 6,625 7,287 7,619 7,947 8,828 9,637 10,341 10,693

0.200 3,555 3,745 6,283 7,116 7,533 6,032 6,359 9,254 10,150 10,597

0.300 2,563 1,721 6,085 7,017 7,484 4,897 4,124 9,027 10,036 10,541

0.400 1,463 -106 5,864 6,907 7,429 3,634 2,101 8,775 9,910 10,478

0.500 1,077 -1,752 5,787 6,869 7,409 3,176 276 8,683 9,864 10,455 1 Cumulative 15-year NPV ($/ac). 2Yield from HLB infected trees reduced 20%, 10% and 5% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

60




14 17

Strategy Strategy

1 2 3 1 2 3

20% 10% 5% 20% 10% 5%

0.001 16,487 13,470 12,895 12,939 12,961 17,101 14,084 13,509 13,553 13,575

0.010 14,488 13,204 12,495 12,739 12,861 15,102 13,818 13,110 13,353 13,475

0.020 13,322 12,910 12,262 12,622 12,802 13,935 13,525 12,876 13,236 13,417

0.030 12,505 12,620 12,099 12,541 12,762 13,118 13,235 12,713 13,155 13,376

0.040 11,978 12,333 12,015 12,488 12,735 12,591 12,947 12,629 13,102 13,349

0.050 11,389 12,049 11,876 12,429 12,706 12,002 12,663 12,490 13,043 13,320

0.060 11,032 11,768 11,804 12,393 12,688 11,644 12,382 12,418 13,007 13,302

0.070 10,521 11,489 11,702 12,342 12,672 11,133 12,103 12,316 12,956 13,287

0.080 10,250 11,213 11,648 12,315 12,649 10,861 11,828 12,261 12,929 13,263

0.100 9,786 10,670 11,555 12,269 12,626 10,396 11,284 12,168 12,883 13,240

0.200 7,799 8,111 11,158 12,070 12,526 8,405 8,725 11,770 12,683 13,140

0.300 6,604 5,790 10,919 11,951 12,466 7,207 6,404 11,531 12,564 13,080

0.400 5,278 3,686 10,653 11,818 12,400 5,877 4,300 11,265 12,431 13,014

0.500 4,779 1,784 10,554 11,768 12,375 5,375 2,399 11,164 12,380 12,988 1 Cumulative 15-year NPV ($/ac). 2Yield from HLB infected trees reduced 20%, 10% and 5% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

61

05

1015

0.10.2

0.30.4

0.5-1

-0.5

0

0.5

1

1.5

x 104

Age of Trees at First detectionHLB Incidence at First Detection

Ne

t P

rese

nt

Va

lue

-5000

0

5000

10000

15000

Figure 4-1. Net Present Value per Acre as a Function of Disease Incidence and

Average Age (Years) of Trees at First Detection with Contour Lines for the Do Nothing Strategy

05

1015

0.10.2

0.30.4

0.5-1.5

-1

-0.5

0

0.5

1

x 104


Ne

t P

rese

nt

Va

lue

-1

-0.5

0

0.5

1

x 104


Average Age (Years) of Trees at First Detection with Contour Lines for Strategy 2

62

05

1015

0.10.2

0.30.4

0.5-5000

0

5000

10000


Ne

t P

rese

nt

Va

lue

-2000

0

2000

4000

6000

8000

10000

12000


Average Age (Years) of Trees at First Detection with Contour Lines for Strategy 3 (30% Yield Penalty)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

2

4

6

8

10

12

14

16

Disease Incidence at First detection

Cu

mm

ula

tive

Ave

rag

e G

rove

Ag

e

Strategy 3

Strategy 2

Strategy 1

Figure 4-4. Dominant Strategy Given Disease Incidence at First Detection and Average

Grove Age (Price = $1.50/pound solid, 30% yield penalty for strategy 3)

63

CHAPTER 5 SENSITIVITY ANALYSIS

In this chapter, the robustness of the model’s conclusions is tested by performing

sensitivity analysis to determine how changes the main parameters of the model affect

the optimal strategy mix. Changes in the age-dependent rate of spread (β) affect the

disease spread, which in turn alter fruit yield and net returns with a resulting impact on

the optimal strategy. Changes in the price per pound solids directly impacts the net

present value estimates. Other parameters that affect the optimal choice of the model

include the period of latency and fruit yield. This chapter considers the effects of

changing prices, betas (rate of spread) and period of latency on optimal strategy. First,

the impact of a price decrease from $1.50/pound solids to $1.20, followed by a price

increase from $1.50 to $1.80/pound solids are examined for each of the three age

cohorts. Next, the age dependent rate of spread and the latency periods are also

adjusted to observe their effect on model results.

The Effects of a Price Decline

Tables 5-1 through 5-3 presents the net present values for the three strategies

for a delivered-in price from $1.50 to $1.20 per pound solid for each of the three age

categories. In Table 5-1, irrespective of the strategy or disease incidence at first

detection, the age cohorts of 0 and 3 produces negative net present values when price

falls. This trend is reversed for the mature groves with average ages of 6, 10, 14, and

17 where net present values are positive, except at high incidence values of 30% to

50%, where some strategies still yield negative net present values. In Tables 5-2 and 5-

3, at low disease incidence of 0.1% - 10.0% (at high incidence of 20% - 50%), Strategy

1 (Strategy 3) is the superior strategy for groves with average ages of 6, 10, 14, and 17.

64

Overall, the lowered price results in lower net present value for all groves at all levels of

disease incidence. A fall in price favors strategy 1 as it completely replaces strategies 2

and 3 at the lower levels of incidence of 0.1% - 10%.

The Effects of a Price Increase

When price is increase from $1.50 to $1.80 per pound solid, the net present

value is still negative for almost all levels of incidence for groves with average age of 0,

but now positive for groves with average ages of 3 or more except at high incidence of

8% to 50% (30% to 50%) in which Strategy 1 (Strategy 2) posts negative net present

values (Table 5-4). In Table 5-4, at low initial disease incidence (0.1% to 7%), Strategy

2 is better than Strategies 1 and 3 for groves with average age of 3. Thereafter, at initial

disease incidence of 8% to 50%, Strategy 3 overtakes Strategy 2 as the best strategy in

net present value. This result again confirms that at higher rates of infection, Strategy 3

is preferred over Strategy 2 because of the high tree removal rates associated with

Strategy 2. For groves with average age of 6 or more, Strategy 1 is only dominant at

0.1% to 1% level of initial incidence, whereas Strategy 2 is dominant for all initial

incidence rates ranging from 2% to 8%. When the initial incidence rate exceeds 10%,

Strategy 3 takes over from Strategy 2 (Tables 5-5 and 5-6). Increased price results in

higher net present value for all groves at all levels of disease incidence. The switch

point (7%) between Strategy 2 and 3 for groves of average age 3 do not change when

price increase. This may be attributed to the fact that as price increase; net present

value of existing fruits increases making it more expensive to remove trees.

In Figure 5-1 (middle subplot), the ranges of initial grove age and initial disease

incidence for which each strategy maximizes net present value shows that when price

falls, Strategy 1 (Strategy 3) is the optimal strategy for all groves, when disease

65

incidence ranges between 0.1% to 10% (20% to 50%). Therefore, when price is

lowered, Strategy 1 replaces Strategy 2 (and some part of Strategy 3) as the optimal

strategy for all groves when disease incidence ranges from 0.1% to 10%. In Figure 5-1

(bottom subplot), when price increase, the optimal strategy is Strategy 2 for initial

incidence of 2% to 8% for all groves and for groves of 6 years or larger, Strategy 1 is

optimal at incidence of 0.1% to 1%. For all groves at 10% to 50% incidence, Strategy 3

is the best strategy. Strategy 1’s area at 2% initial disease incidence for groves over 6

years is taken over by Strategy 2, and Strategy 2’s area at 1.0% initial disease

incidence for groves older than 14 years is taken over by Strategy 3.

The Effects of a Lower Annual Rate of Spread

Tables 5-7 through 5-9 presents results for a lower annual rate of spread of HLB

from Beta (1) = 1.5148125– 0.3= 1.2148125; Beta (2) = 0.8450625 – 0.3 = 0.5450625;

Beta (3) = 0.4440625– 0.3 = 0.1440625, for the respective age cohorts. A lower rate of

spread could be attributed to several factors, but most notably, if a psyllid control

program proves effective, its primary consequence would be a reduction in the rate of

spread. When the betas are lowered, groves with average age of 0 show negative net

present values irrespective of the initial disease incidence (Table 5-7). For groves with

average age of 3, Strategy 2 is superior from disease incidence of 1% to 10%, after

which Strategy 3 becomes superior from disease incidence of 20% to 50%. In Tables

5-8 and 5-9, Strategy 1 dominates from 0.1% to 10% initial disease incidence, whereas

Strategy 3 dominates thereafter from 20% to 50% initial disease incidence, for all

matured groves with average ages of 6 or more. The decreased betas have resulted in

higher net present value for all groves at all levels of disease incidence.

66

The Effects of an Increased Annual Rate of Spread

An increase in the annual rates of spread from Beta (1) = 1.5148125+ 0.3 =

1.8148125; Beta (2) = 0.8450625 + 0.3 = 1.1450625; Beta (3) = 0.4440625+ 0.3 =

0.7440625; for the respective average age category, gives similar results for groves with

average age of 0 and 3, in which the former presents negative net present values, and

the later shows dominance for Strategy 2 at initial incidence of between 0.1% to 2.0%,

and thereafter from 3% to 50%, Strategy 3 is the best strategy. However, for groves with

average age of 6 or larger, Strategy 1 does best for incidences of 0.1% only, Strategy 2

does best for incidences of 1.0% to 6%, and Strategy 3 does best for incidences 7% to

50%. The increased betas have resulted in smaller net present value for all groves at

all levels of disease incidence.

A reduction in the betas also affects the optimal strategy mix (Figure 5-2).

Strategy 1 (Strategy 3) is the optimal strategy for groves 6 years or larger when initial

disease incidence is 0.1% to 10% (20% to 50%). For groves with average age of 0 and

3 (0 or larger, i.e. all groves), Strategy 2 (Strategy 3) is optimal at incidence of 1% to

10% (20% to 50%). As a result of the reduction in the betas, Strategy 1 replaces

Strategy 2 as the dominant strategy for groves older than 6 years at disease incidence

of 3% to 10%. For an increase in the betas (Figure 5-2, bottom subplot), Strategy 1 has

the smallest area of optimality, which occurs only at the lowest level of initial incidence

of 0.1% for groves 6 years or larger. For all groves at incidence of 1% - 6% (7% - 50%),

Strategy 2 (Strategy 3) is the best strategy. Strategy 2 replaces strategy 1 as dominant

strategy for groves older than 6 years when disease incidence is between 1.0% and

2.0%, whereas Strategy 3 replaces Strategy 2 for groves older than 6 years when

disease incidence is from 6% to 8%.

67

The primary consequence of decreased rate of spread is to make Strategy 2

more attractive. This result makes sense as the goal of Strategy 2 is to suppress the

level of disease inoculum. A lower rate of disease spread gives a grower more time to

initiate Strategy 2 and thereby enjoy its benefits. Lower disease spread rate also

means that fewer trees are being removed early in the treatment period. This results in

a smaller decrease in fruit revenue. The contrary effect emerges when the rate of

spread is increased. Faster spread of the disease means the growers have a shorter

window of opportunity to implement Strategy 2; Strategy 3 is preferred at younger ages

of first detection and smaller levels of initial incidences at first detection.

The Effects of a Shortened Latency Period

The latency period refers to the interval between the time a tree first becomes

infected and when is expresses symptoms. The existence of the latency period is one

of the most vexing dimensions of the disease in that a tree removal policy fails to

eliminate all diseased trees. Bové (2012) has recently argued that the latency period

may be shorter than that suggested in earlier literature on HLB. In this section we

investigate the impact of a shorter latency period on the optimal strategy.

Another dimension to this analysis is the efficacy of scouting in detecting the

disease. Futch et al. (2009) argues that one pass through a grove where HLB is present

will result in 50% of symptomatic trees being detected. Bové’s (2012) argument

regarding latency is based upon the observation that symptomatic trees may be

present, but scouts are unable to detect them. Therefore, improved detection

techniques could reduce the latency period.

Tables 5-13 through 5-15 presents results for the scenario when the latency

period is reduced such that groves with ages of 0 and 3 now are assumed to have a

68

latency period of 6 months instead of 1 year, while the latency period of groves 6 years

or larger remain unchanged at 2 years. Results show that all cases in which age of first

detection is 0 display negative net present values. Groves with average age of 3

displays net present values in which Strategy 2 is best when disease incidence is 0.1%

to 10.0%; Strategy 3 is best when disease incidence is 20.0% to 50.0%. For groves 6

years or larger, Strategy 1 does best from disease incidence of 0.1% to 1.0%, after

which Strategy 2 is best at 2.0% to 10.0% disease incidence, followed by Strategy 3,

which is optimal at incidence of 20.0% to 50.0%. In Figure 5-3, the reduction in latency

period favors Strategy 2 more compared to Strategy 1 (and 3), for groves older than 6

years when disease incidence is 2% (10%). Strategy 3 is dominant at disease incidence

of 20% to 50% for all groves. The change in latency has resulted in lower net present

value for all groves at all levels of disease incidence.

Comparison of the results in Table 4-7 and Table 5-13, however, suggest that

shortening the latency period does impact the optimal strategy. Under the baseline

latency period, for groves of three years of age at first detection, Strategy 3 is superior

for initial infection rates of 9% and higher, but with a shortened latency period,

superiority of Strategy 3 shifts to initial infections rates of 10% and higher. While this is a

small change, it does indicate that superior detection methods that could reduce the

period of latency would benefit Strategy 2.

69

Table 5-1. NPV1 for the Three Strategies for Age Classes 0 and 3 from a Price Decline2


Average Age of Trees at First Detection

0 3

Strategy Strategy

1 2 3 1 2 3

0.001 -3,986 -3,397 -4,655 521 347 -1,115

0.010 -5,043 -5,902 -4,972 -1,626 -26 -1,759

0.020 -5,321 -6,950 -5,056 -2,320 -418 -1,967

0.030 -5,436 -7,553 -5,090 -2,794 -788 -2,109

0.040 -5,494 -7,969 -5,108 -3,013 -1,137 -2,175

0.050 -5,610 -8,280 -5,142 -3,174 -1,468 -2,223

0.060 -5,653 -8,529 -5,155 -3,480 -1,782 -2,315

0.070 -5,686 -8,730 -5,165 -3,594 -2,080 -2,349

0.080 -5,712 -8,901 -5,173 -3,690 -2,365 -2,378

0.100 -5,747 -9,174 -5,183 -3,843 -2,895 -2,424

0.200 -5,884 -9,922 -5,225 -4,472 -4,979 -2,613

0.300 -5,905 -10,259 -5,231 -4,887 -6,456 -2,737

0.400 -5,970 -10,436 -5,250 -5,218 -7,568 -2,837

0.500 -5,983 -10,532 -5,254 -5,345 -8,433 -2,875 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is reduced from $1.50 to $1.20. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

70




6 10

Strategy Strategy

1 2 3 1 2 3

0.001 5,980 2,852 2,260 8,149 5,025 4,433

0.010 4,562 2,680 1,834 6,684 4,835 3,993

0.020 3,754 2,490 1,592 5,832 4,626 3,738

0.030 3,196 2,302 1,425 5,238 4,420 3,560

0.040 2,848 2,116 1,320 4,858 4,215 3,445

0.050 2,450 1,932 1,201 4,431 4,013 3,317

0.060 2,219 1,750 1,131 4,175 3,812 3,240

0.070 1,875 1,570 1,028 3,805 3,614 3,130

0.080 1,703 1,392 977 3,612 3,418 3,072

0.100 1,412 1,041 889 3,283 3,031 2,973

0.200 152 -609 511 1,872 1,212 2,550

0.300 -578 -2,099 292 1,036 -435 2,299

0.400 -1,389 -3,446 49 105 -1,925 2,020

0.500 -1,673 -4,659 -36 -232 -3,270 1,918 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is reduced from $1.50 to $1.20. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

71




14 17

Strategy Strategy

1 2 3 1 2 3

0.001 9,575 6,452 5,860 10,028 6,904 6,312

0.010 8,103 6,256 5,418 8,555 6,708 5,871

0.020 7,243 6,039 5,160 7,695 6,492 5,613

0.030 6,642 5,826 4,980 7,093 6,278 5,432

0.040 6,253 5,614 4,863 6,705 6,067 5,316

0.050 5,819 5,405 4,733 6,271 5,857 5,185

0.060 5,556 5,197 4,654 6,007 5,650 5,106

0.070 5,180 4,992 4,541 5,630 5,445 4,993

0.080 4,980 4,789 4,481 5,430 5,242 4,933

0.100 4,638 4,389 4,379 5,088 4,841 4,830

0.200 3,174 2,503 3,939 3,620 2,955 4,390

0.300 2,293 793 3,675 2,738 1,245 4,125

0.400 1,316 -757 3,382 1,758 -305 3,831

0.500 948 -2,159 3,272 1,387 -1,706 3,720 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is reduced from $1.50 to $1.20. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

72

Table 5-4. NPV1 for the Three Strategies for Age Classes 0 and 3 from a Price Increase2



0 3

Strategy Strategy

1 2 3 1 2 3

0.001 -1,371 2,108 314 7,165 9,313 7,176

0.010 -3,241 -2,197 -247 3,480 8,671 6,140

0.020 -3,744 -4,006 -398 2,286 7,998 5,712

0.030 -3,956 -5,050 -461 1,469 7,363 5,467

0.040 -4,065 -5,773 -526 1,090 6,762 5,353

0.050 -4,275 -6,315 -557 810 6,194 5,269

0.060 -4,355 -6,749 -581 282 5,655 5,111

0.070 -4,418 -7,102 -600 85 5,142 5,052

0.080 -4,467 -7,402 -615 -83 4,653 5,001

0.100 -4,533 -7,883 -635 -351 3,741 4,921

0.200 -4,791 -9,216 -712 -1,449 157 4,592

0.300 -4,832 -9,828 -724 -2,175 -2,386 4,374

0.400 -4,954 -10,155 -761 -2,758 -4,305 4,199

0.500 -4,980 -10,334 -769 -2,983 -5,796 4,131 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is increased from $1.50 to $1.80. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

73




6 10

Strategy Strategy

1 2 3 1 2 3

0.001 16,947 14,030 13,384 20,952 18,043 17,397

0.010 14,516 13,734 12,655 18,441 17,717 16,643

0.020 13,131 13,409 12,239 16,982 17,359 16,205

0.030 12,176 13,087 11,953 15,964 17,005 15,900

0.040 11,578 12,768 11,773 15,311 16,654 15,704

0.050 10,896 12,453 11,569 14,579 16,307 15,485

0.060 10,500 12,141 11,450 14,140 15,964 15,353

0.070 9,911 11,832 11,273 13,507 15,624 15,163

0.080 9,615 11,527 11,185 13,175 15,287 15,063

0.100 9,117 10,926 11,035 12,610 14,625 14,894

0.200 6,957 8,098 10,387 10,192 11,506 14,169

0.300 5,705 5,542 10,011 8,759 8,683 13,739

0.400 4,314 3,234 9,594 7,163 6,128 13,260

0.500 3,827 1,154 9,448 6,585 3,822 13,086 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is increased from $1.50 to $1.80. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

74




14 17

Strategy Strategy

1 2 3 1 2 3

0.001 23,398 20,488 19,843 24,174 21,264 20,619

0.010 20,873 20,152 19,086 21,649 20,928 19,862

0.020 19,401 19,781 18,644 20,175 20,557 19,420

0.030 18,369 19,415 18,335 19,143 20,191 19,110

0.040 17,703 19,052 18,135 18,477 19,828 18,910

0.050 16,959 18,693 17,912 17,733 19,469 18,687

0.060 16,508 18,338 17,776 17,281 19,114 18,551

0.070 15,863 17,986 17,583 16,635 18,762 18,358

0.080 15,520 17,638 17,480 16,292 18,414 18,254

0.100 14,934 16,952 17,304 15,705 17,728 18,078

0.200 12,424 13,719 16,551 13,190 14,494 17,324

0.300 10,915 10,787 16,098 11,676 11,563 16,870

0.400 9,239 8,130 15,596 9,996 8,906 16,366

0.500 8,609 5,727 15,407 9,362 6,503 16,175 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is increased from $1.50 to $1.80. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.

75

Table 5-7. NPV1 for the Three Strategies for Age Classes 0 and 3 from a Decline in Beta2



0 3

Strategy Strategy

1 2 3 1 2 3

0.001 -2,065 46 -1,986 5,872 4,859 3,639

0.010 -3,872 -1,462 -2,529 2,498 4,595 2,627

0.020 -4,228 -2,650 -2,635 1,394 4,308 2,296

0.030 -4,526 -3,540 -2,725 637 4,026 2,068

0.040 -4,649 -4,243 -2,762 274 3,750 1,960

0.050 -4,731 -4,817 -2,786 -262 3,479 1,799

0.060 -4,893 -5,298 -2,802 -489 3,213 1,731

0.070 -4,946 -5,710 -2,851 -677 2,951 1,674

0.080 -4,991 -6,067 -2,864 -1,107 2,695 1,546

0.100 -5,059 -6,663 -2,885 -1,373 2,195 1,465

0.200 -5,294 -8,417 -2,955 -2,422 -62 1,151

0.300 -5,346 -9,330 -2,971 -3,106 -1,987 946

0.400 -5,449 -9,909 -3,002 -3,655 -3,649 781

0.500 -5,470 -10,303 -3,008 -4,112 -5,095 644 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) =1.5148125 – 0.3 = 1.2148125 for the 0 Age Class; Beta (2) = 0.8450625 – 0.3= 0.5450625 for age Class of 3; Beta (3) = 0.4440625 – 0.3= 0.1440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

76




6 10

Strategy Strategy

1 2 3 1 2 3

0.001 11,826 8,449 7,931 14,918 11,542 11,025

0.010 11,288 8,285 7,769 14,351 11,361 10,855

0.020 10,759 8,104 7,611 13,791 11,160 10,687

0.030 10,289 7,922 7,469 13,291 10,959 10,537

0.040 9,866 7,742 7,343 12,840 10,759 10,402

0.050 9,483 7,561 7,228 12,430 10,560 10,278

0.060 9,132 7,381 7,123 12,053 10,361 10,165

0.070 8,810 7,202 7,026 11,706 10,162 10,061

0.080 8,513 7,023 6,937 11,383 9,964 9,965

0.100 7,978 6,667 6,776 10,802 9,570 9,790

0.200 6,081 4,914 6,207 8,710 7,629 9,163

0.300 4,827 3,209 5,842 7,306 5,740 8,752

0.400 3,106 1,550 5,393 5,454 3,901 8,266

0.500 1,303 -63 4,774 3,441 2,113 7,582 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) =1.5148125 – 0.3 = 1.2148125 for the 0 Age Class; Beta (2) = 0.8450625 – 0.3= 0.5450625 for age Class of 3; Beta (3) = 0.4440625 – 0.3= 0.1440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

77




14 17

Strategy Strategy

1 2 3 1 2 3

0.001 16,854 13,479 12,962 17,469 14,093 13,576

0.010 16,280 13,290 12,790 16,894 13,904 13,404

0.020 15,712 13,081 12,619 16,326 13,695 13,233

0.030 15,205 12,872 12,467 15,818 13,487 13,081

0.040 14,746 12,664 12,329 15,358 13,278 12,943

0.050 14,327 12,457 12,204 14,940 13,071 12,817

0.060 13,943 12,249 12,089 14,555 12,864 12,702

0.070 13,588 12,043 11,982 14,200 12,657 12,596

0.080 13,259 11,837 11,883 13,870 12,451 12,497

0.100 12,663 11,427 11,705 13,274 12,041 12,318

0.200 10,505 9,407 11,057 11,112 10,021 11,669

0.300 9,043 7,440 10,629 9,646 8,054 11,240

0.400 7,138 5,525 10,127 7,738 6,139 10,737

0.500 5,062 3,661 9,424 5,658 4,276 10,033 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) =1.5148125 – 0.3 = 1.2148125 for the 0 Age Class; Beta (2) = 0.8450625 – 0.3= 0.5450625 for age Class of 3; Beta (3) = 0.4440625 – 0.3= 0.1440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

78

Table 5-10. NPV1 for the Three Strategies for Age Classes 0 and 3 from an Increase in Beta2



0 3

Strategy Strategy

1 2 3 1 2 3

0.001 -3,104 -2,466 -2,298 2,514 4,712 2,632

0.010 -4,388 -6,016 -2,683 60 3,327 1,896

0.020 -4,683 -7,247 -2,772 -784 2,110 1,642

0.030 -4,789 -7,836 -2,804 -1,337 1,123 1,476

0.040 -4,966 -8,237 -2,857 -1,444 297 1,395

0.050 -5,039 -8,535 -2,879 -1,810 -409 1,335

0.060 -5,093 -8,771 -2,895 -1,963 -1,023 1,289

0.070 -5,131 -8,964 -2,906 -2,081 -1,564 1,253

0.080 -5,157 -9,126 -2,914 -2,405 -2,047 1,156

0.100 -5,181 -9,387 -2,921 -2,602 -2,877 1,097

0.200 -5,374 -10,110 -2,979 -3,341 -5,532 875

0.300 -5,378 -10,468 -2,980 -3,640 -7,058 786

0.400 -5,473 -10,691 -3,009 -4,042 -8,090 665

0.500 -5,492 -10,479 -3,015 -4,214 -8,832 613 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) = 1.5148125 + 0.3 = 1.8148125 for age class of 0; Beta (2) = 0.8450625 + 0.3= 1.1450625 for age class of 3; Beta (3) = 0.4440625 + 0.3= 0.7440625 for age classes 6 or larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

79




6 10

Strategy Strategy

1 2 3 1 2 3

0.001 10,474 8,423 7,525 13,551 11,514 10,615

0.010 7,698 8,025 6,692 10,658 11,082 9,747

0.020 6,637 7,597 6,374 9,514 10,617 9,404

0.030 6,085 7,183 6,208 8,901 10,166 9,220

0.040 5,505 6,781 6,034 8,267 9,728 9,030

0.050 5,187 6,391 5,939 7,909 9,303 8,922

0.060 4,929 6,012 5,862 7,615 8,890 8,834

0.070 4,512 5,644 5,737 7,156 8,489 8,696

0.080 4,317 5,286 5,678 6,932 8,098 8,629

0.100 3,992 4,600 5,580 6,558 7,347 8,517

0.200 2,767 1,641 5,213 5,148 4,100 8,094

0.300 1,926 -718 4,961 4,174 1,498 7,802

0.400 1,237 -2,635 4,754 3,370 -629 7,560

0.500 875 -4,197 4,645 2,940 -2,369 7,432 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) = 1.5148125 + 0.3 = 1.8148125 for age class of 0; Beta (2) = 0.8450625 + 0.3= 1.1450625 for age class of 3; Beta (3) = 0.4440625 + 0.3= 0.7440625 for age classes 6 or larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

80




14 17

Strategy Strategy

1 2 3 1 2 3

0.001 15,487 13,450 12,552 16,101 14,064 13,166

0.010 12,580 13,008 11,679 13,193 13,622 12,294

0.020 11,421 12,531 11,332 12,034 13,145 11,946

0.030 10,794 12,068 11,144 11,407 12,682 11,758

0.040 10,147 11,619 10,950 10,760 12,233 11,564

0.050 9,777 11,183 10,839 10,389 11,797 11,452

0.060 9,472 10,758 10,747 10,084 11,372 11,361

0.070 9,002 10,345 10,606 9,613 10,960 11,220

0.080 8,769 9,944 10,536 9,379 10,558 11,149

0.100 8,375 9,171 10,418 8,985 9,785 11,031

0.200 6,889 5,820 9,972 7,495 6,435 10,584

0.300 5,854 3,123 9,662 6,456 3,737 10,272

0.400 4,995 911 9,404 5,594 1,525 10,014

0.500 4,526 -907 9,263 5,121 -293 9,872 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) = 1.5148125 + 0.3 = 1.8148125 for age class of 0; Beta (2) = 0.8450625 + 0.3= 1.1450625 for age class of 3; Beta (3) = 0.4440625 + 0.3= 0.7440625 for age classes 6 or larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

81

Table 5-13. NPV1 for the Three Strategies for Age Classes 0 and 3 from a Lowered Latency Period2



0 3

Strategy Strategy

1 2 3 1 2 3

0.001 -4,195 192 -2,625 1,623 4,861 2,364

0.010 -4,898 -334 -2,836 -940 4,614 1,595

0.020 -5,152 -871 -2,913 -1,417 4,344 1,452

0.030 -5,213 -1,365 -2,931 -2,014 4,077 1,273

0.040 -5,244 -1,821 -2,940 -2,199 3,815 1,218

0.050 -5,259 -2,243 -2,945 -2,340 3,556 1,176

0.060 -5,380 -2,634 -2,981 -2,451 3,301 1,142

0.070 -5,392 -2,999 -2,985 -2,542 3,050 1,115

0.080 -5,402 -3,340 -2,988 -2,950 2,802 993

0.100 -5,417 -3,958 -2,992 -3,075 2,316 955

0.200 -5,437 -6,188 -2,998 -3,751 71 752

0.300 -5,498 -7,590 -3,016 -3,928 -1,907 699

0.400 -5,500 -8,558 -3,017 -4,353 -3,665 571

0.500 -5,501 -9,258 -3,017 -4,440 -5,234 546 1 Cumulative 15-year NPV ($/ac). 2 Latency is now 6 months for ages 0 and 3, and 2 years for ages of 6. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

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Table 5-14. NPV1 for the Three Strategies for Age Classes 6 and 10 from a Lowered Latency Period2



6 10

Strategy Strategy

1 2 3 1 2 3

0.001 11,287 8,447 7,769 14,372 11,540 10,861

0.010 9,181 8,264 7,137 12,193 11,337 10,207

0.020 8,045 8,061 6,796 10,994 11,112 9,848

0.030 7,457 7,859 6,620 10,355 10,888 9,656

0.040 6,849 7,658 6,438 9,703 10,665 9,460

0.050 6,504 7,457 6,334 9,320 10,443 9,345

0.060 6,006 7,258 6,185 8,785 10,223 9,185

0.070 5,761 7,060 6,111 8,509 10,003 9,102

0.080 5,547 6,863 6,047 8,267 9,784 9,030

0.100 4,944 6,471 5,866 7,608 9,350 8,832

0.200 3,533 4,567 5,443 6,006 7,240 8,351

0.300 2,254 2,754 5,059 4,554 5,230 7,916

0.400 1,453 1,031 4,819 3,623 3,320 7,636

0.500 1,075 -603 4,705 3,174 1,507 7,502 1 Cumulative 15-year NPV ($/ac). 2 Latency is now 6 months for ages 0 and 3, and 2 years for ages of 6. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

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Table 5-15. NPV1 for the Three Strategies for Age Classes 14 and 17 from a Shortened Latency Period2



14 17

Strategy Strategy

1 2 3 1 2 3

0.001 16,308 13,476 12,798 16,923 14,091 13,412

0.010 14,118 13,265 12,141 14,732 13,879 12,755

0.020 12,907 13,030 11,778 13,521 13,644 12,392

0.030 12,257 12,797 11,583 12,870 13,411 12,197

0.040 11,594 12,565 11,384 12,207 13,179 11,998

0.050 11,202 12,334 11,266 11,814 12,948 11,880

0.060 10,657 12,104 11,103 11,268 12,718 11,716

0.070 10,372 11,875 11,017 10,983 12,489 11,631

0.080 10,120 11,647 10,942 10,731 12,262 11,555

0.100 9,444 11,195 10,739 10,054 11,809 11,352

0.200 7,770 8,997 10,237 8,376 9,611 10,848

0.300 6,255 6,903 9,782 6,857 7,517 10,393

0.400 5,265 4,912 9,485 5,864 5,526 10,095

0.500 4,777 3,023 9,339 5,372 3,637 9,947 1 Cumulative 15-year NPV ($/ac). 2 Latency is now 6 months for ages 0 and 3, and 2 years for ages of 6. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.

84

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

Strategy 3

Strategy 2

Strategy 1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

Cu

mm

ula

tive

Ave

rag

e G

rove

Ag

e

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15



Grove Age from a Change in Price: Top Subplot is Baseline, Middle and Bottom Subplots Shows Price Decline (from $1.50 to $1.20) and Increase (from $1.50 to $1.80), respectively

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

Strategy 3

Strategy 2

Strategy 1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

Cu

mm

ula

tive

Ave

rag

e G

rove

Ag

e

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15


Figure 5-2. Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age from a Change in Beta: Top Subplot is Baseline, Middle and Bottom Subplots Shows Beta Decline and Increase, respectively

85

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

Cu

mm

ula

tive

Ave

rag

e G

rove

Ag

e

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15


Strategy 3

Strategy 2

Strategy 1


Grove Age from a Change in Latency: Top Subplot is Baseline, Bottom Subplot Shows Decline in Latency from 1 year to 6 Months for Groves with Average Age of 0 and 3 while the Latency for Groves 6 Years or Larger Remain at 2 Years

86

CHAPTER 6 CONCLUSIONS, RECOMMENDATIONS AND LIMITATIONS

The preceding chapters have sought to develop a management strategy for HLB

at the grove level for citrus producers in Florida. A baseline model was developed to

simulate the economic consequences for the “Do nothing” control strategy. This served

as a benchmark for the modeling of the infected tree removal strategy as well as the

enhanced foliar nutritional strategy. The adoption of a particular strategy by a grower is

seen to be a function of certain grove characteristics. This research has identified the

various zones of optimality for each strategy given a grove’s average age and initial

HLB infection rate.

This research attempted to integrate the intricate biological realities of HLB into

an economic decision making framework for producers. The basis of the biological

model is provided by the works of Bassanezi and Bassanezi (2008) and Bassanezi et

al. (2011). This research demonstrate that the complex biological features of HLB can

be transformed into an economic decision making process for citrus growers. The effect

of latency on control effectiveness especially when employing Strategy 2 for example is

addressed in this analysis. The most important contribution of this research is the

incorporation of both symptomatic and asymptomatic trees in the logistic spread curves

used in the analysis. This ensures that even if symptomatic trees are removed (as in

Strategy 2); spread through asymptomatic trees is still accounted for in the model. The

rate of spread of HLB is a function of the grove’s age cohort, which has been intricately

knitted into each of the three models of control strategies in this analysis. Additionally, in

varying the level of initial infection in the analysis, this research also demonstrates the

heterogeneous effects of HLB to NPV at the landscape level, whereby optimal control

87

decisions varies across neighbors. The significance of this research lies in its ability to

address these characteristics and formulate optimal control policy for effective decision

making.

In summary, we find that groves that contain younger trees at first detection have

low or negative net present value due to the faster spread of the disease in younger

groves in addition to low production from young groves. For Strategy 1, all groves with

an average age of 6 years and larger will yield a positive net present value, irrespective

of the initial level of infection. For Strategy 2, except when initial incidence is 40% to

50%, all groves with an average age of 6 or larger yields a positive net present value.

For Strategy 3, all groves with an average age of 3 or larger at all initial incidence levels

yields a positive net present value. Whether cost exceeds revenue in production is a

function of disease incidence and average grove age. The higher the initial incidence

level (the larger the average grove age), the more likely (less likely) that cost of

production exceeds revenue from production.

Finally, we find that the optimal strategy to adopt by a grower depends on the

average grove age at first detection and the initial rate of disease incidence at first

detection. Irrespective of the average grove age, once initial incidence is 20% or larger

in a grove, Strategy 3 should be implemented. The intuition of this recommendation is

that it is better to incur the extra costs of nutritional supplements than remove 20% or

more of productive but sick trees or even do nothing. The marginal revenue from this

action is more than its marginal cost. At higher rates of infection, Strategy 3 is preferred

over Strategy 2 because of the high tree removal rates associated with Strategy 2.

Implementation of Strategy 2 requires that initial incidence should be 3% to 8% for

88

groves 6 years or larger or 0.1% - 2% for groves of average age 0 or 3. Here, the

intuition is that removing 3% to 8% of infected mature trees or 0.1% - 2% of newly

established trees is more cost effective compared to spraying such trees with nutritional

supplements or doing nothing. When there is virtually no infection (0.1% to 1%) in a

grove of age 6 or larger, doing nothing is in the best interest of the producer. The

relationship between the net present value and model parameters such as delivered-in

price, the rate of spread of HLB, and latency has been established through the

sensitivity analysis. It is found that net present value is positively related to price but

negatively related to the rate of spread and the latency period. Changes in these

parameters also results in changes in the optimal strategy mix. In particular, results

indicate that superior detection methods that could reduce the period of latency would

benefit Strategy 2. Results also suggest that the primary consequence of

decreased/increased rate of spread (our proxy for psyllid control) is to make Strategy

2/Strategy 3 more attractive.

The rate of spread of HLB is related to three factors including average grove age,

initial incidence at first detection, and the psyllid population. Even though our model did

not directly incorporate psyllid control into the analysis, reduction in the annual rate of

HLB spread investigated via the sensitivity analysis can serve as proxy for psyllid

control because total elimination of psyllids notably terminates HLB spread.

Effective control of plant diseases that involves spread by vectors and other

weather factors such as HLB requires a model that recognizes landscape management

characteristics, which is missing in this analysis for now. Neighbor effects negatively

affects heterogeneous management protocols by adjacent growers since buildup of

89

bacteria titer in a grove practicing Strategy 1 or 3 could diminish the inoculum reduction

objective of a neighbor practicing Strategy 2. One other drawback is the lack of HLB

spread data from Florida required to estimate the model parameters. Although the

parameters used may not be representative of the HLB situation in Florida, the results

derived here do serve as a guide and reference point for growers and policy makers in

the industry. The assumption of no resetting greatly simplifies the calculation of disease

spread and the accompanying reduction in fruit production per acre. However, this

assumption clearly is a limitation on the derived results. The lack of knowledge on the

underlying distribution of the key variables that affect net present value in the presence

of HLB has forced us to proceed with the analysis in a deterministic framework. Cleary,

stochastic dominance would have been the best estimator of superiority. It is hoped that

future research can be greatly enhanced when most of these limitations are addressed.

90

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BIOGRAPHICAL SKETCH

By the decree of God, Abdul Wahab Salifu was born to a noble couple in a

polygamous home in the heart of Tamale in the northern region of Ghana on a blessed

day. He started school at the Methodist primary school in Tamale and proceeded after 6

years to the Bagabaga Demonstration junior secondary school also in Tamale. He

obtained his high school certificate at Ghana secondary school in Tamale in 1990. From

here, he proceeded to the Ohawu Agricultural College in the Volta region of Ghana

where he obtained the general certificate of agriculture in 1993. He started his work

career as an agricultural extension agent at Zabzugu district in the northern region of

Ghana. In 1999 and 2003, he obtained his national diploma of agriculture and B.Sc.

degree respectively at the University of Ghana. Having worked as assistant regional

MIS officer at the Ministry of Agriculture in the northern region of Ghana from 2003 to

2004, he started his research career as an assistant research officer at Ghana’s CSIR-

Savanna agricultural research institute in Tamale from 2004 to 2006. In the spring of

2009 he obtained his MS degree from Tuskegee University in Alabama. He received his

Ph.D. from the University of Florida in the spring of 2013.

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