Hierarchical Modeling for Hierarchical Modeling for Economic Analysis of Biological Economic Analysis of Biological

Systems: Value and Risk of Systems: Value and Risk of Insecticide Applications for Corn Insecticide Applications for Corn

Borer Control in Sweet CornBorer Control in Sweet Corn

Economics and Risk Economics and Risk of Sweet Corn IPMof Sweet Corn IPMPaul D. MitchellPaul D. Mitchell

Agricultural and Applied EconomicsAgricultural and Applied EconomicsUniversity of Wisconsin-MadisonUniversity of Wisconsin-Madison

University of Minnesota Department of University of Minnesota Department of Entomology SeminarEntomology Seminar

April 11, 2006April 11, 2006

Goal TodayGoal Today

1) Explain and illustrate Hierarchical 1) Explain and illustrate Hierarchical ModelingModeling

2) Provide economic intuition of findings 2) Provide economic intuition of findings concerning the economic value of IPM concerning the economic value of IPM for sweet cornfor sweet corn

Overview work in progress with Bill Overview work in progress with Bill Hutchison and Terry Hurley on sweet Hutchison and Terry Hurley on sweet corn IPM as part of a NC-IPM grantcorn IPM as part of a NC-IPM grant

All work in progressAll work in progress

Problem/IssueProblem/Issue

Use existing insecticide field trial data to Use existing insecticide field trial data to estimate the estimate the value and risk of IPMvalue and risk of IPM for for insecticide based control of European corn insecticide based control of European corn borer (ECB) in processing and fresh market borer (ECB) in processing and fresh market sweet cornsweet corn

Operationally: Operationally: Do I need another spray?Do I need another spray?Estimate the expected value of an Estimate the expected value of an additional additional insecticide applicationinsecticide application for ECB control for ECB control

Use hierarchical modeling to incorporate risk Use hierarchical modeling to incorporate risk into the analysisinto the analysis

Conceptual ModelConceptual Model

Keep key variables random to capture Keep key variables random to capture the risk (uncertainty) in pest controlthe risk (uncertainty) in pest control

Develop a hierarchical model = linked Develop a hierarchical model = linked conditional probability densitiesconditional probability densities

Estimate pdf of a variable with Estimate pdf of a variable with parameters that depend (are parameters that depend (are conditional) on variables from another conditional) on variables from another pdf, with parameters that are pdf, with parameters that are conditional on variables from another conditional on variables from another pdf, etc. … … … … pdf, etc. … … … …

Random Initial ECB

Random % Survival givesRandom Remaining ECB

Observe ECBApply Insecticide?

Random % Marketable

Net Returns

Random Pest-Free Yield

Net Returns = P x Y x %Mkt – Pi x AIi – #Sprys x CostApp – COP

Random Price

Random Initial ECBRandom Initial ECB Mitchell et al. (2002): 2Mitchell et al. (2002): 2ndnd generation ECB generation ECB

larval population density per plant collected larval population density per plant collected by state agencies in MN, WI, ILby state agencies in MN, WI, IL

Empirically support lognormal density with no Empirically support lognormal density with no autocorrelation (new draw each year)autocorrelation (new draw each year)

Sweet corn has more ECB pressure, so use Sweet corn has more ECB pressure, so use MN & WI insecticide trial data for mean and MN & WI insecticide trial data for mean and st. dev., pooling over years 1990-2003st. dev., pooling over years 1990-2003

Lognormal density: mean = 1.28, CV = 78%Lognormal density: mean = 1.28, CV = 78%

Insecticide Efficacy DataInsecticide Efficacy Data Efficacy data from pyrethroid trials (~ 50)Efficacy data from pyrethroid trials (~ 50) Capture, Warrior, Baythroid, Mustang, Capture, Warrior, Baythroid, Mustang,

PouncePounce Most data from: MN, WI, IN and ESA’s AMTMost data from: MN, WI, IN and ESA’s AMT Data include:Data include:

Mean ECB larvae/ear for treated and Mean ECB larvae/ear for treated and untreated (control) plots of sweet cornuntreated (control) plots of sweet corn

Percentage yield marketable for Percentage yield marketable for processing and for fresh marketprocessing and for fresh market

Number of sprays and application rateNumber of sprays and application rate

Model: ECB = ECBModel: ECB = ECB00 x (% Survival) x (% Survival)sprayssprays

Example: ECBExample: ECB00 = 4, 50% survival per = 4, 50% survival per spray, 2 sprays, then ECB = 4(½)spray, 2 sprays, then ECB = 4(½)22 = 1 = 1

Rearrange: % Survival = Rearrange: % Survival = (ECB/ECB(ECB/ECB00))1/sprays1/sprays

Geometric mean of % Survival per sprayGeometric mean of % Survival per spray Use observed ECB, ECBUse observed ECB, ECB00, and number of , and number of

sprays to construct dependent variable: sprays to construct dependent variable: “Average % survival per spray”“Average % survival per spray”

Random ECB after SpraysRandom ECB after Sprays

Random % SurvivalRandom % Survival Dependent variable: Average % Survival per Dependent variable: Average % Survival per

sprayspray RegressorsRegressors

ECBECB00 (density dependence) (density dependence) Number sprays (decreasing returns)Number sprays (decreasing returns) Chemical specific effectChemical specific effect

Beta density (0 to 1) with separate equations Beta density (0 to 1) with separate equations for mean and st. dev. (Mitchell et al. 2004)for mean and st. dev. (Mitchell et al. 2004)

Mean = exp(Mean = exp(00 + + 11ECBECB00 + + 22Sprays + Sprays + iiRateRateii)) St. Dev. = exp(St. Dev. = exp(00 + + 11Sprays)Sprays)

ParameterParameter EstimateEstimate ErrorError

t-t-statististatisti

cc P-valueP-value

00 -1.603-1.603 0.1870.187 -8.587-8.587 [.000][.000]

11 -0.101-0.101 0.04740.0474 -2.126-2.126 [.033][.033]

00 -0.902-0.902 0.1950.195 -4.632-4.632 [.000][.000]

11 -0.0800-0.0800 0.02890.0289 -2.771-2.771 [.006][.006]

22 0.1150.115 0.01690.0169 6.8216.821 [.000][.000]

PouncePounce -2.535-2.535 1.1411.141 -2.221-2.221 [.026][.026]

MustangMustang -4.967-4.967 4.7684.768 -1.042-1.042 [.298][.298]

BaythroiBaythroidd -10.101-10.101 5.1565.156 -1.959-1.959 [.050][.050]

CaptureCapture -12.609-12.609 5.4565.456 -2.311-2.311 [.021][.021]

WarriorWarrior -17.423-17.423 8.2218.221 -2.119-2.119 [.034][.034]

RR22 = 0.192 = 0.192 RMSE = 0.137RMSE = 0.137N = N = 191191

Model ImplicationsModel Implications Mean = exp(Mean = exp(00 + + 11ECBECB00 + + 22Sprays + Sprays + iiRateRateii)) ECBECB00 increase: Mean %S decreases since increase: Mean %S decreases since 11 < 0 < 0

Density dependence: more ECB, lower survival Density dependence: more ECB, lower survival raterate

RateRateii increase: Mean %S decreases since increase: Mean %S decreases since ii < 0 < 0 More insecticide, lower survival More insecticide, lower survival raterate Use Use ’s to compare across insecticides’s to compare across insecticides Warrior>Capture>Baythroid>Mustang>PounceWarrior>Capture>Baythroid>Mustang>Pounce

Spray increase: Mean %S increases since Spray increase: Mean %S increases since 22 > 0 > 0 AverageAverage survival rate per spray increases with survival rate per spray increases with

sprayssprays Total survival rate = %SurivialTotal survival rate = %Surivialsprayssprays decreases decreases

0

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Total %S

Illustration of average %S per spray and total %S with Capture at a rate of 0.04 AI/ac with ECB0 of 2

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Effect of ECB0 on conditional pdf of avg %Survival per spray

RED: ECB0 = 1 GREEN: ECB0 = 3 BLUE: ECB0 = 5

Randomly drawn ECB0 affects % Survival pdf

Effect of sprays on conditional pdf of avg %Survival per spray

RED: 1 spray GREEN: 3 sprays BLUE: 5 sprays

Chosen number of sprays affects % Survival pdf

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Hierarchical Model Hierarchical Model Series of Linked Conditional Series of Linked Conditional

pdf’spdf’s1)1) Draw Random ECBDraw Random ECB00 from lognormal from lognormal

2)2) Draw Average % Survival per spray from beta Draw Average % Survival per spray from beta with mean and st. dev. depending on ECBwith mean and st. dev. depending on ECB00, , number of sprays, chemical, and ratenumber of sprays, chemical, and rate

3)3) Calculate ECB = ECBCalculate ECB = ECB00 x (% Survival) x (% Survival)sprayssprays

4)4) Draw % Marketable depending on ECBDraw % Marketable depending on ECB

5)5) Draw yield and price, calculate net returnsDraw yield and price, calculate net returns Unconditional pdf for ECB or net returns = ???Unconditional pdf for ECB or net returns = ??? Must Monte Carlo simulate and use Must Monte Carlo simulate and use

histograms and characterize pdf with mean, histograms and characterize pdf with mean, st. dev., etc.st. dev., etc.

Random Initial ECB

Random % Survival givesRandom Remaining ECB

Observe ECBApply Insecticide?

Random % Marketable

Net Returns

Random Pest-Free Yield

Net Returns = P x Y x %Mkt – Pi x AIi – #Sprys x CostApp – COP

Random Price

lognormal density

transformed betatimes lognormal

beta densities

lognormal density

Rest of the Model: Quick Rest of the Model: Quick SummarySummary

% Marketable for Processing or Fresh % Marketable for Processing or Fresh Market has beta density (0 to 1)Market has beta density (0 to 1) mean = exp(kmean = exp(k00 + k + k11ECB), constant st. dev.ECB), constant st. dev. More ECB, on average lower percentage More ECB, on average lower percentage

marketable (exponential decrease)marketable (exponential decrease) Pest Free yield has beta density Pest Free yield has beta density

(common)(common) Minimum: 0 tons/acMinimum: 0 tons/ac Maximum: 9.9 tons/ac (mean + 2 st. dev.)Maximum: 9.9 tons/ac (mean + 2 st. dev.) Mean: 6.6 tons/ac (WI NASS 3-yr avg.)Mean: 6.6 tons/ac (WI NASS 3-yr avg.) CV: 25% (increase WI NASS state CV)CV: 25% (increase WI NASS state CV)

Prices and CostsPrices and Costs Sweet Corn: $67.60/tonSweet Corn: $67.60/ton Insecticides ($/ac-treatment)Insecticides ($/ac-treatment) CaptureCapture Warrior Warrior BaythroidBaythroid

$2.82/ac$2.82/ac $3.49/ac$3.49/ac $6.09/ac$6.09/ac MustangMustang PouncePounce

$2.80/ac$2.80/ac $3.76/ac$3.76/ac Aerial Application: $4.85/ac-treatmentAerial Application: $4.85/ac-treatment Other Costs of Production:Other Costs of Production: $200/ac$200/ac No Cost for ECB Scouting, Farmer No Cost for ECB Scouting, Farmer

Management Time, or LandManagement Time, or Land

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Warrior

•Value of 1Value of 1stst spray: $115-125/ac spray: $115-125/ac

•1 Scheduled Spray and use of IPM for 21 Scheduled Spray and use of IPM for 2ndnd spray spray maximizes farmer returnsmaximizes farmer returns

Mean Returns ($/ac)

175

180

185

190

195

200

205

210

IPM Scheduled IPM Scheduled IPM Scheduled

2nd Spray 3rd Spray 4th Spray

Baythroid

Capture

Warrior

Economic Thresholds (ECB larvae/ear)Economic Thresholds (ECB larvae/ear)

22ndnd spray: 0.15 spray: 0.15 33rdrd spray: 0.20 spray: 0.20 44thth spray: 0.25 spray: 0.25

Standard Deviation of Returns ($/ac)

107.40

107.60

107.80

108.00

108.20

108.40

IPM Scheduled IPM Scheduled IPM Scheduled

2nd Spray 3rd Spray 4th Spray

Baythroid

Capture

Warrior

IPM has lower risk (lower standard IPM has lower risk (lower standard deviation) than scheduled spraysdeviation) than scheduled sprays

Value of IPM/Change in Mean Returns ($/ac)

0123456789

10

Baythroid Capture Warrior

Val

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f IP

M (

$/ac

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2nd Spray

3rd Spray

4th Spray

•Source of IPM value is preventing unneeded sprays

•IPM more value for Baythroid and Warrior, since cost more

•IPM more value after more sprays, since need fewer sprays

IPM Risk Effect/Standard Deviation Change ($/ac)

-0.40

-0.35

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Baythroid Capture Warrior

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2nd Spray

3rd Spray

4th Spray

•With proportional yield loss from pest, pests usually reduce st. dev. of returns, so pest control increases st. dev. of returns

•IPM decreases st. dev. of returns since more pests

•More sprays increases st. dev. of returns since fewer pests

CaveatsCaveats

Can’t do “Sequential” IPM: observe and Can’t do “Sequential” IPM: observe and decide multiple times during seasondecide multiple times during season Data only allow estimation of average % survival Data only allow estimation of average % survival

per spay for many spraysper spay for many sprays Need different data for “true” IPMNeed different data for “true” IPM Current data readily available easy to collect Current data readily available easy to collect

while required data are expensive to obtainwhile required data are expensive to obtain Canning companies control sprays and they Canning companies control sprays and they

are not necessarily maximizing farmer are not necessarily maximizing farmer returnsreturns

Processing versus Fresh Processing versus Fresh MarketMarket

IPM for Processing sweet cornIPM for Processing sweet corn 1 scheduled spray and use of IPM for the 21 scheduled spray and use of IPM for the 2ndnd

spray maximizes farmer returnsspray maximizes farmer returns First scheduled spray worth $115-$125/acFirst scheduled spray worth $115-$125/ac IPM increases mean returns $5-$10/ac (~ one IPM increases mean returns $5-$10/ac (~ one

spray), not including scouting costsspray), not including scouting costs IPM decreases st. dev. of returns slightlyIPM decreases st. dev. of returns slightly

Similar analysis for Fresh Market sweet cornSimilar analysis for Fresh Market sweet corn IPM IPM decreasesdecreases mean returns mean returns IPM decreases st. dev. of returnsIPM decreases st. dev. of returns

Fresh Market Sweet CornFresh Market Sweet Corn

Same basic model structure with updatesSame basic model structure with updates Pest free yield: 1100 doz/ac with 25% CVPest free yield: 1100 doz/ac with 25% CV Price: $2.75/doz with st. dev of $0.60/dozPrice: $2.75/doz with st. dev of $0.60/doz % marketable for fresh market% marketable for fresh market

mean = exp(kmean = exp(k00 + k + k11ECB), constant st. dev.ECB), constant st. dev.

Six scheduled sprays maximize returnsSix scheduled sprays maximize returns Optimal IPM threshold = zeroOptimal IPM threshold = zero

Benefit vs. Cost of IPMBenefit vs. Cost of IPM Benefit of IPM: Preventing unneeded Benefit of IPM: Preventing unneeded

sprayssprays Cost of IPM: Missing needed sprays, plus Cost of IPM: Missing needed sprays, plus

cost of information collectioncost of information collection More valuable crop makes missing needed More valuable crop makes missing needed

sprays too costly relative to low cost sprays too costly relative to low cost insecticidesinsecticides

Few will risk $1000/ac to try saving $10/acFew will risk $1000/ac to try saving $10/ac ““Penny Wise-Pound Foolish”Penny Wise-Pound Foolish”

Economic Injury LevelEconomic Injury Level Pedigo’s Classic EIL = C/(V x I x D x K)Pedigo’s Classic EIL = C/(V x I x D x K)

EIL = pest density that causes damage EIL = pest density that causes damage that it would be economical to controlthat it would be economical to control

C = cost of controlC = cost of control V = value of cropV = value of crop I x D = injury per pest x damage per I x D = injury per pest x damage per

injuryinjury K = % Kill of pest by controlK = % Kill of pest by control

As V becomes large relative to C, the As V becomes large relative to C, the EIL goes to zeroEIL goes to zero

Fresh Market Sweet Corn Fresh Market Sweet Corn IPMIPM

Insecticide too cheap relative to value of Insecticide too cheap relative to value of fresh market sweet corn to make IPM fresh market sweet corn to make IPM valuablevaluable

Insect pests vs insect terrorists (IPM or ITM?)Insect pests vs insect terrorists (IPM or ITM?) Insecticide cost must increase so IPM creates Insecticide cost must increase so IPM creates

more value by preventing unneeded spraysmore value by preventing unneeded sprays Market prices increaseMarket prices increase Environmental costs of insecticide useEnvironmental costs of insecticide use

Alternatively: more competitive market for Alternatively: more competitive market for pesticide-free or organic sweet cornpesticide-free or organic sweet corn

ConclusionConclusion Illustrated hierarchical modelingIllustrated hierarchical modeling

Capture effect of production practices on riskCapture effect of production practices on risk Generally requires Monte Carlo simulations Generally requires Monte Carlo simulations Applied to ECB in sweet cornApplied to ECB in sweet corn Also for ECB and corn rootworm in field cornAlso for ECB and corn rootworm in field corn

IPM for commodity vs. high value cropsIPM for commodity vs. high value crops If crop becomes too valuable relative to the If crop becomes too valuable relative to the

cost of insecticide, IPM not economicalcost of insecticide, IPM not economical Processing versus Fresh Market Sweet CornProcessing versus Fresh Market Sweet Corn