Spatio-Temporal Modeling Issues: a Case of Soybean Aphid

Transcription

1 Spatio-Temporal Modeling Issues: a Case of Soybean Aphid Seong Do Yun Project Advisor: Dr. Gramig, Benjamin SHaPE Space, Health and Population Economics Research Group

2 Project: Enhancing Ecosystem Services from Agricultural Lands: Management, Quantification, and Developing Decision Support Tools(EPA-G2008-STAR-K1) Ecology: Dr. Rowe(ASU), Dr. Fargione(Nature Conservancy NGO) Soil Analysis: Dr. Dukes(Purdue) Entomology: Dr. Holland and Dr. Koh(Purdue) Economic Analysis: Dr. Gramig(Purdue)

3 Contents Invasive Species(6) Introduction of Ecosystem Service Project(4) Economic Problem(4) Modeling Method1: Partial Diff. Eqs.(3) Modeling Method2: Kriging(10) Issues and Discussion(7)

4 Invasive Species(Executive Order 13112, NISC 2/3, 1999) Non-native(or alien) to the ecosystem under consideration and whose introduction causes or is likely to cause economic or environmental harm or harm to human health. The National Invasive Species Council Center for Invasive Species and Ecosystem Health Invasive Species 1/6

5 What is economic problem from Invasive Species? Approximately 50,000 alien-invasive species in US and increasing at this time Roughly 400/958 species endangered to extinction Economic damages: $120 billion / year OTA(1993) report: $97 billion / year for 85 years $13.5 billion in loss from crop pest only Pimentel et. al. (2008) Invasive Species 2/6

6 What is economic problem from Invasive Species? Representative Harmful Pest: Soybean Aphid Reference: Dept. of Entomology, Purdue Invasive Species 3/6

7 Soybean Aphid (Koh, 2012) Aphis glycines Matsumura 2000, Wisconsin 2004 Invasive Species 4/6

8 Natural Enemy (Koh, 2012) Harmonia axyridis (Pallas) > 30 species < 10 species Invasive Species 5/6

9 Pest Control: an easy and fast way Use chemical pesticides: Kill them all! Side effect Cost, food safety, water pollution, unsustainability and etc. Invasive Species 6/6

10 Ecosystem Service Project 1/4 Eco-friendly way: Use Agroecosystem (prey-predator) Conservation Planting 21 and 33 Ladybird beetles Pirate bugs Green lacewings Soybean aphid (Aphis glycines) Damsel bugs Conservation planting Newton Co. IN Soybean field IK

11 Study Sites and Sampling Method (Koh, 2012) Ecosystem Service Project 2/4

12 Connectivity Analysis(Koh, 2012) Ecosystem Service Project 3/4

13 Results from Connectivity Analysis(Koh, 2012) Habitat Connectivity influences on native natural enemies flow. Prairie acts as a source for native predators. Biodiversity reduces a risk. Optimization of landscape connectivity is considered. Ecosystem Service Project 4/4

14 Economic Analysis Process Set up Base Model (Toy Model) Scenarios Random Aphid Arrival (Poisson Process) Pesticides Spray Set up new CPs As constraints Solve Optimization Problem (Spatio-temporal mathematical Problem) Get Economic Implications Economic Problem 1/4

15 From the literature review(most recent!) Zhang and Swinton(2009): time only method - exponential growth: total population density determines everything Zhang et. Al.(2010): space only method - research space is homogeneous We need to consider both: time and space - depending on time and space, population density of aphid and predators are different. - research space is never homogeneous. Social scale view not one farm s decision problem Economic Problem 2/4

16 Tentative Economic Optimization Model Space-Time Maximization Problem Maximize Sort of Benefit (private or social) Subject to Economic Constraints Pest Control Carbon Sequestration Current Step Economic Problem 3/4

17 Current Step: Developing Pest Control Constraint Required Data Type: ( x-coord, y-coord, density ) at time t ( Continuous data is better. ) Original Data: collected insects data from Dr. Holland s Team Manage required data from the Original Data Considered data creating process: - First Trial: Partial Differential Equations - Current Trial: Kriging Method Economic Problem 4/4

18 Partial Differential Equations(PDEs): Prey-Predators Model Modeling Method1: PDE 1/3

19 Simulation Example: PDEs 1-D Case 2-D Case: Predators Modeling Method1: PDE 2/3

20 Implausibility of PDEs Improper initial data structures for PDEs Fitting difficulties to the collected data Time Domain Initial data type: nonempty cells are required for numerical PDEs. Spatial Domain Modeling Method1: PDE 3/3

21 Initial Data Analysis Data Collecting Period: 6/22/2011 to 9/22/2011 CP21(10), CP33(5), and Control Field(13) Total Geographical Nodes: 490 Modeling Method2: Kriging 1/10

22 Descriptive Statistics Predators Percentile Obs. Mean JUL AUG SEP Preys Percentile Obs. Mean JUL AUG SEP Modeling Method2: Kriging 2/10

23 Contour Analysis Using Ordinary Kriging Step1: Draw empirical semivariogram cloud to see spatial correlation. Step2: Estimate Ordinary Kriging parameters using Maximum Likelihood Estimation with Exponential covariogram. Step3: Predict 2500 locations inside the given area. Step4: Draw contour plots. Modeling Method2: Kriging 3/10

24 Modeling Method2: Kriging 4/10 Step1: Empirical Semivariogram Cloud August: Predators August: Preys

25 Modeling Method2: Kriging 5/10 Step2: Ordinary Kriging: best unbiased linear predictor Minimize Squared Errors Lagrangian Solution Thus, the only unknown: V

26 Modeling Method2: Kriging 6/10 Step2: Exponential Covariogram (Empirical V) Step2: Estimation Results Predators tausq sigmasq phi Log-Lik JUL , AUG 1, , SEP 3, , Preys tausq sigmasq phi Log-Lik JUL AUG , SEP 49, , , All estimates are significant at 1% level.

27 Step3: Prediction Locations(2500 spots) Modeling Method2: Kriging 7/10

28 Step4: Contour Plots Modeling Method2: Kriging 8/10

29 Step4: Prediction Errors Mean Squared Error(MSE) Predators Preys JUL e e-39 AUG e-30 0 SEP e e-47 All of cases are reached to reliable prediction error. Modeling Method2: Kriging 9/10

30 Results from Base Model Initially high density spots are continuously keeping their high density for aphid. Predators are chasing their food source. But more detail analysis is required. CP locations probably contribute to prey-predator relation. Modeling Method2: Kriging 10/10

31 Issues and Discussion 1/7 Issue1: Constructing Pest Control Data Basic Concept1: Fill out spatial domain Collected Data Prediction(Kriging) At time t Collected Data Prediction(Kriging) At time t+ dt Repeat this process to the final time T

32 Issues and Discussion 2/7 Issue1: Constructing Pest Control Data Basic Concept2: Fill out time domain t1 t2 T Use Spline to each spot for every time: 1-variable(time) spline with (T-t1+1) spots (Alternatives: Exponential growth model or global spline)

33 Issues and Discussion 3/7 Issue1: Constructing Pest Control Data Alternative model for filling out spatial domain? In the case of monthly base: only 28(23) observations are available but the more is the better in any statistical method. Possible way to get more data at each time period? E.g. distance decay function from the nodes: this may be the way Dr. Holland s used. Can we use the calculated flux for this? (Flux from connectivity analysis)

34 Issues and Discussion 4/7 Issue2: Reflecting heterogeneity of spatial domain Important role of spatial heterogeneity: prairie, farmland, river corridor and so forth. Kriging reflects it implicitly(collected numbers already reflected it.) If there is a way to fill out empty data cell reflecting heterogeneity, Kriging may reflect it also. Ex. River corridor, Household zero neighbors of river corridor truncated negative exponential fc.

35 Issues and Discussion 5/7 Issue3: Pest Control Scenario Population density Different population phases at each year. Random Sampling(Assigning) of aphids with Poisson at an initial time step - Calculate predators density through the estimated relation in Dr. Holland s. - Update aphids at t+1 using spline or exponential growth model. - Update predators density. - Repeat this process to the final time T.

36 Issues and Discussion 6/7 Issue3: Pest Control Scenario Pesticides Scenario of spraying out pesticides. Consider spraying-threshold concept. Set up a scenario which farmers sprayed pesticides out in our data. Replace calculated population density with zeros at the spraying time period in scenarios.

37 Issues and Discussion 7/7 Future Works Consider how to reflect carbon sequestration. Set up an economic optimization problem: mutivariate spatio-temporal optimization problem. Your Advices Alternative Method for filling out empty cells or time spline Objective Function: How to reflect social benefit?

38 Questions or Comments?