Estimating the Greening Effect on Florida Citrus

Transcription

1 Estimating the Greening Effect on Florida Citrus Charles B. Moss 1 and Maria Bampasidou 1 1 University of Florida March 26, 2014

2 1 Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Age Structure of the Citrus Grove Aggregate Yield Impact of Greening Econometric Model Bayesian Estimation 3 4

3 Citrus Maladies Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Age Structure of the Citrus Grove Agronomic/Weather Freezes January 1981, December 1983, January 1985, December 1989 Citrus Canker Most recently beginning in 2000 (declared uncontrollable in 2006) Huanglongbing or citrus greening Economics Increased trade Diet fads Decreased housing prices in Florida

4 Citrus Greening - The Disease Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Age Structure of the Citrus Grove Bacterium Candidatus Liberibacter asiaticus Asiatic citrus psyllid (Diaphorina citri Kywayama) This insect was first found in Florida in 1998, and at that time was considered to be a pest of minor importance since the HLB pathogen was not known to be present. The 2005 discovery of HLB in Florida changed the status of this insect to a pest of great importance (Spann et al. 2014, p. 1). Effect of disease Phloem blockage typically leading to loss of root structure Misshapen and bitter fruit Tree decline and death

5 Canker - The Other Citrus Disease Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Age Structure of the Citrus Grove Causes problems with the marketability of fresh fruit Florida experienced periodic bouts Citrus Health Response Program (CHRP) Handling recommendations 1900 foot kill zones Difficulties Florida hurricanes (2004 Charley, Frances, Ivan and Jeanne) Emergence of backyard citrus CHRP abandoned in 2006.

6 Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Age Structure of the Citrus Grove Age Structure of the Citrus Grove Year Orange Colored Set Early Midseason Valencia Grapefruit Pre , , , , , , , , , , , , , , , , , Bearing 21, , , , Non-bearing 1, , Total 22, , , ,838.4

7 Yield by Age in Boxes Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Age Structure of the Citrus Grove Orange Colored Tree Age Non-Valencia Valencia Grapefruit and over

8 Yield per Tree (Boxes) Aggregate Yield Impact of Greening Econometric Model Bayesian Estimation We start with the basic hyperbolic tangent model of Zanzig, Moss, and Schmitz z (a it ) = β 0 2 [1 + tanh (β 1 + β 2 a it )] (1) Tree Age (Years) Predicted Summary

9 Aggregate Yield Aggregate Yield Impact of Greening Econometric Model Bayesian Estimation Yield if age components are known z T t = N i=3 D it β 0 2 [1 + tanh (β 1 + β 2 i)] (2) where D it is the number of trees in each age group.

10 Impact of Greening Aggregate Yield Impact of Greening Econometric Model Bayesian Estimation Integrating the greening impact z T t = N i=3 θ it D it β 0 2 [1 + tanh (β 1 + β 2 i)] (3) θ it = g (i) (θ 0 + θ 1 t) where g (i) is a valid probability density function (generalized density function) N g (i) = 1 i=1 (4) g (i) 0 i

11 Aggregate Yield Impact of Greening Econometric Model Bayesian Estimation Econometric Model Tree Age Structure First defining the total number of trees based on tree ages Taking the discrete change D T t = N D it (5) i=1 N Dt T = [D it D i,t 1 ] i=1 D T t = [D 1t D 1,t 1 ] + [D 2t D 2,t 1 ] + (6) D T t = D 1t + [D 2t D 1,t 1 ] + [D 3t D 2,t 1 ] +

12 Tree Age Structure Continued Aggregate Yield Impact of Greening Econometric Model Bayesian Estimation Note that D 2t D 1,t 1 are the same treee cohorts We replace this with a random tree loss coefficient D T t = D 1t + κ 2t D 1,t 1 + κ 3t D 2,t 1 + (7) where κ it is a random fraction of one. Dividing through by the total tree numbers at time t yields ( d ln Dt T D 1t D T t ) D 1t D T t ( = d ln Dt T + ) N i=2 N i=2 ( ) Dit κ it ln D i 1,t 1 ( ) Dit κ it ln. D i 1,t 1 (8)

13 Bayesian Estimation Aggregate Yield Impact of Greening Econometric Model Bayesian Estimation α N ( α, Σ α ) (9) ˆα = L f (α l α, Σ α ) α l l=1 L f (α l α, Σ α ) l=1 θ (t) = θ 1 + θ 2 (t 2006) + θ 3 (t 2006) 2 (10)

14 Parameter No-Greening Greening β β β θ θ θ

15 The preliminary estimates are showing little aggregate effect of greening on tree yields. Greening may affect tree age cohorts (maybe they are taking diseased trees out). We need to add some things to the model: Tree survival probabilities possibly a function of greening. Possibility that greening affects different tree ages differently.