Stem Diameter Increment P. occidentalis_NEMO_Pr11

Modeling Stem Diameter Increment in Individual Pinus Occidentalis, Sw. Trees in La Sierra, Dominican Republic :

Modeling Stem Diameter Increment in Individual Pinus Occidentalis , Sw. Trees in La Sierra, Dominican Republic Santiago Bueno & Eddie Bevilacqua Department of Forest and Natural Resources Management SUNY-ESF

Range of Pinus occidentalis (Critchfield and Little 1966) :

Range of Pinus occidentalis (Critchfield and Little 1966) 25/02/2011 Modeling Stem Diameter 2

Area of Pinus occidentalis through the years:

Area of Pinus occidentalis through the years 25/02/2011 3 Modeling Stem Diameter

Forestry in the Dominican Republic:

Forestry in the Dominican Republic 25/02/2011 Modeling Stem Diameter 4

La Sierra:

La Sierra 25/02/2011 Modeling Stem Diameter 5

Objectives:

Objectives Fit linear regression models for predicting DBH change over time, using as predictor variables single tree, elapsed time, stand attributes and different indices of competitive status. Determine which statistical technique is best. OLS LME Fixed Effects Fixed + Random Effects Determine from three response variables, which is best d t id 5 ln (id 5 +0.01) 25/02/2011 Modeling Stem Diameter 6

Our model:

Our model Classification Characteristics Predict tree attributes individually Are flexible to forecast growth regardless of age, species mixture or silvicultural system Detailed description of stand structure and dynamics Permit simulation of different silvicultural treatments Design The data The stands Intended use 25/02/2011 Modeling Stem Diameter 7

What to model?:

What to model? DIAMETER OR BASAL AREA? GROWTH OR YIELD FUNCTION? 25/02/2011 Modeling Stem Diameter 8

Data:

Data 25/02/2011 Modeling Stem Diameter 9 Dry Zone Intermediate Zone Humid Zone Number of Stands 10 6 9 Number of Trees for Estimation 417 182 258 Number of Trees for Validation 104 47 64 DBH (cm) 5.1 - 41.7 12.1 - 48.0 7.5 - 42.7 Heights (m) 6.5 - 26.0 13.0 - 31.0 10.0 - 34.2 Age (years) 23 - 45 31 - 37 21 - 52

Data:

Data Plot ID Size (ha) SDI TPH SI BA Observations Interval (yrs) Measurements Initial Final 101 0.10 29.12 250 22 14.5 1984 1989 5 6 102 0.10 24.99 240 13 12.3 1984 1991 7 8 103 0.10 29.80 440 20 13.8 1987 1990 3 4 108 0.10 34.91 660 21 16.2 1989 1994 5 4 109 0.10 29.60 580 18 13.7 1989 1994 5 4 110 0.10 48.59 950 23 22.4 1989 1994 5 4 111 0.10 20.70 580 15 09.3 1989 1994 5 4 112 0.10 28.63 740 15 12.9 1989 1994 5 4 115 0.10 32.45 350 21 15.8 1991 1995 4 2 116 0.10 37.12 420 25 18.0 1991 1995 4 2 25/02/2011 Modeling Stem Diameter 10

DBH projection over time:

DBH projection over time 25/02/2011 Modeling Stem Diameter 11

General approach in model development:

General approach in model development Y = f 1 (tree size) + e Y = f 2 (tree size, stand) + e Y = f 3 (tree size, stand, competition) + e where Y = d t , id 5 , or ln (id 5 +0.01) tree size = d 0 and/or BA 0 stand = TPH, BA, SDI, and/or SI competition = d 0 /d q and/or BAL 0 25/02/2011 Modeling Stem Diameter 12

Testing the goodness-of-fit of the response:

Testing the goodness-of-fit of the response GOODNESS-OF-FIT (Bias, MSE, MAD, etc.) BEST ESTIMATION OF FUTURE DIAMETER ln (id 5 +0.01) id 5 d t 25/02/2011 Modeling Stem Diameter 13 d 5

Statistical techniques:

Statistical techniques 25/02/2011 Modeling Stem Diameter 14

Slide 15:

25/02/2011 Modeling Stem Diameter 15 Explanatory variable subset Parameter estimation and inference method Response variable = d t OLS LME Intercept μ μ μ μ μ μ Time t t t t t t Initial tree size d 0 d 0 d 0 d 0 d 0 d 0 Stand - TPH 0 TPH 0 - n.s. n.s. Competition - - BAL 0 - - BAL 0 G-matrix - - - 0.094 0.094 0.049 R-matrix 0.456 0.439 0.389 0.368 0.368 0.355 AIC 5503 5425 5106 5006 5006 4909

Slide 16:

25/02/2011 Modeling Stem Diameter 16 Explanatory variable subset Parameter estimation and inference method Response variable = id 5 OLS LME Intercept μ μ μ μ μ μ Initial tree size n.s n.s n.s d 0 d 0 d 0 Stand - TPH 0 SDI 0 TPH 0 SDI 0 - n.s. n.s. Competition - - BAL 0 - - BAL 0 G-matrix - - - 0.188 0.188 0.123 R-matrix - 0.888 0.745 0.716 0.716 0.665 AIC - 2267 2131 2130 2130 2068

Slide 17:

25/02/2011 Modeling Stem Diameter 17 Explanatory variable subset Parameter estimation and inference method Response variable = ln ( id 5 + 0.01) OLS LME Intercept μ μ μ μ μ μ Initial tree size BA 0 BA 0 BA 0 BA 0 BA 0 BA 0 Stand - TPH 0 TPH 0 - TPH 0 TPH 0 Competition - - BAL 0 - - BAL 0 G-matrix - - - 0.640 0.652 0.420 R-matrix 2.311 2.206 1.659 1.644 1.644 1.405 AIC 6331 6266 5783 5826 5837 5567

Observed versus predicted Values:

Observed versus predicted Values 25/02/2011 18 Modeling Stem Diameter

Residual versus predicted Values:

Residual versus predicted Values 25/02/2011 19 Modeling Stem Diameter

Slide 20:

25/02/2011 Modeling Stem Diameter 20 Goodness-of-fit statistic* Dependent Variable d t id 5 ln (id 5 +0.01) OLS LME OLS LME OLS LME FIXED FIXED + RANDOM FIXED FIXED + RANDOM FIXED FIXED + RANDOM MSE 2.265 2.273 2.175 2.222 2.220 2.115 19.684 3.240 3.020 RMSE 1.505 1.508 1.475 1.491 1.490 1.454 4.437 1.800 1.738 RMSE% 6.868 6.881 6.732 6.803 6.800 6.637 21.289 8.637 8.338 BIAS 0.083 0.076 0.104 0.130 0.072 0.132 -1.257 -1.395 -1.334 BIAS% 0.378 0.346 0.477 0.594 0.329 0.601 6.029 6.692 6.400 MAD 0.863 0.853 0.810 0.819 0.814 0.749 2.607 1.395 1.334 R 2 0.951 0.951 0.953 0.952 0.952 0.954 0.587 0.932 0.937

Parameter estimates of the best model to predict future diameter (LME fixed + random) :

Parameter estimates of the best model to predict future diameter (LME fixed + random) Covariance Parameter Estimates Response Effect Estimate Stand. Error Pr >t or Z AIC* BIC* G Matrix (p-value) R Matrix (p-value) d t Intercept 0.7027 0.1406 <.0001 4909.4 4911.8 0.049 (0.0008) 0.3551 (<.0001) t 0.2942 0.0069 <.0001 d 0 0.9903 0.0042 <.0001 BAL 0 -0.0428 0.0040 0.001 *Unstructured variance-covariance matrix 25/02/2011 Modeling Stem Diameter 21

Conclusion:

Conclusion d t = f(t, d 0 , BAL 0 ) + e Use is simple Biologically consistent according to forest growth expectations Reasonable when projecting for at most 5 years Sufficiently accurate: LME including fixed and random parameters provided a better fit for both growth and yield functions. In estimating future diameter, accuracy of predictions is within two centimeters for a five-year projection interval. The d t model presents negligible bias in estimating future diameter, although the model slightly over predicts the response variable. Based on the flexibility to provide for a range of stand circumstances, it is proposed that the future diameter model be used to estimate future diameter on individual trees of P. occidentalis in La Sierra, Dominican Republic. 25/02/2011 Modeling Stem Diameter 22