D.J. Leduc , Information Technology Specialist, & J.C.G. Goelz , Principal Forest Biometrician

1. Diameter Distributions for Young Longleaf Pine Plantations: Initial Conditions for a Growth and Yield Model D.J. Leduc, Information Technology Specialist, & J.C.G. Goelz, Principal Forest Biometrician

2. Why Longleaf?

4. Why is this a problem?

5. Mature longleaf pine stands can be unimodal, ….

6. … but they can also be bi- or tri- modal.

7. There are two known causes of this.

8. Suppressed longleaf trees do not die easily.

9. Not all trees exit the grass stage at the same time

10. To produce the irregular diameter distributions observed in older stands , it is essential that initial diameter distributions be irregular.

11. Techniques • Weibull distribution by parameter recovery • Artificial neural networks • Model cohorts of trees beginning height growth

12. What we have to work with • Age • Basal area • Site index • Container stock or not • Trees planted per acre • Number of trees in 0-inch diameter class?

13. Weibull distribution • Included as baseline parametric technique • Pi=0.97 and Pj=0.17 as suggested by Zanakis (1979) • Only used for trees with dbh > 0

14. Artificial Neural Network

15. Artificial Neural Network • Number of grass stage trees is known • Predict proportion of dbh 0 trees • Do not predict proportion of dbh 0 trees • Number of grass stage trees is unknown • Predict proportion of dbh 0 trees • Do not predict proportion of dbh 0 trees

16. Predicting number of dbh 0 trees • Necessary for Weibull distribution that we used and two neural network models. • Used standard logistic model and an evolutionary algorithm

17. Logistic model • logit = 2.1696 + age * (-1.7565) + baa * (-0.1143) + si * 0.1705 + • container * (-12.2144) + tpa * 0.0114 + age*baa * 0.00617 + • age*si * 0.00920 + age*container * 0.8183 + • baa*si * (-0.000960) + baa*container * 0.0383 + • baa*tpa * 0.000013 + si*container * (-0.0640) + • si*tpa * -0.00013 + container*tpa * 0.00184 • predp =exp(logit)/(1+exp(logit)) • pdc00 =predp*tsa

18. Evolutionary algorithm • tmp= (container*11.24+baa)/9.84 • tmp2 =5.08*age+ ((tmp+tsa)/tmp)-148.76+container • pdc00=(((-19.2431+tmp2)*tmp2)/(-46.1721*si)*baa+tmp2)*age/(-22.0538)+tmp2

19. Evolutionary algorithm • Crossover (sexual recombination) • X reproduction • Inversion • Mutation • Hill climbing • Migration and intermarriage

20. Explicitly Modeling Cohorts • Seedlings exit the grass stage over several years. • This is one of the main factors causing diameter distributions to be irregular. • Model diameter distribution as a mixture of distributions for each cohort. • As there are potentially several cohorts, it seems wise to use a very simple distribution.

21. Epanechnikov Kernal • Ki(u) = 0.75 (1-u2) • For (Xmin-.05)<X<(Xmax+.05) • Complete distribution is: Where pi is proportion of stand in cohort i.

22. Using mixture of Epanechnikov-kernals in prediction • Predict the proportion of trees in each cohort. • User-supplied input regarding length of time in grass stage (average length, or years for 75% to leave grass stage…). • Select “Guiding” Dmax (or Dmin). • “oldest” cohort or most populous. • Develop equations to predict other Dmax and Dmin’s from guiding value, and stand variables (age,site index, etc). • Recover guiding Dmax from predicted basal area and trees/acre.

26. Preliminary Results

27. Predicting the number of trees in the grass stage

29. All methods work 410 128 10

30. Weibull works best 203 131 16

31. Neural net works best 203 135 16

32. Conclusions • Evolutionary algorithm better than logistic function for predicting trees in grass stage. • Neural networks show promise for modeling young stand diameter distributions. • Modeling cohorts looks promising, but remains untested • The biggest problem is finding enough easily measured variables to base predictions on