1. United States Department of Agriculture Forest Service, Southern Research Station 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. United States Department of Agriculture Forest Service, Southern Research Station Why Longleaf?

3. United States Department of Agriculture Forest Service, Southern Research Station

4. United States Department of Agriculture Forest Service, Southern Research Station Why is this a problem?

5. United States Department of Agriculture Forest Service, Southern Research Station Mature longleaf pine stands can be unimodal, ….

6. United States Department of Agriculture Forest Service, Southern Research Station … but they can also be bi- or tri- modal.

7. United States Department of Agriculture Forest Service, Southern Research Station There are two known causes of this.

8. United States Department of Agriculture Forest Service, Southern Research Station Suppressed longleaf trees do not die easily.

9. United States Department of Agriculture Forest Service, Southern Research Station Not all trees exit the grass stage at the same time

10. United States Department of Agriculture Forest Service, Southern Research Station To produce the irregular diameter distributions observed in older stands, it is essential that initial diameter distributions be irregular.

11. United States Department of Agriculture Forest Service, Southern Research Station Techniques  Weibull distribution by parameter recovery  Artificial neural networks  Model cohorts of trees beginning height growth

12. United States Department of Agriculture Forest Service, Southern Research Station 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. United States Department of Agriculture Forest Service, Southern Research Station Weibull distribution  Included as baseline parametric technique  P i =0.97 and P j =0.17 as suggested by Zanakis (1979)  Only used for trees with dbh > 0

14. United States Department of Agriculture Forest Service, Southern Research Station Artificial Neural Network

15. United States Department of Agriculture Forest Service, Southern Research Station 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. United States Department of Agriculture Forest Service, Southern Research Station 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. United States Department of Agriculture Forest Service, Southern Research Station 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. United States Department of Agriculture Forest Service, Southern Research Station 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. United States Department of Agriculture Forest Service, Southern Research Station  Crossover (sexual recombination)  X reproduction  Inversion  Mutation  Hill climbing  Migration and intermarriage Evolutionary algorithm

20. United States Department of Agriculture Forest Service, Southern Research Station 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. United States Department of Agriculture Forest Service, Southern Research Station Epanechnikov Kernal  K i (u) = 0.75 (1-u 2 )  For (X min -.05)<X<(X max +.05)  Complete distribution is: Where p i is proportion of stand in cohort i.

22. United States Department of Agriculture Forest Service, Southern Research Station 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” D max (or D min ).  “oldest” cohort or most populous.  Develop equations to predict other D max and D min ’s from guiding value, and stand variables (age,site index, etc).  Recover guiding D max from predicted basal area and trees/acre.

23. United States Department of Agriculture Forest Service, Southern Research Station CohortPiPi D max D min 1p1p1 GF(G,SI,TPA…) 2p2p2 3p3p3 4p4p4

24. United States Department of Agriculture Forest Service, Southern Research Station

25. United States Department of Agriculture Forest Service, Southern Research Station

26. United States Department of Agriculture Forest Service, Southern Research Station Preliminary Results

27. United States Department of Agriculture Forest Service, Southern Research Station Predicting the number of trees in the grass stage CriterionLogistic Function Evolutionary Algorithm Bias19.2-5.3 Largest Deviation 274.6-171.6 Mean Absolute Deviation 29.415.1 Root Mean Squared Error 61.4834.41

28. United States Department of Agriculture Forest Service, Southern Research Station Criterion Neural Networks Weibull Predict 0Don’t predict 0 Known 0Unknown 0 Known 0Unknown 0 MSE482603572521669 FI.84.80.81.82.77  2 lowest 16148 23 KS lowest 1113112319 Mean closest 181412229

29. United States Department of Agriculture Forest Service, Southern Research Station All methods work 410 128 10

30. United States Department of Agriculture Forest Service, Southern Research Station Weibull works best 203 131 16

31. United States Department of Agriculture Forest Service, Southern Research Station Neural net works best 203 135 16

32. United States Department of Agriculture Forest Service, Southern Research Station 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