Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1976 An Examination of Some Subsystems for a Model of Tree Volume Growth. Calvin Junetieh Liu Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Liu, Calvin Junetieh, "An Examination of Some Subsystems for a Model of Tree Volume Growth." (1976). LSU Historical Dissertations and Theses. 2973. https://digitalcommons.lsu.edu/gradschool_disstheses/2973 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This material was produced from a microfilm copy of the original document. 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Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 I I 76-28,814 LIU, Calvin Junetieh, 1943- AN EXAMINATION OF SOME SUBSYSTEMS FOR A MODEL OF TREE VOLUME GROWTH. The Louisiana State University and Agricultural and Mechanical College, Ph.D., 1976 Agriculture, forestry and wildlife Xerox University Microfilmsf Ann Arbor, Michigan 48106 AN EXAMINATION OF SOME SUBSYSTEMS FOR A MODEL OF TREE VOLUME GROWTH A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The School of Forestry and Wildlife Management by Calvin Junetieh Liu B.S., Chungshing University, 1967 M.S., Louisiana State University, 1973 August, 1976 ACKNOWLEDGMENTS The author is indebted to Dr. Thomas D. Keister for his assistance in planning this study and for his guidance toward the completion of this study. The suggestions of Dr. Kenneth L. Koonce, Dr. Norwin E. Linnartz, Dr. David W. Smith, Dr. Bart A. Thielges and Dr. Peter J. Fogg, members of the examining committee, are also appreciated. Acknowledgments are also made to Dr. Barton R. Farth­ ing and Dr. Prentiss E. Schilling of the Louisiana State University Experimental Statistics Department for their advice on statistical analyses. The author is also grateful to Mr. Don Alexander of the Southern Timber Division of the Crown Zellerbach Corpora­ tion for the data he supplied that was used in the study. TABLE OF CONTENT Page ACKNOWLEDGMENT.................................... ii LIST OF TABLES ................................... vi LIST OF FIGURES................................... viii ABSTRACT.......................................... xi CHAPTER I INTRODUCTION................................ 1 CHAPTER II A REVISION OF KEISTER'S COMPETITION INDEX................................. 8 PAST KNOWLEDGE AND EXPERIENCE.............. 9 The Problem of Measuring Stand Density.. 9 The Problem of Defining the Influence Circle.......... 12 The Problem of Calculating the Area of Overlap..........................• 19 PROCEDURES.................................. 34 The Analysis of the Problems...........• 34 A Revision of Keister's Competition Index— A Diagnostic Approach. 38 RESULTS AND DISCUSSION..................... 52 CHAPTER III CONSTRUCTION OF HEIGHT GROWTH CURVE. 56 PAST KNOWLEDGE AND EXPERIENCE.............. 56 Introduction.56 iii Page Height-Diameter Curves and Height- Age Curve s........ ......•••.•••••••• 58 Height as a Measure of Site Pro­ ductivity. .......................... 62 Stand Density, Competition and Height Growth.......... 65 PROCEDURE.................................. 70 Analysis of General Growth Curves...... 70 The Formulation of Tree-Height Growth Curve............. 75 RESULTS AND CONCLUSIONS................... 79 Application of Tree-Height Growth Curve— Case Study I............••••• 79 Application of Tree-Height Growth Curve— Case Study I I 82 Application of Tree-Height Growth Curve— Case Study III . 91 Application of Tree-Height Growth Curve— Case Study IV................ 96 A General Height Growth Curve of Loblolly Pine of Livingston Source.. 105 C o n c l u s i o n . 106 CHAPTER IV CONSTRUCTION OF TAPER FUNCTION AND TREE VOLUME MEASUREMENT................ 113 PAST KNOWLEDGE AND EXPERIENCE................ 113 Introduction........................... 113 Form Expression and Taper Function..... 115 Page PROCEDURES.................................. 120 Method of Defining Stem Taper........... 120 Methods of Curve Fitting and Volume C a l c u l a t i o n . 125 RESULTS AND CONCLUSIONS.................... 127 Defining Loblolly Pine Taper Function... 127 An Elaborative Trace of Butt-Region Taper....... 133 Comparison of Taper Curves of Different Size, Height and Crown-Ratio Groups.. 135 Comparison of Taper Curve of Different L o c a l i t y . 155 Taper Curves of Other Coniferous Specie s................... ........... 158 The Discarding of Variables in Multi­ variate Analysis.. 162 Mathematical Functions and Taper Curve.. 171 Calculation of Log Volume..... 182 Summary and Conclusion.. 184 CHAPTER V MORTALITY AND MORTALITY PREDICTION... 188 PAST KNOWLEDGE AND EXPERIENCE.............. 188 DISCUSSION..................... 193 CHAPTER VI SUMMARY ............................. 196 LITERATURE CITED........ 201 APPENDIX A - DATA GROUPS......................... 212 VITA.............................................. 221 v LIST OF TABLES Table Page 1. Measured and Predicted Height Values of a Single Tree1s Stem Analysis Data........... 81 2. Measured and Predicted Height Values of Irrigated Trees and Non-Irrigated Trees.... 84 3. Measured and Predicted Average Plot Height of Trees Receiving Intensive Cultural Treat­ ment and Trees Receiving No Treatment...... 90 4. Height Growth Patterns of Loblolly Pine Trees From Two Different Geographic Seed Sources. ....... 93 5. A Summary of Data For Loblolly Pine Trees Used in Height-Growth Curve Fitting....... 97 6. Eigenvalues of Stem Taper of Loblolly Pine. 130 7. First Three Eigenvectors of Stem Taper of Loblolly P i n e . 134 8. Eigenvalues of Stem Taper of Loblolly Pine Including Butt-Region Curvature ..... 136 9. First Three Eigenvectors of Stem Taper of Loblolly Pine Including Butt-Region C u r v a t u r e 137 10. Eigenvalues of Three Crown-Ratio Groups.... 141 11. First Three Eigenvectors of Three Crown- Ratio Groups....... 142 12. Eigenvalues of Three DBH Groups........ 146 13. First Three Eigenvectors of Three DBH Groups 147 14. Eigenvalues of Two Height G r o u p s 150 vi Table Page 15. First Three Eigenvectors■of Two Height Groups. ......................... ......... 153 16. Eigenvalues of Trees of Different Locality. 156 17. First Three Eigenvectors of Trees of Different Locality..... ...... ......... 157 18. Eigenvectors of Stem Taper of Slash Pine... 165 19. First Three Eigenvectors of Stem Taper of Slash Pine.• 166 20. Results of Stepwise Regression............. 175 21. Data for Taper Curve Fitting............... 176 22. List of Residual Mean Squares of All Possible Regressions..•••....••••.......... 179 23. List of Residuals of Different Regression Models of Taper Curve 181 LIST OP FIGURES Figure Page 1. Regularized Tree-Growing Spaces and Over­ lapping of Growing Spaces................... 13 2. A Graphical Presentation of Staebler's Circle of Influence, Overlapping Area and Competi­ tion Index.• 23 3. A Graphical Presentation of Newnham's Circle of Influence, Overlapping Area and Competi­ tion Index.■ 26 4. A Graphical Presentation of Keister's Circle of Influence, Overlapping Area and Competi­ tion Index (Part A), and A Sketch of Overlap of Overlapping Areas (Part B)............... 30 5. Relative Competitive Efficiencies........... 37 6 . Sketch