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Use of competition indices in the selection of western hemlock plus trees Thomas, Charles E. 1980

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USE OF COMPETITION INDICES IN THE SELECTION OF WESTERN HEMLOCK PLUS TREES by CHARLES EUGENE THOMAS B. Sc. Stanford Univers i ty , 1962 M. S. F. Northern Arizona Univers i ty , 1974 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Faculty of Forestry) We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1980 ic^) Charles Eugene Thomas, 1980 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ' Date /0'3-%0 ABSTRACT Use of Competition Indices in the Selection of Western Hemlock Plus Trees Western hemlock's primary role in an integrated forestry operation is in high density stands which produce a large cubic volume in relat ively short rotations. This implies an ef f ic ient use of growing space, an important characteristic of the future tree. Selections of individual trees for inclusion in an improvement program should reflect this species management format. The objective of plus tree cruising is to select trees which are phenotypically superior for use in tree improvement breeding programs. The possibi l i ty of obtaining a 10-15% improvement in a selection category without waiting 20 to 40 years for results of progeny tests seems econom-ica l ly tempting. Unfortunately, environmental and genetic components of var iab i l i ty in a given t r a i t resist separation in f ie ld selections. The objective of this study was to develop selection c r i te r ia which ref lect two important characteristics: a) rapid growth rate and b) ef f ic ient u t i l i za t ion of space or growth under stand competition. ^Permanent sample plots in coastal Bri t ish Columbia were used to investigate competition, crown characteristics and growth increment in even-aged, second growth stands of western hemlock. Several cur-rently available competition indices were used in f ive year basal area increment regressions. A regression weighting procedure is described which allows the selection of trees having growth residuals larger than a prescribed confidence interval. The entire plot serves as an environ-i i mental base line (for selection). A second approach ut i l izes low level 70 mm aerial photography of crowns. Crown efficiency regressions are developed based on current crown area and f ive year basal area incre-ment. Again a confidence interval is established with which to select the plus tree candidate. In an additional phase of the study, previously selected trees were visited with the goal of evaluating crown attributes on the basal area increment of these trees. One or more check trees were selected near each of the prior selections; these trees were compared with respect to growth, height, crown area projection, and length of crown. No stat is-t ica l differences could be found between the two groups reaffirming the value of i n i t i a l selection intensif icat ion. i i . i TABLE OF CONTENTS PAGE ABSTRACT i i LIST OF TABLES vi LIST OF FIGURES v i i i ACKNOWLEDGEMENTS xi INTRODUCTION 1 Genetic Improvement 2 Intraspecific Competition 5 Objectives 6 LITERATURE REVIEW 8 Selection Methods 8 Intensive In i t i a l Selection 11 Competition ^ 12 Competition Indices 15 Crown Competition 22 MATERIALS AND METHODS 27 Permanent Sample Plots 27 Computation of Indices 30 Additional Data Collection 32 Existing Phenotypically Selected Plus Trees 41 RESULTS AND DISCUSSION 42 Description of Growth-Competition Index Relationships . . 43 Competition Indices in a Superior Tree Selection Process 49 The Selection Value and Regression Models 50 Elimination of Indices 56 Competition Selections on Sample Plots 56 Analyses of Covariance 58 Crown Area Model 91 Selections Based on Crown Area Models 95 Analysis of Covariance 98 Combining Competition and Crown Parameters 108 Application beyond Permanent Sample Plots I l l Crown Photographed areas and Crown Projection 113 Analysis of Phenotypic Selections and Associated Check Trees 114 Periodic Growth Increment and Age 116 Phenotypic Tree Age-Strata 118 iv Page CONCLUSION 122 Competition Indices 123 Crown Efficiency 124 Crown Area 126 RECOMMENDATIONS 128 LITERATURE CITED 130 APPENDICES 134 Appendix I 135 Appendix I I 146 Appendix I I I 148 Appendix IV 152 Appendix V 155 v LIST OF TABLES Page 1. Date Summary for pure stands of western hemlock at Tournour 31 Is land. 2. Group I - Plot 350 Competition, Select ion and Regression. 59 3. Group I - Plot 351 Competition, Select ion and Regression. 60 4. Group I - P lot 352 Competition, Select ion and Regression. 61 5. Group I - Plot 357 Competition, Select ion and Regression. 62 6. Group I - P lot 358 Competition, Select ion and Regression. 63 7. Group II - P lot 354 Competition, Select ion and Regression. 64 8. Group II - P lot 355 Competition, Select ion and Regression. 65 9. Group II - Plot 356 Competition, Select ion and Regression. 66 10. Group II - Plot 359 Competition, Select ion and Regression. 67 11. Group III - Plot 353 Competition, Select ion and Regression. 68 12. Group III - P lot 400 Competition, Select ion and Regression. 69 13. Group III - P lot 401 Competition, Select ion and Regression. 70 14. Select ion Values for Phenotypic choices Be l l a ' s Model. 71 15. Analysis of Covariance Group I Plots Be l l a ' s Index. 78 16. Analysis of Covariance Group I Plots Ek-Monserud's Index. 79 17. Analysis of Covariance Group I P lots Hegyi's Index. 80 18. Analysis of Covariance Group I P lots L i n ' s Index. 81 19. Analysis of Covariance Group I P lots Newnham's Index. 82 20. Analysis of Covariance Group II P lots Be l l a ' s Index. 83 21. Analysis of Covariance Group II Plots L i n ' s Index. 84 22. Analysis of Covariance Group II Plots Newnham's Index. 85 23. R-Square Comparisons for Competition Indices. 87 24. Reduced set Group II Plots Adjustment Ana lys is . 90 vi Page 25. Adjusted Regression on Group I I Plots. 90 26. Crown Area-Growth Regressions. 96 27. Trees Selected on Crown Area Ef f ic iency. 97 28. Competition Index and Crown Competition Selection Values fo r Phenotypically Chosen Trees. 99 29. Analysis of Covariance Group I Plots Crown Area as Covariate. 100 30. Analysis of Covariance Group I I Plots Crown Area as Covariate. 101 31. Analysis Combining Crown and Competition Covariates. 112 32. Parameter Selection Based on Tumour Island Phenotypic Trees. 114 33. Regression of Crown Area (Aer ia l ) on Crown Project ion. 114 34. Summarized S ta t i s t i cs for Phenotypic Selections and Check Trees. 115 35. Phenotypic Tree Age Strata. 119 36. The Effect of Height, Age and Crown Area on Periodic Growth. 119 vi i / LIST OF FIGURES Figure Page 1. Relative cost increase as a function of increasing selection intensity. 4 2. Mean value (?c) for check trees compared to mean (m) of sample population in a frequency distr ibut ion; k(s) is unknown. 10 3. Selection di f ferent ial in a frequency distr ibution of sample population; k(s) is estimated for the sample. 10 4. Parameters of competition indices. 16 5. The effect of competition for growing space on height growth. 26 6. Location of Tornour Island and permanent sample plots. 28 7. Detail of plot distr ibution 29 8 a. Frequency distr ibution of Arney's Competition Index for al l trees on Tumour Island plots. 33 b. Frequency distr ibution of Bella's Competition Index for al l trees on Tumour Island plots. 33 c. Frequency distr ibution of Ek-Monserud's Competition Index for al l trees on Tumour Island plots. 34 d. Frequency distr ibution of Hegyi's Competition Index for al l trees on Tumour Island plots. 34 e. Frequency distr ibution of Lin's Competition Index for al l trees on Tumour Island plots. 35 f . Frequency distr ibution of Newnham's Competition Index for al l trees on Tumour Island plots. 35 g. Frequency distr ibution of Quenet's Competition Index for al l trees on Tumour Island plots. 36 h. Frequency distr ibution of Staebler's Competition Index for al l trees on Tumour Island plots. 36 9. Balloon location in the crowns, oblique view. 38 10. Vertical view, center of plot marked by balloon. 39 11. Loading f i lm in the helicopter photo boom. 40 vi i i Figure 12. Scatter/p lot of Be l l a ' s Index versus Per iodic Growth (BAGR), Plot #351 Tumour Is land. 13 Scatter/p lot of Ek-Monserud's Index versus Per iodic Growth (BAGR), Plot #351 Tumour Is land. 14. Scatter/p lot of Hegyi's Index versus Per iodic Growth (BAGR), Plot #351 Tumour Is land. 15. Scatter/p lot of L i n ' s Index versus per iodic growth (BAGR), Plot #351 Tumour Is land. 16. S t r a t i f i c a t i o n of competition versus basal area growth Be l l a ' s Index, Plot #351. 17. Periodic basal area growth versus Be l l a ' s Competition index, Plot #359. 18. Per iodic basal area growth versus Be l l a ' s competition index, Plot #400. 19. Back transformed equation with confidence l im i t 20. Natural log transformation of BAGR versus Be l l a ' s Index for Plot #350. 21. Natural log transformation of BAGR versus Ek-Monserud's Index for plot #350. 22. Natural log transformation of BAGR versus Hegyi's Index for P lot #350. 23. Natural log transformation of BAGR versus L i n ' s Index for P lot #350. 24. Natural log transformation of BAGR versus Newnham's Index for Plot #350. 25. Ln(BAGR) versus competition, equation l ines for Newnham's Index, Group I p lo ts . 26. Ln(BAGR) versus competition, equation l ines for Newnham's Index, Group II p lo t s . 27. Combined regression Group I p lo t s , Newnham's Index. 28. Regression l ines for Group I plots BAGR versus Crown Area. 29. Regression l ines for Group II p lots BAGR versus Crown Area. ix Figure Page 30. Regression l i n e s f o r a l l p l o t s i n both Group I and I I BAGR versus Crown area. 104 3 1 . A sample of cumulat ive diameter h i s t o r i e s f o r P l o t #356. 106 32. A sample of cumulat ive diameter h i s t o r i e s f o r P lo t #359. 107 33. Stem map of a p o r t i o n of P lo ts #354 and #355 and crown map o v e r l a y . 110 34. Growth-Crown P r o j e c t i o n Regression l i n e s f o r phenotypic and Check t r e e s . 117 35. Frequency h is togram of Phenotypic-check t r e e age d i s t r i b u t i o n . 120 x ACKNOWLEDGEMENTS I would l ike to express my sincere appreciation to MacMillan-Bloedel, L t d . , for the support they have given direct ly to this project and indirect ly through fellowships. In addition, individuals at MacMillan-Bloedel need to be recognized; D. R. Reimer and D. Handley reviewed and edited an earl ier presentation of much of this study. Rod Stevens, formerly of MacMillan, was central to the original project concept and much of its execution. Formerly with the Canadian Forest Service, now with Brit ish Columbia Forest Service Inventory, Frank Hegyi was very cooperative in the gen-eration of competition indices. The Computing Centre at the University of Bri t i sh Columbia has been a very real source of assistance and in addition has been an example in its commitment to excellence. The largest contributors to the completion of this project have been individuals who encouraged me when serious doubts as to the value of the study interfered with the progress. Dr. D. D. Munro consistently supported my efforts. More than that, I must thank his entire family, Nona, Dean and Lance. To each of the members of the Biometrics Group, Faculty of Forestry at UBC, sincere appreciation for both direct and indirect contributions to the completion of the dissertation are offered. Support for the pursuit of the elusive Ph.D. has come, at no l i t t l e cost from my family, part icularly my wife Jeannine. xi Perhaps the most i m p o r t a n t c o n t r i b u t i o n s have come from d i s c u s s i o n s w i t h o t h e r g r a d u a t e s t u d e n t s , both i n and o u t s i d e the F a c u l t y of F o r e s t r y . In p a r t i c u l a r , I would l i k e t o r e c o g n i z e Kim l i e s f o r h i s r e a d y e a r and c o n s t a n t encouragement. F i n a l l y , I would l i k e t o acknowledge the impetus f o r s e e k i n g a P h . D . I would l i k e t o thank t h e t a l l s k i n n y k i d r i d i n g the b i c y c l e j u s t i n f r o n t of me and over the top of the next h i l l , D r . W i l l i a m Thompson, d e c e a s e d . x i i 1 INTRODUCTION Western hemlock (Tsuga heterophylla, (Rafn.) Sarq.) is one of the four major timber producing species of the Pacific Northwest. Its range extends from southwestern Alaska to north coastal California, with inland regions in the Canadian Rocky Mountains and Idaho, Montana and western Washington in the USA. The most extensive areas are found in coastal area extending from Alaska to Oregon. In early inventories of the region it was often treated as a weed species, at least partly due to its rela-tion to eastern hemlock (Tsuga canadensis (L.) Carr.) which was known to have poor wood quality. Indeed, western hemlock has many desirable qualities for both lumber and pulp production. In British Columbia, western hemlock is currently the major pulping timber. It is preferred in dissolving grade pulps and yields quality pulp in both mechanical and chemical pulping processes (Wellwood, 1960). To escape association with its eastern relative, western hemlock was often referred to as Alaskan pine. S t i l l , it was not until after WW II that Leon Koerner, an immigrant from Czechoslovakia, founded Alaska Pine and Cellulose, Limited, based primarily on hemlock. His enterprise elevated the tree to commercial importance in British Colum-bia. In recent years, i t has in some respects become the most important single species, exceeding in volume cut, the formerly dominant Douglas-f i r jr^ sejjdotsu£a mejizjesij (Mirb.) Franco). In 1976 it exceeded all species harvested, including spruce (Picea spp.), with about 22% of the total cut (5.3 MM cunits of a total 24.5 MM cunits) and.in stumpage returned to the province of B. C, i t contributed $10 million of a total 2 $49 mil l ion (BCFS Annual Report, 1976). In standing mature inventory, western hemlock represents a major component, to ta l l ing approximately 648 mil l ion cunits. Of this volume a total of 350 mil l ion cunits are estimated to be direct ly disposable by the B. C. Forest Service (BCFS, 1975). Today western hemlock's large remaining volume and i ts su i tabi l -i t y for both solid wood and pulp products make i t a very important con-tr ibutor to the wealth and future of the people of Bri t ish Columbia. Genetic Improvement The scient i f ic study of western hemlock, l ike i ts u t i l izat ion by industry, has lagged behind Douglas-fir. Only a few of the papers included in Walters' (1963) annotated bibliography of western hemlock relate to genetics of the tree. So, i t is not surprising to to f ind that interest in the genetic improvement of western hemlock is very recent. At the prompting of the B. C. forest industry the Canadian Forest Service in i t iated a western hemlock tree improvement program in 1968. Piesch (1974) discussed the program and some of the technical d i f f i cu l t ies associated with i ts establishment. Of major concern was the d i f f i cu l t y of i n i t i a l tree selection for inclusion in an improvement program. I t was noted that selection of an individual from a stand, is complicated by tendancy for the establishment period of a stand to extend over several years. Also, the capacity for western hemlock to respond to release further adds to variation in tree size and age with-in stands. These characteristics of the species complicate a selection system based on comparisons of individuals with neighbors growing under similar site conditions. In fact, the importance of i n i t i a l selection is a crucial part of any improvement program and deserves commensurate attention. 3 In i t i a l selection is s t i l l the determinant of ultimate gains in an improvement program. The selected trees determine the genetic base on which species improvement may be achieved. Increasing the amount of attention paid to the selection of individuals increases the amount of improvement in yield or in any other heritable characteristic of interest. The genetic constraints in a selection program are the heri-t a b i l i t y and the variance of the selected character. I f the simplest formula for potential gain is examined, one finds that the intensity of the selection is the only variable which foresters may influence at the i n i t i a l selection. Where G = the gain, h = the her i tab i l i t y , v = the phenotypic variance for the population, and i is the intensity of selection. There is a trade-off between genetic gain and cost of selection. The more stringent the wild stand selection scheme, the higher the costs. Porterfield ( 1 9 7 5 ) performed an economic analysis of the yields and costs of improvement in southern U. S. forests using a marginal cost analysis approach. Figure ( 1 ) represents the increase in cost due to increasing selection intensity in that program. A 6% discounting rate was used. Increased selection intensity must be based on firm grounds. Classical, phenotypic, plus tree selection methods used in the late 1 9 5 0 ' s and early 1 9 6 0 ' s in coastal B. C. for Douglas-fir, expres-sion—are the cumulative product of i ts genetic potential and environ-mental influences. Since the underlying objective of plus tree cruising is the selection of phenotypes which have the greatest probability of being superior genotypes, special care must be taken to account for the modifying environmental factors. Indeed, the purpose of check or ( 1 ) 4 5 comparison trees in current procedures is to minimize edaphic or other microsite bias by comparing the growth rates of several trees in a localized environment. (The assumption is that phenotypic trees are more ef f ic ient in accumulating resources which are equally available to nearby check trees.) In practice, there is no measure of this assumption. Spacing and microsite differences are not quantified. The effects of variation in age, spacing and other environmental influences may also contribute signi f icant ly to differences observed in phenotypic characteristics between candidate trees and other dominant neighbors. Intraspecific Competition Competition can be defined as the demand by more than one individual for a limited v i ta l resource. In forest stands distr ibution of the resource is never even. Although weaker members of the forest community may make more eff ic ient use of those resources they acquire, the large individuals are capable of accumulating a proportionately larger share of the resource (Baskerville, 1965). Unfortunately, competition is not a to ta l l y unambiguous concept. Some portion of a tree's competitive status is probably genetic, another portion may be attributed to f o r tu i -tous spacing or position in the stand and perhaps other contributions to competitive status are possible. Foresters have long been aware of the relation between numbers of trees per unit area and growth rates of individual trees. With the recent prol i ferat ion of computer simulation models, the mathematical expression of competition as a function of tree parameters and distances or areas occupied has become fashionable. These competition indices have helped increase the sophistication of y ield predicting models. 6 In addition, they call attention to the individual tree and i ts relation to i ts neighbors, a characteristic which suggests the possibi l i ty of examining the competitive ab i l i t y of the individual in relation to other members of the population. In view of the requirements for better infor-mation as to the position of a particular phenotype in the population when improvement selection intensity is important, the use of competition index as a covariate to volume growth appears to offer a rat ional, s tat is-t ica l approach to increasing our confidence in the level of improvement selection possible for a given intensity of selection. Objectives The objectives of this thesis are: 1. To examine some stat is t ica l methods for improving quantitative selection in wild and thinned stands of western hemlock, using existing competition indices as a covariate to growth. 2. To evaluate 70 mm crown photography techniques for estimating growth and to establish a selection procedure based on crown parameters. 3. To evaluate, a poster ior i , phenotypically selected western hemlock plus trees with respect to growth and crown parameters. 4. To suggest operational plus tree selection guidelines to incor-porate the findings of this study. With detailed information on permanent sample plots i t is possible to examine the relationship between growth rate and competition. The growth rate of the individual is assumed to be genetically controlled. The competition level is assumed to be expressed by an individual. Determination of the superiority is by examination of the stat is t ica l structure of the population. The data for the study consist of re-measurement records for 12 permanent sample plots maintained by MacMillan-Bloedel, Ltd. They 7 represent both thinned and unthinned second growth stands. These plots were selected to allow a maximum extension of the techniques to f i e ld conditions, as many future selections wi l l probably be made in thinned young growth stands. Data for selected plus trees also came from Mac-Mi 11 an-Bloedel . The study is not intensively genetic in nature. Improvements from alternate selection techniques, such as, family selection, tandem selec-t ion, etc., are not considered. The primary intent is to examine stat is-t ica l techniques as possible adjuncts in an intensified single tree selection scheme. 8 LITERATURE REVIEW Selection Methods There are a number of selection methods employed in tree improve-ment programs. Among them are family selection, tandem selection, clonal selection and mass or phenotypic selection. All are based on s tat is t ica l analysis of components of variance. The f i r s t three mentioned systems are applied to progeny of the original selections. The most important method used in the i n i t i a l selection of trees for inclusion in a f i r s t generation seed orchard is phenotypic selection. Present methods of phenotypic selection in Brit ish Columbia, include check tree, parent tree and roadside selection; al l are very low in reliance on stat is t ica l procedures. Although al l are dependent on the cruiser's ab i l i ty to choose superior phenotypes, the check tree method is relat ively less subjective. Al l methods are heavily dependent on progeny tests for estimate of improvement. For this study only the check tree method is considered further. As practiced in coastal Bri t ish Columbia, check tree cruising in-volves the subjective identi f icat ion of a candidate followed by measure-ment of specific characteristics of the candidate and nearby dominant trees. For example, heights and diameter may be obtained. In the simplest case, measurements are compared with the mean of two dominants. A candidate which fa i l s to exceed the mean of the check trees by a speci-f ied amount is not included in the improvement program. This amounts to evaluating the selection di f ferent ial between the candidate and two of i ts neighbors. 9 The check tree method attempts to correct for the influence of local environment in the selection of plus trees. Instead of deter-mining the mean for the population and comparing the candidate to that standard, the phenotype is compared to the mean of several nearby domi-nant trees. Figure (2) i l lustrates the stat is t ica l basis of this selec-tion procedure. Unfortunately, the mean of the dominants with respect to the population is not known and so intensity of the selection is not known. Indeed, intensity is used in an ambiguous manner. I f the estimated number of trees in an area reviewed is 1,000 per each selec-t ion then an intensity of one in a thousand is quoted. Figure (3) i l l u s -trates the case where the selection di f ferent ial is made with respect to the mean of the population and is the intensity as described in equation (1). This is a more rigorously s tat is t ica l process. A model of the selection can be writ ten: y = m + k * (s) (2) Where y = value of the measured characteristic; m = mean for the popu-lat ion; s = sample standard deviation; and k = a constant. The constant k is the studentized score for the observation. The equation may be re-written in the form: k = (y - m)/s (3) The constant k is analogous to i in equation 1. Ledig (1974) discussed the possibi l i ty that the comparison domi-nants are related to the candidate tree. I f they are, the probability of rejecting superior trees is increased signi f icant ly. The mean for relatives might be expected to be well above the mean for unrelated trees. Ledig further indicates that a baseline regression technique may well avoid this problem. 10 SELECTION VALUE FDR Y Figure 2. Mean value (7c) for check trees compared to mean (m) of sample population in a frequency distr ibut ion; k(s) is unknown. SELECTION VRLUC FOR 1 Figure 3 . Selection di f ferent ial in a frequency distr ibution of sample population; k(s) is estimated for sample. 11 Intensive In i t i a l Selection There is a reasonable precedent for using stat is t ica l methods in processing plus tree cruise data. Brown and Goddard (1961) emphasized growth and crown relationships in their selection program for the southern pines. They used a regression equation, determined from 10 dominants and codominants as a baseline for individual tree volumes. Superior growth efficiency was identif ied by a positive residual of a selection candidate compared to the regression l ine. The authors noted that i f the same amount of wood can be produced on the bole by slimmer, more ef f ic ient crowns, then production of more wood per acre is possible. Final selection was not based solely on the growth efficiency. Several characteristics were measured and given weight in a f inal selec-t ion scheme. S t i l l the efficiency was a key portion of the i n i t i a l selection program. Campbell* selected Douglas-fir plus trees in the mid-1960's for Weyerhaeuser Company by relating growth rate to a measure of present l ive crown extension and the length of dead branch stubs. In effect, the technique was an indirect evaluation of past inter-tree competition since weight was given to a subject with narrow, l ive crown and short, dead branches. Progeny tests of height growth at age four from these selections and from phenotypically selected trees showed a superiority of the competition selected trees. Recently, Weyerhaeuser has developed a regression method for selection of both Douglas-fir and western hemlock. An equation is produced for each selection plot. I t includes growth of competing and subject trees. The predicted growth of the subject tree is compared to the regression line prediction. •^Personal communication, 1977. 12 The Weyerhauser Method has been the subject of some controversy, but clearly reflects the concern of this thesis. Robinson and van Buijtenen (1971) used a summation of mu l t i - t ra i t , weighted scores to select Pinus taeda (L.) plus trees. Among the variables were growth efficiency (crown area/dbh), dry matter (volume x specific gravity) and form. Regression equations were used to establish a check tree volume baseline. Expected volumes for each plus tree candidate were then compared to the actual volume and large positive residual used to assess efficiency of growth. Regressions were calculated based on height, age, and crown measurements. As the baseline data was accu-mulated over a period of time, the number of check trees per selection declined. The authors concluded that their regression only method was most applicable when check trees were more widely scattered and stand density was low. In these cases, few i f any check trees are measured. In dense stands check trees were s t i l l measured and individual regressions used as the baseline. Competition Competition, as used in this study, is defined as the active demand by two or more organisms for a common resource. Competition is commonly classif ied as either interspecific or intraspecific (Kormondy, 1969). While the former is of importance in the establishment of regeneration or managing mixed stands, for this study intraspecific competition is considered most important. A complete model of competition would include l igh t , moisture, nutrients and environmental influences in a dynamic manner. The competition considered here exists when available resources are reduced below an optimal level for individual tree growth. The causes of reduced growth (lack of suff icient resources) are dependent 13 on the number of competing individuals and the amounts and distr ibution of resources. The effects of competition are reduced growth. Current attempts to quantify competition depend on observation of effects. They include measurements of spatial distributions of trees in two dimen-sions and measures of size of individuals. Regardless of claims by modellers current indices are measures of past effects of competition. Most of the indices are concerned with on the ground location of the stems. Ground spatial measures of competition may be divided into several categories, among them stand density, point density and single tree, distance dependent expressions. Stand density measures have been reviewed by Curtis (1970). Reineke's (1933) stand density index and Chisman and Schumacher's (1940) tree area rat io (TAR) are examples. These measures express site occupation as a proportion of normal or open-grown stand conditions for a species. Many of these may be reduced to linear combinations of variables ex-, pressing occupation in terms of diameter square sums. Since they repre-sent stand averages and not the individual case, they are not useful in the investigations of individual tree response to competition. Point density measures attempt to express stand density at a point. Basal area prisms and angle gauges have commonly been used to arrive at expressions of point density. Spurr's (1962) index is an example of this genre, yet i t has some shortcomings for direct application. Competition (and, therefore, zone of influence) does not extend indef i-n i te ly about the individual. I ts extent varies with age, size, and species among other variables. Computation of point density for an individual tree is , therefore, not s t r i c t l y defined mathematically. As there is no clear definit ion of the extent of the zone of influence 14 for individual trees, so too, there is more ambiguity as to the boundary of plots. Attempts to determine the competitive status of individual trees include available growing space defined by polygons. First described by Brown (1965) this geometrical spatial index takes account of irregu-la r i t ies in spatial distr ibution of stems. More recent attempts to describe growing space and competition have been made by several authors (Jack, 1967; Adlard, 1974; and Fraser, 1977). Analysis of periodic annual increment using a polygon spacing index and basal area gave good regression equations for predicting periodic growth. But the index contributed signif icantly to only 4 of the 10 plot models (Adlard, Table 1); diameter or basal area were the main contributors to prediction of growth. One of the possible l imits to the use of current competition indices concerns the variables used to define them. Distances between individual plants is an extrinsic variable ( i . e . , is not a measure on the individual i t s e l f ) , which describes i rregular i t ies in spacing. Zone area or poly-gon area are in t r ins ic , determined by the diameter and/or height of the tree. These intr insic variables ref lect the effects of competition, even i f they are disguised in the form of open-grown crown extent (a function of diameter and height). That the competition between trees for growth requirements exists is beyond doubt. There is considerable vagueness about the exact nature of interactions. There are a large number of variables which seem to be relevant to an expression of compe-t ion. There is also a good deal of ambiguity in the assessment of the causes and the effects of competition. 15 Competition Indices The single-tree, distance-dependent indices of competition have undergone rapid development paralleling their application in various computer simulation models. These indices generally relate zones of influence of individual trees to the physical area occupied by open grown trees of similar diameter or volume. Competition load on a given tree is then estimated as a rat io of space available to the predicted, open-grown space. As these indices relate to individual trees they are obviously candidates to expressing the differences in competition between trees. Figure 4 is a composite representation of the following indices. Arney's (1971) index for Douglas-fir represents competition as the relative occupation of a subject tree's growing space. The growing space for each tree is defined as the expected size of an open-grown tree of equal diameter. The relationship between open-grown crown width and DBH was used to determine the maximum growing space or zone of influence for a tree. The index is expressed: where A- represents the open-grown area for the subject and AO., the area of overlap of the i th competitor with the j t h subject tree. Arney denoted this a percentage overlap. This may be s l ight ly misleading in that a 0 to 100% scale is not obtained, rather i t is a scale of 100(%) minimum with undefined upper l im i t . Bella (1970) developed a model of competition which expresses the relationship between subject and competitor by an exponential function. (4) J 16. Figure 4._ Parameters of competition Indices. where: A = area of influence, CR = Crown radius of an open grown tree, AO = area or Zone overlap, L i j = distance between stems, i = competitor, j = subject 9 i j = sector angle, LOij = linear overlap. 17 Using the findings of Baskerville (1965), Bella modelled the effects of species tolerance by using an exponential weighting of the relative diameters to the growing space overlap. His index is : where D. is the diameter of the subject tree, D. is the diameter of the competitor, ex is a weighting parameter determined by an i terat ive process. Ek and Monserud (1974) also used a weighting to account for rela-t ive tree sizes. However, they included both height and diameter measure-ment in the determination of the proper weight. This means that the weighting is much more proportional to the volume, but computationally depends on more extensive individual tree data. where S., S. express subject and competitor sizes respectively, and tol is a measure of the tolerance of the species. Hegyi (1974) developed a competition index independent of crown overlap, crown extent. His index was formulated as: where L^. represents the distance between the i th subject and the j t h competitor. Although this appears simplistic by comparison to some of the other indices, in combination with a simulation program i t per-forms quite well and is not computationally expensive. The assumption 18 of l inear i ty in the competitive ab i l i t y of trees of different sizes may be quite adequate to represent the situation in even-aged stands and well managed plantations. The advantages of few measurements and few calculations in the application of this index make i t attractive. Lin's (1969) index is somewhat different from the preceding indices. The area about an individual tree is divided into quadrants. Each quad-rant is assigned one quarter of the total growing space for the subject. A maximum of one competitor per quadrant is evaluated in the computation of each tree's index. The range of this index is 0 to 100% and indi-cates the amount of space available to the subject rather than the amount of reduction. This is a true percentage scale. Competitors are selected in each quadrant in a manner similar to the selection of trees by a basal area prism. The tree in each quadrant which subtends the largest angle at the subject tree is chosen as the competitor for that quadrant. Lin's index is : 4 G S I , = 4 j ] T [ 2 5 ~ 9 i ~ 2 , 1 5 * 0.3467 * D i + D j (8) i= l J where 9^  is the observed angle, 2.15 is the minimum angle for competi-t ion to exist. Newnham (1964) used an angular measure to define the competition between trees. His model assumed that crown interactions at the periphery reflected the intensity of competition. His index is formulated as follows: 9 l J . ^ cw. / J (9) 19 where 9— is the interior angle subtended in the j th subject's expected circ le of competition by the intersection of the i th competitor's circle of influence. Quenet (1976) used an index which is independent of the size of the subject tree. As with some early indices this one does not l imi t the distance to a competitor expressly. I t is calculated: where al l symbols are as previously defined. The f inal index which was considered was Staebler's (1951). In this model the linear overlap of growing space along circle radii was used to express the competition between trees. where LOij is the linear over lap and Ri is the radius of the competi-t ion circle based on open grown crown width. These were the indices which were computed for each tree at Tumour Island. There was no information on individual heights so that a height-diameter relation was used to generate S-^ for trees in the Ek-Monserud model. At the time of generation no i terat ive evaluations of exponent was made on the Bella index. These compromises were conceded to be the best in the time available. Comparisons of the performance of competition indices are few. In their respective simulation environments each has proven i tse l f adapt-able to the goal of the modeler. Only Staebler's among these indices (10) (11) 20 was specif ical ly designed to stand alone. Most of them rest on earlier formulations of ecological dispersion or research relating the perfor-mance of individual trees under a variety of thinning, spacing, f e r t i l -ization and mortality regimes. The majority are based on the concept of a l imit ing competition circle or area described mathematically by intr insic measures of the current tree size and extrinsic distances between individuals. Most of the indices (ex. Lin's and Newnham's) are mathematically limited at the low end, but the upper end is undefined. Lin's index is a percentage index and functions inversely with respect to al l the other indices. As previously mentioned Arney's index is termed a per-centage index, but is not. Another of the indices which has definable mathematical characteristics is Newnham's. This index is limited in the open grown case to 0 and in the maximum would approach 4. This can be visualized by imagining a small tree surrounded by four larger trees growing in a very nearly square pattern each overlapping i t s growing space completely. More overlap is impossible in that the com-petitors would begin overlapping each other more than would be consis-tent with their own size! The exception in two storied stands accounts for possible larger values. (Only three observations had a value greater than 4 at Tumour Island.) Three studies comparing competition index performance are cited in the l i terature. Beck (1974) used a model expressing 5-year diameter growth (ln(DG + 1 ) ) as a function of site index, age, diameter and one of four competition expressions; (1) basal area obtained by use of an angle gauge, (2) plot basal area, (3) Gerrard's (1969) competition quo-21 t ient and (4) Bella's competition index. Gerrard's index proved the most valuable addition to common terms. Bella's index was not far different with added R = 12.4% compared to 14.3%. Newnham and Mucha (1971) reviewed a wider selection of the competition indices. Bella's index was selected as the best for predicting diameter growth with the reservation that i t underestimated mortality and was complicated to calculate. In the study both a weighting-factor FC and the adjusting exponent ex, (refer to Appendix I) were determined by i terat ive pro-cedures. A second model selected by the authors included two competi-t ion measures. In a regression model both linear overlap and angular overlap were included. These were the indices of Staebler and Newnham. The authors conclude that the selection of predictive models using competition indices are s t i l l subjective. And, unt i l considerable understanding of the biological mechanics (sic) of competition among trees is accumulated decisions wi l l remain subjective. Daniels' (1976) compared the performance of three of the competi-t ion indices, those of Arney, Ek-Monserud and Hegyi. A modified com-petitor selection technique - using a 10 BAF rule, the same as the one used for selecting competition in this thesis - was described. The three indices plus six modifications of Hegyi's index were correlated with diameter increment and height increment. Ek-Monserud's index had the highest correlation with diameter increment though the modified Hegyi's index was l i t t l e different (-0.424 versus -0.415). Hegyi's index did surprisingly better in height increment correlation (-0.456 versus -.0.276). Unfortunately the note does not indicate the time interval involved in calculating increment. The author also chooses 22 to correlate competition and diameter increment which fa i l s to account for the purely geometric decline in radial growth under constant basal area expansion. Daniels' indicates his belief that Hegyis' index is independent of species and has an advantage in computational simplicity. He indicates further that i t may f ind u t i l i t y as a measure of point density. Crown Competition The crown is the center of the tree's physiological act iv i ty . Photosynthesis, respiration, and metabolism are most important in the crown. The rate of production of metabolic products is certainly genet-ica l ly influenced and has become the center of some attention in genetic improvement studies (Ledig, 1975). Understanding basic biological production processes is important to understanding crown function. Nevertheless, simple qualitative observations indicate the importance of the crown to the success of the individual tree. The social position of the crowns of trees in the development of stands have long been noted in their progression from codominant to intermediate to suppressed and f ina l l y mortality. More precise measurement of the status of the crown with respect to i ts neighbors could supply valuable information concerning the growth, competition or ultimate decline of individual stems. Assmann (1970) devotes a large portion of his book to the description of crown rela-t ions. The role of the crown as a tool of aggression in the competition for l ight and space is treated extensively. Theoretical spatial require-ments of circular crowns are discussed. Forms and geometrical shapes are described as they may relate to growth. Most important for a study in the selection of superior trees, Assmann notes the necessity of 23 considering the efficiency of individual crowns for production of wood. I t seems evident that trees may occupy the same amount of space in a stand and produce different amounts of wood. I f crown form or efficiency is genetically determined as is demonstrated for certain races of Scots pine (Pinus sylvestris, L.), this should be a character of interest in tree improvement (Assmann, 1970). Crown competition has also been recognized by practicing foresters and is often the basis for making s i lv icu l tura l prescriptions (Assmann, 1970), Naturally, crown competition has developed as a tool among com-puter model builders (Mitchell, 1975a). Osborn (1968) found that ratios of crown width and l ive crown length to total tree height provided the best measure of density in western hemlock stands aged 45 to 160 years. However, these variables proved relat ively poor in explaining 5-year radial and basal area growth in his study. Hatch et a l . (1975) developed an individual tree competition model based on the crown surface area exposed to sunlight and the distance from breast height to the base of the l ive crown. The model measures the relative competitiveness of the subject tree and predicts i ts rela-t ive growth potential rather than calculating the competitive pressure exerted on the subject by surrounding trees as in most other models. Both Osborne and Hatch and coworkers assumed that crown form is symmetrical and conical. In rea l i ty , crown shapes are typical ly asym-metrical; the degree of crown deformation appears closely related to size and distance from competitors. Furthermore, a review of crown shape by Assmann (1970) revealed that a variety of species had parabolic or spherical rather than conic crowns. Mitchell (1975a) reached similar 24 conclusions for Douglas-fir, even for open growth trees under no com-pet i t ion. His simulation model treats growing space at the individual branch level, thus incorporating real is t ic variation in crown dimension. In addition, the model considers foliage retention and volumes. This model has demonstrated the v iab i l i t y of crown characteristics as pre-dictors of individual tree growth. The profound influence of crown size, shape and position in the stand on diameter growth are well recognized by the practical forester. The correlation between height growth and crown class is also obvious. Mitchell (1975a) has i l lustrated the relation of potential to achieved height growth for the range of crown classes of Douglas-fir (Figure 5). Other recent studies have cast doubt on the wisdom of accepting prima facia the forestry dictum which indicates that height growth is not affected by density or competition. Curtis and Reukema (1970) observed mean top height differences of suff icient magnitude to warrant re-evaluation of site index in Douglas f i r . The studies indicated that changes in site index between ages 5 and 35 were associated with establishment densities and could not be accounted for by soils or topographic differences. Differences in apparent site index were a t t r i -buted principal ly to effects of dif fering intensity of competition on height growth of dominant and codominant trees. Husch et a l . (1972 p.353-354) also notes height-density dependence in some species. Crown variables offer a functional relation to the growth of indi-vidual trees. I t might even be expected that a future development of physiological information as to biological efficiency of needles or needle retention times could be added direct ly to models of individual 25 crowns. This approach has an advantage over a s t r i c t l y mathmatical model in that the new information may be incorporated in the model without returning to basic model building and evaluation. 26 Competition Load where h = height of individual tree and H = height of an open grown tree, and tree ideograms indicate the upper l imi t of an indicated crown class. Figure 5. (Adapted from Mitchell 1975a) The effect of competition for growing space on height growth. MATERIALS AND METHODS This study had as a goal (objective number 1) intensive modelling of growth, competition, and ( indirect ly) genetics of individual trees on permanent sample plots. In addition, i t was hoped to extend the work to existing plus trees and to develop f i e l d methods for future selections. MacMillan-Bloedel, Ltd. , has many permanent sample plots with growth records for 20 years or more. There were also in existence a number of phenotypically chosen plus trees cruised by the company's personnel over the years. I t was decided that the f i r s t tests would be done with the selected sample plots of nearly pure western hemlock. I n i t i a l model results were to be applied to the phenotypic selections. The study was contracted to MacMillan-Bloedel, Ltd. by the Canadian Forestry Service under a scient i f ic subvention. Permanent Sample Plots Permanent sample plots located on Tumour Island (Figures 6 and 7) were chosen as the basis for this study because of their age, uni-formity of site and the length of recorded data available. Two plots were established in 1932, the remainder in 1949 and 1950. At estab-lishment they were wel1-stocked, predominantly young western hemlock. The stands have been measured at five-year intervals and stem maps were constructed for al l the plots at or shortly after plot establishment. The plots were divided for analysis into three groups by age and loca-t ion: 28 Figure 6. LOCATION OF STUDY PLOTS Location of Tumour Island and permanent sample plots Figure 7. DETAIL OF PLOT DISTRIBUTION 30 Group I Breast height age 60 - 65, located near Tumour Bay t idal f l a t s . Al l but one plot have been thinned at least once since 1950. They are plots 350, 351, 352, 357, (al l thinned), 358 (unthinned). Group I I Breast height age 45 - 50, located parallel to a single drainage, plots 354 and 359 (thinned), 355 ( l igh t l y thinned), and 356 (unthinned). Group I I I Breast height age 80 - 100. These stands contained a larger proportion of other species, (age of the plot is indicated in parenthes): plots 353 (80), 400 (100), and 401 (100) (al l thinned). A summary for the plots based on the original plot and an internal buffered subplot is presented in Table (1). (See table & notes.) Computation of Indices Eight distance-dependent, inter-tree competition indices were selected for this study on the basis of their high potential for appli-cation in operation, growth prediction, systems in Bri t ish Columbia (Hegyi, 1975, Glew, et a l . , 1976). The indices were computed for trees lying within a buffered region of each plot. Computational algorithms were modified and programmed by Hegyi and Oxtoby (1976). Mitchell 's model (1975a) seemed to be the most real is t ic of those emphasizing crown competition. His concepts were used to test western hemlock plus tree selection c r i te r ia based on crown photography. Distribution histograms of frequency versus competition index were plotted in an attempt to understand more precisely the ranges of com-pet i t ion values for each index. For some of the indices theoretical l imits could be calculated or estimated as was discussed in the l i terature 31 TABLE 1. DATA SUMMARY FOR PURE STANDS OF WESTERN HEMLOCK AT TURNOUR ISLAND Year Original Current Total Buffered Plot # Thinned Stems Stems Area Density Area Density AC St/Ac • AC St/Ac GROUP I 350 50,65 340 145 .5 290 .30 306 351 '50 303 109 .5 218 .30 194 352 '59 376 127 .5 254 .30 213 357 '50 281 160 .5 320 .30 233 358 '55 367 190 .5 360 .31 403 GROUP I I 354 '59 434 159 .26 577 .16 462 355 '59 485 195 .26 750 .16 775 356 418 225 .26 865 .11 755 359 '54 425 100 .26 384 .13 377 TABLE 1. DATE SUMMARY FOR PURE STANDS OF WESTERN HEMLOCK AT TURNOUR ISLAND (CONTINUED) DIAMETER BASAL AREA BUFFERED AREA INCHES Square-feet BA / AC PLOT # MEAN (SD) MEAN (SD) GROUP I X100 350 12.0(4.06) 88.3(58.9) 270 351 14.8(3.70) 127.0(64.4) 240 352 15.8(4.30) 146.0(76.6) 311 357 13.5(4.06) 108.0(63.3) 251 358 11.6(3.92) 81.5(56.4) 328 GROUP I I 354 9.97(2.72) 56.3(30.5) 260 355 7.73(2.88) 37.1(29.5) 288 356 7.74(2.90) 37.2(28.9) 281 359 11.2 (3.61) 76.9(50.7) 286 32 review. Graphing the relationship allows us to identify extreme values and detect discontinuities i f they should exist for an index. Figure 8(a-h) i l lustrates the results of graphing al l 8 indices. Additional Data Collection In early June 1976 the plots were visited by experienced plus tree cruisers of MacMillan-Bloedel Ltd. and phenotypic selections on each plot were made. The trees were selected using procedures as close to operational techniques as possible given that trees on the plot were to be selected. These were to be compared with trees selected later by computed models. Thinned plots were included in the study since many existing, thinned stands are suitable for plus tree selection. In addition, 25 trees were selected using an estimation of competi-t ion computed by MacMillan-Bloedel's hemlock simulator (Company pro-pr ietary). Stem distributions were f i e ld checked and errors corrected on stem maps. Ground measurements of crown area projection (CPRO) were made on the phenotypic trees. The phenotypic trees were climbed and marked for identi f ication in aerial photographs. Breast height increment cores and some addi-tional upper stem cores were obtained and plot record diameters and ages were ver i f ied. The cores were sent f i r s t to Dr. R. W. Kellogg at Western Forest Products Laboratory of the Canadian Forestry Service for analysis of specific gravity; the results to be used to determine specific gravity of phenotypes. They were then measured by an Addo-X operator at U.B.C. for radial growth. These measurements were used to cross check the diameter increment recorded on the MacMillan-Bloedel f i e l d sheets. 2 0 C H o Z UJ => o UJ (fc u. ICOA 200 400 COMPETITION GOO INDEX BOO Figure 8a. Frequency distr ibution of Arney's Competition Index for al l trees on Tumour Island plots. o Uj => O UJ tt u. 100 50 2*2 4 ' 4 COMPETITION INDEX Figure 8b. Frequency distr ibution of Bella's Competition Index for al l trees on Tumour Island plots. 34 o LU o LU tt LL /ocM T T T V T T COMPETITION INDEX Figure 8c. Frequency distr ibution of Ek-Monserud's Competition Index for al l trees on Tumour Island plots. 20QJ >• o Z LU => O LU tt JOQJ 2 2 4 4 ~r~ 6 7 — r ~ 8 9 COMPETITION INDEX Figure 8d. Frequency distr ibution of Hegyi's Competition Index for al l trees on Tumour Island plots. o UJ o UJ ct u. lOOA 50-— • i 1 1 i 1 2 2 4 4 6 7 COMPETITION INDEX Figure 8 e . Frequency distr ibution of Lin's Competition Index for a l l trees on Tumour Island plots. COMPETITION INDEX Figure 8 f . Frequency distr ibution of Newnham's Competition Index for al l trees on Tumour Island plots. 36 200J >-o z LU =) o LU C t u. 1004 7¥" 11^1 K>'7 COMPETITION INDEX 225 Figure 8g. Frequency distr ibution of Quenet's Competition Index for al l trees on Tumour Island plots. o z Ul => o L u C t u. IOCH 50-2'2 4*4 € T7 COMPETITION INDEX If Figure 8h. Frequency distr ibution of Staebler's Competition Index for al l trees on Tumour Island plots. 37 Low-level photographs were taken of each plot from a helicopter (Mitchell, 1975b). Plot centers were marked by a "double" weather balloon, helium f i l l e d (Figures 9 and 10). The Brit ish Columbia Forest Service (BCFS) supplied a 20-foot boom equipped with synchronized, twin 70 mm cameras and a technician for operating this stereophoto-graphic system. The system is designed to give high resolution stereo-photographs suitable for measurement of crown dimension when slow, uniform speed and low, constant f l i gh t altitude are maintained (Figure 10). The boom was mounted on a contractor's helicopter (Figure 11). Both color reversal and black and white f i lm were exposed and processed by the BCFS. The photographs were then scanned, identif ied with their respective plot numbers and taken to a commercial, photointerpretation laboratory (Integrated Resource Photography Ltd. , Vancouver, B. C ) . The stereo pairs were mounted and a corrected, stereo model was estab-lished. In a few cases i t was necessary to use consecutive photos from a single camera to obtain suitable stereo models due to asynchrony in exposures. Measurements of crown area at and crown heights above, the estimated level of canopy closure were made on al l visible trees within a plot. Unfortunately, the f l i gh t altitude was inadequately maintained. Because of the short photo base of the boom this lack of control resulted in large differences in the r e l i a b i l i t y of the measurements for height and some errors in estimation of crown areas. Photo coverage could have been better; too few exposures were made, many series terminated before the subject plot was at the center of an exposure. Due to these problems, the estimated total tree heights were not usable. This was a major disappointment in the project, but costs did not allow the correction of the problem. Balloon location Figure 9. in the Crowns, obiique view co Figure 1 0 . Vert ical view, center of p lo t marked by balloon Figure 1 1 . Loading Film in the Helicopter photo boom 41 Existing Phenotypically Selected Plus Trees In July, 1976, measurements of a sample of the existing plus trees were made. The locations of these trees represented a broad spectrum of habitat types throughout the coastal western hemlock zone on Mac-Mi 11 an-Bloedel Timber Farm Licenses (TFL's). Near each plus tree at least one check tree was selected for apparent crown efficiency and position of the crown in the canopy; dominant check trees were preferred, but some codominants were purposely, selected. Height, diameter, crown rad i i , and competitor distr ibution were measured for each plus and check tree. Growth on the selected trees was determined from Addo-X measurements performed at U.B.C. 42 RESULTS AND DISCUSSION Considerable effort went into the creation of s ta t is t i ca l ly rele-vant decision models. Eventually, successful models emerged. The pro-cess which led to different models seems to be as important as the actual results, because serious reservations developed to the use of basal area increment as a decision variable when volume is the true variable of interest. Therefore, attention is focused on the process of developing decision models for the selection of superior trees. In s ta t is t ics , we are frequently faced with accepting or rejecting a particular observation as a reasonable member of a population. We have information on the population and the values of the observations on individuals. This is a problem in s tat is t ica l inference. The rules and procedures of stat is-t ica l inference can be applied to the selection of superior phenotypes. Several practical problems must be dealt with in applying stat is-t i ca l decision rules to a set of observations. The population must be clearly defined. This is not a t r i v i a l problem (Steele and Torie, 1964). In the case of selection of western hemlock plus trees, i t is easy to eliminate spruce trees growing on the plot , but not so easy 1 2 to recognize "residual" western hemlock. •'•The word residual is used commonly in two ways. F i rs t , i t refers to trees le f t after a harvesting operation and which have a decided advan-tage in stand competition especially in western hemlock. Second, i t is used in stat is t ics to indicate the distance of an individual observa-tion from a mean or a regression l ine. In this paper "residual" trees wi l l always be referred to in quotes. I t is clear that "residual" hemlock are not members of the "population" as they have a decided head start on the even aged seedlings. 43 A sample plot chosen for measuring components of growth should have a uniform distr ibution of nutrients, moisture and l ight . I f the sampled plot conditions are optimal, competition index represents the effects of the environmental variation on the growth of the individual tree and the residual represents genetic variation. I t is true that current competition may be partly genetically determined and additional variation includes the influence of age, microsite and minor crown posi-tion differences among other factors. These factors serve to emphasize the importance of selection of uniform sample plots since the objective is to isolate as much of the genetic variance in the residual as is possible. While i t is recognized that an actual parti t ioning of genetic and environmental effects is not possible, a model should attempt to isolate a biologically rational component affecting tree growth. Selection of a model on which to establish l imits for inferential decisions should be consistent with biological rea l i t ies . Thus, one objective (#1) of this study was to investigate stat is t ica l c r i te r ia for selection of western hemlock based on the regression of growth on competition. The use of a simplistic model such as selection based only on the growth rate or total size would not be consistent with the objectives, even though this could be considered a possible model for the establishment of a selection rule. Competition indices seems to be a rational covariate to growth in attempt to describe genetic superiority. Description of Growth - Competition Index Relationships Scatter plots of the growth competition relationship are i l lustrated in Figures 12 to 15. Throughout this study growth is measured as the difference between squared diameters at the two measurement periods. This is the equivalent of basal area growth (BAGR). 44 Conversion to metric area units is made by multipl ication by 5.067 2 2 cm / in . Conversion to square feet is by multipl ication using .00545415 2 2 f t / i n . These conversions were not made as they are constants and not real ly crucial to selection. To further i l lust rate the value of information concerning growth competition relationships the Tumour Island data was sorted into ascen-ding values for competition and divided by competition into several strata on three of the plots using Bella's index of competition. Means and standard deviations were computed for the strata. The result of this procedure is i l lustrated in Figures 16 to 18. Not surprisingly, both the mean and the standard deviation change from stratum to stratum. Two points have been made: 1) there is a functional relation between BAGR and competition index, and 2) there is a spread about the line representing this relat ion. A simple model of the functional form of growth competition may be gained by examining these figures'. There is an obvious curvilinear relationship for these as well as others examined (with the exception of Lin's index which increases with increasing competition and seems l inear) . A brief analysis of l imit ing situations for the majority of indices can add to the picture. F i rs t , the competition free situation; while the exact value is not certain, we know that growth is not i n f i -nite when there is no intraspecies competition. Second, in relat ively even-aged stands there must be an upper l imi t to competition. Again we are not certain at what exact value competition is a maximum, but beyond some point growth ceases and mortality is probably imminent. Altogether this suggests an overall quadratic model with both x and 45 PLOT 351 +-> <4-CT to LO CO oo 348 ^  X CD <: CO o ct: CD 23.2 J CC < CO CO OH — i 1 r — ti.t 34.0 47 O BELLA'S INDEX i 600 75 0 Figure 12. Scatter Plot of Bella's Index versus periodic growth (BAGR), Plot #351 Tumour Island. 46 58 IJ PLOT 351 46-4 J 3484 23 21 we A ft 77 I 4 9 0 EK-MONSERUD'S INDEX T 116 Figure 13. " 1 — 14 2 Scatter Plot of Ek-Monserud's Index versus periodic growth (BAGR), Plot #351 Turnous Island. 47 58 0 u-c r L O C O co or CD <: CO o CD < co CO 46-5 J 34-flJ 23 2 ll>6 J PLOT 351 7 7 7 7 7 7 HEGYI'S INDEX Figure 14. Scatter Plot of Hegyi's Index versus periodic growth (BAGR), Plot #351 Tumour Island. 48 PLOT 351 T 1 1 1 1 1— 0 15.t 1 0 J 4 I . T *0.9 76 2 LIN'S INDEX Figure 15. Scatter plot of Lin's Index versus periodic growth (BAGR), Plot #351 Tumour Island. 49 y intercepts, i t does not rule out linear models or more generalized logarithmic models. From a general picture of competition we proceed to examine the nature of individual competition indices and their case dependence on computer and simulation models. Competition Indices in a Superior Tree Selection Process I t is possible to include other parameters in a competition model of growth. Among the candidate parameters i n i t i a l dbh is often used. For simulation purposes, models must have good or excellent growth predictive ab i l i t y . To be most effective both the genetic and environ-mental variation should be explained in a single model. For this reason, one or more i n i t i a l size parameters are often included. Typically, five-year periodic growth rates may be predicted by such models with R values of .70 to .90 or higher. R is a measure of the proportion of the variance of growth which is explained by a regression. A growth model would have the general form Y = f (CI (d,s),D) + e (12) where Y is periodic basal area growth, CI is the competition index, a function of d, the subject and competitor diameter, s their spatial d istr ibut ion; and D, the i n i t i a l diameter. The unexplained portion is represented by e. In the development of computer simulation growth prediction is paramount. Functional or causal roles of predictors is secondary. For the purpose of plus tree selection a model which maximizes growth predictive power could be completely inappropriate. Our goal is the development of a selection cr i ter ion which is closely associated 50 with the genetic superiority of an individual. This suggests a model incorporating the environmental portion of influences which control growth and segregating those influences which could be genetic. In s ta t is t ica l terms, the expected growth in the population is accounted for by expl ic i t terms of the regression equation and the genetic varia-tion is associated with the residual. I f a model is driven by an i n i t i a l size term (e.g. , diameter), any genetic variation tends to be masked since this term is a result of both genetic and environmental factors and i t becomes i l logical to expect to identify plus trees using regres-sion or any other stat is t ical procedure. As a result the following model was chosen: where these terms s t i l l have their original denotations. The Selection Value and Regression Models Once the functional models have been proposed, a process for selecting individual trees is easily obtained. In the simplest case a confidence interval for each tree is obtained. This value can be used to select superior trees. For a linear model of growth versus competition, confidence l imits for the growth of an individual tree can be expressed: where Y = BAGR and X = a competition index. X is the mean and S indi-yx cates the sample standard deviation from regression. Using this rela-tion the residual for any observation may be standardized. Comparison of residuals for any value of competition can then be made. One way Y= f (CI (s,d)) + e ( 1 3 ) ( 1 4 ) PLOT 351 4 COMPETITION STRATA 16 TREES I STRATUM + overall mean I I I + I I 10 2 0 30 4 0 COMPETITION INDEX (Bella) 5 0 Figure 16. Strat i f icat ion of competition versus basal area growth Bella's Index Plot 351. , J PLOT 3 5 9 - 5 Strata 49 trees 10 t rees/point + I IX i t i i -overal l mean I I 4-I I -T I 10 20 30 40 Figure 17. Periodic basal area growth versus Bel la 's Competition index. PLOT 400 ( Mixed Species) 60 trees 10 trees/point ( 7 trees>I00 C. I . not Included) tr I X o CC < UJ CC < < < oo ce < ui >-U l > .109 .054 T J L "H— 20 1 1 — 30 T I T I 1 T + 1 + — i — 40 1 — 50 I — 6 0 1 — 70 "T— 80 "T— 90 COMPETIT ION INDEX cn co Figure 18. Periodic basal area growth versus Bella's competition index. 54 of obtaining the selection value is to divide each residual by the CL (confidence l imi t ) for the corresponding competition value. (Standard-ization of the variables prior to regressing them is another way.) Pro-cedures for calculating confidence l imits and hence obtaining a selec-tion value are part of the most current computer regression packages. As we have seen the relation for most of the competition indices is not a simple linear one, nor is the variance of growth rate constant for al l values of competition (see Figures 12-18). Direct application of linear regression models of relation and confidence intervals is not appropriate. Stat is t ica l ly , both the curvilinear relation and the non-uniform variance can be handled by common computer routines and s t i l l y ield a selection value. A number of regression models were investigated. Data from four of the plots and al l indices were processed and the results analysed for distr ibution of residuals, standard errors, and probability of residuals. Complete output is analagous to crown regressions on a single plot and is included in Appendix I I . The f i r s t regression model to yield reasonable results for al l the c r i te r ia mentioned was: Y = bQ + b x (CI) + b 2 (CI)2 + e (15) The polynomial model typical ly gave R-square values of 0.50 to 0.60 for the better indices. Examination of the residual pattern for these models again revealed nonhomogeneous variance with respect to the indices. Referring again to the i l lustrat ions for s t ra t i f ied com-peti t ion using Bella's index (Figures 16-18) selection probability is not the same for each strata. In order to obtain equal probability at al l levels a weighted regression procedure could be used. This 55 procedure was suggested but not implemented as a resu l t of the fol lowing considerat ions. I n i t i a l resu l ts from computer runs using standard confidence in te r -val se lect ion ru les , l e t alone weighted ru les , were discouraging. F i e l d examination of the select ions revealed many small suppressed or in te r -mediate trees were chosen. Addit ional select ions were made in MacMillan-Bloedel, Ltd. PSP 710 near Port Alberni on Vancouver Is land. The se lec-t ions were reviewed by a group of simulation and tree improvement foresters in the f a l l of 1976. Discussions during th i s meeting led to a d i f ferent approach to the s t a t i s t i c s of se lec t ion . I t was agreed that in dense young stands suppressed or intermediate trees were not expected to be candidate t rees. These trees represent a d i f ferent "populat ion". They u t i l i z e the resources e f f i c i e n t l y in that they survive on f i l t e r e d l i gh t and reduced nutr ients , but in terms of producing wood useful to man they are not e f f i c i e n t . A new approach was taken to estab l i sh a model which re f l ec t s the prac t i ca l fo res te r ' s interest in the more dominant t rees. A t ransfor-mation of the equation already invest igated was adopted. The procedure i s much l i k e the weighting of a regression to equalize the variance except the opposite i s done. The regression maintains the information on small t rees, but emphasizes the variance observed among the larger stems. The resu l t ing equation i s : Y/CI = b Q/ (CI) + b x + b 2 (CI) + e (16) Notice that the l e f t side of equation (16) has dimensions, per iodic growth/unit competit ion. This reca l l s other fo res ters ' interest in concern for e f f i c i ency in superior tree select ions (Brown and Goddard, 1961). In prac t i ca l terms the model el iminates the select ion of most 56 small , suppressed or intermediate t rees. Examination of the residuals and the trees selected coincided more closely with subjective ideas of plus t rees. El imination of Indices Of the eight or ig ina l indices four were eliminated quick ly . Staebler 's (1951) index was an early attempt at describing spacing re lat ions and Quenet's (1976) index is a very simple model. These two indices f a i l e d to explain a su f f i c ien t amount of the growth variance. Selection using only the mean value for growth gave resul ts qui te comparable to these two indices disregarding any ef fect fo r competit ion. L in 's index posed both computational and theoret ica l problems. The problems are examined in Appendix I I . Arney's index is mathematically sophist icated and has a biological basis. I t s performance in growth simulation is not questioned here. I t was eliminated in view of i t s consistent ly low correlat ions with growth in the regression model developed to select plus tree candidates. Competition Selections on Sample Plots Figure 19 i l l u s t r a t e s the select ion in terval obtained by back-transforming equation 16 to the or ig ina l basal area growth and compe-t i t i o n values. The regression and a l i s t of the selected plus trees along with the i r select ion values (standardized residuals) is presented in Tables 2 through 13. The complete regression resul ts of the analysis of Plot 358 are presented in Appendix I I I . Be l la 's index i l l u s t r a t e s the method. Examination of the trees selected by the competition indices i n d i -cate that they are not the fastest growing in terms of periodic incre-.218 ^ .103 .109 ki kj . 0 3 4 P L O T 3 5 9 -SELECTION LIMITS .f tree candidates REGRESSION - PREDICTION 10 2 0 30 4 0 COMPETITION INDEX (Bella) Figure 19. Back transformed equation with confidence l imi t . 58 ment nor are they the largest basal area trees. However, selected trees are high on the l i s t of trees based on basal area growth; they might be classed as t h r i f t y dominants or, occasionally, codominants. In general, the selected trees have competition indices which place them in the lower th i rd of the plot of CI. A few of these trees might be classed as open-grown, but the majority do not have unlimited growing space; they support the hypothesis that a superior tree should express dominance over i ts competitors. Those phenotype choices at Tumour Island which could have an index computed, are represented in Table 14. Among them only one tree has an index greater than the mean value for i ts plot. Two of them actually represent the tree of least competition (Bella's index). The extremely low competition value associated with phenotypes supports the idea that phenotypic selections may be growing under conditions of low competition in relation to their neighbors. Analyses of Covariance I f each plot has i ts own regression equation due to original spacing or thinning or age, a tedious, expensive repetit ion of the process for developing models would have to be undertaken each time a new condition was encountered. Certainly this would be unacceptable economically. However, i f the results from plot regressions can be combined, a base-line established, and reduced sampling schemes designed, the process may be quite economical. Snedecor and Cochran (1967) give a clear discussion of the use of analysis of covariance for comparison of regression lines. I f the relations between independent and dependent variables are investigated 59 Table 2. Group I - Plot 350 Competition, Selection and Regression Competition Competition Average for Tree Selection* Competition Index Plot #350 Number Value Index Value Bella 30.0 64 2.8 27.8 29 2.4 14.3 53 1.5 18.2 Ek-Monserud 4.4 64 3.4 3.8 29 2.8 2.3 53 1.8 3.1 Hegyi 1.5 64 3.2 1.4 29 2.5 .8 53 1.7 1.0 Newnham 1.8 64 2.0 1.8 29 2.6 .8 Y/CI = bQ/CI + bl + b 2 CI + e Coefficients for the Regression h h ** b Competition Index ?1 ^0 Bella - .692 - 37.4 Ek-Monserud - 5.08 - 38.5 Hegyi -15.8 - 39.2 Newnham - 9.63 - 34.5 * Standard deviation units above regression. N.B. This is not the same selection value as used in quantitative genetics. ** Absence of a b 2 value indicates that the coefficient was not signif icantly different from 0 and did not enter the regression. 60 Table 3. Group I - Plot 351 Competition, Selection and Regression Competition index Bella Ek-Monserud Hegyi Newnham Competition Average for Plot #351 23.2 3.3 1.1 1.61 Tree Number 238 254 304 254 370 238 Selection Value 1.7 1.5 1.5 1.4 2.0 1.6 Competition Index Value 2.6 2.8 .8 .9 1.0 .9 Competition Index Bella Ek-Monserud Hegyi Newnham Y/CI = bQ/CI + bj_ + b 2 CI + e Coefficients for the Regression - .853 - 4.56 -57.5 17.8 - 6.70 35.9 31.1 56.3 28.0 61 Table 4. Group I - Plot 352 Competition, Selection and Regression Competition Competition Average for Tree Selection Competition Index Plot #352 Number Value Index Value Bella 25.1 476 1.8 12.8 488 1.4 15.1 437 1.1 25.6 Ek-Monserud 3.6 476 2.6 3.5 613 2.2 2.6 442 1.8 3.3 488 1.7 2.4 Hegyi 1.2 476 2.6 .8 613 1.7 .7 442 1.6 1.0 437 1.2 1.2 Newnham 1.66 488 1.5 1.1 442 1.1 1.0 613 1.1 .7 Y/CI = b 0/CI + bj_ + b 2 CI + e Coefficients for the Regression Competition Index ^1 2 _0 Bella - .0435 - 37.2 Ek-Monserud - .943 - 41.4 Hegyi -17.1 - 38.6 Newnham -34.1 6.51 52.3 62 Table 5. Group I - Plot 357 Competition, Selection and Regression Competition Competition Average for Tree Selection Competition Index Plot #357 Number Value Index Value Bella 30.3 1873 2.1 14.2 1906 1.7 24.6 Ek-Monserud 4.5 1873 2.8 3.1 1959 1.8 3.6 1906 1.6 3.2 Hegyi 1.5 1873 2.0 .8 1906 1.7 1.2 1959 1.2 .9 Newnham 1.7 1873 1.4 .3 1906 1.2 1.3 Y/CI = bQ/CI + b x + b 2 CI + e Coefficients for the regression Competition Index 11 ^2 2°_ Bella - .694 - 33.4 Ek-Monserud - 3.93 - 30.5 Hegyi -13.2 - 33.1 Newnham -12.2 - 33.1 63 Table 6. Group I - Plot 358 Competition, Selection and Regression Competition Competition Average for Tree Selection Competition Index Plot #358 Number Value Index Value Bella 35.7 2110 2.5 19.8 2220 1.7 20.1 2212 1.3 17.0 Ek-Monserud 5.8 2097 2.2 3.9 2110 1.9 2.9 2093 1.8 4.9 Hegyi 2.1 2110 2.4 1.2 2093 1.7 2.0 2212 1.6 1.2 2298 1.5 1.3 Newnham 1.8 2346 1.4 0.5 2054 1.2 0.8 Y/CI = b 0/CI + b 1 + b 2 CI + e Coefficients for the Regression Competition Index bA b^ Bella - 1.35 .0108 41.5 Ek-Monserud -11.6 .623 51.0 Hegyi -23.9 3.34 42.3 Newnham -23.6 3.83 36.6 64 Table 7. Group I I - Plot 354 Competition, Selection and Reg ression Competition Competition Average for Tree Selection Competition Index Plot #354 Number Value Index Value Bella 29.4 883 2.7 16.9 1016 1.6 22.1 992 1.4 26.4 Ek-Monserud 4.5 883 2.7 3.7 896 2.1 1.6 1027 1.6 3.0 Hegyi 1.6 883 3.5 1.2 922 1.8 1.6 1012 1.4 1.5 Newnham 1.7 883 3.0 .9 Y/CI = bQ/CI + b x + b 2 CI + e Coefficients for the Regression Competition Index _ i _ i _0 Bella - 2.88 .0328 65.0 Ek-Monserud - 5.34 37.1 Hegyi -72.9 15.9 85.2 Newnham -57.3 13.0 67.6 65 Table 8. Group I I - Plot 355 Competition, Selection and Regression Competition Competition Average for Tree Selection Competition Index Plot #355 Number Value Index Value Bella 41.6 1039 1.8 14.1 1219 1.3 13.8 Ek-Monserud 6.5 1219 1.9 2.5 1039 1.8 2.6 Hegyi 2.5 1207 no trees chosen -Newnham 1.7 1039 1.3 .4 Y/CI = bQ/CI + b x + b 2 CI + e Coefficients for the Regression Competition Index \\Wl ^0 Bella - 2.07 .0182 58.1 Ek-Monserud -13.6 .771 57.4 Hegyi -51.0 8.36 76.8 Newnham -57.1 14.6 55.2 66 Table 9. Group I I - Plot 356 Competition, Selection and Regression Competition Index Competition Average for Plot # 356 Tree Number Selection Value Competition Index Value Bella 40.0 1574 1592 1742 2.4 1.3 1.2* 24.0 17.4 44.3 Ek-Monserud 7.5 1574 1592 1639 2.6 1.9 1.9 4.5 3.3 3.2 Hegyi 3.1 1574 1592 1665 1639 2.2 1.4 1.4 1.2 2.5 1.3 2.4 1.2 Newnham 1.7 1592 1639 1574 2.3 1.9 1.7 .8 .5 .5 Y/CI = bQ/CI + b 1 + b 2 CI + e Coefficients for the Regression Competition Index hA ^0 Bella - 1.32 .0105 39.8 Ek-Monserud - 5.53 .21 33.0 Hegyi -13.1 1.32 32.6 Newnham - 8.05 _ 21.0 * Tree wi l l be checked in the future for mismeasurement. 67 Table 10. Group I I - Plot 359 Competition, Selection and Regression Competition Competition Average for Tree Selection Competition Index Plot #359 Number Value Index Value Bella 25.4 2193 1.7 16.4 2147 1.2 17.4 Ek-Monserud 4.0 2147 1.7 3.0 2193 1.4 2.4 2212 1.1 3.0 Hegyi 1.4 2193 1.3 .8 2212 1.3 1.2 2147 1.1 1.0 Newnham 1.8 2147 1.6 1.3 2193 1.4 .8 2212 1.0 1.3 Y/CI = bQ/CI + bj_ + b 2 CI + e Coefficients for the Regression Competition Index _ I _ i _0 Bella - 0.936 - 39.0 Ek-Monserud -16.5 1.25 58.4 Hegyi -20.1 - 42.7 Newnham -12.3 - 37.7 68 Table 11. Group I I I - Plot 353 Competition, Selection and Regression Competition Competition Index Average for Plot # 353 Tree Number Selection Value Competition Index Value Bella 37.2 749 1.8 16.9 683 1.2 36.1 723 1.2 24.4 Ek-Monserud 4.6 749 1.8 2.7 670 1.6 3.5 723 1.4 3.3 Hegyi 1.7 749 1.6 .8 683 1.5 1.7 Newnham 1.9 723 1.4 1.6 749 1.3 .5 750 1.2 1.3 Y/CI = bQ/CI + b1 + b 2 CI+ e Coefficients for the Regression Competition Index ^1 ^2 ^0 Bella - 1.30 .0137 43.7 Ek-Monserud -16.4 1.1 60.2 Hegyi -42.0 8.63 55.0 Newnham -23.6 3.62 41.9 69 Table 12. Group I I I - Plot 400 Competition, Selection and Regression Competition Competition Average for Tree Selection Competition Index Plot #400 Number Value Index Value Bella 66.5 199 1.9 29.4 206 1.7 28.8 116 1.3 31.1 Ek-Monserud 10.3 206 1.6 J 4.1 295 1.5 3.7 119 1.1 4.8 Hegyi 2.9 119 1.8 2.0 206 1.4 1.4 116 1.3 2.0 Newnham Y/CI = bQ/CI + b x + b 2 CI + e Coefficients for the Regression Competition Index H_ ^2 ^0 Bella - .447 .00196 23.2 Ek-Monserud -2.23 .0517 19.4 Hegyi -9.18 .878 22.9 Newnham 4.62 - 15.8 70 Table 13. Group I I I - Plot 401 Competition, Selection and Regression Competition Competition Average for Tree Selection Competition Index Plot #401 Number Value Index Value Bella 38.8 97 2.2 25.5 106 2.0 31.2 152 1.9 28.8 69 1.6 21.9 Ek-Monserud 6.2 268 2.2 3.7 265 2.0 3.8 69 1.5 3.0 106 1.5 2.9 Hegyi 2.0 152 2.1 1.4 106 2.1 1.3 97 1.9 1.3 Newnham 1.7 106 2.1 1.1 265 1.9 1.5 97 1.9 1.5 268 1.8 .9 152 1.7 1.0 Y/CI = bQ/CI + b x + b 2 CI + e Coefficients for the Regression Competition Index bA bA ^0 Bella - .510 .0035 18.7 Ek-Monserud - 3.48 .150 18.8 Hegyi -17.1 2.60 27.2 Newnham - 4.20 _ 12.8 71 Table 14. Selection Values for Phenotypic choices: Bella's Model. Mean Group Plot Bella's Index Tree No. Bella's Index Selection Value I 350 30.0 31 11.2 -0.10 I I 354 30.0 904 954 32.6 15.3 0.58 1.63 355 41.6 1039 14.1 1.80* 359 25.4 2147 2160 2165 17.4 23.9 24.3 1.24* 0.37 0.44 I I I 353 37.2 670 749 13.0 16.9 -0.18 1.77* 401 38.8 265 268 20.8 19.2 1.43 1.31 * / Tree selected by competition index, also. 72 in different times or environments, analysis of covariance answers the questions, "Can the results be considered the same?" I f not, in what respects are they different? In addition, analysis of covariance can be viewed as a method to improve our examination of the relation of randomized experiment treatments. Thinning levels and levels of basal area and age may be considered the treatments on these plots. Differ-ences which arose in regression lines which can be attributed to these "treatments" might be correctable in f i e ld applications of the selection method. In applying the analysis of covariance to the plot data only the re lat ively pure hemlock stands were considered. The older, mixed stands were eliminated because, 1) there was indication that the classical methods actually correspond to the competition based methods in these stands, and 2) the species mixture must certainly color the competition value assigned to individual trees; some trees being mainly influenced by f i r or spruce. Additional reflection on the application of indices indicated that al l indices should be re-examined and models rechecked. For this reason scatter plots of the now quite well edited data were made and correlations between the indexes and different transformations of the dependent variable were examined again. Figures 20 to 24 i l l u s -trate some of the plot data. The best model for each index was selected and some preliminary analyses of covariance run on combinations of plots from Group I and Group I I . Several of these analyses are presented in Tables 15 to 22. I t should be noted that somewhat better results were obtained for Lin's index using untransformed growth (BAGR) and transformation of the index by arcsin improved performance, neither of these transfor-73 4.06 r r 3.22 2 . 3 6 to * 1.54 • • c o o • • • e 09 • e e e • • • 0 0 0 0 0 9 • mao e e e o o « • o o o • c e e • e e t o o • • • e o • • .70 - . 1 4 8.1 » o o © c • e as • e e J 1 I I L J L ,J 21.0 34.0 4 6 . 9 BELLA'S INDEX 5 9 . 6 7 2 . 8 Figure 20. Natural log transformation of BAGR versus Be l l a ' s Index for p lot #350. 74 4 . 0 6 3 . 2 2 <0 2 . 3 8 5 1 5 4 . 7 0 - . 1 4 |_ o moo o e oo O O C* O O h o o o> © OOOM OO) CB O O O O O O o e so oo o oo o o o a*>o o o o o o e o o oo oo o o o JL 1.2 JL ooao J L o J L 3 6 6 . 4 9 . 0 ||.6 EK-MONSERUD'S INDEX 14.24 Figure 21. Natural log transformation of BAGR versus Ek-Monserud1s Index for plot #350. 75 4 . 0 6 3.22 Ci 2 .38 h to o e • m © o • «e o o m> m I— • ee e e - e>o e e e e e * e e e> e e e o e e e e m e e e e e e < • c e o e e e e e w 1.54 .70 - . 1 4 e e e e • e • ee e e e e © J L J I ©J L .5 I.I 1.6 2.1 H E G Y l ' S I N D E X 2.7 J I 3.2 Figure 22. Natural log transformation of BAGR versus Hegyi's Index for plot #350. 76 4 .06 3.22 O 2 38 -<0 I © e e e e e • e e moo « • o mo ooo ooo • e o ee eee eo e e e • • e to i 1.54 .70 e e • e e e e e es e-o - 1 4 L - e I | | I I I I l I 15.2 30.5 45.7 L I N ' S I N D E X 6 0 . 9 76.2 Figure 23. Natural log transformation of BAGR versus Lin's Index for plot #350. 4 . 0 6 0- © • © • e> • e 3 2 2 * 2 . 3 8 to < v l 1.54 . 7 0 e e e e • o © •>© • © • 0) 0 • • 9 0 O • 0 0 O 0 0 © • © O 0 0 0 O © 0 0 0 0 0O - . 1 4 .2 J JL . 9 1.6 2 3 NEWNHAM'S INDEX 3.0 3.7 Figure 24. Natural log transformation of BAGR versus Newnham's Index for plot #350. 78 Table 15. Analysis of Covariance Group I Plots Bella's Index SOURCE DF BETWEEN MEANS 4 COVARIATE 1 ERROR 402 SUM SQRS MEAN SQR F-STAT SIGNIF 32.344 227.91 162.18 227.91 564.94 .40342 .0000 ** EQUAL SLOPES 4 2.1032 ERROR 398 160.07 .52581 1.3074 .2666 NS .40219 EQUAL ADJ MEANS 4 4.2286 1.0571 2.6205 .0346* ERROR 402 162.18 .40342 TOTAL 407 422.43 COEFFICIENTS COVARIATE COEFF BELLA'S INDEX -.0562 T-STAT -23.8 SIGNIF .0000 REGRESSIONS PLOT # (1) 350 (2) 351 (3) 352 (4) 357 (5) 358 N 92 62 64 70 120 CONSTANT 4.34 3.86 4.04 3.69 3.72 BELLA'S -0.0651 -0.0536 -0.0576 -0.0520 -0.0527 SE OF REGR 0.542 0.589 0.571 0.738 0.687 R-SQR 0.75 0.36 0.53 0.49 0.60 NS The s tat is t ica l test indicates no significant difference among parameters * The stat is t ica l test indicates a significant difference ** Probabilities too small to pr int , there is a significant s ta t is t ic 79 Table 16. Analysis of Covariance Group I Plots Ek-Monserud's Index SOURCE DF SUM SQRS MEAN SQR F-STAT BETWEEN MEANS 4 32.344 COVARIATE 1 202.28 ERROR 402 187.81 202.28 432.97 .46718 SIGNIF .0000 EQUAL SLOPES 4 4.3784 1.0946 ERROR 398 183.43 .46087 2.3751 .0516 NS EQUAL ADJ MEANS 4 3.5581 ERROR 402 187.81 .88951 .46718 1.9040 .1089 NS TOTAL 407 422.43 COEFFICIENTS COVARIATE EK-MONSERUD'S INDEX COEFF .33438 T-STAT -20.8 SIGNIF .0000 REGRESSIONS PLOT # N CONSTANT EK-MONSERUD'S SE OF REGR R-SQR (1)350 92 4.02 -0.367 0.610 0.679 (2)351 62 3.78 - .352 0.611 0.313 (3)352 64 4.07 -0.402 0.621 0.442 (4)357 70 3.96 -0.418 0.762 0.452 (5)358 120 3.51 -0.288 0.737 0.536 80 Table 17. Analysis of Covariance Group I Plots Hegyi's Index SOURCE BETWEEN MEANS COVARIATE ERROR DF SUM SQRS MEAN SQR F-STAT SIGNIF .0000 4 32.344 1 191.16 402 198.92 191.16 186.32 .49483 EQUAL SLOPES 4 11.335 ERROR 198 187.59 2.8337 6.0121 .0001 EQUAL ADJ MEANS 4 4.0148 ERROR 402 198.92 1.0037 2.0284 .0897NS .49483 TOTAL 407 422.43 COEFFICIENTS COVARIATE HEGYI'S INDEX COEFF -1.03 T-STAT -19.7 SIGNIF .0000 REGRESSIONS PLOT # (1)350 (2)351 N 92 62 CONSTANT 4.50 3.78 HEGYI'S -1.43 -1.03 SE OF REGR 0.613 0.621 R-SQR 0.68 0.29 (3)352 (4)357 (5)358 64 70 120 4.21 3.86 3.57 -1.35 -1.14 -0.823 0.594 0.751 0.772 0.49 0.47 0.49 81 Table 18. Analysis of Covariance Group I Plots Lin's Index SOURCE DF SUM SQRS MEAN SQR F-STAT SIGNIF BETWEEN MEANS 4 32.344 COVARIATE 1 ' 127.61 ERROR 402 262.47 127.61 195.46 .65290 .0000 EQUAL SLOPES 4 7.6238 ERROR 398 254.84 1.9059 .64031 2.9766 .0192 EQUAL ADJ MEANS 4 15.252 ERROR 402 262.47 3.8129 .65290 5.8399 .0001 TOTAL 407 422.43 COEFFICIENTS COVARIATE LIN'S INDEX COEFF .0331 T-STAT 14.0 SIGNIF .0000 REGRESSIONS PLOT # (1)350 (2)351 (3)352 (4)357 (5)358 N 92 62 64 70 120 CONSTANT 1.20 1.75 1.59 1.59 0.885 LIN'S 0.0402 0.0244 0.0281 0.0205 0.0394 SE OF REGR 0.755 0.634 0.701 0.968 0.850 R-SQR 0.51 0.26 0.29 0.12 0.38 82 TABLE 19. Analysis of Covariance Group I Plots Newnham's Index SOURCE DF SUM SQRS MEAN SQR F-STAT SIGNIF BETWEEN MEANS 4 32.344 COVARIATE 1 226.35 ERROR 402 163.53 226.56 .40678 556.95 .0000 EQUAL SLOPES 4 4.7440 ERROR 398 158.78 1.1860 .39895 2.9728 .0193 EQUAL ADJ MEANS 4 34.214 ERROR 402 163.53 8.5536 .40678 21.027 .0000 TOTAL 407 422.43 COEFFICIENTS COVARIATE NEWNHAM'S COEFF -.938 T-STAT -23.6 SIGNIF .0000 REGRESSION PLOT # (1)350 (2)351 (3)352 (4)357 (5)358 N 92 62 64 70 120 CONSTANT 4.18 3.81 3.90 3.54 3.71 NEWNHAM'S -1.01 -0.729 -0.778 -0.835 -1.09 SE OF REGR 0.595 0.547 0.526 0.824 0.622 R-SQR 0.69 0.45 0.60 0.36 0.67 TABLE 20. Analysis of Covariance Group I I Plots Bella's Index 83 SOURCE DF SUM SQRS MEAN SQR F-STAT SIGNIF BETWEEN MEANS 3 51.132 COVARIATE 1 211.41 ERROR 325 133.19 211.41 515.88 .4098 .0000 EQUAL SLOPES 3 3.8911 1.2970 ERROR 322 129.30 .40154 3.2301 .023 EQUAL ADJ MEANS 3 2.2789 ERROR 325 133.19 .75963 .40981 1.8536 ,137 NS TOTAL 329 395.73 COEFFICIENTS COVARIATE COEFF BELLA'S INDEX -0.0514 T-STAT -22.7 SIGNIF .0000 REGRESSIONS PLOT # N CONST BELLA'S SE REGR R-SQR 354 74 3.90 -0.00568 0.619 0.56 355 124 3.85 -0.00547 0.644 0.67 356 83 3.24 -0.0430 0.704 0.59 359 49 4.21 -0.0662 0.485 0.66 84 TABLE 21. Analysis of Covariance Group I I Plots Lin's Index SOURCE BETWEEN MEANS COVARIATES ERROR DF SUM SQRS MEAN SQR F-STAT SIGNIF 3 1 325 51.132 138.07 206.52 138.07 217.29 .63545 .0000 EQUAL SLOPES 3 1.7311 .57703 ERROR 322 204.79 .63599 .90729 .433 NS EQUAL ADJ MEANS 3 21.790 ERROR 325 206.52 7.2632 11.430 .63545 .0000 TOTAL 329 395.73 COEFFICIENTS COVARIATE COEFF T-STAT SIGNIF LIN'S INDEX 0.0398 14.7 .0000 REGRESSIONS PLOT # (1) 354 (2) 355 (3) 356 (5) 359 N 74 124 83 49 CONSTANT 1.13 0.313 0.326 1.16 LIN'S -0.0307 -0.0429 -0.0425 -0.0376 SE OF REGR 0.829 0.859 0.831 0.449 R-SQR 0.21 0.42 0.41 0.71 85 TABLE 22. Analysis of Covariance Group I I Plots Newnham's Index SOURCE DF BETWEEN MEANS 3 COVARIATES 1 ERROR 325 SUM SQRS MEAN SQR F-STAT SIGNIF .0000 51.132 217.18 127.41 217.18 553.97 .39205 EQUAL SLOPES 3 4.1788 1.3929 ERROR 322 123.24 .38272 3.6396 .0131 EQUAL ADJ MEANS 3 58.021 19.340 ERROR 325 127.41 .39205 49.332 .0000 TOTAL 329 395.73 COEFFICIENTS COVARIATE NEWHAM'S COEFF -1.06 T-STAT -23.5 SIGNIF .0000 REGRESSIONS PLOT # N CONSTANT NEWNHAM'S SE OF REGR R-SQR (1) 354 74 4.06 1.09 0.633 0.54 (2) 355 124 3.72 1.23 0.608 0.71 (3) 356 83 3.14 0.981 0.717 0.56 (5) 359 49 4.05 0.836 0.403 0.77 86 mations radically improves R-square or reduces standard error over the log model. For comparison's sake i t was deemed better to report al l indices under the log transformation. The model for analysis of covariance was based on the natural log of basal area growth. As before basal area growth was determined as: BAGR = ( D ? 5 )2 - ( D 7 Q )2 (17) where subscript indicates the year of measurement. Basal area in square feet is obtained by the usual factor .005454 ( i . e . , graph scales are 1/.005454 or 183.35 times the area growth in square feet ) , and square cm can be obtained by multiplying the value by 5.0671. The best models were obtained using natural log transformations of the dependent var i -able. The comparison of R-square values was deemed appropriate as the intent of these analyses was to assay the val id i ty of one model in combining data on several plots. The comparison is made in Table 23. The best relationships appear to be Bella's index and Newnham's. Com-plete covariance analysis of these indices were run. Again Lin's index was included because of i ts specif ic i ty to western hemlock. (Figures 25 through 26 i l lus t ra te regressions on al l plots for Newnham's index.) 87 Table 23. R-Square Comparisons for Competition Indices PLOT 350 351 352 357 358 354 355 356 359 INDEX BELLA .751 .36 2 .53 2 .49 1 .60 2 .55 1 .67 2 .58 1 .66 EK-MSRD .68 .31 .44 .45 .53 HEGYI .68 .29 .49 .48^ .49 LIN .51 .26 .29 .12 .38 .21 .42 .41 .712 NEWNHAM .692 .45 1 .60 1 .36 .67 1 .54 2 . 7 1 1 .56 2 .77 1 Note: raised numerals indicate highest and second highest value. The analysis of covariance tables were interpreted as follows: 1) the value of the covariance analysis is tested, i f the covariate is not significant at this point the analysis is abandoned; 2) slopes of individual lines within the group are tested, significance at this point indicates that separate regression models are required stat is-t i c a l l y and further analysis should be abandoned (for this grouping); 3) on plots with equal slope further analysis can be made on the levels of the l ines. This f inal test indicates that there is a factor acting uniformly on the sampled population and in the case of the logarithmic model adopted here a mult ipl icative factor is indicated. For purposes of i l lus t ra t ion , the analysis of covariance was rerun 0 on three Group I plots using Newnham's index, (Table 24). In this case slopes are the same and only levels are dif ferent. To combine plots for selection the lines from the individual plots are corrected for differences in level. The adjusted means presented in Table 24 are subtracted from the grand mean for al l observations. This difference GROUP REGRESSION 1.29 . 7 6 J . 2 2 - . 3 1 Figure 25. .46 126 2 06 COMPETITION INDEX (NEWNHAM) 2.85 3 . 6 5 LN (BAGR) versus Competition equation lines Newnham's Index, Group I plots. COMPETITION INDEX (NEWNHAM) Figure 26. Ln (BAGR) versus Competition equation lines Newnham's Index, Group I I plots. Table 24. Reduced Set Group I I Plots Adjustment Analysis SOURCE DF SUM SQRS MEAN SQR F-STAT SIGNIF BETWEEN MEANS 2 38.225 COVARIATES 1 111.54 111.54 284.38 .0000 ERROR 202 79.229 .39222 EQUAL SLOPES 2 1.0597 ERROR 200 78.169 REGRESSION EQUAL ADJ MEANS ERROR TOTAL 205 229.02 COEFFICIENTS COVARIATE COEFF NEWNHAM'S INDEX -.963 REGRESSIONS PLOT # 354 MEAN 2.19 ADJ MEAN 2.20 GRAND MEAN 2.01 ADJUSTMENT 0.188 CONSTANT 4.06 NEWNHAM'S INDEX -1.09 SE OF REG 0.63 R-SQR 0.54 Table 25. SOURCE DF SUM SQRS REGRESSION 1 111.87 ERROR 204 79.229 TOTAL 205 191.10 COEFFICIENTS COEFF CONSTANT 3.65 NEWNHAM'S INDEX -.963 SE OF REG .623 R-SQR .585 .52986 1.3557 .2601 NS .39084 T-STAT SIGNIF -16.86 .0000 356 359 1.52 2.57 1.47 2.63 2.01 2.00 0.537 0.625 3.14 4.05 -0.981 -0.836 0.72 0.40 0.56 0.77 MEAN SQR F-STAT SIGNIF 111.87 288.06 .0000 .38838 T-STAT SIGNIF 34.4 .0000 17.0 .0000 Adjusted Regression on Group I I Plots 91 is then added to observations on the corresponding plot. The adjusted growth was then entered into a regression model as the new dependent variable. Now a single model can be used to select trees from al l three plots. This is an important result as i t indicates that thinned and unthinned plots can be combined in a selection of parent trees. The regression model is presented in Table 25. Figure 27 i l lustrates the scatter of data points once the effect of average tree size is removed. The regression line is indicated. Crown Area Model A related approach to evaluating competition is available in Mit-chel l 's simulation model (1975a). This model, while recognizing the effect of growing space on the development of the trees, places i ts major emphasis on the actual development of the crown. The idea of the crown as the photosynthetic producer of wood laid down in the annual growth ring is central to the model concept. Quantitative measures of branch elongation, needle retention and needle efficiency are al l integrated in Mitchell 's growth simulation model. In the model, competitive status of a tree is expressed as the rat io of a tree's actual foliage volume to the maximum fo l ia r volume of a tree of similar dimension growing under open conditions. CI. = ln {^j (18) J c where CI. = competition index of the j th subject tree. FV. = fo l iar J J volume of the j th subject tree. FVc = fo l ia r volume of a comparable open-grown tree. 3 9 6 r 3 . 4 9 3 . 0 3 2 . 5 7 »j •i 2.10 i * S 1.64 «: 1.17 H - . 7 1 <~ c: - . 2 5 - . 2 2 . 6 0 .86 1 6 6 2 ^5 C O M P E T I T I O N I N D E X ( N E W N H A M ) Figure 27. Combined regression for Group I plots, Newnham's Index. vo ro 93 While objections to using current crown dimensions as an index of competition have been raised (Bella, 1970), they do not apply to Mitchell 's index, since i t relates current size of crown to the open-grown condition. This process is analogous to the competition indices which are derived from zones of influence based on the crown extent of open-grown trees. In addition, expressions of crown dimensions and growth are immediately noted to have the dimensions of growth per unit of area occupied; a direct measure of the ut i l izable efficiency of production of wood. An ef f ic ient crown implies one which produces wood at the minimum expense in occupation of space. This definit ion differs from Baskerville's (1965) definit ion of efficiency in that recoverable wood product must be produced. He compared the efficiency of trees of different crown classes and found that the suppressed trees were the most ef f ic ient ones. How-ever, the context of the investigation must be considered. In the purely biological sense smaller trees at a given time in the development of a stand u t i l i ze a smaller proportion of the resources required to produce wood fiber than the larger trees. The dominants accumulate proportionately more resources; they grow more, but are more wasteful. I f our interest and understanding of the situation is primarily the total biomass produced on a given unit area this information may be useful to us direct ly. However, i f our interest is in the eventual economic u t i l iza t ion of resource, we must remember that much of the wood f iber is accumulated in small stems which are never going to be economically valuable. Moreover, the presence of a larger number of stems means slower growth for those stems which conceivably can become harvestable resource. Uti l izable efficiency connotes managed stand 94 production at high, recoverable rates. For the purposes of this portion of the investigation, a crown competition index was not calculated for each tree. In fact, open-grown crown information necessary for calculations is not available for hem-lock. Because of the method of collection of the crown data ( i . e . , the current crown was photographed), the period of growth used was the preceding five-year interval. I t was assumed that the current crown is not much different from the crown at the start of the period and that the short duration of the period would not have seen major changes in the status of the crown. Thus, crown area is an estimate of growth potential for a short span of time. When related to other trees in the plot , crown area (CRAR) can be used as an estimator of ut i l izable efficiency when related to basal area growth. Estimation of CRAR is possible from the ground, but much better estimates should be possible using low-level aerial photography. Low speed (30 mph), low-level (200') photographs should yield high resolu-tion stereophotographs for the measurement of crown dimensions and, under good conditions, could yield information on tree heights and crown volumes (Mitchell, 1975b). This approach was applied to the Tumour Island hemlock stands, but the crown photographs seldom showed the ground, which is necessary i f tree heights and ground level changes are to be determined. Ground markers of various color and markings for plot identi f icat ion were made on each plot. Only one marker actually appeared in the photographs! Individual crowns are d i f f i c u l t to delineate in aerial photographs of dense hemlock stands; in fact , many suppressed or intermediate crown 95 class trees were not v is ible. They are, however, a source of uncer-tainty in the delineation of crowns of codominant and dominant trees. In effect, most of the smaller trees, those having high competition indices, were removed from the population being sampled as a consequence of the method. In addition, several dominant or codominant trees had to be excluded from the population because the actual crown extent could not be identi f ied (a problem arising at least in part from the lack of control over al t i tude). Furthermore, positive assignment of a mea-sured crown to an individual tree on the stem map was not always possible. In most cases, these problems could be reduced with better f l i gh t con-t r o l . As a practical technique, creating small openings near the plots would also be worthwhile in obtaining ground registrat ion. Selections Based on Crown Area Models The regression model for basal area growth increment on CRAR was a simple linear one. The absence of many suppressed and intermediate trees meant that i t was less important to deal with their contribution to var iab i l i ty than in the competition index approach; selection was based direct ly on the size of the residual. There was also no problem associated with trees growing near the border of the plot as the "index" of environmental effects is the crown i t se l f . Coefficients of the regressions are presented in Table 26. Each plot regression was examined for probability of distribution of residuals and uniformity with respect to the independent variable, CRAR. While a stat is t ical test was not performed, regressions for Group I I (Plots 354 to 356 and 359) appear to have the same slope (b j ) . The pattern of change for the intercept (b n) for these plots corresponded 96 with the past level of thinning and current basal area. A similar relation was suggested for the t idal f l a t plots of Group I. The d i f -ferences between these two groups may be site and/or age variation. There was insufficient range in the data to test this hypothesis. Table 26. Crown Area-Growth Regressions Y = b n + bi (CA) + e* Group Plot o^ (S 6 b 0 ) bA (s eb 0) R2. I 350 3.59 1.35 .102 .0074 .63 351 .306 1.70 .100 .0085 .63 352 .249 1.30 .106 .0076 .67 357 2.59 1.56 .086 .0086 .50 358 1.64 1.20 .092 .0078 .58 I I 354 3.11 1.60 .128 .0164 .39 355 .669 .646 .142 .0078 .69 356 1.04 .795 .136 .0096 .69 359 4.14 1.39 .134 .0119 .63 I I I 353 3.59 1.56 .098 .0152 .55 400 2.69 1.34 .061 .0083 .51 401 .870 .740 .065 .0073 .47 * Standard errors of estimation are included in computer output. The f inal selection of plus trees was performed in the same manner as the competition index selections. The upper confidence l imi t for an individual observation was used. A l i s t of the selected trees with their residual is presented in Table 27. The trees indicated with an 97 Table 27. Trees Selected on Crown Area Efficiency Observation Tree Standardized Plot Number Number Residual 350 41 64° 4.86* 350 17 29° 2.66 351 1 220 4.54* 351 44 317 1.63 352 6 437° 3.20 352 85 613° 3.00 353 36 693 4.53* 353 61 750° 1.83 354 32 1016° 2.52 354 57 1033 2.12 354 45 1027° 1.99 355 75 1219° 4.85* 355 1 1039° 3.52** 356 48 1590 4.43 356 8 1411 2.49 357 30 1826 3.01 357 65 1915 2.49 358 29 2110° 4.32* 358 70 2212° 2.06 358 91 2294 2.09 359 59 2204rt 3.85* 359 51 2193° 2.07 400 25 199° 1.75 400 42 323 1.74 401 3 12 3.02 401 17 97° 2.86 * These values are suspect. Trees are either mismeasured or older than rest of stand. ** Phenotypically selected tree. 0 Trees selected by one or more competition models. 98 asterisk (*) are of such large residual that further measurement of age and growth should be taken to check for i r regular i t ies. In one or two cases, large residuals were def ini tely associated with an indi-vidual tree which was 5 to 10 years older than the stand average age. These trees were removed from the succeeding analyses. However, as only a small proportion of the trees had their total age measured, i t is possible that some of the asterisked trees are simply older trees (advanced regeneration). Table 28 shows a comparison of phenotypically selected candidate trees and their associated crown and competition residuals. Analysis of Covariance As with the results of competition indices the results of indi-vidual regressions obtained on each plot are discouragingly expensive to obtain i f each local population must be treated as were the permanent sample plots at Tumour Island. There are some enticements to further analysis. The b^  coefficients for groups of plots (especially I and I I ) are very similar and the regressions are of untransformed linear nature. Furthermore, differences noted in intercepts can be associated with the number of stems per acre and increment per stem, fewer stems per acre accruing larger per stem increment." I t seems advantageous to apply the methods of analysis of covariance to the plots in Group I and I I . Results of the analysis of covariance including regressions for the model BAGR = constant + b(CRAR) are summarized in Tables 29 and 30. The coefficients were used to plot individual regression lines in Figures 28-30. Examinations of the figures indicates a difference 99 Table 28. Competition Index and Crown Competition Selection Values for Phenotypically Chosen Trees Bella's Index Crown Competition Plot Tree Standard Residual Standard Residual 354 904 .58 -0.38 954 1.63 355 1039 1.80* 3.52° 1165 ** 0.53 356 1431 ** -0.23 1697 ** -1.10 1725 ** -0.97 1745 ** 1.28 359 2147 1.24* -0.23 2160 0.37 2165 0.44 2176 0.38 350 31 -0.10 1.06 85 -1.43 -0.11 352 519 ** -0.61 583 ** -0.81 357 1806 •* -0.30 1894 ** -0.02 358 2258 ** 0.65 2239 ** 0.31 400 159 ** 0.20 206 ** 1.22 401 265 1.43 0.59 268 1.31 2.43 353 670 -0.18 -0.20 749 1.77* -0.13 * Tree selected by competition index. ** Trees located in buffer str ip for which no competition selection value was obtained. 0 Tree selected on crown area efficiency. 100 Table 29. Analysis of Covariance Group I Plots Crown Area as Covariate SOURCE DF BETWEEN MEANS 4 COVARIATES 1 ERROR 462 SUM SQRS MEAN SQR F-STAT SIGNIF 813.6 .0000 1982.8 33718. 19147. 33718. 41.44 EQUAL SLOPES 4 104.3 26.07 ERROR 458 19043. 41.56 .6272 .643 NS REGRESSION 1 34893. EQUAL ADJ MEANS 4 807.5 201.8 ERROR 462 19147. 41.44 4.871 .000 TOTAL 467 54848. COEFFICIENTS COVARIATE CRAR COEFF .09147 STD ERROR .00321 SIGNIF .0000 REGRESSIONS PLOT # 350 351 352 357 358 N 109 80 89 95 95 CONSTANT 4.44 2.76 1.42 2.04 1.23 CRAR .092 .082 .098 .095 .090 SE REG 6.46 5.76 6.47 7.72 5.48 R-SQR .65 .66 .65 .60 .67 All regressions highly signif icant. 101 Table 30. Analysis of Covariance Group I I Plots Crown Area as Covariate  SOURCE DF SUM SQRS MEAN SQR F-STAT SIGNIF BETWEEN MEANS 3 3929.4 COVARIATES 1 19570. 19570. 614.59 .0000 ERROR 392 12482. 31.843 EQUAL SLOPES 3 65.871 21.957 ERROR 389 12416. 31.919 .68790 .55 NS REGRESSION 1 22838. EQUAL ADJ MEANS 3 661.68 220.56 ERROR 392 12482. 31.843 6.9265 .00 *** TOTAL 396 35982. COEFFICIENTS COVARIATE CRAR COEFF .12994 STD ERROR .0052414 SIGNIF .0000 REGRESSIONS PLOT # 354 355 356 359 N 89 144 87 77 CONSTANT 4.41 1.38 .609 3.43 CRAR .115 .133 .128 .137 SE REG 7.01 4.78 5.22 5.86 R-SQR .40 .69 .62 .69 All regressions highly signif icant. 3 5 0 , 5 3 . 8 h 47 .2 5 4 0 . 5 to to 2 33 .8 27.1 20.5 13.8 7.1 0 .4 ± J L J L J L _L JL - 8 . 0 4 6 . 8 101.5 156.4 211.2 2 6 6 . 0 320 8 375 .6 CRAR (SQ. FT.) Figure 28. Regression lines for Group I plots BAGR versus Crown Area. 430.4 435.2 540 .0 o ro 53 ef-47.2 h to Ti 40.51 to 3 3 . 8 | to 3 5 6 3 5 4 5 to to to to 27.1 20 .5 13.8 7.1 r J L ± JL 0.4 i ' » - 8 . 0 4 6 . 8 Figure 29. 101.5 156.4 211.2 266 .0 3 2 0 . 8 3 7 5 . 6 4 3 0 . 4 435.2 5 4 0 . 0 CRAR (SQ. FT.) Regression Lines for Group I I plots BAGR versus Crown Area. CRAR (SQ. FT.) Figure 30. Regression lines for al l plots in both Groups I & I I BAGR versus Crown Area. 105 in slopes between Groups I and I I (confirmed by preliminary analysis). Covariance analyses were run on the separated Groups. Differences between regressions are in the levels. I t seems quite possible that between group slope differences are related to age through the cumulation of current annual increment which is being measured in this study. This hypothesis should be tested by measurement of relations on growth plots of s l ight ly older and s l ight ly younger PSP's of similar site index. To i l lust rate the possibi l i ty of combining crown regressions into a single model for selection of individual trees, the common mean was subtracted from each adjusted mean and this value added to each obser-vation on i ts corresponding plot . This process corrects each line to the common model. A test regression was run with al l plots within a group to confirm the procedures effect. Residuals on the covariance adjusted model were calculated and then examined. In general the same trees were selected, as were with the individual plot regression models. The relative sizes of residuals were maintained so that some of the trees selected on individual plots are less outstanding when viewed in this context. Differences in the selections are due to editing of the data as the addition or subtraction of a constant to the regression should not change the sizes of residuals though their standardized value w i l l be based on the pooled model. I t is only possible to examine genetic potential of the selected trees in long term genetic experiments. The historical performance of individual trees can lend some credence to our selections at Tumour Island. The data were sorted into ascending crown area. Then a sample of trees having positive and negative residuals, after the effect of crown area is removed, was plotted. Figures 31 and 32 i l lust rate example 106 _ j I I J 1~ 5 0 5 5 6 0 6 5 7 0 Y E A R Figure 31. A Sample of cumulative diameter histories for Plot #356. 107 Figure 32. A sample of cumulative diameter histories for Plot #359. 108 trees from the unthinned plot 356 and heavily thinned plot 359 respec-t ive ly . I t is evident that across the competition spectrum, trees with positive residuals are continuing to out-perform trees having negative residuals. Crown selection trees were included in the sample of trees i l lustrated purposely. The selected trees are indicated by a paren-thetical number. The residual indicated by (a) is a phenotypic selec-tion which had a positive residual. A closer examination of the per-formance not presented in detail indicated that the size of the residual correlates well with the current slope of the growth record l ine. This analysis serves to allay the suspicion that some trees might represent sudden, fortuitous release rather than the established competitive advantage. The results offer encouragement for the use of the proposed selection method, even though the encouragement is not s t r i c t l y genetic. The results also suggest the importance of setting biologically sound management goals in the establishment of plus tree selection for western hemlock. There are trees in the stand which continue to grow better than their neighbors under the influence of intense crowding. Trees capable of high production under intense competition contribute more volume per acre than large trees which require disproportionately large amounts of growing space. Combining Competition and Crown Parameters Competition indices ref lect the differences in growth due to spatial patterns on the ground. The ab i l i t y of crown measures to predict growth especially as this related to treated stands confirms the importance of considering the aerial competition in hemlock. The ab i l i ty of hemlock 109 crowns to seek openings in the canopy and not direct ly above the stem distr ibution at breast height make the crown a possible component in the construction of growth models which have a value in the selection of superior individuals. Figure 33 i l lustrates a small portion of plots 354 and 355 stem map. The accompanying overlay shows the capability of crowns to shif t into more open areas of the canopy. Thus in thinned stands i t might be expected that crown parameters would be more apt to predict the growth of the remaining trees than competition index derived from stem maps. Indeed, this is the case for the Tumour Island PSP's. On plots which have been recently thinned, or do not have a completely closed canopy, crown parameters contribute a larger proportion of the reduction in sums of squares than competition indices or in the case of plot 359 a larger proportion than past diameter. I f crown parameters and the competition indices express different qualit ies in the environment of an individual tree i t would be reason-able to combine them in a single growth model. Three of the plots were chosen to represent extremes in condition. Plots 350 and 359 currently have open canopies due to thinnings. Plot 355 is one of the densest and one whose growth was poorly described under tree assumptions of al l the previously investigated models. A linear model including crown area projection (CRAR), crown class (CC) as assigned by MacMillan-Bloedel foresters, and Bella's index was f i t , BAGR = bQ + b^ (CRAR) + b0(CC) + bg(CRAR) + e . The data were limited to trees which had the index computed ( i . e . , those I l l within the buffered area on the plot) and photographed crowns. In al l three cases the R-square value was increased over that obtained using CRAR alone. Plot 350, the most recently thinned, showed the least improvement over regressions involving CRAR alone. Comparison of R-square for multiple variable models and Bella's index alone shows higher values for 355 and 359. Plot 350 has a lower R-square value. These latter comparisons should be interpreted carefully. The R-square value should increase with the addition of predictive values. The coefficients of the added variables are signi f icant ly different from zero indicating that they do add to the regression. The comparisons are of logarithmic transformations. Plot 350 has lower quality photographs which should tend to decrease the chance that i t would contribute more information to the competition model. The results of the regressions are summarized in Table 31. These models were considered exploratory and no selec-tions were made using this approach. The reduction in standard errors of regression are noticeable, but genetic interpretation is less clear, also the analysis of covariance becomes extremely d i f f i c u l t to inter-pret. Until some methods of constructing common models becomes avail-able there seems l i t t l e possibi l i ty of constructing models of general application to the problem of selecting superior trees. Coefficients (b^'s) are signif icantly different even in the closely related plots 355 and 359. The attempt to combine competition indices and crown information has been discussed br ie f ly and has not been used to select candidate trees. Application Beyond Permanent Sample Plots I t was an objective of this study to examine the possibi l i ty of 112 TABLE 31. Analysis Combining Crown and Competition Covariates. SOURCE DF SUM SQRS MEAN SQR F-STAT SIGNIF BETWEEN MEANS 2 3236.5 COVARIATES 3 14611. 4870.4 158.86 .0000 ERROR 212 6499.6 30.658 EQUAL SLOPES 6 1113.7 185.61 7.0993 .0000 ERROR 206 5385.9 26.145 EQUAL ADJ MEANS 2 162.79 81.397 2.6550 .0726 NS ERROR 212 6499.6 30.658 TOTAL COEFFICIENTS COVARIATE CRAR CC Bella COEFF .71784-1 •2.6372 -.15441 T-STAT 9.6075 -4.4644 -3.4765 SIGNIF .0000 .0000 .0006 REGRESSIONS PLOT # N CONSTANT CRAR CC BELLA SE OF REGR R-SQR 350 72 25.348 .43834--2.7501 -.27795 6.3058 .67509 355 103 7.3258 .12856 -1.4685 -.58770 4.3676 .77471 359 43 37.042 .33358-1 -5.4105 -.45680 4.5105 .81993 113 developing a f i e ld procedure based on the results from the permanent sample plots. Descriptive analysis of individual phenotypic selections were undertaken. First trees selected on the permanent sample plots are described, then characteristics of the wider sample of phenotypic selections are reviewed. Crown Photographed Areas and Crown Projection With a view to extending the crown photography results of Tumour Island baseline plots to dispersed, phenotypic selections, stepwise multiple regressions were run on Tumour Island trees which had both crown photographs (CRAR) and crown projectional (CRPRO) measurements. Again, the expression of growth was basal area growth over the last f ive years. Several transformations were t r ied , but simple linear models proved suff ic ient. The results are indicated in Table 32. I t appears that ground measurements of crown area projection in young growth stands are best and that aerial photographs are better in older stands. I t is possible that use of an instrument to assure perpendicular viewing of the crown would improve measurements from the ground in the older ( ta l le r ) stands. In the interim, crown area in stands aged 70 and above can s t i l l be predicted from crown projection using the results from Tumour Island trees presented in Table 33. 114 Table 32. Parameter Selection Based on Tumour Island Phenotypic Trees  Y = bQ + b1 CRPRO + b 0 CRAR + b 3 (HT to BLC—^*) + e Group _n ^0 h h H ^_ SEE—/ I 11 6.155 .08552 .75 6.57 (less than 60 years) I I 7 6.136 .0760 .75 4.38 (between 60-80 years) Table 33. Regression of Crown Area (Aerial) on Crown Projection CRAR = bQ + bx CRPRO + e _n_ ^0 ^1 R£ SEE 22 41.17 .4982 .75 48.38 Analysis of Phenotypic Selections and Associated Check Trees How do the results of the Tumour Island research plots apply to the practical cruising for plus trees? May we apply some of the findings to individual trees? In order to look into these possible applications previously selected hemlock plus trees were visited and nearby check trees established. Because of the ease of obtaining crown data, the crown projection measurements were emphasized for comparison of the performance of the plus and check trees. 1/ BLC = base of l ive crown. 2/ Standard error of estimate. 1 1 5 A variety of stat is t ical techniques, paired t tests, elimination of outl iers and the regression analysis of variance were applied to the data. Basal area growth differences were not signif icant, height differences approached significant probability levels ( 0 . 9 1 ) . Check trees were signif icantly smaller in d.b.h. than plus trees, but this difference was expected since we purposely selected a number of codomi-nant and smaller dominants as check trees (Table 3 4 ) . Otherwise the phenotype and check trees are equivalent in the categories which are of interest to this study. Table 3 4 . Summarized Statist ics for Phenotypic Selections and Check Trees Phenotypic Trees ri Minimum Maximum Mean Std Dev SEE Diameter (inches) 2 6 1 3 . 0 2 6 . 3 1 9 . 0 3 . 5 0 . 6 6 Height (feet) II 9 0 . 0 1 3 9 . 0 1 1 4 . 1 1 3 . 6 2 . 5 3 Ht to BLC* (feet) II 2 0 . 0 8 5 . 0 6 5 . 3 1 3 . 1 2 . 4 5 Age (years) II 3 8 . 0 7 9 . 0 6 0 . 4 1 3 . 0 2 . 3 0 Diameter growth (inches) II . 2 3 1 . 6 8 . 8 0 0 . 3 2 0 . 0 5 9 Check Trees Diameter (inches) 2 9 9 . 8 0 2 4 . 0 1 6 . 9 3 . 6 0 . 7 2 Height (feet) it 8 4 . 0 1 5 0 . 0 1 1 0 . 7 1 5 . 1 2 . 9 6 Ht to BLC (feet) n 3 0 . 0 8 5 . 0 6 4 . 2 1 6 . 8 3 . 2 9 Age (years) " 3 8 . 0 1 1 0 . 0 6 2 . 2 1 6 . 1 3 . 0 7 Diameter growth (inches) n . 2 4 1 . 3 4 . 7 6 8 . 3 2 . 0 6 5 * Height to base of l ive crown. 116 Separate regression lines for phenotypic plus and check tree strata were tested against the pooled regression and against each other. They did not di f fer signif icant ly. The pooled regression (Figure 34) is thus used for both: Y = 16.46 + .3154 (CRPRO) (19) The residuals were examined to determine i f phenotypic trees having positive residuals were predominant among the best trees. Of the best ten trees, f ive were check trees and f ive were phenotypes. This is strong evidence that plus trees selected in the past have not been notably more ef f ic ient than their neighbors. I f a quantitative improvement in i n i t i a l selection is to be effected in the future, a baseline selec-tion technique offers the highest probability of success; recall that small differences between nearby trees may be attributed to relationship of the plus phenotype and i ts nearby neighbors (Ledig, 1974). Rejection of the current plus trees should not be contemplated without establish-ment of a baseline approach or other genetic analysis. The implied lack of difference between trees merely points out the lack of quanti-f ied difference in growth efficiency between trees. I t should either be quantified or investment in the current method of selection be reduced. Periodic Growth Increment and Age The periodic growth rate of trees is not constant over time. Growth accelerates during juvenile growth stages and begins decelerating before culmination of mean annual increment. The rate of change of the growth function is quite rapid. I t is d i f f i c u l t to compare stands or individual trees i f growth is not adequately defined in terms of competition and Figure 34. Growth-Crown Projection Regression lines for Phenotypic and Check trees. 118 age. Because per iodic growth rate has been the dependent var iable in th i s study, an examination of age s t r a t i f i e d regressions was undertaken. Age has two roles in the se lect ion of plus trees: 1) re l a t i ve or d i f f e ren t i a l age and, 2) absolute or stand age. A few years' age advan-tage for ind iv idual trees overshadows potent ia l genetic di f ferences. An analysis of the effect of age for r e l a t i v e l y small age differences (1 to 3 years) in the Tumour Island data was not poss ib le. Ages for a l l , or at least a large majority of t rees, would be necessary. Abso-lute age involves the changes in growth rate associated with the current annual increment. Nonetheless, two indicat ions corroborating the impor-tance of age were noted: 1. Unusually large values for the residual (more than three standard deviat ions) were pos i t i ve l y associated with trees of +7 to +10 years age d i f f e r e n t i a l . 2. The difference in regression slope between Groups I and II is probably associated with the age difference between these groups. There i s one drawback to the regression ana lys is . Each regression i s descr ipt ive of a s ingle stand and age. Thus, without comparable stands of several ages, no method i s avai lab le for ca lcu lat ing the ef fects of age on select ions for growth e f f i c i ency . A funct ional re la t ion has not been discovered which would allow overlaying independently deter-mined age-increment re lat ionships on the competition-growth re lat ionships fo r ind iv idua l t rees. Phenotypic Tree Age-Strata S t r a t i f i e d regression analyses based on age were performed using data from the 54 of the 57 phenotypic trees after removal of one i nd i -vidual with unusually large basal area growth and two trees having 119 extremely large crowns and consequently, low basal area growth efficiency. Age s t ra t i f icat ion was based on the pattern obtained on Tumour Island plot Groups I to I I I . Figure 35 is a histogram of phenotypic age d i s t r i -bution. Table 35. Phenotypic Tree Age Strata Strata Aqe Number of Trees True Mean Aqe Std. Dev^ Range 30-49 16 42.1 2.9 38-47 50-69 21 62.7 5.2 51-68 70-89 17 73.4 3.98 70-84 Stepwise regression analysis indicated that crown dimension was the best predictor of growth in a l l cases. In the youngest group, CRAR was the only variable that entered the regression; CRAR, height and age, and CRAR and age, entered the 50-69 and 70-80 group regressions respectively. These findings offer some confirmation that our suspi-cions regarding age are jus t i f i ed . Table 36. The Effect of Height, Age and Crown Area on Periodic Growth Y = b 0 + b1 CRPRO + b2Ht + b3Age + e Age n b 0 b l b 2 b 3 R2 SEE 30-49 16 17.98 .0389 .24 9.34 50-69 21 9.80 .0386 .4391 -.7178 .46 7.37 70-90 17 -108.67 .0542 - 1.522 .84 6.11 These results also suggest that age and additional crown dimensions (length of l ive crown or a linear regression combination of height and 1/ Sample standard deviation > 10-1 55 3->^ 3 r> i 5 2 + H 33 4 0 4 3 3 0 53 6 0 6 3 AGE (YEARS) Figure 35. Frequency histogram of age distr ibut ion. 7 0 7 3 8 0 8 3 -121 height to the base of the l ive crown) may be of importance in expanding our selection technique from the research plots to f i e ld selections. These analyses are not equivalent to the Tumour Island study. The check trees do not provide a suff icient baseline to define the relat ion-ship between CRAR and basal area growth. They are included to i l lus t ra te that the concern for age in selection of plus trees is well founded. A baseline is required which defines the basal area growth-crown relations as well as giving an estimation of the variation in the popu-lat ion. The var iab i l i ty in the population is the factor which deter-mines the size of a standardized residual. A larger number of check trees would be required to establish confidence l imi ts , as in the Tumour Island portion of this study. 1 2 2 CONCLUSION This study was in i t iated by MacMillan-Bloedel L td. , under a scien-t i f i c subvention of the Canadian Forest Service in an attempt to resolve disparate selection c r i te r ia for western hemlock. The current c r i te r ia were not uniform for government agencies and forest industries. I t was early in the selection phase of an improvement program for western hemlock. The expectation was that increased attention to environmental influences on the growth of individual trees would lead to more valuable genetic material for inclusion in tree breeding programs. The evidence does not lead to unqualified conclusions. Examination of past pheno-typic selections and comparisons of them to check trees showed that phenotypes have not been notably more ef f ic ient in the last five-year growth period than the check trees. Regression analyses of phenotype-check trees, applied to age-stratif ied data, suggests that stand age and possibly other characteristics of the stand may bias the c r i te r ia used in current selections. Independent regression models applied to each age stratum. Even though some significant differences between phenotypes and check trees were discovered, the lack of clear superi-or i ty of past selections confirms the value of investigating the o r ig i -nal hypotheses. For increased i n i t i a l gains in an improvement program a more s ta t is t i ca l l y rigorous selection procedure including some measure of competition is desirable. 123 Competition Indices An attempt to rationalize growth, genetics and environment into mathematically and biologically consistent models was made. Periodic growth was predicted from competition. The residual variation in the model was equated with genetic variance and selection was then based on well-defined stat is t ica l procedures. Eight competition indices were applied to stem-mapped stands of western hemlock. Four of the indices were eliminated as unsuitable for complete evaluation. Of the four remaining, two indices seemed best, Newnham's and Bella's. I t is some-what disappointing that no clear trend in performance of the indices was discovered. This lack of model superiority plus the relat ively low R-square values suggest that current competition expressions do not adequately explain purely environmental relationships between individual trees. For selection of trees other than those on PSP's, competition index alone does not seem to have suff icient predictive precision to be used with confidence in a selection model based on periodic basal area growth on other than permanent sample plots. None-theless, there was some encouragement for the analysis. Both Newnham's and Bella's indices reflected the history of thinning on Plots 354-359 and 357-358, where an increased mean value of the index indicated increased density (no thinning). Slopes of regression were similar for these plots, but suff icient ambiguities existed to require a careful analysis of covariance. The analyses of covariance using competition indices i l lust rate the possibi l i ty of combining information from several of the plots. Newnham's index was used as covariate on Group I I Plots, s t i l l al l 124 the plots did not have the same slope. The example was extended by eliminating the plot having signif icant ly different slope. While i t is not necessary to reject combined models which show s t a t i s t i -cally different slopes for individual plots at a given probability level, in practice inclusion of plots having different slopes increases the variance due to competition-environment. The competition index approach does not seem to be one which offers immediate application to selection. Large stand-mapped plots are required along with exten-sive data processing. The theoretical construction of the indices is primarily abstract-mathematical. They include both internal and exter-nal measures of var iab i l i t y , spacing and diameter. These indices work admirably in the computer simulation environment for which they were designed. Their shortcoming for this application lies in the absence of a causal relation to biological and environmental competition. Crown Efficiency The second approach to selection ut i l ized low-level aerial photo-graphs to evaluate trees on the plots and to select candidates with ef f ic ient crowns. Despite problems with f l i gh t control and lack of coordination in the processing of aerial photographs, this approach seems worthy of further t r i a l . The s tat is t ica l procedures for selec-t ion seem quite sound even in the shadow of less than reliable data. Basal area growth/unit crown area is a measure of efficiency of space u t i l i za t ion . This concept has been successfully employed in southern pine selection (Brown and Goddard, 1961). An adaptation of this method should be extensively investigated. I t is necessary to reiterate that the decision variable used in this study was basal area growth and not 125 tree volume change. To f u l l y validate the approach, volume should be the selection cr i ter ion. This study has demonstrated that use of additional individual tree information and standard s tat is t ica l procedures can select trees growing better than expected by a given model. Exactly which trees are selected remains a problem for the definit ion of the manager. I t can be argued that selections from among the largest crowned trees, even i f they are more "ef f ic ient" than other large trees now, had an i n i t i a l advantage over their neighbors, or that i f grown in stands they would result in less wood per acre because of their large area occupancy. Trees grown in closer competition to their neighbors on the other hand might be smaller because they have the same spatial requirement of larger trees and simply have not had access to i t during their l i f e . Nonetheless, the results of examining growth patterns of trees at Tumour Island indicate that some smaller trees are s t i l l growing at a constant rate compared to the deceleration of trees of similar crown area occupancy. For the managed stand of the future larger numbers of stems capable of sustained growth rate mean increased harvestable wood production per acre. Studies of both agricultural crops and trees indicate the exist-ence of different physical and physiological growth strategies, (Duncan, 1971, Pienaar, 1965, and Ledig, 1975). Some plants convert the products of photosynthesis into supporting tissues (wood f iber in trees), others reinvest these products in leaf area. I t is obvious that juvenile selection would favor plants having the former qual i t ies. Later exami-nation of selections might f ind that the plants which emphasized produc-tion of leaf early had grown more rapidly in the long run and had contr i -126 buted more to the total volume in a stand. These ideas support the value of crown functional relations in the selection of superior trees. Crown Area As with the study of competition indices analyses of covariance for crown area-growth relations were undertaken to determine the gen-eral i ty of this relation among plots. The analyses were consistent with hypotheses predicting differences between plots receiving thinning treatments. The slope of a growth-crown area regression line for plots within groups were s ta t is t i ca l l y consistent. Levels of the lines were correlated to the number of stems or average i n i t i a l diameter of the plots. These findings suggest the possibi l i ty of combining plots of similar age, site and growth type and selecting trees from a single regression baseline. Slope differences between the two groups dictate further research to determine the cause or an appropriate covariate to account for these differences. The limited range in age, location and site prescribes speculation as to the reason for differences at this time. Both methods of measuring competition's influence on the growth of western hemlock select trees with a s ta t is t i ca l l y interpretable meaning. The standardized residual indicates the probable position of a tree with respect to a model of environmental influences. Many of the trees selected would not have been considered under current f i e l d selection procedures. The methods are not as prone to the bias of subjective evaluation as happens with individual cruisers. While individual experience is irreplaceable for some characteristics, auto-mated selection of quantifiable characteristics seems desirable. Both 127 the competition index and crown efficiency methods attempt to overcome the effect of fortuitous spacing and other undefined advantages on the phenotypic c r i te r ia used to select genetically superior parent trees. Simplicity of models and future sample size reductions possible in the application of crown models recommend the value of crown measure-ments. Direct application of the competition index approach in stem mapping entire stands is impractical. However, some modification of phenotypic selection coupled with stand basal area or competition measurement could prove feasible. Cruisers did pick trees with rela-t ive ly low levels of competition. Crown area measurements could easily be added to a selection cruise procedure with l i t t l e additional time in the f i e l d as was done in the analysis of phenotypic selections (see f i e ld form, Appendix V). Application of selection c r i t e r ia , as is practiced in southern pines, (Robinson and van Buijtenen, 1971), would be possible. In the f inal analysis, f i e l d testing of seedlings or clones is the only certain method for determining the genetic value of the selection. Seed and cuttings of some of the Tumour Island selections were collected in September 1976 and sent to Mr. Dick Piesch of the Canadian Forestry Service for vegetative propagation and progeny test ing. Additional collections are needed, however, before halfsib and fu l l - s i b and clonal tests can be carried out. Competitive ab i l i t y should be a primary cr i ter ion in evaluation of the famil ies, clones and individual offspring. Variable spaced f i e ld tests, e.g., as recommended by Lin and Morse (1975), could assist in making more objective evaluations of present plus trees progency, and in making recurrent selections for advanced generation breeding. 128 RECOMMENDATIONS The research in i t iated here should be consolidated. Results obtained to date should also have interesting implications for al l ied growth and yield studies. 1. Two approaches which increase object ivi ty in the selection of plus trees can be suggested, based on the finds of the current project: a) Individual baseline construction at each candidate tree, consisting of the sampling of suff icient trees to define the competition or crown efficiency trend line and computation of the residual of the selected trees—similar to present Weyerhaeuser method and also suggested in Ledig (1974). b) A method of establishing a multiple regression similar to the one suggested by Robinson and van Buijtenen (1971) using crown dimensions, height, site index and age. In the la t ter , check trees would be sampled in the i n i t i a l phases of the program, but gradually phased out as the data bank increased. Eventually, selections would be compared to the appropriate strata regression with few, i f any, check trees being selected in the f i e l d . A baseline regression need not consist of an entire plot of 100 or more trees as in the Tumour Island study. Knowledge of the form and var iab i l i ty of the regression could be used to reduce the sample size to the order of 10-30 trees, each mapped as above. A few trees chosen to represent the extremes of the regression could yield quite adequate estimates of the slope against which to compare a subject tree's performance. These trees would come from the dominant and intermediate crown classes. The subject tree's residual would be compared to the regression line to determine i ts periodic growth performance. Integration of the growth rate selections with other phenotypic c r i te r ia is also being studied. 2. A f i e ld form which could be readily adapted to either of these approaches was designed for f i e ld work on phenotypically selected trees and is included in Appendix IV crown dimensions and competitor diameters and distances are included. Integration of the forms into the current plus tree cruising procedures should make future application of either of the methods of selection with computer assistance practical. 1 2 9 3. Scion material and open-pollinated seed must be collected from the appropriate Tumour Island selections. The vegetative material should be propagated for subsequent clone bank estab-lishment and breeding work. 4. An expanded, basic study of the relationships between western hemlock crown characteristics and growth rates should be under-taken. Tree height and possible form measurement should be specified as c r i t i ca l i f the high correlation between crown area and volume growth rate is ver i f ied, the results could warrant further modification of plus tree selection methods as well as supplying relevant information for future physiological, ecologi-cal and growth and yield studies of western hemlock. 130 LITERATURE CITED Adlard, P. G. 1974. Development of an empirical competition model for individual trees within a stand. JJN: Growth Models for tree and stand simulation (J. Fries, ed. p 22-37), Royal College of Forestry, Stockholm, Sweden Res. Note 30, 379 p. Arney, J. D. 1971. Computer simulation of Douglas-fir tree and stand growth. Ph.D. thesis. Oregon State University, Corvallis, Oregon. 79 p. Assman, E. 1970. The principles of forest yield study. Pergamon Press, Oxford. 560 p. Baskerville, G. L. 1965. Dry matter production in immature Balsam f i r stands. For. Sci. Monograph 9. 42 p. Beck, D. 1974. Predicting Growth of Individual trees in thinned stands of Yellow-Poplar. IH: Growth models for tree and stand simulation (J. Fries, ed. p 47-55), Royal College of Forestry, Stockholm, Sweden Res. Note 30, 379 p. . Bella, I. E. 1970. Simulation of growth, yield and management of aspen. Ph.D. thesis. Faculty of Forestry, University of B.C. 190 p. Bri t ish Columbia Forest Service Annual Report. 1976. Bri t ish Columbia Forest Service Resource Inventory Report. 1975. Brown, B. S. 1965. Point density in stems per acre. N. Z. For. Res. Notes No. 38. Brown, C. L., and R. E. Goddard. 1961. Silvical considerations in the selection of plus phenotypes. Journal of Forestry 59:420-426. Chisman, H. H. and F. X. Schumacher. 1940. On the tree-area rat io and certain of i ts applications. Journal of Forestry 38:311-317. Curtis R. 0. 1970. Stand density measures: an interpretation. Forest Science 16:403-414. Curtis R. 0., and D. L. Reukema. 1970. Crown development and site estimates in a Douglas-fir plantation spacing test. Forest Science 16:287-301. 131 Daniels, R. F. 1976 Simple competition indices and their correla-tion with annual loblol ly pine tree growth. For. Sci. 22(4) 454-456. Duncan. W. G. 1971. Leaf angles, leaf areas and canopy photosyn-thesis. Crop Sci. vol (11) 482-485. Ek, A. R., and R. A. Monserud. 1974. Trials with program FOREST: Growth and reproduction simulation for mixed species even-or uneven-aged forest stands. IN: Growth models for tree and stand simulation (J. Fries, ed. p. 56-73), Royal College of Forestry, Stockholm, Sweden Res. Note 30, 379 p. Fraser, A. R. 1977. Triangle based probability polygons for forest sampling. For. Sci. 23(1) p. 111-121. Gerrard, D. J. 1969. Competition quotient: a new measure of competition affecting individual forest trees. Michigan State Univ. Agric. Exp. Sta. Res Bull 20. 32pp. Glew, D. R., F. Hegyi and T. G. Honer. 1976. Data base requirements for growth models in the Computer Assisted Resource Planning System in Brit ish Columbia. Proc. XVI IUFR0 World Congress, Division IV. Norway, p. 74-85. Hatch, C. R., D. J. Gerrard and J. C. Tappeiner, I I . 1975. Exposed crown surface area: A mathematical index of individual tree growth potential. Canadian Journal of Forest Research 5:224-228. Hegyi, F. 1974. A simulation model for managing jack pine stands. IN: Growth models for tree and stand simulation (J. Fries, ed. p 74-90), Royal Colege of Forestry, Stockholm, Sweden Res. Note 30, 379 p. Hegyi, F. 1975. Growth modeling in an operational planning context. Proc. C.I.F. Workshop on Canadian Forest Inventory Methods. University of Toronto Press, p. 224-238. Hegyi, F. and L. D. Oxtoby. 1976. A set of FORTRAN algorithms for evaluating inter-tree competition indices. Canadian Forestry Service, Burnside Laboratory Report. 15 p. Husch, B., C. I . Mil ler and T. W. Beers. 1972. Forest mensuration. The Ronald Press Co., N.Y., 410 p. Jack, W. H. 1967. Single tree sampling in even-aged plantations for survey and experimentation. Paper Sect. 25, 14th IUFRO Congress. Kormondy, E. J. 1969. Concepts of ecology. Prentice Hall , Englewood C l i f f s , N.J., 209 p. 132 Ledig, F. T. 1974. An analysis of methods for the selection of trees from wild stands. Forest Science 20:2-17. Ledig, F. T. 1975. Increasing the productivity of forest trees. IN: Forest Tree Improvement - the Third Decade. 24th Annual Forestry Symposium. Louisiana State University p. 189-207. Lin, C. S. and P. M. Morse. 1975. A compact design for spacing experiments. Biometrics 31(3):661-671. Lin, J. Y. 1969. Growing space index and stand simulation of young western hemlock in Oregon. Ph.D. thesis. School of Forestry, Duke University 182 p. Lowe, R. G. 1971. Some effects of stand density on the growth of individual trees of several plantation species in Nigeria. Univ. of Ibadan. Ph. D Thesis. Marsh, E. K. 1957. Some preliminary results from O'Connor's corre-lated curve trend (C.C.T.) experiments on thinnings and espace-ments and their practical significance. Paper presented at 1957 Brit ish Commonwealth Forestry Conference. Mitchell , K. J. 1975a. Dynamics and simulated yield of Douglas-fir. Forest Science Monograph 17. 39 p. Mitchell , K. J. 1975b. Stand description and growth simulation from low-level stero photos of tree crowns. Journal of Forestry 73:12-16. Newnham, R. M. 1964. The development of a stand model for Douglas-f i r . Ph.D. thesis. Faculty of Forestry, University of Bri t ish Columbia, Vancouver. 201 p. Newnham. R. M., and H. Mucha. 1971. A test of the effectiveness of different competition indices in predicting diameter growth in a young red pine plantation. Forest Management Inst i tute Ottawa, Ontario. 16pp. Osborn, J. E. 1968. Influence of stocking and density upon growth and yield of trees and stands of coastal western hemlock. Ph.D. thesis. University of Bri t ish Columbia, Vancouver. 395 p. Pienaar, L. V. 1965. Quantitative theory of forest growth. Ph.D. thesis. University of Washington, Seattle. 167 pp. Piesch, R. F. 1974. Eastablishment of a Western Hemlock tree improve-ment program in coastal Brit ish Columbia. Canadian Forest Service Information Report. BC - X - 89. Porterf ield, R. L. 1975. Economic aspects of tree improvement pro-grams IN: Forest Tree Improvement - the Third Decade. 24th Annual Forestry Symposium. Louisiana State University p. 99-107. 133 Quenet, R. V. 1976. Personal Communication. Unpublished File report. Brit ish Columbia Ministry of Forests. Reineke, L. H. 1933. Perfecting a stand density index for even-aged forests. Journal of Agricultural Research 46:627-638. Robinson, J. F., and J. R. van Buijtenen. 1971. Tree grading without the use of check trees. _In: Eleventh Conference on Southern Forest Tree Improvement, p. 207-211. Snedecor, G. W., and W. G. Cochran. 1967. Stat ist ical Methods, 6th Ed. The Iowa State University Press. Ames. IA 593 p. Spurr, S. H. 1962. A measure of point density. Forest Science 8:85-96. Staebler, G. R. 1951. Growth and spacing in an even-aged stand of Douglas-fir. M.F. thesis. School of Forestry, University of Michigan. 46 p. Steel, R. G. D., and J. H. Torrie. 1960. Principles and Procedures of Stat ist ics. McGraw-Hill, NY. 481 pp. Walters, J. 1963. An Annotated Bibliography of Western Hemlock, Tsuga heterophylla (Raf.) Sarg. Vancouver, Faculty of Forestry, University of Bri t ish Columbia. 86p. Wellwood, R. W. 1960. Specific gravity and tracheid length variations in second growth western hemlock. Jour, of Forestry. 58(50) 361-368. APPENDICES 134 APPENDIX I A SET OF ALGORITHMS FOR EVALUATING INTER-TREE COMPETITION INDICES From F. Hegyi and L.D. Oxtoby NOT FILMED DUE TO COPYRIGHT MATERIAL APPENDIX I A SET OF ALGORITHMS FOR EVALUATING INTER-TREE COMPETITION INDICES From F. Hegyi and L. D. Oxtoby 136 INTRODUCTION Since 1964, when Newnham (1964) introduced his distance-dependent stand model for Douglas-fir, inter-tree competition indices have played an important role in growth simulation methodology. In fact , the subsequent development of distance-dependent single tree growth simu-lators stimulated different formulations of inter-tree competition indices (Newnham 1964, Lin 1969, Bella 1970, Arney 1971, Ek and Mon-serud 1973, Hegyi 1973). While these indices al l require data on inter-tree distances, the actual calculations provide some variations which may be explained in terms of crown overlap calculations, angle measures, and d.b.h. ratios of competitors over subject trees. In recent years, single tree growth modeling picked up considerable momentum in Bri t ish Columbia (Hegyi 1975, Glew, et a l . 1976). How-ever, because the main differences between the various single tree growth simulators appear to be due to the formulations of inter-tree competition, i t was considered essential that an evaluation of competi-t ion indices be carried out before some of the models are implemented operationally. Therefore, a set of FORTRAN algorithms was developed at the Pacific Forest Research Center which fac i l i ta tes the calculations of competition indices by Staebler (1951), Newnham (1964), Lin (1969), Bella (1970), Arney (1971), Hegyi (1973), Ek and Monserud (1973), and Quenet (1975). The above indices were selected on the basis of having high potential of application in our operational growth predic-tion system (Hegyi 1975, Glew, et a l . 1976). ARNEY'S COMPETITIVE STRESS INDEX CSIj = 100 * ZAj ZA| WHERE: CSI = COMPETITIVE STRESS INDEX ZO «= AREA OF ZONE OVERLAP ZA - INFLUENCE—ZONE AREA n = NUMBER OF COMPETITORS i «= SUBJECT TREE j = COMPETITOR REQUIRES: - OPEN—GROWN CROWN RADIUS FUNCTION - CW = f(DBH) - X - Y COORDINATES - DBH APPLICATION - SPATIAL PATTERNS (X-Y COORDINATES) - GENERATE POTENTIAL HEIGHT AND DBH INCREMENTS PER TREE - CALCULATE CSI FOR EACH TREE - ADJUST POTENTIAL INCREMENTS BY CSI . - HEIGHT AND DBH REDUCTION: 0—1 - MORTALITY = f(CROWN LENGTH, CSI) - CALIBRATION: REDUCTION FACTORS - INCREMENT PERIOD: FIXED (1 YEAR) - INPUT PARAMETERS: GENERATED OR SUPPLIED BELLA'S COMPETITIVE INFLUENCE—ZONE OVERLAP INDEX WHERE: CIO «• COMPETITIVE INFLUENCE—ZONE OVERLAP INDEX ZO = AREA OF ZONE OVERLAP ZA = INFLUENCE—ZONE AREA D = DBH EX « EXPONENT n «= NUMBER OF COMPETITORS I = SUBJECT TREE j COMPETITOR REQUIRES: - OPEN—GROWN CROWN RADIUS FUNCTION CR .= f(DBH) - ADJUSTING FACTOR (FC) INFLUENCE = CR x FC - X - Y COORDINATES - DBH APPLICATION: - SPATIAL PATTERNS (X-Y COORDINATES) - GENERATE POTENTIAL HEIGHT AND DBH INCREMENTS PER TREE - CALCULATE CIO FOR EACH TREE - ADJUST POTENTIAL INCREMENTS BY CIO . - HEIGHT AND DBH REDUCTION: 0—1 - MORTALITY = f(CURRENT INCREMENT, CIO, RANDOM) - CALIBRATION: FC, EX, REDUCTION FACTORS - INCREMENT PERIOD: VARIABLE - INPUT PARAMETERS: GENERATED OF SUPPLIED EK 'S COMPETITION INDEX n Z O j j H; x CRi ZA; x H; * C R j ClAj = ClUj x TOLj WHERE: CIU = UNADJUSTED COMPETITION INDEX CIA = ADJUSTED COMPETITION INDEX ZO = AREA OF ZONE OVERLAP ZA = INFLUENCE-ZONE AREA H = HEIGHT CR = OPEN-GROWN CROWN RADIUS TOL= SHADE TOLERANCE VALUE n NUMBER OF COMPETITORS REQUIRES: - OPEN-GROWN CROWN RADIUS FUNCTION - HEIGHT OR HEIGHT = f(DBH) - TOL OR SHADE TOLERANCE FUNCTION - X - Y COORDINATES - DBH APPLICATION - SPATIAL PATTERNS (X-Y COORDINATES) - GENERATE POTENTIAL HEIGHT AND DBH INCREMENTS PER TREE - CALCULATE CIA FOR EACH TREE - ADJUST POTENTIAL INCREMENTS BY CIA - HEIGHT AND DBH REDUCTION: 0—1 - MORTALITY = f(CR0WN RATIO, CIU, PERIOD, RANDOM) - CALIBRATION: TOL, REDUCTION FACTORS - INCREMENT PERIOD: VARIABLE - INPUT PARAMETERS: GENERATED OR SUPPLIED H E G Y I ' S C O M P E T I T I O N I N D E X W H E R E : C l '« C O M P E T I T I O N I N D E X D = D B H DIS = D I S T A N C E n ' « N U M B E R O F C O M P E T I T O R S A S D E T E R M I N B Y A 1 0 B A F A N G L E G A U G E i - S U B J E C T T R E E j - C O M P E T I T O R R E Q U I R E S : - D B H - X - Y C O O R D I N A T E S A P P L I C A T I O N : - S P A T I A L P A T T E R N S ( X - Y C O O R D I N A T E S ) - G E N E R A T E P O T E N T I A L H E I G H T A N D D B H I N C R E M E N T S P E R T R E E - C A L C U L A T E C I F O R E A C H T R E E - A D J U S T P O T E N T I A L I N C R E M E N T S B Y C l - H E I G H T A N D D B H R E D U C T I O N : 0 - 1 - M O R T A L I T Y = f ( S T O C K I N G O R C A I , C l , R A N D O M ) - C A L I B R A T I O N : R E D U C T I O N F A C T O R S - I N C R E M E N T P E R I O D : F I X E D (1 Y E A R ) - I N P U T P A R A M E T E R S : G E N E R A T E D O R S U P P L I E D 141 L I N ' S G R O W I N G S P A C E I N D E X n GSI; Z(25-RF) RF j=l f ( K ) DISii 2 * D i i K Dj Dj + Dj x W H E R E : GSI G R O W I N G S P A C E I N D E X R F = GSI R E D U C T I O N F A C T O R (^25) A S O B T A I N E D F R O M A T A B L E K « W E I G H T E D K R A T I O DIS = D I S T A N C E D = D B H n «= N U M B E R O F C O M P E T I T O R S A S D E T E R M I N E D B Y A 10 B A F (OR L E S S ) A N G L E G A U G E U P T O A M A X I M U M O F 4 ( T H E L A R G E S T T R E E . I N E A C H Q U A D R A N T ) i = S U B J E C T T R E E j • C O M P E T I T O R R E Q U I R E S : - C R O W N R A D I U S ( F O R R F ) - R E D U C T I O N F A C T O R T A B L E - X - Y C O O R D I N A T E S - D B H A P P L I C A T I O N : - S P A T I A L P A T T E R N S ( X - Y C O O R D I N A T E S ) G E N E R A T E P O T E N T I A L H E I G H T A N D D B H I N C R E M E N T S P E R T R E E - C A L C U L A T E GSI F O R E A C H T R E E - U S E GSI IN G R O W T H F U N C T I O N S - M O R T A L I T Y = f (PAI, GSI) - C A L I B R A T I O N : R F , K . G R O W T H F U N C T I O N S - I N C R E M E N T P E R I O D : F I X E D (2 Y E A R S ) - I N P U T P A R A M E T E R S : G E N E R A T E D O R S U P P L I E D N E W N H A M ' S C O M P E T I T I O N I N D E X ci5 - ^ ( ^ c w f ) 2 tr C l = C O M P E T I T I O N I N D E X 6 - A N G L E F R O M T H E C E N T R E O F S U B J E C T T R E E C R O W N T O T H E T W O P O I N T S O F I N T E R S E C T I O N W I T H T H E C O M P E T I T I V E C R O W N C W = O P E N - G R O W N C R O W N W I D T H TT = 3 .141596 n « N U M B E R O F C O M P E T I T O R S i = S U B J E C T T R E E j = C O M P E T I T O R R E Q U I R E S : - O P E N - G R O W N C R O W N R A D I U S F U N C T I O N C W = f ( D B H ) - X - Y C O O R D I N A T E S - D B H A P P L I C A T I O N : - S P A T I A L P A T T E R N S ( X - Y C O O R D I N A T E S ) - G E N E R A T E P O T E N T I A L D B H I N C R E M E N T S D B H G R O W T H = f ( D I A M E T E R , A G E ) B Y S I T E S - C A L C U L A T E C l F O R E A C H T R E E - A D J U S T P O T E N T I A L D B H I N C R E M E N T S B Y C l - D B H R E D U C T I O N : 0 - 1 - M O R T A L I T Y = f ( D B H I N C R E M E N T , C l ) - C A L I B R A T I O N : R E D U C T I O N F A C T O R S - I N C R E M E N T P E R I O D : F I X E D (5 Y E A R S ) - I N P U T P A R A M E T E R S : G E N E R A T E D O R S U P P L I E D QUE NET'S COMPETITION INDEX n • m j=1 DlSij Cl = COMPETITION INDEX D = DBH D1S = DISTANCE n «= NUMBER OF COMPETITORS AS DETERMINED BY A 10 BAF ANGLE GUAGE i « SUBJECT TREE j - COMPETITOR REQUIRES: - X - Y COORDINATES - DBH S T A E B L E R ' S C O M P E T I T I O N I N D E X ( M O D I F I E D ) W H E R E : Cl = C O M P E T I T I O N I N D E X LO = L I N E A R O V E R L A P R = R A D I U S O F C O M P E T I T I O N C I R C L E n = N U M B E R O F C O M P E T I T O R S I «= S U B J E C T T R E E j = C O M P E T I T O R R E Q U I R E S : - O P E N - G R O W N C R O W N R A D I U S F U N C T I O N — C W = f ( D B H ) - X - Y C O O R D I N A T E S - D B H n Cl; 2R; FLOWCHART OF THE COMPETITION INDICES PROGRAMS DATA INPUT AND CONTROL MAIN PROGRAM ARNEY'S INDEX J BELLA'S INDEX EK'S INDEX J LIN'S INDEX TERMINAL £ \ • I/O 3 HEGYI'S INDEX NEWNHAM'S INDEX QUENET'S INDEX STAEBLER'S INDEX -> CORRELATION RESULTS T PLOT APPENDIX I I LIN'S GROWING SPACE INDEX 147 Lin's competition index was included in the proposal for this project as i t is specif ically designed for western hemlock. The index obviously performs well in the simulation i t was designed for. However, several problems developed with i ts application to the current project. The f i r s t was not serious, i t is the only index which can assume value zero. This means that calculations which involve division transformations must be replaced by an arbitrary small value. In addition the index is based on competitors found in fixed quadrants around the subject tree. This condition does not seem apropos measurements of individual trees required by consideration of genetic var iab i l i ty . Note the following sketch: \ \ \ \ 51 0 o o \ \ \ \ \ In the f igure, because large trees are growing in two quadrants, GSI is reduced to 50%. The upper r ight quadrant has two large trees, but only one is necessary to reduce the growing space to zero for the quadrant. I f the reference axes are rotated to the position indicated by dashed l ines, the GSI for three quadrants is reduced to zero; GSI = 25% for the same tree! The dependence of GSI on arbitrary orientation of the f i e ld plot axes (XY-axes are not oriented identically on Tumour Island plots) is not equivalent to simulation of stand growth in a computer model. The GSI would be expected to average out over the plot but not ref lect perfectly individual tree differences. These observations do not ref lect in any way deprecatory to the function of Lin's index in the computer model environment. However, for these reasons GSI was eliminated from the f inal evaluation at this time. APPENDIX I I I EXAMPLE OF COMPUTER OUTPUT USED TO SELECT CROWN EFFICIENT CANDIDATES DEP.VAR. I U 0 C P . V A R . BAG* TH CA A I C C N S T . I 1 . 6 4 1 D I C O E F F . » 0 . 9 2 4 3 E-01 FN AT 1 0 ( 0 ) FPP .OB(H) 1 3 6 . 7 C . 7 6 2 3 E SID.SR'.A -16 1 . 2 0 1 STU.ERf.fi S T O . F S R . V 0 . 7 B 4 3 E-02 6 . 1 1 4 -fSO 0.5 8 6 0 f^tci CF y vs * #NC F I C T C F F F G P E S S I C N L I N E . THE " . " AND " • " A P E LSEU TC PLOI Thfc R F G R E S S I O N 11NE;'TftE " • " IS 4 2 . 0 0 U S E D WHEN A P L O T P O I N T CJVCt<S D A T A P O I N T S 42.00 >-/ Plot 358 1 • 1 4 1 . 1 0 40 . 2 0 3 9 . 3 0 / Unthlnned Hemlock • • • 3b. 4 0 3 7 . 5 0 3 6 . 6 0 i»rowrn / 1 1 1 • 3 5 . 7 0 3 4 . 0 0 3 3 . 9 0 33.00 D?^2 .'- D702 ' • • 1 I . 3 3 .OJ 3 2 . 1 0 3 1 . 2 0 -(square Inches J 1 1 • • • • 3 0 . 3 3 2 9 . 4 0 2 8 . 5 3 / 1 11 1 1 1 . • 1 • 2 7 . 6 0 2 6 . 7 0 2 5 . S 3 24.00 1 * 1 .. 1 2 4 . SO 2 4 . 0 0 2 3 . 1 0 1 . . . • 1 - 2 2 . 2 0 2 1 . 3 0 2 3 . 4 3 / 1 • • 1 .*. 1 . 1 1 11 1 19.SO IV.(JO 1 7 . 7 3 15.00 1 1 1 1 .* 1 I ic . eo 1 5 . 9 3 1 5 . 0 3 I 1 1 11 * . . 1 . * . 1 1 1 1 1 1 4 . 1 C 1 3 . 2 0 1 2 . 3 0 J 1 i 1 1 . . 1 . * . 1 1 1 1 . 4 0 1 0 . 5 3 9.tC0 J 1 • ... 1 ». 1 1 1 1 e . 7uo 7 . E 0 3 6 . 9 C 0 6.COO 1 .* 1 . . * 1 * . l 1 1 1 1 1 1 1 1 1 1 6 . 0 0 0 5 . 1 0 3 4.?UU .. i l 11 1 1 1 11 1 1 1 1 1 1 1 1 3 . J O 0 2 . 4 3 3 l.buO / • 1 1 0 . 6 0 0 0 -0.iOJO - 1 . 2 C 0 -3.000 / / I / / / / I I H I M I I I I I i i i i i i i M i i i i i i m n i t l l l t l M l l l t t l i i \ I I I I I I I I n i i i i i i n n 1 1 1 1 utit -2. 100 - 3 . 0 0 3 1 -2C.C0 C1STM.CE 6 0 . 0 0 1 4 0 . 0 E E T K E E N S L A S H E S u THE X - A M S I S 4.00J 220.0 3 J 3 . 0 3 8 0 . 0 Crovrn Area ' (sauare feet) ( D ^ . V A * . u.utr.^r. a t l t W . i . tcoEH . i r R A t i o i d l F P R O B C B J i '0 .*55, , A S T5'5!!.'5 0 ? S T D : ' S i ; T FIsTo J BACMM CA 1.6*1 0 .92*3F-0 i 13d.7 0.7033E-16 1.201 0.78*oF-02 6 .61* 0.5860 I ———• ""rt j z r c t i t P Y S I L U A L £ 1 * 2 . J -Y h A t VtbSlS R E S I C U A L S ( p r e d i c t e d J 363. CA rffF.SUS P E S I L O A L S . 1 / • > J P l o t 358 , / / • • ' / . 1 " / / 1 / / I • / 33 .0 / l . / 300. / 1 ' / 1 ' .1 / • * 1 1 / / 1 1 1 ' / • ; .1 1 / l l / / • ' / 1 ' / 2 / : J 1 / 2 / ' / . 1 . * • / 1 L 2*.o f • ' 2 ' / . 1 1 1 2 2 0 . . 11 1 ' / 1 1 • f J 1. 1 : L ', -1 i l l / l . l / 2 1 / / 2 ' / 1 . 2 / / 1 ' 1 : — n / i / n i . ' ) I • ' / l i 1 ' / • t i l 1 L . 15.3 L 1 2 1 I ' / 2 1 1 . / . 1 1 1 1 1 f 1*0. / • I I • ' - 11 1 2 . 1 . ' / 1 1 1 f -; • 1 I 1 1 ' 1 1 . 1 1 / • / 1 1 1 ' / 1 1 1 1 1 1 ; I l l / • i u i i u i 1 1 U l 1 / 1 1 1 ' / 1 1 I t ' . / 1 1 111 1 f 6*00 ; 2 1 1 1 / 1 1 1 / 1 1 2 . ' 60.0 • i 1 1 . I l l ' / 211 1 ' 1 1 . ' ; 131 1 I 2311 / 11 1 1 / / 11 1 ' / 1 2 . ' / 3 1 1 ' ; .1 ' / 2J11 ' / 11 1 / / . . 1 1 L ; • * / • i\iniiim\iimn-ti\imimi\inmin\iiinmi\ -4H.U - 3 7 . 0 - 9 . 0 0 9 . 0 3 2 7 . U . * 5 . 0 -20.6 i \ i i m n n \ i m t j i t t \ i i i i i m t \ m i t i t i i \ i i i i i i i n \ - * 5 . 0 - 2 7 . 0 - 9 . 0 0 9 . 0 0 2 7 . 0 o i S t A N C i BETWEEN SLASHES OH TMF. X-AXES I S O.V'OOO D E P . V A * . i V D E P.VAR. ' A I C O N S T . ) O I C O E F F . I FRAT t U ( U I F P K C B I O I ST 0 .ERR • A S T O . f F . O S T O . t A B . Y RSO B A O n T H CA 1 . 6 4 1 C . 9 2 4 3 F - 0 1 1 3 8 . 7 0 . 7 6 3 3 E - 1 6 1 . 2 0 1 0 . 7 B 4 J P - C 2 6 . 6 1 4 0 . 9 8 6 0 1 1 \ F F i b o A B I l l T V C I P L C t TO VER1 2.6C0 t F E J l C U A l S v i F ES ICUALS FT TFE tiCFCALITT OF THE CIST CF RFSIOUALSI I 2. t O O r — / P l o t 358 2.490 2.380 2.270 / * 2.163 't . P r o b a b i l i t y of Residuals . m\ 2.053 1.S4S i ) . l / . i / . 1 1.635 1.720 1.613 1.5-0 l / • l / *• 1 . S 3 J 1.390 l . T c O i \* i l * . / 2*. 1 . 1 7 J 1.C60 C r t J O 7 12. / 3. / 1 3. 0.840C C.730O 0.62 JO o.*ccu / l i . . " 5 . . / 2 2 . . C . 5 1 0 0 0.4000 0 . 2 9 J O ) 22. / * * / 3.. C.lflUS C.7L0.E-01 - I . 4 0 3 J E - 3 1 / »• / *. / . • • -C . 1 5 0 C , - C . 2 C J 3 - C . 3 7 J 3 -3.7JVJ3 7 : .« / . . l . .3 -C.460C - 3 . 5 S J 3 - 3 . 7 C U 0 . / . i l / . .11 / .2 -C.8 I 0 0 - C . V J 3 J - 1 . C 3 0 7 . . 1 1 / . . 2 / . 2 - l . l « i 0 • -1.253 - l . r u O 1 ' .11 / . 1 / . 1 • • - 1 . 4 7 J -1.563 -1.690 •' •-1.600 . 1 / 1 / # - l . L O O -1.910 -2.C20 7 1 / • - 2 . 1 3 3 -2.240 -2.350 / 1 -2 . « . 0 3 -2.57o -2.teo -2.sua / - 2 . 7 S J -2.SOU //I/////////I/////////I/ ////////1// / / / / / / /1/ / / / / / / / /!/////////I///////// \UJAtl 11 t\l.UJ.ii.llJ'ltllil HI 1 _^ -6.804 -4.CB2 • -1.361 1.361 C1STAKCE EEThtEN SLASHFS CN THE X-AXIS IS 0.1361 4 . 0 8 2 6.P3-. APPENDIX IV LIST OF "PLUS" TREES SELECTED BY FOUR COMPETITION MODELS, CROWN AREA MODEL AND ON BASIS OF PHENOTYPE Number Number Number Bella Ek-Monserud Hegyi I 350 29 2.4 2.8 2.5 53 1.5 1.8 1.7 64 2.8 3.4 3.2 31 - .10 85 -1.43 351 238 - 1.7 254 1.5 1.4 304 1.5 370 220 317 332 437 1.14 1.18 442 1.81 1.65 476 1.79 2.63 2.63 488 1.43 1.74 613 2.18 1.74 519 583 357 1873 2.1 2.8 2.0 1906 1.7 1.6 1.7 1959 1.8 1.2 1826 1915 1806 1894 358 2054 2093 1.81 1.68 2110 2.54 1.93 2.44 2212 1.31 1.65 2220 1.74 2346 2294 2258 2239 II 354 883 2.7 2.7 3.3 896 2.1 992 1.4 1012 1.4 1016 1.6 1027 1.6 922 1.8 1033 904 .58 954 1.63 355 1039 1.8 1.8 1219 1.3 1.9 1165 356 1574 2.4 2.6 2.2 1592 1.3 1.9 1.4 1639 1.9 1.2 1742 1.2* 1411 1590 1431 1697 1725 1745 * Tree olsmeaaured or older. Newnham Competition Phenotypes Commenta 2.6 2.0 1.6 2.0 1.13 2.66 4.86* 4.54* 1.63 3.20 Inside plot Inside plot Phenotype I'a 7 1.52 1.08 3.00 Seed & scions In buffer In buffer 1.4 1.2 1.16 3.01 2.49 4.32* 2.06 In buffer In buffer 1.43 2.09 In buffer In buffer 3.0 2.52 1.99 2.12 1.3 3.52 4.85* 1.7 2.3 1.9 2.49 4.43 X Inside plot X Inside plot X Inside X Buffer X In buffer X In buffer X In buffer X In buffer Appendix Vb Group Number I t ! Plot Tree Crown Huober Number Bella EV-Monscrud Hegyi Newnham ( Competition Phenotypes 359 2147 1.24 1.69 1.10 1.35 (- .23) X 2193 1.69 1.43 1.30 1.37 2.07 2212 1.10 1.27 1.02 2204 3.85* 2160 .37 - X 2165 .44 X 2176 X 3J3 670 1.6 X 683 1.2 1.5 723 1.2 1.4 1.4 749 1.8 1.8 1.6 1.3 750 1.2 1.83 X 693 4i 53* 400 116 1.3 1.27 119 1.14 1.80 199 1.9 1.73 206 1.7 1.64 1.42 X 295 1.56 323 1.74 159 X 401 69 1.6 1.3 97 2.2 1.9 1.9 2.86 106 2.0 1.5 2.1 2.1 152 1.9 2.1 1.7 265 (1.43) 2.0 1.9 X 268 (1.31) 2.2 1.8 X 12 3.02 QpiMueute Inside, 1clone Inside Inside Buffer Inside Seed & scions Seed & scions Inside Buffer Inside Inside APPENDIX V COMPETITION INDEX - PLUS TREE SELECTION FORM V» \J IYI r C I I I I V l » l i i i 7 L . n i i i» w. i_ w i— i— • PROJECT 221.6 L o c o t i o n : /^^J^fjjT 1 1 3 0 TREE BLC Bose Live CrowrJ 0 (o 1 O DBH 4 HT. / 2 2 o AG! 0 CORE# 2 / / 9 7 9 30 31 32 34 Crown 55 56 Dimensions N | N E |i E it S E •Cr. A. -\ At t. -K A fell I 14 i SW w NW 1 - Dom 2 - Codo/n 3 - Inter 4 - Sup 37 3^"S404lT ti^.3*4" , 5 4* <7 48 49 50 51 52 53 S4 55 56 57 58 59 60 CC: 5 - Deod Sp-'- I — Hemlock Sp.« 5 - Spruce 6 _ Cut 2 — Fir 6 - Other Conif. • 3 - Bolsom • 7 - Mople A - Cedar 8 - Alder 9 - Other De:i< Com Tre petitors' t No.!! c )i 5 t 0 r c e Beori || Diome te i l r jppsc l | C r o w n j M | ! c i o s s i Dbservotfons Plus Tree-Enter tree#ofterK o 1 o i 0 1 :j 0 / 0 • o 1 0 Q | 0 j / I ' M ! / - -! / ' I 1 • i 1 ij / i i 1 n ' I 1 o i z i; • JL 9 4--* i—-- -t-^ ! 0 : l l / i f f - i l / I I 2. & OQ>/l * • 0 3 '! 1 $ flail ! 19' J II 3 0 4 II 1 i —* $1 il / 1 / 1 / il ;i / / ! 2 0 0 6 !j J-1 7 3 -L 1 $M 19!-1 |i II T ^ 1 0 7 ii JL / 0 •il 1 1\C\ Xl£ l 2101 •I 1 2 0 8 ! | 0 ft A •1 ii /!! / 0 9 ; / Z / 0 / — 1 o jl J— % 2\?\0\ \2\3\- 1 ii 2i| / I 1 I « — 1 1 1 r; 2 ij 1 ft 2 m & i < ? P T i l / / A 1 1 3:1 I I 6 1 * U l 4 i ' i II / ?li 1 1 — 1 Il i i 1 » ii ! 1 1 5 !': 6 1; 1 1 !j ti 1' !i I I -1 7 P • i ii ii ! -1 — L — ! — s l i ! it i 1 I 1 — 1 — ii 1! jl — 1 2 9 | i 1 Ol: 1 1 ii- i 1 ! ! i H r II il • 2 1 ! j ii i ! K T r I 2 C i ! ~ n — ii 1! 1 2 3 1 ! 1 — 1 i il j — j 2 2 4 5 1 t 1 Ii I" _ . — ... , — , 11 1 -Time. y//(. Slgnoturoi Q,~J~ TAT 

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