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Ecological and height growth analysis of some sub-boreal immature lodgepole pine stands in central British… Wang, Qingli 1992

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E C O L O G I C A L A N D H E I G H T G R O W T H ANALYSIS O F S O M E S U B - B O R E A L I M M A T U R E L O D G E P O L E P I N E S T A N D S IN C E N T R A L BRITISH C O L U M B I A by Q I N G L I W A N G B.Sc. Shenyang Agr icul tural Univers i ty , C h i n a , 1977 M.Sc . The Northeast Forestry Univers i ty , C h i n a , 1981 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y i n T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Faculty of Forestry) We accept this thesis as conforming to the reqvdred standard T H E 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 A p r i l 1992 © QingK Wang, 1992 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. 1 further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of irOf^ ^ C^g-^t ^ The University of British Columbia Vancouver, Canada Date -6 (2/88) A B S T R A C T This study investigated relationships between lodgepole pine {Pinus contorta Dougl. ex Loud.) height growth and ecological site quality. Vegetation, environmental, and stand data, obtained from seventy-two sample plots established i n immature stands over wide range of soil moisture and soil nutr ient conditions i n the montane boreal climate i n central B r i t i s h Columbia, were analyzed using the methods of biogeoclimatic ecosystem classification and numerical analysis. The analysis produced categorical and continuous measures of ecological site quality which were then related to measures of height growth obtained from stem analysis of one hundred and sixty-two site trees. The seventy-one diagnostic species and ten vegetation units identified by tabular analysis were strongly correlated wi th , and occupied relatively narrow segments of climatic, soil moisture, and soil nutrient gradients. Heat index was used to characterize the climatic gradient represented by three biogeoclimatic subzones. Actual/potential evapotranspiration ratio and the depth of the growing-season water table or gleyed soil horizons were used to characterize the soil moisture gradient and to classify the study plots into eleven soil moisture regimes. Soi l mineral izable-N and the sum of exchangeable bases were used to characterize the soil nutr ient gradient and to classify the study plots into five soil nutrient regimes. Correlations between vegetation and categorical or continuous measures of ecological site quality impl ied that these measures had a meaning relative to moistvire and nutrient conditions experienced by plants. Eleven site associations circumscribed by vegetation units and characterized by a range of climatic, soil moisture, and soil nutrient regimes, stratified the study plots into qualitatively and quantitatively distinct, field recognizable, segments of regional gradients of ecological site quality. Regression analysis showed that the most strongly related ecological variables to lodgepole pine site index were: (1) ecotopes, defined either by a combination of categorical variables (biogeoclimatic subzone, soil moisture regime, and soil nutrient regime) (adj. R2 = 0.85) or by a combination of continuous variables (potential evapotranspiration, and the depth of water table or gleyed soil horizons, and soil mineralizable-N) (adj. R^ = 0.82), (2) site associations (adj. R2 = 0.81), (3) site series (adj. R2 = 0.84), and (4) vegetation units (adj. R2 = 0.83). Lodgepole pine appears to have a potentigd to grow on nitrogen-rich sites w i t h p H < 7. The three-parameter Chapman-Richards growth fimction precisely described height growth of site trees over a wide range of sites. The pattern of height growth changed w i t h ecological site quality. Site series and ecotope (defined either by a combination of categorical or continuous variables) h a d a stronger relationship w i t h the function parameters than site index. The two site-specific height growth models developed—^the site un i t model and the ecotope model—were more effective than an existing site-index driven growth models. The above results support the use of either categorical or continuous synoptic ecological variables i n describing the var iat ion of lodgepole site index i n relation to ecological site quality, which can be inferred from the understory vegetation developed i n mid-seral stands. The derived site index and site-specific height growth models showed strong relationships between height growth and several measures of ecological site quality produced by biogeoclimatic ecosystem classification. In consequence, categorical or continuous ecological variables could be used i n polymorphic growth modelling to predict lodgepole pine height growth so that the effects of site, and environmental changes, inc luding management practices, on forest productivity can be better understood. T A B L E O F C O N T E N T S A B S T R A C T i i T A B L E O F C O N T E N T S v LIST O F T A B L E S v i i i LIST O F F I G U R E S x i i A C K N O W L E D G M E N T S xv i 1. G E N E R A L I N T R O D U C T I O N 1 2 . T H E S T U D Y A R E A 7 3. E C O L O G I C A L ANALYSIS O F T H E S T U D Y E C O S Y S T E M S 1 3 3 . 1 . I N T R O D U C T I O N 1 3 3 . 2 . M A T E R I A L S A N D M E T H O D S 1 6 3 . 2 . 1 . Sample Plots and Sampl ing 1 6 3 . 2 . 2 . F o l i a r Nutr ient Analysis 1 9 3 . 2 . 3 . So i l Phys ica l and Chemical Analyses 1 9 3 . 2 . 4 . So i l Moisture Analysis 2 2 3 . 2 . 5 . Indicator P lant Species Analys is 2 4 3 . 2 . 6 . Vegetation and Site Classification 2 4 3 . 2 . 7 . Stat ist ical Analysis between Vegetation, So i l , and Foliage Variables 2 5 3 . 3 . R E S U L T S A N D D I S C U S S I O N 2 6 3 . 3 . 1 . Vegetation Classification and Indicator Plants 2 6 3 . 3 . 2 . So i l Moisture Analysis 4 0 3 . 3 . 3 . So i l Nutr i en t Analysis 4 9 3 . 3 . 4 . Site Classification 6 4 3 .4 . C O N C L U S I O N S 7 3 4. R E L A T I O N S H I P S B E T W E E N L O D G E P O L E P I N E SITE INDEX A N D M E A S U R E S O F E C O L O G I C A L S I T E Q U A L I F Y 76 4.1. I N T R O D U C T I O N 76 4.2. M A T E R I A L S A N D M E T H O D S 78 4.3. R E S U L T S .83 4.4. D I S C U S S I O N 101 4.5. C O N C L U S I O N S 110 5 . SITE S P E C I F I C H E I G H T G R O W T H M O D E L S B A S E D O N S T E M ANALYSIS A N D M E A S U R E S O F E C O L O G I C A L SITE Q U A L I T Y I l l 5.1. I N T R O D U C T I O N I l l 5.2. L I T E R A T U R E R E V I E W 113 5.3. M A T E R L ^ A N D M E T H O D S 116 5.4. R E S U L T S A N D D I S C U S S I O N 121 5.4.1. Averaging Height Growth D a t a 121 5.4.2. Height Grovrth and Stand Density 123 5.4.3. Height Growth i n Relation to Ecological Variable and Site Index 125 5.4.4. Site-Specific and Site Index D r i v e n Height Growth Models 129 5.4.5. Increment Chgiracteristics of Height Growth 144 5.4.6. Test ofthe Site-Specific Height Growth Models 152 5.4.7. Comparison ofthe Site U n i t Model and Goudie's Models 155 5.4.8. Physiological Characteristics of Height growth 158 5.4.9. Potential Appl icat ion of the Site-Specific Height Growth Model 161 5.5. C O N C L U S I O N S 161 6. S U M M A R Y A N D C O N C L U S I O N S 163 R E F E R E N C E S 166 Appendix 1 183 Appendix II 189 Appendix III 191 LIST O F T A B L E S Table Page 2.1. Selected climatic characteristics for the study area 8 3.1. Synopsis of the vegetation imits distinguished i n the study plots 28 3.2. Diagnostic combinations for the plant alHances (all.), associations (a.), and subassodations (sa.) distinguished i n the study plots 29 3.3. The eigenvalues (1) and ctraiulative accounted-for variance of P C A applied to a covariance matr ix w i t h the diagnostic species significance values 31 3.4. Means of selected climatic, soil, and stand characteristics of the ten distinguished vegetation imits 34 3.5. Diagnostic species correlated positively or negatively w i t h the first P C A component and their edaphic indicator values 35 3.6. Diagnostic species correlated positively or negatively w i t h the second P C A component and their edaphic indicator values 36 3.7. The eigenvalue (1), variance, and canonical correlation for the canonical variâtes obtained fi'om analysis of concentration on the diagnostic species stratified according to their indicator values of climate, soil moisture and soil nitrogen into indicator species groups (ISGs) 38 3.8. Comparisons of soil water deficit calculated on the 30 year normals i n a monthly time-step, annual data i n a monthly time-step or i n a daily t ime-step using the Energy/Soi l -Limited water balance model 42 3.9. The cr iteria used for the characterization and classification of actual soil moisture regime of the study plots (sites w i t h fluctuating water table are not included) (after K l i n k a et al. 1989b) 43 3.10. Megin values of selected components of the annual water balance for the study plots stratified according to soil moisture regimes (SMRs) 44 3.11. Mul t ivar ia te statistics and F approximations for testing group means i n the canonical discriminant analysis of 11 soil moisttire regimes (SMRs) under HO: £dl group means i n the poptilation are equEil 47 3.12. Results of the canonical discriminant analysis for five soil nutrient regimes using on mineral izable -N (kg ha"^) and stmi of exchangeable bases (kg ha"^) as variables 51 3.13. Percentage of study plots identified by canonical discriminant analysis into the source soil nutrient groups on the basis of minerahzable-N (kg ha"^) and sum of exchangeable bases (kg ha"-'^ ) 52 3.14. Mult ivar iate statistics and F approximations for testing group means i n the canonical discriminant analysis of five soil nutrient groups vmder HO: a l l group means i n the population are equal 53 3.15. Means and standard deviations (in parentheses) of a l l available soil nutr ient v£iriables and fi*equency of nitrophytic plants for five soil nutrient regimes.55 3.16. Comparisons of the means of mineraUzable-N (mN) and s imi of exchangeable C a , M g , and K (SEC) for soil nutrient regimes (SNRs) stratified from this study and the studies on the coastal B . C 58 3.17. Means of foliar macronutrient concentrations i n the study stands stratified according to soil nutrient regimes (SNRs). Symbols i n colimms are: a -adequate, nd - no deficiency; smd - slight-moderate deficiency, sd - severe deficiency 61 3.18. Regression models based on foliar nitrogen dry mass (fNw) and soil mineralizable nitrogen (mN) 62 3.19. Synopsis and differentiating characteristics of the site associations distinguished i n the study plots 68 3.20. Means of selected climatic, soil, and stand characteristics of the distinguished site associations (SAs) 69 3.21. Mult ivar iate statistics and F approximations for testing group means i n the canonical discriminant analysis of 11 site associations (SA) vmder HO: a l l group means i n the population are equal 72 4.1 Synopsis of the ecological variables stratified according to origin, mode, and expression (categorical variables are i n normal face, continuous variables are i n i ta l i c face) 79 4.2 Synopsis of the general forms of categorical models used to test the relationships between lodgepole pine site index and selected ecological variables. SI is site index (m @ 50 years of breast height age) 81 4.3 Synopsis of the general forms of analytical models used to test the relationships between lodgepole pine site index and selected ecological variables. SI is site index (m @ 50 years of breast height age) 82 4.4. Models for the regression of lodgepole pine site index on selected vegetation variables 88 4.5. Categorical models for the regression of lodgepole pine site index on selected environmental variables (n = 72) 92 4.6. Anal j^ ica l models for the regression of lodgepole pine site index on selected environmental variables (n = 72) 97 5.1. Synopsis of the ecological variables used i n the height growth models a n d stratified according to expression (categorical or continuous) 118 5.2. A summary of average height growth curves for each ofthe 40 sample plots. 122 5.3. Testing for site index i n relation to the parameters estimated for the Chapman-Richards function using regressions w i t h site imits as dummy variables. Site vmits were defined i n Table 5.6 126 5.4. Coefficients of determination (R^) and standard errors of estimation ( S E E ) from p£irameter prediction models for ecological variables ( N = 40) 130 5.5. Comparisons of parameter predictions for b j , and b3 based on site index, site series, and ecotopes ( N = 40) 131 5.6. Parameter prediction equations for hi, b2, and b3 based on site tmits ( S U p ( N = 38) 133 5.7. Comparisons of parameter prediction equations for site series, ecotope, and site imi t height growth models 134 5.8. Height growth parameters computed for site un i t height growth model [5.4.15] using equations [5.4.12], [5.4.13], and [5.4.14] 136 5.9. Lodgepole pine height growth by site units based on equation [5.4.15] and parameters given i n Table 5.8 137 5.10. Comparisons of lodgepole pine height growth predicted by the site uni t and ecotope models based on equations [5.4.11] and [5.4.15] and parameters given i n Tables 5.8 and 5.12 140 5.11. Height growrth parameters computed for the site series height growth model us ing equations [5.4.4], [5.4.5], and [5.4.6] 142 5.12. Height growth parameters computed for the ecotope height growth model us ing equations [5.4.7], [5.4.8], and [5.4.9] 143 5.13. Comparisons between lodgepole pine site index estimated using equation [5,3.3] w i t h parameters calculated from site index equations [5.4.1], [5.4.2], and [5.4.3], and the height corresponding to the index age of 50 years. . . 145 5.14. Cumulat ive growth (H), o i r rent annual increment (CAI), and mean annual increment (MAI) for each site i in i t . Bo ld fonts indicate the total age of maximtun mean annual increment and its corresponding growth. Breast height age is i n parentheses 151 5.15. Residual einalysis based on equation [5.4.15] at 5-year intervals at breast height age for each stsind 154 5.16. Comparison of site index estimated from the site un i t model, Goudie's site index driven model, and measured site index 156 5.17. The physiological parameters derived from Chapman-Richards fimction for site units stratified according to climate, soil moisture, and soil nutrient. 160 A l . Site series, lodgepole pine height growth based on equation [5.4.10] and peirameters given i n Table 5.11 195 A 2 . Ecotope, lodgepole pine height growth based on equation [5.4.11] and parameters given i n Table 5.12 202 LIST O F F I G U R E S Figure Page 2.1. Locations of the three sampHng areas i n the S B P S and S B S zones of B r i t i s h Columbia 9 3.1. Scree plot of P C A eigenvalues on diagnostic species 30 3.2. Ordination of sample plots along the first two P C A axes on diagnostic species showing 70% confidence ellipsoids for each basic vegetation tmit. E a c h sample plot is represented by an alphabetical symbol that designates a vegetation uni t (Table 3.1) 32 3.3. Ordinations of vegetation units and climatic (a), soil moisture (b), and soil nitrogen indicator species groups (ISGs) as a fimction of the first two canonical variâtes determined by analysis of concentration. Symbols for vegetation units (A - J ) are defined i n Table 3.1; symbols for ISGs are explained i n the legend 39 3.4. Categorical plots showing means and standard deviations of (a) actual/potential évapotranspiration (^t^xaax^ ratio and (b) soil water deficit i n relation to soil moisture regimes (SMRs) 45 3.5. Ordination of the study plots as a fimction of the first two canonical variâtes determined by canonical discriminant analysis showing 75% confidence regions for soil moisture regime means. E a c h plot is represented by an alphabetical symbol that designates S M R : excessively dry (A), very dry (B), moderately dry (C), slightly dry (D), firesh (E), moist (F), very moist (G), wet (H), moderately dry-moist (I), s l ightly dry-very moist (J), and fi-esh-wet.. .48 3.6. Ordination of the study plots as a fimction of the first two canonical variâtes determined by canonical discriminant analysis showing 95% confidence regions for soil nutr ient regime (SNR) means. E a c h study plot is represented by an alphabetical symbol that designates soil nutrient group: A - very poor, B - poor, C - medium, D - r ich , and E - very r ich 54 3.7. Categorical plots showing means and standard deviations for (a) soil mineral izable-N (mN) (kg ha'-*^), (b) sum of exchangeable C a , K , and M g (kg ha"-'^), and (c) fi-equency of nitrophytic species (FNj'rR39j,) i n relation to soil nutrient regimes (SNRs) 56 3.8. Scattergremi and regression of forest floor mineral izable-N (kg ha'-'^) against fi*equency of nitrophytic plants (FNITR3%) 60 3.9. Scattergram and regression of forest floor mineral izable -N (kg ha'-'^) against foliar N (mg/100 needles) us ing equation [3,3.4] 63 3.10. Ordinat ion ofthe study stands as a function ofthe first pair of soil and foliar nutrients canonical variâtes determined by canonical correlation analysis. E a c h study plot is represented by an alphabetical S3nnbol that designates SI»fR: A - very poor, B - poor, C - medium, D - r i ch , and E - very r i ch 65 3.11, A n environmenteJ chart showing the site associations distinguished i n the study plots i n relation to biogeoclimatic subzones, relative (Arabic mmibers) and actual soil moisture regimes, and soil nutr ient regimes 71 3.12, Ordinat ion of the study plots as a function of the first tv^o canonical variâtes determined by canonical discriminant analysis on selected environmental variables. E a c h study plot is represented by a n alphabetical symbol that designates site association (SA) 74 4.1, Categorical plot of lodgepole pine site index i n relation to soil nutrient regimes (SNRs) 85 4.2, Categorical plot of lodgepole pine site index i n relation to soil moisture regimes (SMRs) 86 4.3, Categorical plot of lodgepole pine site index i n relation to site associations (SAi) 87 4.4, Relationship between estimated ( V U model, equation [1]) and measxired lodgepole pine site index values and probability plot of residuals fi:om regression analysis 89 4.5, Relationship between estimated (LAI model, equation [15]) and measured lodgepole pine site index vedues and probability plot of residuals fi-om regression analysis 90 4.6, Relationship between estimated ((1) B G C model [2], (2) S N R model [4], and (3) S M R model [3]) and measured lodgepole pine site index values and probability plot of residuals from regression analysis 93 4.7, Relationship between estimated (combined B G C , S M R , and S N R model [10]) and measured lodgepole pine site index values and probability plot of residuals fi-om regression angJysis 94 4.8, Relationship between estimated (model [6]) and measiu-ed lodgepole pine site index values and probability plot of residuals fi*om regression analys is , . . 95 4.9, Relationship between estimated ( P E T model [16], D G W model [17], and m N model [18]) and measured lodgepole pine site index values and probability plot of residuals fi-om regression analyses 98 4.10. Relationship between estimated (combined P E T , D G W , and m N mode [27]) and measxired lodgepole pine site index values and probability plot of residuals from regression anedysis 100 4.11. Response surface showing the relation between estimated lodgepole pine site index, soil moisture regime, and soil nutrient regime i n the SBPSxc subzone using equation [10] 103 4.12. Response surface showing the relation between estimated lodgepole pine site index, soil moisture regime, and soil nutrient regime i n the SBSmc subzone using equation [10] 104 4.13. Response surface showing the relation between estimated lodgepole pine site index, soil moisture regime, and soil nutrient regime i n the S B S w k subzone using equation [10] 105 4.14. A n edatopic grid showing S B P S x c site series (1, 2, 3, 10, and 13) and lodgepole pine site index isolines calculated from equation [10] and fitted using a distance weighted least squares smoothing algorithm 107 4.15. A n edatopic grid showing S B S m c site series (4, 6, 8, 11, and 14) and lodgepole pine site index isoUnes calculated from equation [10] and fitted using a distance weighted least squares smoothing algorithm 108 4.16. A n edatopic grid showing S B S w k site series (5, 7, 9, 12, and 15) and lodgepole pine site index isolines calculated from equation [10] and fitted using a distance weighted least squares smoothing algorithm 109 5.1. Relationships between site index and nvmiber of stems per hectare for each stand and site series, and according to biogeoclimatic subzones 124 5.2 Height growth curves for (A) cl imatically different and edaphically s imilar sites series and (B) c l imatically s imi lar and edaphically different site series.. 128 5.3. Lodgepole pine height growth curves by site imits based on equation [5.4.15] and parameters given i n Table 5.8 139 5.4. Comparison of site un i t and ecotope, lodgepole pine height growth curves based on equations [5.4.15] and [5.4.11] 141 5.5 Lodgepole pine height growth ctirves derived by using site index i n parameter prediction equations ([5.4.1], [5.4.2], and [5.4.3]) 146 5.6. The plot of estimated current annual increments (CAE) for site imits stratified according to biogeoclimatic subzones 148 5.7. The plot of estimated mean emnual increments (MAI) for site imits stratified according to biogeoclimatic subzone 149 5.8. The plot of estimated current annual increments (CAI) and mean annual increments (MAI) for site imits 150 5.9. Relationships between measured and estimated heights for site i m i t s . . . . 153 5.10. Comparison between site imi t (solid lines) and Goudie's (dotted lines) height growth curves 157 A l . Site series, lodgepole pine height growth curves based on equation [5.4.10] and parameters given i n Table 5.11 198 A2 . Site series, lodgepole pine height growth curves for S B P S x c subzone based on equation [5.4.10] and parameters given i n Table 5.11 199 A 3 . Site series, lodgepole pine height growth curves for S B S m c subzone based on equation [5.4.10] and parameters given i n Table 5.11 200 A4 . Site series, lodgepole pine height growth curves for S B S w k subzone based on equation [5.4.10] and psirameters given i n Table 5.11 201 A 5 . Ecotope, lodgepole pine height growth curves for S B P S x c subzone based on equation [5.4.11] and parameters given i n Table 5.12 205 A6 . Ecotope, lodgepole pine height growth cim^es for S B S m c subzone based on equation [5.4.11] and parameters given i n Table 5.12 206 A7 . Ecotope, lodgepole pine height growth curves for S B S w k subzone based on equation [5.4.11] and parameters given i n Table 5.12 207 A C K N O W L E D G M E N T S I a m very grateful to D r . K . K l i n k a for the guidance and support through a l l stages of the study. I thank the members of my supervisory committee, D r . T . M . Ba l lard , Department of Soi l Science, D r . G . E . Bradfield, Department of Botany, £md Dr . P . L . M a r s h a l l , Forest Resource Management Department, for advice and comments on the earlier draft of the thesis. Appreciation is also expressed to P . Bemardy , D.S. M c L e n n a n , D . Nevr, J . A . P . Newmann, G . Wang, and H . J . Wi l l iams for assistance i n collecting field data, to R . E . Carter , my research colleague, and G . J . K a y a h a r a , my fellow graduate student, for their advice i n general, and to D r . T .A. Black (Department of Soi l Science, Univers i ty of B r i t i s h Columbia) for his valuable comments on the use of the Energy/Soi l L i m i t e d water balance model. F inanc ia l support for the study was provided by the B r i t i s h Col imibia M i n i s t r y of Forests, and the Nat ional Science and Engineering Research Counci l of Canada. This support i s gratefully acknowledged. 1. G E N E R A L I N T R O D U C T I O N Lodgepole pine (Pinus conforta Dougl. ex Loud.) is the most widely distributed coniferous tree species i n western N o r t h America (Wheeler and Critchfield 1985). Its distribution extends approximately from 64° N latitude and 1440 w longitude i n the Y u k o n Territory to 31° N latitude i n B a j a Cal i fornia and 105° W longitude i n South Dakota (Bums and Honka la 1991). Lodgepole pine is a major t imber species—cranking second i n volimae among tree species harvested i n B r i t i s h Col imibia and Alberta , exceeded only by spruce (Kennedy 1985). I n this wide geographical range, lodgepole pine grows under a wide variety of ecological conditions both i n extensive, pure stands and i n association w i t h many other conifers ( B u m s and H o n k a l a 1991). It is one of a few tree species w i t h a remarkably wide climatic and edaphic amplitude (Kraj ina 1969). In view of lodgepole pine's importance for timber production, i t is important to know the relationships between its growth performance and site conditions. Gr ier et al. (1989) recommended systematic quantitative research into relationships between forest productivity and both extrinsic and intr insic site factors. Th i s dissertation focusses on the relationships between height growth and ecological site quality i n order to establish a stronger l i n k between the provincial system of biogeoclimatic ecosystem classification (BEC) and growth and yield studies. The l imited quantitative information on how site conditions affect forest growth constitutes an imfortimate void i n the ecology of trees species and forest management of B r i t i s h Columbia. Two major theses were adopted: (1) Soxind forest management reqmres an ecological basis and ecosystem-specific approach. This is necessary because each tree species is adapted to a certain range of ecological conditions; therefore each species w i l l grow a n d behave i n ways that depend on the ecosystems or sites i n which i t grows ( K l i n k a and Fel ler 1984). Understanding ecosystems means imderstemding the ecological basis of productivity (Van Dyne 1969). (2) The application of an ecosystem-specific approach reqviires that a forest, which consists of many different ecosystems, be stratif ied into ecologically uniform segments. When i t is stratified, management of that forest can be simplified and, at the semie time, given a soimd ecological foundation ( K l i n k a et al. 1990b), A consistent and ecologically meaningful stratification requires, i n t u r n , an appropriate ecological classification system. If the B E C system is an appropriate ecological classification system, then i t should y ie ld a useful means for explaining the variat ion i n growth performance of different tree species on different forest sites. I f this assxmiption can be convincingly confirmed, then this study w i l l provide pr inc ipal evidence of the usefiilness of the B E C system to forest research and management. Ecosystem studies carried out i n B r i t i s h Colmnbia by K r a j i n a and his students resulted i n the development of the biogeoclimatic ecosystem classification (BEC) system. The B . C . Forest Service adopted this system, and i n the past decade, the B E C system has become entrenched i n forest research and management as a means of recognizing different types of forest sites and of cheu-acterizing their ecological quality (e.g., K r a j i n a 1972, K i m m i n s 1977, Pojar et al. 1987, K l i n k a et al. 1990b, Meidinger and Pojar 1991). In a l l forest site-productivity studies, the question at once arises as to what is the concept and definition of site, and on what basis are site data to be evaluated i n order to clarify site-productivity relationships. The B E C system considers site (habitat or ecotope) to be the physical environment (climate, topography, and soil) of a geographically circtmascribed ecosystem, and organizes ecosystems into environmentally characterized classes (Pojar et al. 1987). This implies the recognition of environmentally different kinds (types) of sites, each wi th different ecological conditions or quality for plant growth. Thus, from the ecological perspective, the extrinsic and intr insic environmental factors affecting the biotic commvmity of an ecosystem define quality of a site (e.g., Daubenmire 1968, D a n i e l et al. 1979, Spurr and Barnes 1980, Gr ier et al. 1989). Whi le i t i s fairly easy to work w i t h ind iv idual environmental factors, i t is very difficult to determine their integrated effect on plants due to compensating effects (Bakuzis 1969, D a m m a n 1979, Assmann 1970, Ol iver and Larson 1990). A s a result, sites w i th different combinations of environmental factors can have s imi lar ecological qualities. To clarify plant-site relationships and to define ecological site quality, the B E C system uses the pr imary factors that have a direct £md major influence on plant establishment, survival , and growth: climate (light and temperature), soil moisture, soil nutrients, and soil aeration (e.g., Cajander 1926, Pogrebnyak 1930, H i l l s 1952, Major 1963, K r a j i n a 1969, Gr ier et al. 1989). To determine ecological quality of a site means to determine the expression or value of these pr imary factors on that site. As forest productivity is the consequence not the cause of ecological site quality, i t can not be a true measiire of ecological qual ity of the site (although i t can be considered an associated characteristic), and ecological site quality can not be a true measure of forest productivity. Forest productivity has alvrays been an essential consideration i n stand management, and site index has always been the most widely used measure of site quality, i.e., the inherent capacity of a site to support forest growth. It is recognized that site index is an indirect and incomplete measure of forest productivity (i.e., the growth performance of a tree species on a given site) or site productivity (i.e., the capacity of the site to support the growth of the species), as i t on ly indicates the height growth performance at a given po int In t ime (e.g., Jones 1969; Burger 1972, Carmean 1975,1982; Haggl imd 1981; S p u r r a n d B a r n e s 1981; Clutter et al. 1983; Monserud 1984,1988). As this study investigates only how height growth changes w i t h ecological site quality, site index was adopted as the measure of lodgepole pine growth performance on ecologicedly different sites. The most prevalent restriction i n us ing site index to estimate height growth is that i t must be estimated from trees whose height growth has not been affected by anything other than the factors constituting ecological quality of the site. The top height concept (i.e., using only dominant trees of the stand that have been l ikely dominant throughout the life of the stand) has been widely accepted as a reasonable measure of height for site index (op. cit.) and a better measure of site quality t h a n diameter or total volume growth (Oliver and Larson 1990). The goal of the research carried out i n this study was to answer two questions for immature lodgepole pine stands growing i n the Sub-boreal P i n e -Spruce (SBPS) and Sub-boreal Spruce (SBS) zones of central B r i t i s h Col iunbia: (1) H o w does height growth change w i t h ecological site quaUty? and (2) What is the strength of the relationships between the measures of ecological site quality and height growiih? Specific objectives of this ecological investigation were: (a) to locate study stands along climatic and edaphic gradients w i t h i n the montane boreal region of central B r i t i s h Colxmibia; (b) to obtain qualitative and quantitative climatic, soil , imderstory vegetation, and stand data for characterizing plant commimities, soil moisture and nutr ient regimes, ecological site quality, foliar nutrients, and height growth ofthe study stands; (c) to stratify and classify the study stands according to their vegetation and ecological site quality; (d) to develop regression models that use categoriced or continuous measures of ecological site quality, for the prediction of site index; (e) to specify a height growth model, which uses categorical or continuous measures of ecological site quality, for the prediction of site index and for the prediction of height growth. The dissertation is comprised of six chapters. Chapter 1 gives the general introduction and Chapter 2 describes the study area. Chapter 3 through 5 each include introduction, materials and methods, results and discussion, and conclusions sections. These three chapters are related, but also independent of each other. Ecological analysis of the study sites is reported i n Chapter 3 which lays a foimdation for the central part of this dissertation—Chapter 4 investigating the relationships between lodgepole pine site index and measures of ecological site quality, and Chapter 5 i n which stem analysis data are combined w i t h the most useful measures of ecological site quality i n the three-parameter Chapman-Richards growth function to derive and evaluate site-specific height growth models. Conclusions are given i n Chapter 6. 2 . T H E S T U D Y A R E A The study area is situated i n the central interior of B r i t i s h Columbia between 52-55^ N latitude and 123-1250 W longitude. Physiographically, the area occurs w i t h i n the Interior P lateau (Holland 1976), and climatically, w i th in the Sub-boreal Spruce (SBS) and Sub-boreal Pine—Spruce (SBPS) zones (B.C. M i n . For . 1988, Meidinger and Pojar 1991). The study plots were distributed i n three distinct segments of a regional cl imatic gradient (biogeoclimatic subzones) based on precipitation and temperature (Table 2.1) and i n three widely separated sampling areas: south of A n a h i m L a k e , north of B u m s Lake , and east and southeast of Prince George (along Bowron River and Wi l low Roads) (Figure 2.1). The A n a h i m Lake area lies w i t h i n the V e r y D r y and Cold S B P S subzone (SBPSxc) , the B u m s Lake area w i t h i n the Mois t and Cold S B S subzone (SBSmc), and the Prince George area w i th in the Wet and Cool S B S subzone (SBSwk) (Meidinger and Pojar 1991). The Interior P lateau ranges from 600 m to 1200 m above sea level and is covered w i t h glacial t i l l which usually bears a close association mineralogically w i th the underlying bedrock (Valentine and Dawson 1978). The predominant basic basalt lavas contribute to the high base saturation of many soils. The A n a h i m Lake area occurs on the gently ro l l ing Fraser P lateau formed pr imar i ly by basaltic lava flows. The Bxims Lake area is wi th in the low relief Nechako P lateau which was also formed from lava flows covering older volcanic and sedimentary rocks, w i th a few granitic intrusions (Pojar et al. 1984, Meidinger and Pojar 1991). The Bowron River and the Wil low Road sampling areas are located on a large and deep glaciofluvial deposit i n the eastem comer of the Fraser Bas in . Table 2.1. Selected climatic characteristics for the study area». Subzone Samphng area SBPSxcb Anahim Lake SBSmc Bums Lake SBSwk Prince CJeorge Climatic station Elevation (m) Anahim Lake Kleena Kleene 1097 (899) Bums Lake Topley Landing 704 (722) Aleza Lake 625 Mean annual precipitation (mm) 305 492 897 Mean annual snowfall (%MAP) 49 48 38 Mean precipitation May-Sept, (mm) 118 221 353 Mean precipitation ofthe driest summer month (mm) 15.5 32.8 54.7 Mean precipitation of the wettest winter month (mm) 36.4 54.8 97.8 Mean annual temperature (^ 'C) 0.4 2.4 3.0 Mean temperature of the warmest month (°C) 1L4 14.0 15.3 Mean temperature ofthe coldest month («C) -13.7 -12.9 -12.9 Potential évapotranspir-ation (mm/year)c 411 439 460 Heat indexe 13.4 18.5 2L5 Index of continentalityc 36.9 34.4 38.8 «Climatic data are from Canadian Climate Normals 1951-1980 (Environm. Canada). ''SBPSxc - Very Dry and Cold SBPS subzone, SBSmc - Moist and Cold SBS subzone, and SBSwk -Wet and Cool SBS subzone. •^Calculated from Canadian Chmate Normals using methods described in Chapter 3. The S B S Eind S B P S zones are parts of the Canadian Boreal Forest region which is a part of Microthermal Coniferous formation (Kraj ina 1969, 1972). The climate of both zones is montane boreal (Dfc, Koppen i n Trewartha 1968). It can be best described as drier ( in the S B P S zone) to wetter ( in the S B S zone), continental (warm summer and cold winter), w i t h a short growing season, less precipitation i n spring than i n siunmer, autiman, and winter, frequent cloudiness, and l ight (in the S B P S zone) to heavy (in the S B S zone) snow cover. In comparison to a tj^jical boreal climate, sub-boreal climate is sl ightly less continental or polar/arctic, thus slightly warmer i n January and cooler i n J u l y . Consequently, sub-boreal winters are shorter and the growing season slightly longer w i t h a smaller loss of water due to the lower évapotranspiration than i n the typical boreal climate (Kraj ina 1969). A s a result of favorable cUmatic characteristics, forest productivity i n the S B S zone is higher than i n the S B P S zone, which is located i n the r a i n shelter of the coastal movmtains. Boreal White and Black Spruce (BWBS) zone, which is located at higher latitudes, and subalpine boreal Engelman Spruce-Subalpine F i r (ESSF) zone, which is located at higher altitudes. Major tree species i n the prevail ing upland coniferous forest i n the S B S and S B P S zones include: lodgepole pine, white spruce {Picea glauca Moench), subalpine fir (Abies lasiocarpa Hook.), and black cottonwood (Populus trichocarpa Torr. et Gray ex Hook.); minor tree species are: black spruce [Picea mariana (Mil l . ) B.S.P.] , trembling aspen (Populus tremuloides Michx.) , paper b irch (Betula papyrifera Marsh. ) , and Engelmann spruce (Picea engelmannii P a r r y ex Engelm.) (Hosie 1979). Due to the fi-equent occurrence of forest fires, a large area of the S B S and S B P S zones is occupied by pure, even-aged lodgepole pine and trembl ing aspen stands i n various stages of secondary succession. There is a general tendency for lodgepole pine to dominate early serai forests on coarse-textured and acidic soils. I n the S B S zone, the old-growth forests are dominated by white spruce, but may contain significant amounts of lodgepole pine on drier sites and subalpine fir on wetter sites (Pojar et al. 1984). In the S B P S zone, due to a drier climate, lodgepole pine appears to be more shade-tolerant than i n the S B S zone, and constitutes a significant component i n a few scattered old-growth forests. Old-growth forests on zonal sites are dominated by white spruce and/or i ts hybrids, w i t h a significant proportion of lodgepole pine i n the S B P S zone. Poorly to moderately developed shrub and herb layers typically contain Arctostaphylos uva-ursi, Rosa acicularis, Shepherdia canadensis, and Spiraea betulifolia etc, (in the S B P S zone), Vaccinium caespitosum, V. membranaceum, V. myrtiloides, Amelancher alnifolia, Sorbus scopulina, Cornus canadensis, and Arnica cordifolia etc, ( in the S B S zone), Hylocomium splendens, Pleurozium schreberi, Ptilium crista-castrensis, Dicranum polysetum (in the S B S zone), and Cladonia spp. ( in the S B P S zone) are the major species i n the moderately to wel l developed moss and l ichen layers. T i l l , lacustrine, and fluvial materials derived from volcanic (less often granitic) rocks are the most common soil parent materials. The soils formed fi-om the t i l l and lacustrine materials on zonal sites are typically moderately deep, loamy-skeletal, weakly acidic Gray Luvisols , less fi-equently Brunisols and Podzols (Agric. C a n . Expert Committee on Soil Survey 1987) w i th t h i n and poorly decomposed forest floors (Valentine 1978), or poorly developed Mors ( K l i n k a et al. 1981). The presence of a fine-textured and angular blocky B t horizon at the 30 to 50 cm depth, i n which clay has been accumulated, tends to restrict drainage, permeability, and aeration characteristics of the soils (Pojar et al. 1984). As a result, these soils become extremely wet i n the spring causing root mortal ity and inducing a shallow rooting pattern. The soil formed from the fluvioglacial materials on zonal sites are basically deep, sandy-skeletal, more acidic Dystr ic Bnmiso ls or Podzols due to more effective precipitation and intensive leaching of bases wi th a bleached sandy Ae horizon and better developed M o r or Moder hvunus forms (op. cit.). The occurrence of the coarse-textured sandy soils leads to good permeability, drainage, and aeration of the soils, therefore, causing a deeper rooting system. Nevertheless, leaching of bases is intense i n these soils. Organic materials have also been found i n depressions and water-receiving sites. 3. E C O L O G I C A L ANALYSIS O F T H E S T U D Y E C O S Y S T E M S 3.1 I N T R O D U C T I O N Apply ing the ecosystem concept to forest management and research requires that a forest be ecologicedly stratified i n order to determine the k i n d and pattern of component ecosystems. Ecological stratification implies identification, description, and mapping of ecosystems which must be based on taxonomic classification and carried out effectively and consistently. The ecological stratification also implies that recognized strata or units reflect and clarify to the greatest extent vegetation-environment relationships (Kraj ina 1965a). The most pervasive ecological classification i n western Canada is a biogeocHmatic ecosystem classification, adapted by the B r i t i s h Columbia Forest Service from the pioneering work by V . J . K r a j i n a and his students (e.g., K r a j i n a 1965b, 1969; Pojar 1983, 1985; Pojar et al. 1986, 1987; K l i n k a and K r a j i n a 1986; Green et al. 1989; Meidinger and Pojar 1991). This classification (also referred to as the B E C system) results from an analysis and synthesis of vegetation, climate, and soil data. The approach to classification is hierarchical , w i th three interrelated levels of integration: local, regional, and chronological. The multiple-category vegetation and site classifications organize local ecosystems, the multiple-cateory zonal classification organizes regional ecosystems, and, us ing the framework of the site classification, the vegetation classification deals w i t h vegetation dynamics. The product of any multiple-category taxonomic classification are classes, units , or taxa which were distinguished by using a chosen set of differentiating characteristics and arranging them into a hierarchy. If the vegetation, zonal, and site classifications of the B E C system eire t ru ly ecological, then differentiating characteristics or classes produced by each of the component classifications should express and signify certain kinds of vegetation-environment relationships. In consequence, the major theme of the study described i n this chapter was to carry out ecosystem classification using the methods and system of biogeoclimatic ecosystem classification, and to demonstrate the ecological relationships discovered or integrated by the result ing classifications. In further chapters, the differentiating characteristics applied, and the classes produced, w i l l be used to establish the l i n k to forest productivity. The classes produced by the vegetation classification represent floristically imiform classes of plant coromunities i n the sense of the Braim-Blanquet approach (1932), which is based on the floristic composition of the entire plant commvmity. This approach has been vridely used i n Etirope (e.g. Becking 1957; D a h l 1956; Poore 1955; Moore 1962), Soviet U n i o n (Sukachev 1964), C h i n a (Wu 1980), the U n i t e d States (Daumenmire 1952; 1968), and Canada (Kraj ina 1969). The approach identifies and uses species w i th relatively narrow ecological amplitudes as the basis for grouping (differentiation); such species are termed 'diagnostic', and a group of them constitute a 'diagnostic combination of species' (Pojar et al. 1987). The underlying assimaption is that diagnostic species provide, at the same time, floristically as wel l as ecologically uniform classes of ecosystems. Apar t from classification, some diagnostic species have been used for the direct indication of synoptic, and to a lesser degree, ind iv idual factors of ecological site quedity ( K l i n k a et al. 1989a, 1989b). The actual vegetation that develops on a particular site depends on and reflects the site, disturbance, chance, and time, whereas cl imax vegetation reflects principally the influence ofthe site. As this study analyzed mid-seral successional stages, their vegetation classification might have been confounded by the effects of disturbance and site factors. To deal w i t h temporary variations i n vegetation, the B E C system uses the vegetation of late-seral, near-climax, and chmax successional stages to develop site classification for organization of ecosystems into site imits on the basis of more or less stable environmental attributes and the concept of ecological equivalence. This principle implies that sites w i t h the same or equivalent properties have the same vegetation and productivity potential (Cajander 1926, 1949, Bakuz i s 1969, O d u m 1971). Considering physiological and ecological perspectives implic i t i n literatiu-e, and addressing the problem of environmental compensation (Assmann 1970), the site classification i n the B E C system employs three synoptic environmental factors w i th a direct and major influence on plant establishment, svirvival, and growth: climate (radiation, temperatvire, and precipitation), soil moisture, and soil nutrients (Pojar et al. 1987). Where appropriate, other environmental factors directly affecting vegetation development are included as differentiating characteristics. Independently fi*om classification, these factors have been used for direct indication of ecological site quality i n coastal B r i t i s h Col imibia ( K l i n k a et al. 1984,1989a; K l i n k a and Carter 1990). Therefore, to faciUtate the use of indicator plants and the direct assessment of the ecological qual ity of forest sites i n the study area, special attention was given to quantitative characterization and classification of soil moisture and nutr ient regimes. The m a i n objective of the research reported i n this chapter was to lay a foundation for investigating relations of lodgepole pine height growth to measures of ecological site quality (Chapters 4 and 5). Secondary objectives were to investigate (1) the usefiilness of the understory vegetation i n immature lodgepole pine stands i n site classification, (2) the applicability of the imderstory species as indicators of ecological site quality, (3) the usefiilness of minersdizable-N as an index of soil nutr ient availabil ity, and (4) vegetation-environmental relationships between the study plots. The objectives were accomplished by analyzing, synthesizing, and interpreting the vegetation and environmental data obtained from 72 sample plots using phytosociological and nimaerical techniques. 3.2 M A T E R I A L S A N D M E T H O D S 3.2.1 Sample Plots and Sampling The study plots were located i n three geographically disjxmct biogeoclimatic subzones: (1) V e r y D r y and Cold Sub-boreal Pine—Spruce (SBPSxc), (2) Moist and Cold Sub-boreal Spruce (SBSmc), and (3) Wet and Cool Sub-boreal Spruce (SBSwk), each representing a distinct segment of a regional, montane boreal, climatic gradient (B .C. M i n . For. 1988; Meidinger and Pojar 1991) (Figure 2.1; Table 2.1). A l l sample plots used i n the study were located i n even-aged (30 to 80 years), unmanaged, natura l ly established, lodgepole pine-dominated stands, which were imiformly and f i i l ly stocked, but not overstocked (60% to 95% tree canopy cover, exceptionally < 50% on wet sites), and which were free of disturbance and damage. These conditions provide the best estimation of site index at a given index age of 50 years (Fries 1978, Clutter et al. 1983). In each sampling area, sample plots were selected across the widest possible range of soil moisture and nutrient gradients (Harrington 1986, Verbyla and Fisher 1989). Soi l moisture regimes were estimated i n the field us ing selected topographic and soil properties and indicator plant species follovdng the methods described by K l i n k a et al. (1984, 1989b). In each study stand, a 400 m^ (0.04 ha) sample plot was subjectively selected (Orlôd 1988) to represent an ecosystem relatively uniform i n topography, soil, understory vegetation, and stand characteristics. O f the 72 plots was used i n the study — 18 SBPSxc plots were located south of A n a h i m Lake , 18 S B S m c plots north of Bxu-ns Lake , and 36 S B S w k plots east and southeast of Prince George. Site descriptions for each plot included measurements or identification of elevation, slope position, slope aspect, slope gradient, bedrock geology, and soil parent material . The vegetation description followed the procedure outlined by Walsmley et al. (1980) and Luttmerd ing et al. (1990), inc luding identification of a l l vascular plants, mosses, liverworts, and lichens and estimation of species cover by percentage or significance values according to the A (tree), B (shrub), C (fern, herb, emd graminoid), and D (moss and lichen) layers. The Domin-Kra j ina scale (Kraj ina 1933 cited by Mueller-Dombois and EUenberg 1974) was used to estimate species significance. Species nomenclature followed Hitchcock and Cronquist (1973) for vascular plants, Ireland et al. (1980) for mosses, Stotler and Crandall-Stotler (1977) for liverworts, and Hale and Curberson (1970) and V i t t et al. (1988) for lichens. A complete checklist of plant species on the study ecosystems is given i n Appendix I. Four domingmt trees w i th no obvious evidence of abnormal growth performance i n each plot were measured for breast height age, us ing an increment bore, and top height, using a Suunto clinometer. Site index of each sample plot was then determined using appropriate tables for lodgepole pine (Goudie 1984). In each sample plot, four sample points were systematically located i n each quadrant and soil pits were dug down to the root-restricting layer (highly compacted B t horizon or water table), or to a depth of 1 m fi:om groxmd surface i f the restricting layer was absent. The forest floor emd minergJ soil were described and identified according to K l i n k a et al. (1981) and Agriculture Canada Expert Committee on Soi l Survey (1987), respectively. The major rooting depth, the depth of water table, gleyed horizon, or other restricting layers were recorded. Four forest floor samples were taken as close as possible on each side of the soil pit and composited for chemical analysis; s imilarly , mineral soil for chemical analysis was seimpled on each side of the soil pit to a depth of 30 cm, or less i f a root restrict ing layer was present, and composited. Projected leaf area index (LAI) was estimated for 58 plots by converting canopy transmittance (QJ/QQ) using the Beer-Lambert law: [3.2.1] L A I = -hi(Qi/Qo)/k, where = photosynthetically active radiation below canopy; Q Q = photosynthetically active radiation above canopy. A n average of 50 sample points of Qi was taken on a systematic basis i n each plot using the Sunfleck Ceptometer (Model SF-80 , Decagon Devices, Inc., 1987). Q Q was measured using the same Ceptometer immediately before, during, and after the measurements for 40 plots, and measured continuously using the LI-1000 Datalogger (Li -Cor Inc. 1986) for the additional 18 plots. Measures were taken either imder clear sky or continuous cloud cover i n order to minimize variation i n both and Q Q . A l l data were measured from 10:00 am to 2:00 p m during the month of September. Cal ibrat ion for Qj from the Ceptometer and Q Q from the Datalogger was recently carried out ( H . Q ian , Department of Forest Sciences, Univers i ty of B r i t i s h Col imibia , pers. comm.). The Ceptometer measures (Qp were consistently 5-10% lower than the Datalogger measures (QQ), therefore, adjustment to the Qj was made; k = the l ight extinction coefficient and was calculated using the ellipsoidal leaf emgle distribution function (Campbell 1986, Carter et al. 1991): [3.2.2] k = ( X U l/tan28)(l^) 1.47 + 0.45X + 0.1223X2 - 0.013X3 + 0.000509X4 where 9 = the sun elevation angle and X = the ratio of horizontal to vertical semi-axes of the ellipsoid. The Beer-Lambert law assimies that the foliage is randomly distributed i n space and leaf incl ination angles are spherically distributed (Jarvis and Leverenz 1983); therefore, X was asstuned to have a value of 1. The sun elevation angles ranged from 56.3 to 68.4 degrees from vertical. The average corresponding value for k was calculated as 0.55, which falls just above the mid -point of the range of extinction coefficient reported for conifer canopies by Jarvis and Leverenz (1983). 3.2.2. Fo l i a r Nutr ient Analysis Fo l iar sampling and chemical analysis followed the gmdelines and procedure given by B a l l a r d and Carter (1986). In brief, the current year's foliage from the upper crown of fifteen dominant or codominant healthy trees on each of 54 plots was sampled i n early October using a shot gun. The analyses for total N , P , K , S, C a , M g , Fe , A l , M n , C u , Zn , B , available SO4 -S , and active Fe , were conducted by Pacific Soi l Analysis Inc., Vancouver, B . C . Both the concentration (dry-mass basis) and the total weight (mg) per 100 needles were used i n evaluating the nutrient status of each stand. 3.2.3. Soi l Physical and Chemical Analyses F r o m each soil pit , coarse fragments larger than 2.5 cm i n diameter were weighed and the pit dimensions were measured to determine total soil volume. Seventy-two forest floor samples for bulk density were collected by cutting out a small piece of forest floor, measuring its dimensions, and weighing its mass after oven-drjdng at 105^ C for 24 hours. Seventy-two minered soil samples for bulk density were determined by cutting out a core, measuring its volimae using a water replacement method after filling the result ing hole w i th a t h i n plastic bag and recording i ts mass after oven-drying at lOS^C for 24 hours. Subsequently, these bulk density samples were sieved and the total weight, and the weight of coarse fi-agments larger ihan 2 m m i n diameter, were recorded. The coarse firagment-fi*ee bulk density was then calculated using the following equation (Nuszdorfer 1981): [3.2.3] Db = ^ ^ ^ ^ ^ , ^<2 mm where = bulk density (kg/m^); (M<2 mm) ~ (naass of soil < 2 m m i n diameter) = (total dry mass of sampled soil) - (mass of the soil > 2 m m i n diameter); (V< 2 mm) - (volimie of the soil < 2 m m i n diameter) = (total voltraie of the sampled soil) - (volume of the soil > 2 m m i n diameter) which equals to the mass of soil ^ 2 m m i n diameter divided by 2.65 (kg/m^) (average solid particle density). Soi l particle size i n the < 2 m m fi-action was determined by the hydrometer method (Day 1965, Gee and Bauder 1986) using a < 2 m m soil suspension (50 g/L) i n disti l led water and sodiimi-hexametaphosphate ( H M P ) solution i n a 1 L sedimentation cylinder. The analysis was done by Pacific So i l Analysis Inc., Vancouver. After being air-dried to a constant mass, forest floor samples were ground using a Wi ley m i l l , and mineral soil samples were sieved through a 2-mm sieve to remove the coarse fi-agments larger than 2 m m i n diameter. Subsequent chemical analysis was carried out on the basis of the fine fi*action. A l l chemical analysis was ceirried out by Pacific Soi l Analysis Inc. Vancouver. The p H of the forest floor was determined using a 1:5 suspension i n dist i l led water and measured w i t h a p H meter (Peech 1965). M i n e r a l soil p H was measured wi th a p H meter us ing a 1:1 suspension i n dist i l led water. Total carbon (C^) was determined using a Leco Induction Fxxmace (Bremner and Tabatabai 1971). Tota l nitrogen (Nj.) of the mineral soil was determined by the semimicro-Kjeldahl digestion method (Bremner and Mulvaney 1982) followed by colorimetric analysis for N H 4 , us ing a Technicon Autoanalyzer (Anonymous 1976). Mineral izable nitrogen (mN) was measured using the anaerobic incubation procedure of W a r i n g and Bremner (1964), modified by Powers (1980). Exchangeable potassium (K) , magnesi imi (Mg), and calcium (Ca) were extracted using 1 M N H 4 O A C adjusted to p H 7 (Page 1982) and measured by atomic absorption spectrophotometry (Price 1978). M i n e r a l soil extractable phosphorus (Pg^) was determined using the extraction procedure of Mehl i ch (1978). The extractable sulphate-sulphur (S04-S)ex of the minera l soil was determined by ammonium acetate extraction (Bardsley and Lancaster 1965) and turbidimetry. Total nitrogen (N^) and total phosphorus (P|.) of the forest floor were determined using a modified Parkinson and A l l e n (1975) procedure. Total sulfur of the forest floor (S^) was determined using a F isher Sul fur Analyzer Model 475 (Lowe and Guthrie 1984). Soi l nutrient variables were expressed as concentrations on a dry mass basis and on a mass per uni t eirea basis. The mass per i m i t area conversion used bulk density (D^) corrected for coarse fi-agments content for both forest floor and mineral soil , and represented kilograms of nutrients per hectare (kg/ha) i n the forest floor and the surface 0-30 cm on average of mineral soil w i t h some exceptions (shallow soils). The formula that was used for both forest floor and mineral soils (see Nuszdorfer 1981) was: [3.2.4] Z ( k g h a - l ) = ( l - C F ) ( con<2mm 102 or 106 103g cm" where X (kg ha-l) = a nutrient mass i n k g per hectare; CF = fraction of coarse fragments on a voltmie basis; ^con<2mm = nutrient concentration i n the fine soil fraction (% or ppm); kg/lO^g = a conversion factor; Vg = volume of soil i n one hectare = (soil depth i n cm)(10^cm2 ha"^). The soil nutrient values obtained from chemical analysis were used as potential variables for characterizing soil nutrient gradient and for discr iminating between soil nutrient regimes following the approach described by Kabzems and K l i n k a (1987), and K U n k a et al. (1989b). 3.2.4. Soi l Moisture Analysis The mean monthly growing-season precipitation (mm), temperature (^C), and solëir radiation flux density (MJ/m^/day) for each subzone were obtained from the nesirest climatic station (Anonymous 1982) for calculation of the actual évapotranspiration and the annual water balance using the Energy /Soi l -Limited model of Spittlehouse and B lack (1981). The model was expressed as: where 6 = the average volumetric water content ofthe rooting zone [(mm)^ water/(mm)3 soil); P = precipitation (mm/day); E = évapotranspiration (mm/day); D = drainage from the rooting zone (mm/day); R = r u n off (mm/day) which is usual ly neglected for forested area on a flatter [3.2.5] ei = e i . i + ( P i - S i - D i - ^ i ) V C . landscape; = time intervals of one day; Ç = soil rooting depth (mm); i = 1, 2, , n (1 = the first day of the growing season, n = the last day of the growing season). The model, driven by solar radiation, temperature, and precipitation, uses soil rooting depth (mm), soil texture, and fi-action of soil coarse fragments (CF) to estimate available water storage c a p a c i t y T h e soil rooting depth i n mm was adjusted by using the equation as follows^: [3.2.6] the "adjusted" C = measured C( l - CF) Soil texture was used to estimate 5 parameters required by the model-^r the water content at field capacity (0niax)' water content at wi l t ing point (6niin)» water potential at a i r entry (\|/g), an empirical coefficient (m), and aeration porosity (63). Potential or energy l imited évapotranspiration (i^niax) actual or soil l imited évapotranspiration (E^) were calculated as monthly toteds during the growing-season (May to September). Total growing-season water deficit (A^) was calculated as the s imi of ^^nax niinus for each month dviring the growing-season, i.e., [3.2.7] /^=^(E^^^-E,) , where m is the number of months i n the growing season. The ^max' ^ t ' \v depth of the soil water table and gleyed horizon were used to characterize actual soil moisture regimes for the study plots as suggested by K l i n k a et al. (1989b). ^Instructions to the computer program to calculate simple water balances by D. L . Spittlehouse, 1987. In addition to the Spittlehouse and Black method, the Thomthwaite (1948) procedure was also used for calculating potential évapotranspiration (PET) and heat index (HI). The Rose and Grant method (1976) was used for calcvdating the index of continentality (see Table 1.1). 3.2.5. Indicator P lant Species Analysis A computer-assisted spectral analysis (Emanuel 1987, Mueller-Dombois and EUenberg 1974; K l i n k a et al. 1989b) was carried out to characterize vegetation and site units and to determine the usefulness of indicator plants for inferring ecological site quality. The relative frequencies of indicator species for a given indicator species group (ISG) (e.g., very poor to poor, medimn, and r i ch to very rich) and a given site attribute (climate, soil moisture, or soil nitrogen) for each plot, or group of plots (imit) was calculated according to K l i n k a et al. (1989b) w i t h a correction: [3.2.8] Fjk = — 100 , 1=1 where Fj^^ = relative frequencies for a given I S G j and a given site attribute k; Z Cy]j = sum of midpoint percent cover value of species i (i = 1, 2, , m) for a given I S G j and a site attribute k; X = sum of midpoint percent cover value of species i (i = 1, 2, , n) for a given site attribute k. Frequency values were used to produce spectral histograms for each study plot, to £iid the interpretation of soil moisture and nutrient analysis, and to serve for further regression analysis. 3.2.6. Vegetation and Site Classification Study plots were classified according to the methods of biogeoclimatic ecosystem classification as described by Pojar et al. (1987). Vegetation classification was based on a tabtdar method (Mueller-Dombois and El lenberg 1974), diagnostic criteria proposed by Pojar et al. (1987), and a computerized tabl ing program (VTAB) (Ememuel 1987). The diagnostic species identified for the distinguished vegetation units were then used i n a principal components analysis (PCA) (Dillon and Goldstein 1984), for the purpose of (1) aiding i n the formation of floristically imiform groups of study plots, (2) obtaining ordination scores for diagnostic species, and (3) examining floristic affinities among the distinguished vegetation units. The P C A was performed using the S Y S T A T statistical package (Wilkinson 1990). Analys is of concentration (AOC) (Feoli and Orldci 1979; L a u s i and N i m i s 1985) was used to examine the relationships between the vegetation units and indicator plant species groups (ISGs). Site classification was based on climate (biogeoclimatic subzones), soil moisture regime, and soil nutrient regime determined for each study plot. A site association was only recognized when i t could be characterized by an exclusive combination of climate, soil moisture, and soil nutrients (i.e., when i t could be distinguished by an exclusive range of climate, soil moisture, and soil nutrient regimes). To delineate site associations, i t was further necessary to determine whether the distinguished basic vegetation units reflected differences i n ecological site quality. This examination was carried out i n a process of successive approximation (cf. Poore 1962). 3.2.7. Statist ical Analys is between Vegetation, S o i l , and Foliage Variables A l l data were summarized and analyzed using the S Y S T A T , S Y G R A P H (Wilkinson 1990), and S A S (SAS Institute Inc. 1985) statistical packages w i t h the aid of the Quattro Pro (Borland International, Inc. 1989) spreadsheet package on a I B M compatible personal computer. The M I D A S statistical package (Fox and Guire 1976) on the U B C mainframe computing system was also used for the analyses. Pr io r to statistical analysis, soil chemical variables and foliar nutrient variables used i n the angdyses were examined for normality using a probability plot (Chambers et al. 1983). Those variables that exhibited non-normality were logarithmically transformed and tested again. Variables that appeeired to have non-homogeneity of variance between groups i n discriminant analysis were handled using Smith's (1947) quadratic function (Dil lon and Goldstem 1984). Pr inc ipa l components anedysis (PCA) (Di l lon and Goldstem 1984) was used for vegetation ordination based on a reduced data base (diagnostic species) ( K l i n k a et al. 1990a). Cluster aneJysis (CA) (Sneath £md Sokal 1973) was used for pre-identifying imderljdng soil nutrient groups. Stepwise discriminant analysis (SDA) was used for variable selection. Canonical discriminant analysis (CDA) (Dillon and Goldstem 1984) was applied for finalizing soil moisture and soil nutrient groups. Relationships between vegetation, soil factors, and foliar nutrients were explored using canonical correlation analysis (CCA) (Gitt ins 1985; D i l l o n and Goldstem 1984) combined wi th P C A , which summarized the original variables into a small number of components. Regression analysis (Chatterjee and Price 1977) was used to examine the relationships between nitrophj^ic indicator species, soil nitrogen, and foliar nitrogen. 3.3. R E S U L T S A N D D I S C U S S I O N 3.3.1. Vegetation Classification and Indicator Plants A l l 72 sample plots were classified into a hierarchy of vegetation imits (plant alliEmces, associations, and subassodations) consisting of ten basic vegetation imits (six assodations and four subassodations) (Table 3.1). These ten units , each representing a mid-successional stage of lodgepole pine-dominated forest communities, were delineated according to the floristic differences (diagnostic combinations of spedes) between the groups of plots, and named by the generic names of the dominant plemt spedes (Tables 3.1 and 3.2). For the sake of brevity, 'Pinus' was omitted fi"om the name and only the generic names of diagnostic and/or dominant understory spedes were used; spedfic names were used only to prevent ambiguities. The classification produced implies that there are ten different ecological strata represented among the study plots using floristic criteria. The 71 diagnostic species summarized i n Table 3.2 were submitted to p r i n d p a l components analysis (PCA) to explore floristic affinities among the distinguished vegetation units and their relation to environmental gradients. The first two components extracted accounted for 38% of the total variance i n vegetation data, w i t h the first component accounting for 23% of the total variance and the first ten components accounting for 75% of the total variance (Table 3.3). A scree plot (Di l lon and Groldstem 1984) (Figure 3.1) also showed that the first ten components were good enough to explain the variat ion i n the data. The P C A results suggested the presence of structure i n the vegetation data and, i n conjunction w i t h environmental characteristics and indicator values (Tables 3.4, 3.5, and 3.6), the potential for evaluating environmental affinities between vegetation units . Ordination of plots on the first two P C A axes. Table 3,1. Synopsis of the vegetation units distinguished i n the study plots. P lant alliance P l a n t association P lant subassociation Stereocaulon Arctostaphylos Arctostaphylos-typic (A)^ Arctostaphylos-Shepherdia (B) Arnica (C) Empetrum Empetrum (D) Vaccinium Vaccinium myrtiloides (E) Vaccinium membranaceum (F) Ribes Ribes (G) Gymnocarpium Gymnocarpium-typic (H) Gymnocarpium-Equisetum (I) Sphagnum Sphagnum (J) ^ A n alphabetical symbol for a basic vegetation unit . Table 3.2. Diagnostic combinations for the plant alliances (all.), associations (a.), and subassodations (sa.) distinguished in the study plots. G H I < Vegetation unit Number of plots vegetation \init ^Diagnostic and species value 5 ? f I t 2presence class and %ean species significance Juniperus 'sibirica solid— - ' -stereoCAulon a l l . ArctosCaphyloB uva-ursi cladonia cornqta cladonia gracilis Stereocaulon tcmentoBum Arctostaphylos a, Arctostap • -  rr-^ — idago apathulata Arctoataphyloa-typic sa. Cetraria islandica Arcto3taphylo3-Shepherdia sa. Anyone multifida Aster ciliolatUB Carex concinnoide3 Ceratodon purpureus Cladonia gracilis Eguiaecum scirpoides Fragaria virginiana shepherdia canadensis Arnica a. Arnica cordifolia Calamagrostia canadensis Festuca Dccidentalis orthilia secunda , Spiraea betulifolia vaccinium membranaceum En^etram a l l . & a. Empetrum nigrum Eguisecum arvense Salix drummondiana Sanguiaorba canadensis Vaccinium a l l . Abies lasiocarpa Dicranum polysetum , Pieurorium schreberx sparaea betulifolia_ Vaccmiura myrtilloides Vaccinium myrtilloides a. Cladonia gracilis Maiantb&num canadense Rubus parviflorus Tsuga heterophylla Vaccinium membranaceum a. Amelanchier alnifolia Clintonia uniflora Geocaulon lividum Oryzopsis asperifolius Rubus pedatuB Sorbus scopulina Vaccinium caespitosum Vaccinium membranaceum viola orbiculata Ribes a l l . Lycopodium annotinum Ribes lacustre Ribes triste Ribes a. Arnica cordifolia Aster foliaceus Dicranum fuscescens Osmorhiza chilensis Vaccinium caespitosum Gymnocarpium a. Gymnocarpium dryopteria Rubus parviflorua Smilacina racemoaa Tiarella trifoliata viburnum edule Gymnocarpium-typic sa. Aralia nudicaulia Petasitea palmatua Polytrichum commune Populus tr&ouloidea Rhytidiadelphus triquetrua Rubua parviflorus Gymnocarpium-Equiaetum sa. Alnus sinuata Aster subspicatus , Athyrium filix-fmama Betula papyrxfera Dryopteris expansa Bauisetum palustre Galium triflorum Heracleum lanatum Sphagnum a l l . & a. Betula alandulosa Carex diapezToa Ledum groenlant,. Potentilla paluL Salix sitchensia Sphagnum nenoreum i^iraea douglaaii lUentaliB arctica dicum ' stria II + IV 2 II + I II I (d) I 3 1 d d ,d d r d,cl del ,d c) ,d d,c| d.o dâ) d,o) d,cd) a) i,c) ,od) III 1 + III + + III 1 III + I + 1 V 2 V 1 III + IV 2 III 2 3 V S IV II + V 2 III 1 V 1 IV 1 I + IV + 2 III 2 IV 3 III 3 III 1 II + I + I + II I II II III II I II 4 1 1 1 1 2 3 1 III III II I V IV I 1 4 2 III 1 V 1 I + II + V 4 III 3 '\ 1 II 1 I + IV 3 lY Î II + III 4 II + V 2 3 1 II + 1 2 III + II + 4 2 III 1 V 4 2 1 III 2 V 3 IV 1 I 3 I • 1 1 1 3 I 1 I + I + I + I + I II I II I II I I + II + II 3 I + IV 3 II 1 II I -f I 1 V II 2 + V 3 V I 3 + V II II + III 1 IV 1 IV 1 II 1 V 4 V 4 III IV 3 I + I II 3 V 6 III 2 III 2 II 1 I + \ Î II 1 IV 4 V 3 IV 3 V 4 II 2 I V 2 V 4 IV 2 IV 1 II + 2 V a V 8 V 6 V 5 IV 4 III 1 V V 4 III 1 IV 3 I + I V 6 V 5 I + III 1 I + I III 1 II + I + I I III 3 II 1 I + II 3 III 3 IV 4 III 1 I + II + II + IV 2 II 1 I + III 1 III 2 III 2 II 1 I 1 II 1 III 2 V 2 II + I + V 2 V 2 V 3 III 1 IV 2 IV 2 I + IV 3 II 1 II III 1 I + II + IV 1 I + I 1 IV + I + 1 IV 2 II 1 + III 1 I + V 5 V 6 II 1 V 4 I I 4 II + II + IV 1 tv 1 I + IV 1 rv 3 II + II 1 V 4 [V 3 I + I + V 3 II 3 II II + III + I II + 1 + I + III 2 V 2 II + I V 2 II 2 I 1 IV 3 II + I III 1 3 V 2 V 2 III 2 III I 1 III 3 II + II 2 IV 3 II 3 III I + I + 2 2 II 1 II 1 V 4 II 3 I + I + I 1 rv 2 II + I + IV 1 II 1 V 4 III 4 III 2 I 1 IV 4 II 2 I + III 3 IV 2 I + II 1 I + III 2 I + III 2 IV 3 IV 1 V 5 III 3 I II 1 IV 2 II + III 2 I + + IV 5 I -f III 2 + II + V III S 1 + I + II 1 III 4 + II 1 V 7 I 2 II 3 III 3 II + H I 1 noscic values: d - d i f f e r e n t i a l , dd - dominant: differential, cd - constant dominant, c - constant, ic - important Ispecie» diagnostic values: d companion (Pojar et a i . 1987). ^presence classes as percent o 70.d), 9 = 85.6 (70.1 - ioOl. 1.6 (1.1 - 2.1) 0), 8 = 60.0 (5( , 3 = .1 -Figure 3.1. Scree plot of P C A eigenvalues on diagnostic species. Table 3.3. The eigenvalues (A,) and ciunulative accounted-for variance of P C A applied to a covariance matrix w i th the diagnostic species significance values. Component X Cumulat ive % of total variance 1 34.49 22.9 2 22.08 37.5 3 14.96 47.4 4 10.24 54.2 5 7.46 59.2 6 6.61 63.6 7 5.41 67.2 8 4.46 70.1 9 4.02 72.8 10 3.81 75.3 w i t h 70% confidence elHpses superimposed for the ten vegetation units , portirays the m a i n s imi lar i ty relationships among the units (Figure 3.2). The study plots of a l l S B P S vegetation imits (A, B , and D and distinctly azonal C and J ) were scattered i n the left region of the ordination, while the majority of the S B S units occurred toward the right (Figure 3.2). Thus, the first P C A axis coincided w i t h a climatic gradient from relatively dry and cold (the S B P S subzone) to relatively wet and warm (the S B S w k subzone) montane boreal climate. W i t h the notable exception of Pleurozium schreberi, a l l positively correlated diagnostic species w i t h the first P C A component were either absent or occurred wi th a low fi*equency i n the S B P S x c subzone; the negatively correlated species (Arctostaphylos uva-ursi—group) occurred i n the S B P S x c subzone and, i n the S B S m c and S B S w k subzones, on azonal (driest or wettest) sites (Tables 3.2, 3.4, and 3.5, F igure 3.2). The second P C A axis represented a combined moisture and nutrient gradient: water-deficient and nitrogen-poor study plots [vegetation units A , B , C, D (in part), E , and F] occurred i n the lower region of the ordination, whereas the remaining plots [vegetation units D (in part), G , H , I, J , and K ] were scattered i n the upper region (Figure 3.2). The negatively correlated diagnostic species (Arctostaphylos uva-ursi—group) were typically indicators of very dry and nitrogen-poor sites, and the positively correlated diagnostic species (Ribes lacustre—group) were predominantly indicators of fi*esh to very moist and nitrogen-rich sites (KHnka et al. 1989b) (Tables 3.2, 3.3, and 3.6, Figures 3.2 and 3.3.). The P C A pointed out a few inconsistencies i n indicator values for some plants; for example, Vaccinium caespitosum, reportedly an indicator species of fi-esh to very moist on a poor site ( K l i n k a et a l . 1989b), exhibited a wide amplitude along a soil moisture gradient i n this study (Tables 3.2 and 3.5). -10 -10 - 4 2 8 14 First PCA component Figure 3.2. Ordination of sample plots along the first two P C A axes on diagnostic species showing 70% confidence ellipsoids for each basic vegetation \mit. Each sample plot is represented by an alphabetical symbol that designates a vegetation unit (Table 3.1). Table 3.4 Means of selected climatic, soil, ïind stand characteristics of the ten distinguished vegetation units. Symbols for vegetation units are given in Table 3.1. Vegetation unit A B C D E F G H I J Number of plots 5 7 9 5 9 8 8 6 8 7 Biogeoclimatic subzone SBPSxc SBPSxc SBSmc SBPSxc SBSwk SBSwk SBSmc SBSmc SBSmc SBSwk SBSwk SBSwk (mm/yr)l 101 W^max^ 0-42 Growing-season 140 water deficit (mm^) Depth of soil water table(w) na or gleyed horizon (g) (cm)^  Forest floor C/N 68 Mineral soil C/N 105 Forest floor & mineral 3.7 soUmN(kgha-l) Forest floor & mineral soil exchangeable Ca, Mg, andK(kgha-l) Measured site index 10.6 (m 9 50 years B.H.age) 119 194 205 217 0.50 0.79 0.86 0.93 120 52 33 16 4(^1 38^ 2 4382,w3 53 50 37 41 70 56 38 50 9.9 12.2 45.6 15.6 1330 4177 1510 6030 535 12.3 17.4 13.7 17.3 231 246 235 234 0.99 1.0 1.0 1.0 1.6 0 0 0 SBPSxc SBSmc SBSwk 246 1.0 0 na 48^2,wl 53g2,wl 44g4,w3 25"''^ 36 41 39 29 32 26 43 31 26 41 37.8 33.8 36.4 133 61.8 637 4149 2175 6608 3680 18.9 20.1 21.87 22.5 13.5 ^actual growing season évapotranspiration; ^actual growing seasson evapotranspiration/potential évapotranspiration ratio; ^number of plots used to calculate the mean value is given by a numerical superscript after g or w. Table 3.5. Diagnostic species correlated positively or negatively w i th the first P C A component and their edaphic indicator values (after K l i n k a et al. 1989b). Pearson Indicator value Indicator species correlation soil soil coefificient(r) moisture nitrogen Pleurozium schreberi 0.88 P Dicranum polysetum 0.87 MD-F P Vaccinium myrtiloides 0.84 MD-F P Vaccinium membranaceum 0.77 MD-F P Amelancher alnifolia 0.73 MD-F M Abies lasiocarpa 0.72 Sorbus scopulina 0.72 MD-F P Geocaulon lividum 0.62 P Viola orbiculata 0.60 MD-F M Spiraea betulifolia 0.57 VD-MD M Oryzopsis asperifolia 0.54 P Maianthemum canadense 0.52 P Rubuspedatus 0.49 F-VM P Clintonia uniflora 0.32 MD-F P Vaccinium caespitosum 0.31 F-VM P Arctostaphylos uva-ursi -0.53 VD-MD P Fragaria virginiana -0.39 M Calamagrostis canadensis -0.38 M-W M Solidago apathulata -0.38 VD-MD P Cladonia cornuta -0.38 ED-VD P Shepherdia canadensis -0.35 VD-MD M Sphagnum nemoreum -0.31 W-VW P Betula glandulosa -0.31 P Stereocaulon tomentosum -0.30 ED-VD P Empetrum nigrum -0.30 P Equisetum scirpoides -0.29 R Ledum groenlandicum -0.28 W-VW P Carex concinnoides -0.28 MD-F M Carex disperma -0.26 W-VW P Sanguisorba canadensis -0.25 VM-W Salix drummondiana -0.25 VM-W R Table 3.6. Diagnostic species correlated positively or negatively w i th the second P C A component and their edaphic indicator values (after K l i n k a et al. 1989b). Pearson Indicator value Indicator species correlation soil soil coefificient(r) moisture nitrogen Ribes lacustre Equisetum palustre Gymnocarpium dryopteris Tiarella trifoliata Ribes triste Galium triflorum Calamagrostis canadensis Viburnum edule Athylium filix-femina Aralia nudicaulis Petasites palmatus Smilacina racemosa Rubus parviflora Betula papyrifera Lycopodium annotinum Aster subspicatus Alnus sinuata Heracleum lanatum Rubus pedatus Polytrichum commune Spiraea douglasii Populus tremloides Dryopteris expansa Clintonia uniflora Rhytidiadelphus triquetrus Trientalis arctica Arctostaphylos uva-ursi Stereocaulon tomentosum Shepherdia canadensis Vaccinium caespitosum Cladonia cornuta Cladonia gracilis Solidago spathulata Spiraea betulifolia Juniperus sibirica 0.75 R 0.73 VM-W P 0.71 F-VM R 0.67 F-VM R 0.65 VM-W P 0.63 F-VM R 0.56 VM-W M 0.56 F-VM R 0.53 VM-W R 0.53 F-M R 0.52 VM-W R 0.52 R 0.51 R 0.50 0.43 MD-F M 0.42 VM-W R 0.40 F-VM R 0.40 F-VM R 0.39 F-VM P 0.38 F-VM P 0.37 VM-W M 0.37 F-VM R 0.34 F-VM R 0.33 MD-F M 0.33 F-VM M 0.29 W-VW P -0.53 VD-MD P -0.52 ED-VD P -0.46 VD-MD M -0.46 F-VM P -0.43 ED-VD P -0.39 ED-VD P -0.38 VD-MD P -0.37 VD-MD M -0.28 VD-MD M The results of the tabii lar comparison and P C A impl ied that diagnostic species and, i n consequence, vegetation imits have relatively narrow ecological amplitudes. To further explore the affinities of the vegetation units to their diagnostic combinations of species, an analysis of concentration (AOC) was carried out. The purpose of this analysis was to quantify relationships between the vegetation units and the diagnostic species grouped according to their cUmatic and edaphic indicator values ( K l i n k a et al. 1989b) (Table 3.7, Figure 3.3). The first and second canonical correlations (r) between the vegetation units and the climatic indicators were 0.35 and 0.31, respectively. Seventy-three percent of the total variance was explained by the first two canonical variâtes. The majority of vegetation units were clearly associated wi th the indicators of boreal and cool temperate climates. The Arctostaphylos-typic unit (A) showed a strong affinity to alpine tundra & boreal and cool temperate & semiarid climates, the Gymnocarpium-Equisetum uni t (I) showed a weak affinity to cool temperate & mesothermal and subalpine boreal & cool mesothermal climates, and the Sphagnum uni t (J) showed a weak affinity to a cool mesothermal climate (Tables 3.3 and 3.7, Figure 3.3). The vegetation imits showed a stronger relationship to soil moisture ISGs w i t h first and second canonical correlations of 0.75 and 0.47, respectively. Eighty-seven percent of the total variance was explained by the first and second variâtes. The Arctostaphylos-typic uni t (A) was strongly related to the indicators of excessively dry to very dry sites (suggestive of uniformity i n available soil moisture i n the study plots), whereas the Ribes uni t (G) was intermediate between the indicators of fresh to very moist and very moist to wet sites (suggestive of heterogeneity i n available soil moisture i n the study plots). Table 3.7. The eigenvalue (X), variance, and canonical correlation for the canonical variâtes obtained from analysis of concentration on the diagnostic species stratified according to their indicator values of climate, soil moisture and soil nitrogen into indicator species groups (ISGs). Canonical Eigenvalue variâtes (K) Percent variance Ciimulative variance Canonical correlation(r) Climatic ISGs 1 2 3 I 0.123 0.095 0.063 0.297 41.0 32.0 21.2 41.0 73.0 94.2 0.349 0.308 0.251 Soil moisture ISGs 1 2 3 I 0.563 0.223 0.098 0.902 62.4 24.7 10.9 62.4 87.1 98.0 0.750 0.472 0.313 SoU nitrogen ISGs 1 2 I 0.217 0.099 0.315 68.7 31.3 68.7 100.0 0.466 0.314 (a) (b) r 1 c i a i * * I 1 - I •• SBCU 0 j • a i 1 1 H T $ 1 e n » * • AUUB . 1 1 -6.0 -3.8 -1.6 0.6 ^8 F i r s t canonical variate 5.0 ZJ5 13 0J5 -QJ5 -1J5 -2J5 1 1 V tvi D 1 1 EVD 4 ! VDIID G rvu it B * r 1 1 I C U D F 1 1 -2.0 -1.1 -0J3 0.7 1.6 F i r s t canonical variate as (c) -0.7 --1.6 -1 •- I — \ FOOR T A 0 J . . " T • 1 B 1 • R K H C H E 1 ' SIUll B Legend: A - J v e g e t a t i o n u n i t s - 2 - 1 0 1 2 F i r s t Canonical Variate ISGs of c l i m a t i c regimes : A L T U - t u n d r a & boreal ; SBCM — s u b a l p i n e boreal & cool m e s o t h e r m a l ; B C r - m o n t a n e boreal & cool t e m p e r a t e ; CM - cool m e s o t h e r m a l ; CTCM - cool t e m p e r a t e k m e s o t h e r m a l ; CTCSA — cool t e m p e r a t e k s e m i a r i d . ISGs of soi l m o i s t u r e r e g i m e s : E V D - excessively d r y to v e r y d r y ; VDMD - v e r y d r y to m o d e r a t e l y d r y ; M D F - m o d e r a t e l y d r y t t o fresh ; F V M - f resh to v e r y m o i s t ; VMTf - v e r y m o i s t to wet; TfVW — wet to v e r y wet. ISGs of so i l n u t r i e n t regimes : POOR - v e r y poor to poor; M E D I U M - m e d i u m ; RICH — r i c h to v e r y r i c h . Figure 3.3. Ordinations of vegetation units and climatic (a), soil moisture (b), and soil nitrogen indicator species groups (ISGs) as a fimction of the first two canonical variâtes determined by analysis of concentration. Symbols for vegetation units (A -J) are defined i n Table 3.1.; symbols for ISGs are explained i n the legend. In relation to soil nitrogen ISGs, the first and second canonical correlations were 0.47 and 0.31, respectively. Almost 100% of the total variance was explained by the first and second variâtes. The Gymnocarpium-Equisetum unit (I) was very strongly related to the indicators of nitrogen-rich sites (suggestive of imiformity i n available soil nitrogen i n the study plots), whereas the Ribes unit , plotted close to the center of ordination, was intermediate between the indicators of nitrogen-poor and -r ich sites (suggestive of heterogeneity i n available soil nitrogen i n the study plots) (Tables 3.3 and 3.7, Figure 3.3). 3.3.2. Soi l Moisture Analysis In the B E C system, the soil moisture regime (SMR) is one of the basic components of ecological site quality and one of the differentiating characteristics used i n site classification (Pojar et al. 1987). Unambiguous characterization of soil moisture conditions for plant growth requires quantitative criteria which can then be used to divide a soil moisture gradient into ecologically meaningfii l regimes (classes). This study adopted the criteria proposed by K l i n k a et al. (1989b) for coastal B r i t i s h Columbia (Table 3.9), and used the Energy/Soi l -Limited model {equations [3.2.5], [3.2.6], and [3.2.7]} to calculate the annual water balances for each study plot. E a c h study plot was then assigned an appropriate actual S M R either according to the depth of growing season water table or depth of the gleyed soil horizon, or according to the value of the actual/potential évapotranspiration ratio (Et/Emax). The absence of either of the above cr iteria resulted i n the study plot being assigned to the fresh S M R (Table 3.10). K l i n k a and Carter (1990) pointed out several shortcomings using the soil water balance model of Spittlehouse and Black (1981) i n their study for coastal Douglas fir. One of the l imitations was that the monthly time-step of 30 year normals used i n the calcidations l ike ly resulted i n an underestimation of soil water deficit. In the present study, 30 year climate normals were also used since dai ly or annual data were not accessible at the time when the model was applied. Th i s might also have restilted i n some underestimation of soil water deficit for lodgepole pine stands. I n order to compare the differences between using annual data i n a monthly time-step, annual data i n a daily time-step, and 30 year climate normals i n a monthly time-step, a test, based on 3 plots representing slightly dry, fresh, and moist S M R s , was carried out later when the annual and daily data were available. A s was suggested by A . T . Black (Department of Soi l Science, Univers i ty of B r i t i s h Coltimbia, pers. comm.), the daily measvu-ements i n 1977 were combined into 5 day time-steps since the amoxmt of water could be held i n the soil for at least 2-3 days after saturation by a ra infa l l . The results showed that there was no difference for moist S M R , but a slight underestimation of the water deficit using normals was found for fresh and slightly dry S M R s (Table 3.8). As S M R s are quite broadly defined classes, this underestimation for fresh, sl ightly dry, and other 'drier' S M R s would not strongly affect the original allocation of the study sites, and 30 year normals could s t i l l be used for soil water balance modelling i f annual or dai ly data are not available. Another shortcoming i n the model was that no adjustments were made for aspect and slope. I n this study, this was recovered by comparing similarit ies and consistency i n topographic and soil properties ( K l i n k a et al. 1984) and soil moisture spectra ( K l i n k a et al. 1989b). A s a result, some plots were reassigned, £md three special S M R s were recognized to characterize soil moisture conditions on sites w i t h a strongly fluctuating water table (Table 3.10, F igure 3.4). These special S M R s pEirallel those defined for coastal B r i t i s h Colimabia by B e m a r d y (1989) {cf. Banner et al. 1990). They occurred i n situations where the Table 3.8. Comparisons of soil water deficit calctdated on the basis of 30 year normals i n a monthly time-step, annual data i n a monthly time-step, or annual data i n a dai ly time-step using the Energy/Soi l -Limitted water balance model. Plot number S M R 70 S D 68 F 60 M Soi l water deficit (mm/year) 5 day-step monthly-step monthly-step annual annual normals 26.5 0 7.4 14.1 0 0 0 0 0 Table 3.9. The criteria used for the characterization and classification of actual soil moisture regime of the study plots (sites w i th fluctuating water table are not included) (after K l i n k a et al. 1989b). l a . Water deficit occurs 2a. E^/Ej^gJ^ 0.40 excessively dry (ED) 2b. E^IE^^ > 0.40 but < 0.60 very dry (VD) 2c. E^E^g^ > 0.60 but < 0.90 moderately dry (MD) 2d. ^t/^max ^  0-90 sUghtly dry (SD) l b . Water deficit does not occur 3a. Ut i l i za t i on of soil-stored water occurs and growing-season soil water table or gleyed horizons absent fresh (F) 3b. No ut i l izat ion occurs or growing-season water table or gleyed horizons present 4a, Growing-season soil water table or gleyed horizon > 60 cm deep moist (M) 4b. Growing-season soil water table or gleyed horizon > 30 cm but < 60 cm very moist (VM) 4c. Growing-season soil water table or gleyed horizon < 30 cm deep wet (W) 1 ^ t / ^ m a x " actu£d/potential évapotranspiration ratio during the growing season. Table 3.10. M e a n values of selected components of the annual water balance for the study plots stratified according to soil moisture regimes (SMRs). Actual S M R Ntunber of plots 'Et (mm/yr) (mm/yr) 3^t/^max 4Wd (cm) (cm) Excessively dry 2 92 152 0.38 na n a Very dry 8 110 128 0.46 na na Moderately dry 5 191 46 0.80 n a n a SHghtly dry 16 212 25 0.90 na n a Fresh 7 242 0 1.00 na n a Moist^ 11 235 0 1.00 53(3) 60(2) Very moist^ 9 239 0 1.00 35(5) 53(3) Wet6 6 246 0 1.00 24(5) n a Moderately dry to moist^ 2 136 104 0.57 na 40(1) SHghtly dry to very moist^ 5 202 33 0.86 40(2) 48(3) Fresh to wet^ 1 244 0 1.00 30(1) n a 1F^ - soil actual évapotranspiration. 2 - growing-season soil water deficit. 3 E^/Ej^oy. - actual evapotranspiration/potential évapotranspiration ratio. - depth of soil water table. 5 - depth of soil gleyed horizon. 6 Number of plots used to calculate the mean value is given by a munerical superscript i n parenthesis. 200 150 J 100 u 50 r;3 0 o CO -50 1 r T 1 r J I I L 1 r J L ED VD MDf SDf F f MD SD F M V M W Soil moisture regime ED VD MDf SDf F f MD SD F Soil moisture regime M V M Figure 3.4. Categorical plots showing means and standard deviations of soil water deficit (upper) and actual/potential évapotranspiration ( E ^ j ^ ^ x ) '"^tio (lower) i n relation to soil moistiire regimes (SMRs). Symbols for S M R s are explained i n Table 3.8. soils were moderately to slowly pervious and imperfectly or poorly drained (typically located on flats or i n depressions), but surplus water was not evident i n the soils for a large part of the growing season. Precipitation normals and soil characteristics suggested that the soils are at, or above, field capacity i n late fal l and dur ing and after snowmelt. This was quite evident from the presence of gleyed soil horizons w i t h i n 20 to 60 cm of the ground surface, and a frequently observed above-ground or near-surface water table following major growing-season precipitation events. D u r i n g relatively dry and w a r m periods, the water table gradually receded to a greater depth to a point where excess water was no longer evident i n the soil , and soils were below field capacity and vdth a water deficit i n the upper soil layer. A combination of two adjectives was used to describe the upper and lower l imits i n variat ion of soil moisture conditions. For example, slightly dry-very moist S M R described soil moisture conditions of the sites which show both slight growing-season water deficit and periodic waterlogging (Tables 3.9 and 3.10, Figure 3.5). Such S M R s were denoted by the superscript f (fluctuating) attached to the adjective describing the 'drier' l i m i t of soil moist;u*e conditions (e.g., S D ^ . To confirm the recognized S M R s from soil characteristics, and to determine their relations w i t h the understory vegetation, canonical discr iminant analysis based on logarithmic transformed fi-equencies of soil moisture ISGs and recognized S M R s was carried out. The analysis assigned 78% of the study plots into the source S M R s . 'Misclassifications' of indiv idual ssraiples suggested by the analysis were mostly confined to adjacent S M R s . A n ordination of the study plots as a function of the f irst two canonical variâtes showed that a l l S M R s were significantly different from each other (Table 3.11) and were separated wi th no overlap of their 75% confidence regions (Figure 3.5). Confidence regions could not be shown for excessively dry (ED), moderately dry-moist (MD^), and fi*esh-wet (F^) S M R s as they Table 3.11. Multivariate statistics and F approximations for testing group means in the canonical discriminant analysis of 11 soil moisture regimes (SMRs) under HO: all group means in the population are equal. Statistic Value F df P > F Wilks' lambda (A) 0.008 7.521 60,298 0.000 Hllai's trace (V) 2.748 5.155 60,366 0.000 Hotelling-Lawley trace (U) 12.170 11.021 60,326 0.000 - 9 - 4 1 6 First canonical variate Figure 3 . 5 . Ordinat ion of the study plots as a function of the first two canonical variâtes determined by canonical discriminant analysis showing 7 5 % confidence regions for soil moisture regime (SMR) mesms. E a c h plot is represented by an alphabetical symbol that designates S M R : excessively dry (A), very dry (B), moderately dry (C), sl ightly dry (D), fi-esh (E), moist (F), very moist (G), wet (H), moderately dry-moist (I), slightly dry-very moist (J), and fi'esh-wet (K). included too few study plots. The ordination arranged S M R s along the first canonical variate i n order of decreasing water deficit fi^om left to right, and eJong the second canonical variate i n order of decreasing depth of water table or gleying. 3.3.3. Soi l Nutr ient Analysis A s was the case for the soil moisture regime, the soil nutrient regime (SNR) is one of the basic components of ecological site quality and one of the differentiating characteristics used i n site classification (Pojar et al. 1987). Unambiguous characterization of soil nutrient conditions for plant growth requires quantitative criteria which can then be used to divide a soil nutrient gradient into ecologically meaningfiil regimes (classes). This study adopted the approach used by Court in et al. (1988) and Kabzems and K l i n k a (1987). Since nitrogen appeared to be the only l imi t ing factor to lodgepole pine growth i n this study according to foliar nutrient analysis (reported later i n this section), the use of soil nitrogen as a one dimensioned representation of the soil nutrient gradient was justi f ied (T .M, B a l l a r d , Department of Soi l Science, Univers i ty of B r i t i s h Colvmibia, pers. comm.). The variables selected for the analysis included: p H and C / N ratio for forest floor and mineral soil , and for both forest floor and mineral soil , minerahzable-N (mN) (kg ha-l ) and stun of exchangeable C a , M g , and K (kg ha-l) (SEC) . Due to the curvi l inearity of the veiriables, transformations were made. I n the first step, cluster analysis, based on the selected six variables and Eucl idean distance and Ward's m i n i m u m variance algorithm (Sneath and Sokal 1973), was used to recognize the presence of five natural groups of study plots to be consistent w i t h the existing S N R classification. In the second step, the five groups produced by cluster analysis were subjected to stepwise discriminjmt analysis for the selection of variables which woxild explain the largest amount of variation i n the data set. This analysis identified two variables—^mN and SEC—determining the structure i n the data set at a 95% confidence level w i t h part ia l of 0.84 and 0.41, respectively. In the last step, canonical discriminant anedysis was used to determine to what extent m N and S E C would assign the study plots into the five groups created by the cluster analysis. Incorrectly assigned plots were reassigned into the groups indicated by the analysis, and the analysis was repeated u n t i l the resvdts stabilized, i.e., further reassignments did not improve the success of discrimination (Tables 3.12 and 3.13), The final analysis resulted i n 96% of the study plots being assigned into their soxirce groups. The first canonical variate was mainly correlated to m N (loading = 0.97) and was accoimted for 94% of the total variance. The S E C was main ly correlated to the second canonical variate (loading = 0.69) (Tables 3.12 and 3,13), Figure 3,6 showed an ordination of the study plots on the first two canonical variâtes, w i th the five S N R s indicated by 95% confidence ellipses centered on the group means. A l l means were significantly different from each other (Table 3.14), and a l l groups were separated w i t h no overlap of their 95% confidence regions. The ordination arremged the study plots along the first canonical variate, which represents a soil m N gradient, rank ing from nitrogen-poorest (group 1 on left) to nitrogen-richest (group 5 on right). A t this point, the five delineated soil nutrient groups were considered to represent five S N R s , perhaps more appropriately, soil nitrogen regimes: 1 - very poor, 2 - poor, 3 - meditmi, 4 - r i ch and 5 - very r ich. A s immiary of a l l the soil nutrient variables of the study plots stratified according to the five delineated soil nutrient regimes, indicated that the two selected differentiating characteristics—mN and SEC—prov ided a a good basis for Table 3.12. Results of the canonical discriminant analysis for five soil nutrient regimes using on mineral izable-N (kg ha-1) and sum of exchangeable bases (kg ha" 1) as variables Variable Canonical loadings on the first two canonical variâtes 1st 2nd m N 0.956 -0.292 S E C 0.722 0.692 Canonical variate 1st 2nd Canonical correlation ( R ) 0.95 0.60 Squared R (R2) 0.90 0.36 Eigenvalue 8.91 0.57 Proportion of variance 0.94 0.06 Cumulative variance 0.94 1.00 Table 3.13. Percentage of study plots identified by canonical discriminant analysis into the source soil nutrient groups on the basis of mineral izable-N (kg ha'^) and siun of exchangeable bases (kg ha-l) . Percent Number of plots assigned by discriminant analysis Source correct 1 2 3 4 5 2 1 100 6 0 0 0 0 6 2 100 0 16 0 0 0 16 3 90 0 0 18 2 0 20 4 95 0 0 1 19 0 20 5 100 0 0 0 0 10 10 I 96 72 Table 3.14. Multivariate statistics and F approximations for testing group means in the canonical discriminant analysis of five soil nutrient groups under HO: all group means in the population are equal. Statistic Value F df P > F Wilks' lambda (A) 0.057 52.722 8, 132 0.000 Pillai's trace (V) 1.265 28.818 8, 134 0.000 Hotelling-Lawley trace (U) 10.939 88.880 8, 130 0.000 Figure 3.6. Ordination of the study plots as a function of the first two canonical variâtes determined by canonical discriminant analysis showing 95% confidence regions for soil nutrient regime (SNR) means. Each study plot is represented by an alphabetical symbol that designates soil nutrient group: A - very poor, B - poor, C -medium, D - rich, and E - very rich. Table 3.15. Means of all available soil nutrient variables and frequency of nitrophytic plants for five soil nutrient regimes. Variable VP (n=6) Soil nutrient regime ^  P M R (n=15) (n=21) (n-20) VR (n=10) Forest floor pH C/N total P (kg/ha) total S (kg/ha) 4.3 63 15 21 4.4 50 33 39 4.4 39 67 58 5.3 39 94 118 5.9 33 302 474 Mineral soil pH 5.9 C/N 95 available P (kg/ha) 142 available SO4-S (kg/ha) 5.3 5.5 65 81 4.3 5.1 35 54 3.3 6.1 39 40 3.2 6.1 29 17 3.5 Forest floor & mineral soil mNQtg/ha) Ca (kg/ha) Mg (kg/ha) K (kg/ha) SEC (kg/ha) 2.7 539 599 65 1203 9.7 535 398 107 1040 29.7 1002 214 160 1376 38.3 3188 372 400 3960 130.1 7206 497 576 8278 Others Frequency of nitrophytic ISG 1.5 3.7 9.3 25.2 38.2 1 VP - very poor, P - poor, M - medium, R - rich, and VR - very rich. Soil nutrient regime Figure 3.7. Categorical plots showing mesms and standard deviations for soil mineralizable-N (mN) (kg ha'l) (upper), sum of exchangeable Ca, K, and Mg (kg ha'"^ ) (middle), and frequency of nitrophytic species (FNITR3%) dower) in relation to soil nutrient regimes (SNRs). Symbols for SNRs are: very poor (VP), poor (P), medium (M), rich (R), and very rich (VR). classification (Figure 3.7), as they are strongly correlated w i t h a number of the other variables (Table 3.15). Near ly a l l the accessory variables showed either an increase or decrease along the soil m N gradient, i.e., from very poor through to very r i ch S N R s . Positive correlations were apparent for the forest floor p H , total P and S, and the total soil C a and K , while negative correlations were noted for both forest floor and mineral soil C / N and the mineral soil available-P and SO4-S. No obvious trend was detected for the mineral soil p H and M g . The soil nutrient properties identified i n this study for characterization of soil nutrient gradients, and the S N R themselves, are consistent w i t h the resvdts of previous studies carried out by Court in et al. (1988), Kabzems (1985), and Carter and K l i n k a (1991). For example, mineral izable-N and exchangeable C a , K , M g were identified by Coiu-tin et al. (1988) as differentiating variables for the soil nutrient gradient i n southwestern B r i t i s h Columbia and by Kabzems (1985) as the best properties for characterization of the soil nutrient gradient on southern Vancouver Island. The mean values of m N for the five S N R s reported by Carter and K l i n k a (1991) for the S N R s of 149 Douglas-fir stands i n the Very D r y and D r y Mar i t ime subzones of the Coasted Western Hemlock zone of southern B . C . are comparable to those determined i n this study for a population of ecologically entirely different stands (Table 3.16). I f the delineation of S N R s is ecologically sovmd and not merely an arbitrary artifact of the data and the procedure used, then relationships should exist between the m N or S N R s and understory vegetation and lodgepole pine foliar N , and between soil nutrient and foliar nutrients. To quantify the relationship between the fi'equency of nitrophytic plants (FNITR3%) ( K l i n k a et al. 1989b) and forest floor mineral izable-N, a nonlinear Table 3.16. Comparisons of the means of mineral izable-N (mN) and sum of exchangeable C a , M g , and K (SEC) for soil nutrient regimes (SNRs) stratified fi-om this study and the studies on the coastal B . C . S N R s V P P M R V R This study m N (kg/ha) 2.7 9.7 29.7 38.3 130.1 S E C (kg/ha) 1202 1040 1376 3960 8278 Other studies I m N (kg/ha) 7.3 13.1 25.2 46.6 176.5 2 S E C (kg/ha) 1386 873 1225 1743 5066 1 F r o m Carter and K l i n k a 1991. 2 F r o m Court in et al. 1988. regression model us ing the natural logarithm of FNITR3% and untransformed forest floor m N was developed (equation [3.3.1], Figiu-es 3.8): [3.3.1] FNITR3% = exp[0.597(mN)(û.45i)] I2 = 0.73 S E E = 3.5 % n = 68. The model indicates that FNITR3% increases exponentially as soil nitrogen avai labi l i ty increases. The use of FNITR3% as an index of soil nitrogen avai labi l i ty is strongly supported by variation i n forest floor m N . This result is s imi lar to that obtained by K l i n k a et al. (1990) i n their study among humus forms, forest floor nutrients, and tmderstory vegetation. Fifty-three foliar samples were evaluated for stand macronutrient status. Comparing measured concentrations to the l imits proposed by B a l l a r d and Carter (1986) suggested that there were no deficiencies for P , C a , M g and SO4-S i n any of the study stands, possible slight-moderate K deficiency i n a l l study stands, and severe N deficiency i n 80% of the study stands. Stratif ication of foliar macronutrient concentrations according to the S N R s showed the presence of a nitrogen gradient (Table 3.16). Although almost a l l stands were diagnosed to have severe N deficiencies, there was a slight increase i n N concentrations fi-om very poor through very r i ch S N R s . Regressions of soil mineral izable-N against foliar N were developed (Table 3.18), These nonlinear models (Table 3.18) using foliar N dry mass (mg/100 needles) as the dependent variables and various measm-es of soil m N as independent variables, had similar good fits. Equation [3,3,4] was chosen to i l lustrate the relations between fl!^w and soil m N (Figm-e 3,9), A s was the case for Figure 3.8. Scattergram gind regression of forest floor minergdizable-N (kg ha-^) against frequency of nitrophytic plants (FNITR3%). T a b l e 3.17. M e a n s of foliar m a c r o n u t r i e n t concentrations i n the study stands stratified according to soil nutrient regimes (SNRs) . Symbols i n columns are: a - adequate, n d - no deficiency, psd - possible deficiency, smd - slight-moderate deficiency, sd - severe deficiency. N u m b e r F o l i a r macronutrients (%) S N R of stands N P K C a M g S S 0 4 - S V e r y poor 6 l .OSsd* 0.15a 0.46smd 0.21nd 0.103nd O.OSSpd 0.0096nd Poor 13 l .OSsd 0.15a 0.44smd 0.19nd 0.107nd O.OSlpd 0.0098nd M e d i u m 9 1.13sd 0.15a 0.45smd 0.19nd O.lOSnd 0.085pd 0.0099nd R i c h 17 l . l S s m d 0.16a 0.46smd 0.19nd 0.116nd 0.089pd 0.0109nd V e r y rich 8 1.19smd 0.16a 0.44smd 0.19nd O . l l G n d O.OQOpd 0.0099nd * Interpretations are based on B a l l a r d a n d C a r t e r (1986). Table 3.18. Regression models based on foliar nitrogen dry mass ( M w ) and soil mineralizable nitrogen (mN). [3.3.2] fNw = 0.955(fmNcon)^-2^'^ N =50 I2 = 0.962 (corrected l2 = 0.553) S E E = 0.870 (mg) where finN^^j^ = forest floor m N concentration (ppm). [3.3.3] flSTw = 0.905(fmmNcon)0-295 N =50 12 = 0.964 (corrected l2 = 0.567) S E E = 0.855 (mg) where finmNc^j^ = combined m N concentration of forest floor and mineral soil [3.3.4] fNw = 2.178(fmmNkg)0-224 N = 50 I2 = 0.962 (corrected 12 = 0.549) S E E = 0.872 (mg) where finmNkg = combined dry mass of forest floor and mineral soil m N ( k g h a - i ) . Figure 3.9. Scattergram and regression of forest floor mineral izable -N (kg ha-l) against foliar N (mg/100 needles) using equation [3.3.4]. the and forest floor m N , equation selected, the content of foliar N increases as a power function of combined dry mass of forest floor and minera l soil m N (kg ha"^). The performance of the models was comparable to that of foliar N concentrations and minera l soil m N reported by Powers (1980) for Pinus jeffreyi and P. ponderosa (quadratic fimction), and by K l i n k a and Carter (1990) for Pseudotsuga menziesii us ing either concentrations or contents (mg/100 needles) of foUar N . A canonical correlation analysis (CCA) was used to summarize the general relationships between foliar macronutrients (mg/100 needles) (N, P , K , C a , M g , S, and SO4-S) and soil macronutrients (kg/ha) (forest floor C / N , total P , and total S, mineral soil C / N , and combined forest floor and minera l soil m N , K , C a , and Mg) . A l l these variables were transformed using a common logarithm since non-normality existed i n the data. The first and second canonical correlations, 0.85 and 0.79, suggested strong l inear relationships between the logarithms of foliar and soil macronutrients. Graphica l ordination of the 53 study plots on the first foliar canonical variate and the first soil canonical variate associated w i t h the classified S N R s (Figure 3.10) showed general l inear relationships between these two sets of measurements. Although overlaps between S N R s occurred, the plots classified to a particular S N R tended to be associated together. 3.3.4. Site Classification Classifying study plots into vegetation units , and knowing the regional climate (biogeoclimatic subzone), S M R , and S N R for each study plot, made i t possible to stratify the study plots into classes that have s imi lar ecological site quality and, hence, s imi lar potential vegetation and productivity. This quality and potential are best indicated by near-cHmax or climax plant communities, but can be - 4 - 3 - 2 - 1 0 ' 1 2 3 First canonical variate of foliar nutrients Figure 3.10. Ordinat ion of the study stands as a function of the first pair of soil and foliar nutrients canonical variâtes determined by canonical correlation analysis. Each study plot is represented by an alphabetical symbol that designates S N R : A -very poor, B - poor, C - medi imi , D - r ich , and E - very r ich . also inferred from imderstory vegetation i n late-seral commimities. Deal ing w i t h mid-seral lodgepole pine-dominate commmiities, any inferences of vegetation potential were avoided i n this study, as they would be merely speculation. The basic rniit of site classification is the site association, each site association representing a group of ecologically-equivalent sites. Site associations are circumscribed by late-seral, near-climax, or climeix vegetation units and characterized by a range of climatic, soil moistmre, and soil nutrient regimes. Site series simply represent a climatically uniform segments of a site association, i.e., that portion of a site association that occiurs w i th in a biogeoclimatic subzone forms a site series (Pojar et al. 1987). When developing site classification, one to one correspondence between vegetation imits and site associations can not be expected. Different combinations of diagnostic species do not always reflect differences i n ecological site quality; thus, vegetation imits do not always have equal importance or value for site classification (Pfister and A m o 1980). For example, the difference i n late-seral to climax vegetation on ecologically-equivalent sites can often be attributed to var iat ion i n the composition and cover of a tree layer or ground surface materials. I n order to delineate site associations, i t was necessary to examine whether the floristic differences among the recognized vegetation units (Table 3.2) manifested, i n fact, differences i n ecological site quality. The objective was to eliminate variat ion i n vegetation due to non-site influences, i.e., disturbance, chance, and time. A site association was only recognized when i t could be distinguished from a l l other site associations by an exclusive range of climatic, soil moisture, soil nutrient regimes, and, eventually, by an additional environmental factor. The examination was carried out i n several steps resembling the process of successive approximation (Poore 1962) and was assisted by computerized tabl ing programs and ordination techniques. In the first step, the tabulated environmental plot data were exgmained to determine whether each vegetation vmit had an exclusive range i n climatic, soil moisture, soil nutrient regimes, w i t h appropriate considerations for additional controlling environmental factors (e.g., fluctuating water table). Those units that met this condition were set aside, the others were submitted to a further analysis. In the second step, the vegetation imits that overlapped i n ecological site quality were inspected. The sample plots identified as outiiers and the borderline plots were assigned to the environmentally most closely related unit . The relocation of these plots brought about another set of differentiable site associations. I n the th i rd step, the remaining, usual ly nearly completely overlapping, vegetation units were grouped, considering both floristic and environmental affinities. The newly tabulated environmental data were inspected and differentiable groups were identified. Grouping was continued unt i l a l l groups could be differentiated. I n the last step, new vegetation and environment tables were produced (Tables 3.19 and 3.20), App ly ing the principles of environmental pattern analyses (WhittEiker 1957,1967,1978), the recognized site associations were plotted on a mosaic chart (Shimwell 1971) composed of climatic, soil moisture, and soil nutrient gradients (Figure 3.11). The tables and the chart were used to compare site associations for floristic and environmental affinities and conformity to a general pattern of relationships. Table 3.19. Sjmopsis and diflferentiating characteristics of the site associations distinguished i n the study plots. Name (symbol) C K m a t e l S M R 2 S N R 3 Stereocaulon (A) S B P S x c E D V P - P Arctostaphylos (B) S B P S x c V D V P - M Sherpherdia (C) S B P S x c M D f M - V R Aulacomnium (D) S B P S x c SDf M - V R Salix (E) S B P S x c F f M - V R Pleurozium (F) S B S m c M D V P - M Vaccinium myrtiloides (G) S B S w k M D V P - M Vaccinium membranaceum (H) SBSmc , S B S w k S D V P - M Gymnocarpium (I) SBSmc , S B S w k F - M M - V R Equisetum (J) S B S m c , S B S w k V M R - V R Carex (K) SBSmc, S B S w k W M - V R represented by biogeoclimatic subzones: S B P S x c - V e r y D r y and Cold Sub-boreal Pine Spruce Subzone, S B S m c - Moist and Co ld Sub-boreal Spruce Subzone, S B S w k - Wet and Cool Sub-boreal Spruce Subzone. ' soil moisture regimes: E D - excessively dry, V D - very dry, M D ^ - moderately dry to moist, S D ^ - slightly dry to very moist, F ^ - fresh to wet, M D - moderately dry, S D - sl ightly dry, F - fresh, M - moist, V M - very moist, W - wet. ' soil nutrient regimes: V P - very poor, P - poor, M - medi imi , R - r i ch , V R - very r ich . Table 3.20. Means of selected climatic, soil, and stand characteristics of the distinguished site associations (SAs). Symbols for SAs, biogeoclimatic subzones, soil moisture regimes (SMRs), and soil nutrient regimes (SNRs) are explained in Table 3.19. Site association Number of plots A 2 B 8 C 2 D 5 E 1 F 1 G 4 H 16 I 18 J 9 K 6 Subzone Actual SMR -SBPBxc—• SBSmc MD SBSwk MD SBSwk ED VD MDf SDf F SD F-M VM W Actual SNK VP VP-M R R-VR VR P P-M P-M M-R R-VR M-VR El (inni/year)i 92 110 136 202 244 168 202 212 227 239 246 ^t/^max. 0.38 0.46 0.57 0.86 1.00 0.63 0.86 0.90 1.00 1.00 1.00 Growing-season water deficit (mm^ear) 152 128 104 32 0 93 32 26 0 0 0 Depth of gleyed horizon^ or water tabled (cm) na na 402 (1)4 482.3 (5) 303 (1) na na na 532.3 (7) 442.S (8) 243 (5) Forest floor C/N 71 60 46 37 25 62 42 42 39 32 34 Mineral soil C/N 138 80 51 38 31 70 47 47 33 32 43 Forest floor & mineral soil min-N (kg ha"^) 2.1 6.4 16.1 45.6 104 7.5 15.8 19.4 34.8 121.6 54.8 Forest floor & mineral soil exchangeable Ca,Mg,andK(kgha-l) 1006 2628 6425 6029 5523 499 488 839 2059 7740 3257 Foliar N (mg/100 needles) 2.71 2.94 3.28 3.91 6.39 3.79 3.47 3.84 4.88 5.25 4.66 Measured site index (m/50 yr of b.h.age) 8.2 12.1 12.9 13.7 11.4 15.6 15.9 18.2 20.6 21.3 13.9 FNrrR3% 0.8 3.1 11.1 21.1 42.8 4.1 2.3 3.0 27.3 36.4 11.6 1 Et - actual évapotranspiration. 2 Denotes the depth of gleyed horizon. 3 Denotes the depth of water table. Numerical numbers in parenthesis indicate the number of plots used to calculate the soil water table and depth of gleyed horizon. The sample plots were classified into 11 site associations and 15 site series (Table 3.19), named for brevity by the generic or specific names of a dominant indicator plemt. These were selected fi*om a diagnostic species smaimary table for site associations, as potential climax tree species could not be determined. The classification impUed that there are eleven different ecological strata w i th in the population of the study plots, each representing a segment of a n ecological site quality gradient. To support the significance of, and to quantify the environmental affinities between the recognized site associations, canonical discriminant ansdysis using selected environmental variables was carried out. The environmental variables were: heat index (Table 2.1), EiJE^^ ratio, growing-season water deficit or the depth of water table or gleyed soil horizon, and soil miner£dizable-N (Table 3.20). Mult ivar iate statistics showed that a l l site associations were significantly different based on the means of those selected environmental variables (Table 3.21). The analysis assigned 74% of the study plots into their source site associations. 'Misclassifications' of study plots by the analysis were confined to Gymnocarpium (I) and Equisetum (J) plots. Overlap between I- and J-plots is l ike ly a reflection of difficulties or inaccuracies i n precisely characterizing or measiiring growing-season soil water svirplus conditions using a single point i n time, i.e., the depth of water table or gleyed soil horizons (Table 3.20). Ordinat ion of the study plots as a function of the first two canonical variâtes showed a remarkable pattern (Figure 3.12). F i rs t ly , the study plots were clearly separated along the first canonical variate according to climate i n order from the S B P S x c subzone (left) to the SBSmc subzone to the S B S w k subzone (right), w i th the S B P S x c plots appearing more cl imatically dissimilar than S B S m c and S B S w k 1 Sulnone SBPSxc SBSmc 1 SBSwk Very poor ( V P X poor (P), and medium (M) b oU nutrient reflmea eioeniTely dry SiereocÊUIoa 0-2/YP-P Tery dry ArdosUpbjlca 3-4/YP-M modeniely dry P/euroBum 1-2/VP-M j Y. myrUUoides 1/VP-M •lifhUy dry y. membnaaceum 3-4/VP-M 2-3/VP-M freth moist Tery moUt Tret Medium (MX rich (R), and Tery rich (VR) •oil nutrient regime ezceaaiTely dry Tery dry moderately dry ali(hUy dry freah Gjrmaocarpium 4-s/y-vp moist Sbepberdia Sf/M-VR Tery moiat AuJaaxmnJum er/M-YR Squisetum eym-YP e/u-VR •wet Salix 7f/M-VR Carex 7/M-YP 7/M-VR Figure 3.11. A n environmental chart showing the site associations distingmshed i n the study plots i n relation to biogeoclimatic subzones, relative (Arabic numbers) and actual soil moisture regimes, and soil nutrient regimes. Table 3.21. Multivariate statistics and F approximations for testing group means in the canonical discriminant analysis of 11 site associations (SA) imder HO: aU group means in the population are equal. Statistics Value F df P > F Wilks' lambda (A) 0.003 14.117 50,263 0.000 Hllai's trace (V) 2.883 8.308 50,305 0.000 Hotelling-Lawley trace (U) 17.400 19.279 50,277 0.000 plots. This justif ied classification of the S B P S x c plots into a different site association, whereas climatic affinities between the S B S m c and S B S w k subzones justif ied classification of ecologically-equivalent sites into the same site associations but different site series. Secondly, the study plots were arranged i n order of increasing soil moisture and nitrogen along the second canonical variate, wi th most water- and nitrogen deficient plots shown on bottom and most waterlogged and nitrogen-rich plots shown on towards the top. The pattern of the study plots along the second canonical variate indicated that they represent points on a combined soil moisture and nitrogen gradient. I n consequence, the distingxiished site associations were floristically inferred segments of climatic, soil moisture, and soil nitrogen gradients (i.e., an ecological site quality gradient). It was recognized that climate, soil moisture, and soil nitrogen, are continuous properties, and so site associations are not discrete groups, they change along each gradient into other associations. The l imits of a partictdar site association should be based on statistics derived fi:om observed and measured properties of samples of that association. 3.4. C O N C L U S I O N S U s i n g nimierical techniques and the methods of biogeoclimatic ecosystem classification, ecological analysis of the study plots produced indirect and direct categorical and continuous measures of ecological site qugdity for investigating their relations to lodgepole pine height growth. Flor ist ic analysis showed that the imderstory vegetation i n mid-seral lodgepole pine stands was sufficiently developed to indicate differences i n ecological site quality between the study plots. Diagnostic species of the distinguished vegetation units were found to be strongly correlated w i t h regional cUmatic, soil moisture, and soil nutrient gradients. 5.0 2.3 --0.4 --3.1 --5.8 --8.5 -7.5 -4.9 -2.3 0.3 2.9 5.5 First canonical variate Figure 3.12. Ordinat ion of the study plots as a function of the first two canonical variâtes determined by canonical discriminant analysis on selected environmental variables. E a c h study plot is represented by an alphabetical symbol that designates site association (SA). Symbols for S A are given i n Table 3.18. The application of the criteria proposed by K l i n k a et al. (1989b), and those of the Energy /Soi l -Limited model (Spittlehouse and Black 1981), resvdted i n successful stratification of the study plots into actual soil moisture regimes. Soil mineral izable-N and the sum of exchangeable C a , M g , and K were the properties used to characterize a soil nutrient gradient and five tradit ionally used soil nutrient regimes. Correlations between imderstory vegetation and categorical or continuous measures of soil moistvu-e suggested that these measures were not arbitrary, but had a meaning relative to soil moisttire conditions experienced by plants. S imi lar ly , correlations between soil m N and the fi-equency of nitrophytic plgmts, between foliar N and soil m N , and between foliar and soil macronutrients suggested that (1) a complex soil nutrient gradient can be exemplified, but not replaced by a soil nitrogen gradient, and (2) the criteria and l imits used to stratify the study plots into classes of the soil nitrogen gradient were not arbitrary, but might have a meaning relative to general nutrient supply for plants. The criteria used to classify the study plots into site associations resulted i n recognition of queditatively and quantitatively distinct, field recognizable, segments of regional gradients of ecological site quality. 4. R E L A T I O N S H I P S B E T W E E N L O D G E P O L E P I N E SITE INDEX A N D M E A S U R E S O F E C O L O G I C A L SITE Q U A L I T Y 4 . 1 . I N T R O D U C T I O N Classification of forest ecosystems is recognized as being an essential prerequisite for the implementation of site-specific s i lv icultural management. To make si lvictdtural decisions that have a desirable effect on both forest and site productivity, a forester should know ( 1 ) the ecological quahty of different sites, ( 2 ) the ecological characteristics of different trees, and ( 3 ) the relationship between growth performance of tree species and ecological site quality. This knowledge can then be used to select specific species and s i lv icultural regimes that w i l l sustain or enhance forest and site productivity. Although there are some l imitations to site index, i t has been widely used for its practicality as a measure of ( 1 ) growth performance or productivity of a particular tree species on particular site and (2 ) site quality, i.e., a site's capacity to support forest growth (e.g., Spurr and Barnes 1 9 8 1 , Hagglund 1 9 8 1 , Monserud 1 9 8 4 ) . Evident ly , site index can be neither a complete nor a precise measure of forest productivity as i t only indicates the height growth performance of a tree species, at a given point i n time. However, there are some conceptual problems i n relat ing site index to site quality. F i r s t l y , the site index of two different tree species growing on the same site may be different; thus site index is the measure of forest productivity or site quality relative to a given species, not a measure of a site's quaUty to support forest growth, i n general. Secondly, the same tree species may have the same site index on two ecologically different sites; hence, these two sites gire said to have the same site quality i n supporting growth of the species. However, this contradicts the ecological perspective that defines site quedity as the sum of a l l the many environmental factors affecting the biotic community of an ecosystem (Daniel et al. 1979, Spurr and Barnes 1980), Therefore, i t is more appropriate to use the term ecological site quality than site quality i n describing ecological characteristics of forest sites. In B r i t i s h Coltmibia, biogeoclimatic ecosystem classification is widely used to recognize different types of forest ecosystems according to the ecological quality of their sites (Pojar et al. 1987). Although the classification has improved s i M c u l t u r a l decision-making, the l i n k between the classification (or ecological site quality) and forest productivity has not yet been established. In consequence, one cannot determine potential forest productivity of different tree species on different forest sites as the relationship between forest productivity and measm'es of ecological site quality has not yet been examined for a l l major crop tree species. Relationships between environmental factors and site index have been the subject of mêiny studies and reviews. Most of these studies had l imited success i n accoimting for a major portion of the variat ion i n site index over a large area, and i n advancing the imderstemding of relationships between ecological site quality and tree growth. Kabzems and K l i n k a (1987), Court in et al. (1988), Green et al. (1989), Carter and K l i n k a (1990, 1991), and K l i n k a and Carter (1990) applied various measures of ecological site quality for estimating and describing the influence of these measiires on Douglas-fir site index. U s i n g the approach and principles of biogeocKmatic classification, they identified several ecological variables that were strongly related to Douglas fir site index. However, there is a need to expand and test the results of their studies for other tree species and i n different environments. The usefuhiess of the measures of ecological site quality determined by biogeoclimatic ecosystem classification i n site-productivity studies was examined i n this Chapter by asking one pivotal question: how does lodgepole pine productivity vary w i t h measures of ecological site quality? In consequence, the specific objective was to evaluate relationships between severed selected ecological variables determined i n Chapter 3 and the site index of immatxire sub-boreal lodgepole pine stands. This objective was accomplished by relating environment, vegetation, and site index data fi-om these stands through simple and multiple regression analysis. 4.2. M A T E R I A L S A N D M E T H O D S The 72 plots described previously were used for this analysis. The ecological analysis reported i n Chapter 3 produced a number of variables that were used as independent variables i n regression analysis. These variables, representing various measures of ecological site quality, were categorized according to origin (environment and vegetation variables), mode of measuring ecological site quality (indirect and direct variables), and expression [categorical and continuous (analytical) variables] (Table 4.1). The same categorization was adopted for regression analysis i n order to avoid redimdant combinations and collinearity of variables, and complexity of models. For example, vegetation variables were not used together w i t h environmental variables, indirect variables were not used together w i t h direct variables, and categorical variables were not used together wi th continuous variables. Simple and multiple least squares regression analyses (Rawlings 1988, Wi lk inson 1990) were used to regress site index on selected combinations of ecological variables. The analysis considered several categorical models (Table 4.2) and analytical models (Table 4.3). Table 4.1 Synopsis of the ecological variables stratified according to origin, mode, and expression (categorical variables are in normal face, continuous variables are in italic face). ORIGIN Mode Indirect Direct VEGETATION Vegetation imit (VU) Frequency of indicator species groups (ISGs) (Fjj^ Q-type PCA scores on diagnostic species (PCAj^ Leaf area index (LAI) Q-type PCA scores on foliar nutrients (PCA^ ENVIRONMENT Biogeoclimatic subzone (BGrC) Site association (SA) Site series (SS) Forest floor carbon-nitrogen ratio (C/N) Mineral soil carbon-nitrogen ratio (C/N) Q-type PCA scores on soil nutrients (PCAg) Soil nutrient regime (SNR) Soil moisture regime (SMR) Potential évapotranspiration (PET) Water deficit (Aj^ Depth of water table (W^) Depth of soil gleying (G^i) Mineralizable nitrogen (mN) Sum of exchangeable Ca, Mg,K(SEC) Site index (m/50 yr) was investigated for normality using graphical analysis (probabiUty plot) (Chambers et al. 1983; Wi lk inson 1990). A l l soil nutrient variables and foliar nutrient variables were transformed using a common logarithm to reduce their heterogeneity of variance. In order to specify appropriate l inear models, the relationships between the dependent variable and the independent variables were checked for nonlinearity using a graphical display (Chambers et al. 1983; Wi lk inson 1990). M i n - N and S E C were transformed due to their curvil inear relationship w i t h site index. D u m m y variables (qualitative variables or indicator variables) (Chatterjee emd Price 1977) were used i n categorical models. MulticoUinearity (Rawlings 1988), a common problem of ecological data, was examined using Pearson correlation analysis (Wilkinson 1990). Pr inc ipa l component regression (Rawlings 1988) was introduced due to multicol l inearity among the variables studied. Means and standard deviations of site index i n relation to vegetation units , site associations, S M R s , and S N R s , were shown i n categorical plots (Wilkinson 1990). A distance weighted least square (DWLS) smoothing method (McLa in 1974, Wi lk inson 1990) was used to superimpose the isolines of site index onto a two-dimensional edatopic grid. The relationship among site index, S M R s , and S N R s was displayed i n a three-dimensional space w i t h a projected contour plot. Table 4.2 Synopsis of the general forms of categorical models used to test the relationships between lodgepole pine site index £ind selected ecological variables. SI is site index (m @ 50 years of breast height age). where VUj are diunmy variables representing vegetation units from 1 through 10; YUi = Arctostaphylos-typic, VU2 = Arctostaphylos-Shepherdia, VU3 = Arnica, VU4 = Empetrum, VU5 = Vaccinium myrtiloides, VUg = V. membranaceum, VU7 = Ribes, VUg = Gymnocarpium-typic, VUg = Gymnocarpium-Equisetum, or V U j ^ q ~ Sphagnum. [2] SI = /(BGCi) where BGCj are dummy variables representing biogeoclimatic subzones: SBPBxc, SBSmc, or SBSwk. [3] SI = /(SMRs) where SMRs are dummy variables representing soil moisture regimes from ED through W; ED = excessively dry, VD = very dry, MD = moderately dry, SD = slightly dry, F = fresh, M = moist, VM = venr moist, W = wet, MD^ = moderately dry to moist, SD^= slightly dry to very moist, and F'= fresh to wet. where SNRs are dummy variables representing soil nutrient regimes from VP through VR; VP = very poor, P = poor, M = medium, R = rich, and VR = very rich. [6] SI = /(SSi) where SSj are diunmy variables representing site series from 1 through 15; SSj^  = SBPSxc/Stereocaulon, SS2 = SBFSxc/Arctostaphylos, SS3 = SBFSxc/Shepherdia, SS4 = SBSmc/Pleurozium, SS5 = SBSwkA^occinium myrtilloides, SSg = SBSmcA .^ membranaceum, SS7 =SBSwk/V.membranaceum, SSg = SBSmc/Gymnocarpium, SSg = SBSwkJGymnocarpium, S S i q = SBPSxcJAulacomnium, SSn = SBSmc/Equisetum, SS]^ 2 = SBSyfk/Equisetum, SS13 = SBPSxc/SaZa, SS14 = SBSmc/Carac, SS15 = SBSwk/Carac. [7-10] SI = /(B(5Ci, SNRs, SMRs) where BGrCi, SNRs, and SMRs are explained above. [1] SI = / (VUi) [4] SI = /(SNRs) [5] SI = /(SAi) Table 4.3 Synopsis of the general forms of analjrtical models used to test the relationships between lodgepole pine site index and selected ecological variables. SI is site index (m @ 50 years of breast height age). [11] SI = /(Fjk) where Fj^ is relative frequency of selected ISG j (EVD = excessively dry to very dry, VDMD = very diy to moderately dry, MDF = moderately dry to fresh, FVM = fresh to very moist, VMW = very most to wet, WVW = wet to very wet, P = very poor to mediiun, M = poor to rich, and R = medium to very rich) of site attribute k (SMR and SNR). [12-13JSI = / (FCAy) where PCAy are Q-tjrpe PCA scores on diagnostic species. [14] SI = /(PCAf) where PCAf are Q-type PCA scores on foliar nutrient variables. [15] 81 =/(LAI) where LAI is projected leaf area index. [16] SI = / (PET) where PET is potential evapotrsinspiration. [17] SI = / (DGW, Dummy) where DGW is the combination of the depth of soil water table (W(j) or the depth of soil gleying horizon (G )^ and soil water deficiency (A^); Dummy is a dummy variable representing Gj, Wj, and A^. [18-20]SI = / (mN, SEC) where mN is soil mineralizable nitrogen and SEC is siun of exchangeable CA, Mg, and K. [21-22]SI = / (fC/N, mC/N) where fC/N and mC/N are representing forest floor and mineral soil carbon-nitrogen ratios, respectively. [23-291SI = / (PET, DGW, Dummy, mN, SEC) where PET, DGW, Diunmy, mN, SEC are explained above. [30] SI = /(PCAs) where PCAg are Q-type PCA scores on soil nutrient variables. 4.3. R E S U L T S Stratif ication of a l l sample plots (n = 72) according to site associations (SAj), soil moisture regimes (SMRs) , and soil nutrient regimes (SNRs), manifested three important trends i n the variation of lodgepole pine site index (Figiires 4.1, 4.2, and 4.3). Site index was lowest on very poor sites and clearly different fi*om a l l other sites, but the differences emiong the poor, medium, r i ch , and very r ich sites were not obvious (Figure 4.1). This indicated that the lodgepole pine productivity gradient is poorly related to the soil nutrient gradient, i.e,, increase i n available soil nitrogen over the level defined for the poor S N R has a negligible influence on site index. Stratif ication of the sample plots according to S M R s produced different results than the stratification based on S N R s (Figure 4.2). The categorical plot showed the presence of two distinct populations of sample plots and a strong productivity gradient coinciding w i t h the soil moisture gradient. A l l low-site index (SI < 15 m, except for the wet S M R ) S M R s occurred i n the S B P S x c subzone, while a l l high-site index (SI ^ 15 m) S M R s occurred i n the S B S m c and S B S w k subzones. This suggests (1) a strong climatic influence on the soil moisture gradient and (2) affinity between S B S m c and S B S w k climates. Lodgepole site index increased w i t h an increasing available soil moistxire to a maximima, and then i t decreased wi th an increasing temporary (fresh S M R ) or permanent (wet S M R ) water table. Stratif ication of the sample plots according to site associations (SAj) produced nearly identical results (Figure 4.3), i.e., the presence of two populations of sample plots and a strong productivity gradient coinciding w i t h an ecological site quality gradient. A l l low-site index [SI < 15 m, except for the S A ^ (Carex site association)] SAj were confined to the S B P S x c subzone, whereas a l l high-site index (SI ^ 15 m) SAj were confined to the S B S m c and S B S w k subzones. This indicates that (1) the ecological site quality gradient coincides w i t h climatic and soil moistvire gradients and (2) SAj represent vegetation-inferred segments ofthe combined climatic and soil moisture gradient. W h e n the results of these three trends are taken into account, i t appears that the climatic and soil moisture regimes of the study stands are strongly related to a lodgepole pine productivity gradient (measured by site index). To quantify relationships between lodgepole pine site index and selected measures of ecological site quality (Table 4.1), various categorical and analytical regression models were examined (Tables 4.2 and 4.3). A total of 30 models were developed, and a l l models were significant at p < 0.01, except for model [19] (Table 4.6). The models using vegetation variables (Table 4.4) had moderate to strong relationships w i t h site index (0.41 < R2 < 0.83), but the V U model (equation [1]) accounted for the largest proportion of the variation i n site index of a l l vegetation models examined (R2 = 0.83) (Figure 4.4). Tak ing into account the strength of the models using various expression of understory vegetation (equations [11], [12], and [13]), i t appears that the understory vegetation i n eeirly-seral lodgepole pine stands is wel l enough developed as to serve as a good indicator of ecological site quahty. The L A I model (equation [15]) showed a quadratic relationship between site index and L A I , and indicated that site index did not increase wi th increasing L A I across the complete L A I gradient, but appears to reach a max imum when L A I s are approximately at 3.0 m^ m-2, w i th higher L A I s not necessarily result ing i n higher lodgepole pine site indices or productivity (Figure 4.5). S, 30 ^ 25 20 h 15 h 10 h .t^  5 GO VP P M R Soil nutrient regime VR Figure 4.1. Categorical plot of lodgepole pine site index i n relation to soil nutrient regimes (SNRs). Symbols for S N R s are defined i n Table 4.2. S, 30 'S 25 eu 20 h o O 15 B P! 10 -0) •t^  5 GO ED VD MDf SDf F f MD SD F M VM W Soil moisture regime Figure 4.2. Categorical plot of lodgepole pine site index i n relation to soil moisture regimes (SMRs). Sjrmbols for S M R s are defined i n Table 4.2. 20 h 30 •iH CD W «3 «M O >^ o (§; 10 - 0 S A l SA2 SA3 SA4 SA5 SA6 SA7 SA8 SA9SA10SA11 Site association Figure 4.3. Categorical plot of lodgepole pine site index i n relation to site associations (SAj). Symbols for SAs are defined i n Table 4.2. Table 4.4. Models for the regression of lodgepole pine site index on selected vegetation variables. S3rmbols for all variables are defined in Table 4.2 and 4.3. [I] SI = 13.529 - 2.909(VUi) - 1.229(VU2) + 3.871(VU3) + O.lSimJ^) + 3.783(VU6) + 5.421(VU6) +6.534(VU7) + 8.238(VU8) + 8.959(VU9) + O.O(VUio) adjusted R2 = 0.83 SEE = 1.68 m n = 72 [II] SI = 17.263 - 10.165(EVD) - 5.636(VDMD) + 3.965(MDF) + 4.522(FVM) - 7.018(WVW) + 3.558(R) adjusted R2 = 0.64 SEE = 2.41 m n = 72 [12] SI = 17.185 + 0.340(PCAi) + 0.534(PCA2) - 0.320(PCA3) + 0.040(PCA4) + 0.322(PCA5) + 0.067(PCA6) - 0.045(PCA7) - 0.189(PCA8) - 0.004(PCA9) + 0.055(PCAio) adjusted R2 = 0.75 SEE = 2.00 m n = 72 [13] SI = 17.185 + 0.340(PCAi) + 0.534(PCA2) - 0.320(PCA3) + 0.322(PCA5) adjusted R2 = 0.76 SEE = 1.97 m n = 72 [14] SI = 15.709(PCAi) + 0.651(PCA2) + 0.996(PCA4) + 1.228(PCA5) - 0.983(PCA8) + 1.096(PCA9) + 0.919(PCAio) adjusted R2 = 0.45 SEE = 3.00 m n = 53 [15] SI = 6.235 + 8.655(LAI) - 1.285(LAI)2 adjusted R2 = 0.41 SEE = 3.08 m n = 58 Figure 4.4. Relationship between estimated ( V U model, equation [1]) and measured lodgepole pine site index values and probability plot of residuals from regression analysis. Figure 4.5. Relationship between estimated (LAI model, equation [15]) and measured lodgepole pine site index values and probabiHty plot of residuals from regression analysis. The P C A f model (equation [14]), us ing stepwise selected P C A components ( P C A i , P C A g , P C A 4 , P C A 5 , and PCAg) that accounted for 88% of the total var iat ion i n foliar nutrients , explained 45% of the variat ion i n site index. The categorical models using selected environmental variables (Table 4.5) showed poor to very strong relationships w i t h site index (0.23 < R2 < 0.85). Ranking according to adjusted R^ and S E E for the three single factor models (equation [2], [3], and [4]), their performance improved i n order from the S N R model (equation [4]) to the B G C model (equation [2]) to the S M R model (equation [3], Figure 4.6). The S M R model accoimted for the largest proportion of the variation i n site index of a l l nine categorical models examined (R^ = 0.84, S E E = 1.60 m) (Figure 4.7). The performance of the S A model (equation [5]), SS model (equation [6], F igure 4.8), combined B G C and S M R model (equation [8]), combined S M R and S N R model (equation [9]), and combined B G C , S M R , and S N R model (equation [10], F igure 4.7) were very comparable to that of the S M R model. The combined B G C , S M R , and S N R model (equation [10]) was the best model for explaining lodgepole pine site index i n terms of adjusted coefficient of determination (R^ = 0.85) and standard error of estimate ( S E E = 1.54 m). Comparison of model performance implies that (1) S N R , as a categorical variable, was found to be significant but did not improve the performance of the models using S M R s , B G C s , or their combination, (2) S M R and B G C exhibit a h igh collinearity, (3) S M R is the major determinant of lodgepole site index, and (4) more complex S A , S S and combined B G C , S M R , and S N R models do not necessarily produce better results than a simple S M R model. Table 4.5. Categorical models for the regression of lodgepole pine site index on selected environmental variables (n = 72). Symbols for categorical variables are defined in Table 4.2 and Table 4.3. [2] SI = 19.18 - T.OKSBPSxc) - 0.95(SBSmc) - O.OO(SBSwk) adjusted R2 = 0.52 SEE = 2.80 m [3] SI = 13.88 - 5.73(ED) - 1.75(VD) - 0.98(MDO - 0.20(SDl) - 2.48(F<) + 1.92(MD) + 4.30(SD) + 5.29(F) + 7.84(M) + 7.44(VM) + 0.00(W) ac^ justed R2 = 0.84 SEE = 1.60 m [4] SI = 18.48 - 7.91(VP) - 1.97(P) - 0.46(M) - 0.33(R) - 0.0(VR) adjusted R2 = 0.23 SEE = 3.53 m [5] SI = 11.40 - 3.25(SAi) + 0.74(SA2) + 1.50(SA3) + 4.20(SA4) + 4.45(SA5) + 6.78(SA6) + 9.33(SA7) + 2.28(SA8) + 9.92(SA9) + O.OO(SAio) + 2.48(SAii) adjusted R2 = 0.81 SEE = 1.74 m [6] SI = 11.40 - 3.25(SSi) + 0.74(SS2) + 1.50(SS3) + 4.20(SS4) + 4.45(SS5) + 6.13(SS6) + 7.17(SS7) + 8.02(SS8) + 9.99(SS9) + 2.28(SSio) + 8.70(SSii) + 10.53(SSi2) + 0.00(SSi3) + 3.80(SSi4) + 1.83(SSi5) adjusted R2 = 0.84 SEE = 1.64 m [7] SI = 20.05 - 2.72(VP) - 2.20(P) - 1.23(M) + 0.15(R) + O.OCVR) - 6.77(SBPSxc) - 1.09(SBSmc) - O.O(SBSwk) a^usted R2 = 0.58 SEE = 2.62 m [8] SI = 12.12 - 4.75(ED) - 0.762(VD) + 0.00(MO + 0.78(VMf) - 1.5(Wf) + 1.149(MD) + 4.014(SD) + 5.157(F) + 7.409(M) + 7.122(VM) - 0.316(W) + 0.78(BGCi) where BGC = 1 for SBPSxc, 2 for SBSmc, and 3 for SBSwk. adjusted R2 = 0.85 SEE = 1.58 m [9] SI = 14.69 -3.89(ED) -0.27(VD) -0.93(MDf) - 0.33(SDO - 3.29(Fl) + 3.25(MD) + 5.46(SD) + 5.84(F) + 8.15(M) + 6.92(VM) + 0.0(W) - 2.65(VP) - 2.29(P) - 1.57(M) - 0.86(R) - O.OCVR) a4justed R2 = 0.84 SEE = 1.60 m [10] SI = 9.379 - 2.682(ED) + 0.788CVD) + 0.00(M^ + 0.642rVMO - 2.189(Wf) + 2.7663(MD) + 5.114(SD) + 5.67(F) + 7.687(M) + 6.688(VM) - 0.292(W) + 0.689(SNRs) + 0.765(BGCi) where SNR = 1 for VP, 2 for P, 3 for M, 4 for R, and 5 for VR; BGC = 1 for SBPSxc, 2 for SBSmc, and 3 for SBSwk. adjusted R2 = 0.85 SEE = 1.54 m Srtimale SI (m @50 y n of BH >ge) Renduala (m) 28 •s E. 22 -16 -10 -1 1 1 1 1 1 r • 2 -§ 1 -1 V (2) ? 1 • 3 0 -1 -1 -• • -2 -1 1 1 1 1 1 a 10 12 M 16 18 20 22 btimate SI (m @60 jn ot BH age) -10 -8 0 Residuals (m) 28 "S fi. C3 22 -16 -10 -- 1 — 1 1 • 1 t 1 4 10 16 22 28 EatimaU SI (m @a0 y n of BU age) (3) -4 -2 0 2 Rcaiduala (m) Figure 4.6. Relationship between estimated ((1) B G C model [2], (2) S N R model [4], and (3) S M R model [3]) and measiired lodgepole pine site index values and probability plot of residuals from regression analysis. Figure 4.7. Relationship between estimated (combined B G C , S M R , and S N R model [10]) and measured lodgepole pine site index values and probability plot of residuals from regression analysis. Figure 4.8. Relationship between estimated (SS model [6]) and measured lodgepole pine site index values and probability plot of residuals from regression analysis. The analytical models using selected environmental variables produced comparable results and trends to the categorical models (Table 4.6). W h e n ranked according to adjusted R2 and S E E for four single factor models, their performance improved i n order from the soil nutrient models (equations [18], [19], and [21]) to the climatic model (equation [16]) to the soil water model (equation [17]). The combined model (equation [27]) had the best fit and accoimted for the largest proportion of the var iat ion i n site index of a l l analytical models examined ( R ^ = 0.82, S E E = 1.72 m) (Figure 4.9). A s w i t h the comparable categorical variables, analytical soil nutrients showed significemt but poor relationships w i t h lodgepole pine site index (Figure 4.9). The models us ing £iny of the selected direct soil nutrient measiu-es (mN, S E C and C/N) accoimted for less than 35% of the variation i n site index. W h e n used w i t h other analytical variables, performance of the resulting models was only m£u-ginally improved. In addition, S E C showed a strong collinearity to m N and had no significant relationships w i t h site index i n the study (equation [19]) ( R ^ = 0.00, S E E = 4.06 m). This indicated that there were no differences i n terms of the stun of exchangeable C a , M g , and K i n the study sites. Lodgepole pine site indices increased without correspondence wi th S E C because the S E C was rich enough for lodgepole pine growth throughout a l l the study sites. The relationship between lodgepole pine site index and m N (equation [18], Figure 4.9(3)} revealed that site index did not increase w i t h increasing m N across the complete m N gradient, but reached a maximum as m N approached approximately 63 kilograms per hectare. Continuously increasing soil nitrogen does not necessarily promote lodgepole pine height growth or productivity [Figure 4.9 (3)]. Table 4.6. Analytical models for the regression of lodgepole pine site index on selected environmental variables (n = 72). Symbols for analytical variables are defined in Table 4.2 and 4.3. [16] SI = -706.01 + 3.181(PET) - 0.003(PET2) adjusted R2 = 0.52 SEE = 2.80 m [17] SI = 3.64 + 0.034(DGW) + 14.78(Dummy) adjusted R2 = 0.62 SEE = 2.50 m [18] SI = 7.509 + 10.9081og(mN) - 2.51inog(mN)]2 R2 = 0.28 SEE = 3.43 m [19] SI = 16.845 +0.1051og(SEC) R2 = 0.00 SEE = 4.06 m [20] SI = 18.462 + 5.6871og(mN) - 2.7851og(SEC) adjusted R2 = 0.32 SEE = 3.34 m [21] SI = 35.30 - 11.19log(mC/N) R2 = 0.35 SEE = 3.28 [22] SI = 36.47 - 1.251og(fC/N) - 10.671og(mC/N) adjusted R2 = 0.33 SEE = 3.30 [23] SI = -692.199 + 3.126(PET) - 0.003(PET)2 + 2.231og(mN) a4justed R2 = 0.57 SEE = 2.65 m [24] SI = -687.554 + 3.108(PET) - 0.003(PET)2 + 0.026(DGW) + 11.35(Dummy) adjusted R2 = 0.79 SEE = 1.85 m [25] SI = 0.64 + 0.03(DGW) + 14.20(Dummy) + 2.771og(mN) adjusted R2 = 0.69 SEE = 2.25 m [26] SI = 5.02 + 3.421og(mN) - 1.431og(SEC) + 0.03(DGW) + 13.46(Dummy) adjusted R2 = 0.70 SEE = 2.19 m [27] SI = -702.504 - 3.179(PET) - 0.004(PET)2 + 0.025(DGW) + 11.615(Dummy) + 1.826log(mN) a<ijusted R2 = 0.82 SEE = 1.72 m [28] SI = -610.288 + 2.703(PET) - 0.003(PET)2 + 0.024(DGW) + 11.073(Dummy) + 1.8691og(SEC) adjusted R2 = 0.82 SEE = 1.72 m [29] SI = -656.058 + 2.939(PET) - 0.003(PET)2 + 0.024(DGW) + 11.365(Dummy) + 1.1041og(mN) + 0.981og(SEC) ac^ justed R2 = 0.82 SEE = 1.71 m [30] SI = 17.185 + 0.667(PCAi) - 0.764(PCA2) - 0.695(PCA4) + 0.650(PCA5) + 2.412(PCA6) adjusted R2 = 0.44 SEE = 3.03 m 400 410 420 430 440 4S0 4«0 470 Potentikl erkpolruiapirmUoD (mm) 4 10 16 28 EiUmaled SI (m @&0 y n of BH afe) 34J0 g 27^  h •s I 20.4 -B "J8 -I 00 • • • • • OJO 0.7 lA ZA ZJB log tr tnsfonned mineralizable N (3) I - a 2 HealduBli (m) Residuala (in) -6 0 5 ResiduBls (m) 10 Figure 4.9. Relationship between estimated ( P E T model [16], D G W model [17], and m N model [18]) and measured lodgepole pine site index values and probability plot of residuals from regression analyses. Comparing the analytical to the categorical models, the P E T model (Figure 4.9, equation [16]) and the B G C model (equation [2]) showed identical performance (R2 = 0.52, S E E = 2.80 m), the D G W model (equation [17], Figure 4.9) was inferior (R2 = 0.62) to the S M R model (equation [3]), and the combined P E T , D G W , and m N model (equation [27], Figure 4.9) was s imilar (R2 = 0.82, S E E =1.72 m) to the S M R model (equation [3]) ( R ^ = 0.84, S E E = 1.60 m) or the combined B G C , S M R , and SISTR model (equation [10]) (R2 = 0.85, S E E = 1.54 m). Thus, two relatively simple direct measures of climate and soil water appear to be sufficient to explain a large amoimt of the variat ion i n site index i n the study plots. The P C A g model (equation [30]), using stepwise selected P C A components ( P C A i , P C A g , PCA4, PCA5, and PCAg) which accounted for 91% of the total variat ion i n soil nutrients, explained 44% of the variat ion i n site index. The first P C A component (PCA^), which was highly correlated to m N , N|^ C .^, S^, and P^, explained 60% of the total vEiriation. Relat ing the soil nutrient P C A model (equation [30], Table 4.6) to the foliar nutrient P C A model (equation [15], Table 4.5), the former showed almost identical fit (R2 = 0.44, S E E = 3.03 m) as d id the later (R2 = 0.45, S E E = 3.00 m). This implies that soil and foliar nutrients appear to play the same role and contribute the same value i n evaluating lodgepole pine site index or productivity. I I I I I I I I I 1 - 4 - 3 - 2 - 1 0 1 2 3 4 Residuals (m) Figure 4.10. Relationship between estimated (combined P E T , D G W , and m N mode [27]) and measured lodgepole pine site index values and probability plot of residuals from regression analysis. 4.4. D I S C U S S I O N K l i n k a and Ceirter (1990) suggested that i t is possible to use a simple conceptual model—site index = f(heat, soil moisture, soil nutrients, soil aeration)—for investigating growth-site relationships under certain assmnptions. Despite a Kmited representation of climates and some combinations of S M R s and S N R s , the large amoimt of variat ion i n site index explained by this model revealed the presence of strong relationships between lodgepole pine site index and selected measures of ecological site quality, us ing either categorical or anal3^cal and indirect or direct measures. Indirect measures of heat, soil moisture and soil nutrients had good relationships w i t h their direct measures. However, i t was necessary to recognize and characterize soil moistvire conditions featuring fluctuating water table. The results obtained for lodgepole pine conformed well w i t h those reported for Douglas-fir i n the Very D r y and D r y Mar i t ime Coastal Western Hemlock subzones by Green et al. (1989), Carter and K l i n k a (1990), and K l i n k a and Carter (1990), and a few studies involving lodgepole pine (IlHngworth and Arl idge 1960, Duffy 1964, Youngberg and Dahms 1970, Mason and Tigner 1972, Mogren and Dolph 1972, Corns and P l u t h 1984). How does lodgepole pine productivity measured by site index vary w i t h ecological site quality? It is clear that lodgepole pine' productivity increases w i t h increasing potential évapotranspiration i n B r i t i s h Columbia, i.e., from cool to w a r m climates. K r a j i n a (1969) concluded that the potential for the most productive lodgepole pine growth is i n the Coastal Western Hemlock and Interior Western Hemlock zones. W i t h i n montane boreal chmates, the productivity w i l l be lower than i n cool mesothermal and temperate climates, and the productivity gradient w i l l coincide w i t h a growing-season temperature gradient, presumably reflected by zonal classification. Biogeoclimatic subzones, eventually variants , provide a first order of site stratification, while soil moisture and nutrient regimes provide a second and th i rd order, respectively. The ecological amplitude of lodgepole pine i n relation to a soil moistm-e gradient is very wide; i t extends fi'om excessively dry through wet sites (e.g., K r a j i n a 1969, Lo tan and Perry 1983, Cochran 1985, B u m s and Honka la 1990). Th is study showed that the rate of increase i n site index firom excessively dry to moist and the rate of decrease fi*om moist to wet sites was evidently higher than the rate of change along a soil nutrient gradient (Figures 4.11, 4.12, and 4.13). Surpris ingly , l i tt le is known about lodgepole pine nutr ient relations (e.g., K r a j i n a 1969, Lotan and Perry 1983, Cochran 1985). Some studies have shown no or weak relationships between soil nutrient levels and growth (e.g., Holmes and Tackle 1962, Duffy 1964), whereas others claimed significant responses to nitrogen ferti l ization (Sander 1966, Et ter , 1969, Cochran 1975, Weetman et al. 1985). O n the basis of this study, i t is suggested that lodgepole pine is a relatively low demanding species for nitrogen to mainta in i ts growth level w i t h i n given cl imatic and soil moisture conditions. In a l l three subzones, the most productive growth occurred on moist and nutrient-very r i ch sites (Figures 4.14, 4.15, and 4.16). This finding differs fi*om the proposition of K r a j i n a (1969) who suggested that the most productive sites are nutrient-r ich, and that nutrient-very r ich sites do not support lodgepole pine growth. It is suggested that this discrepancy is due to the difference i n characterizing the soil nutrient gradient and diflferentiating soil nutrient regimes between this study (of. Chapter 3) and K r a j i n a (1969). K r a j i n a considered nutrient-very r i ch sites to have not only high avai lable-N levels but also to be Ca-r ich, wi th p H > 6 i n the smface mineral soil horizon. It appe£irs that lodgepole pine is absent Figure 4.11. Response surface showing the relation between estimated lodgepole pine site index, soil moistvu-e regime, and soil nutrient regime i n the S B P S x c subzone using equation [10]. Sjonbols for soil moisture regimes and soil nutrient regimes are defined i n Table 4.2. Figure 4.12. Response surface showing the relation between estimated lodgepole pine site index, soil moistiu*e regime, and soil nutrient regime i n the S B S m c subzone using equation [10]. Symbols for soil moisture regimes and soil nutrient regimes are defined i n Table 4.2. Figure 4.13. Response surface showing the relation between estimated lodgepole pine site index, soil moistm-e regime, and soil nutrient regime i n the S B S w k subzone using equation [10]. Symbols for soil moisture regimes and soil nutrient regimes are defined i n Table 4.2. on alkaline soil w i t h p H approaching 8 (Cochran 1985), Implementation of site-specific management requires good information on forest productivity. W i t h biogeoclimatic ecosystem classification i n place, and relationships between site index and ecological site quality analyzed, i t is possible to use the models developed to estimate lodgepole site index. The analytical models should be most useful i n determining the effects of environmental change on forest growth, whereas categorical models shoidd be appropriate for operational applications. Considering the wide usage of edatopic grids and S M R s and S N R s i n site identification, i t is proposed that site index estimated by the combined B G C , S M R , and S N R model (equation [10]), and plotted for each subzone onto an edatopic grid (Figures 4.14, 4.15, and 4.16), represents both an effective means and format for predicting site index for any given site by forestry personnel. Although the site series model (equation [6]) is also suitable, i t s imply assigns the estimated mean site index for a given site series to a stand that falls w i th in that site series, regardless of the S M R and S N R present. The application of the combined model requires site diagnosis, i.e., stratification of a given area into component ecosystems, examination of each component, and site identification according to basic ecological site qualities (biogeocHmatic unit , S M R , and SNR) . In B r i t i s h Colimabia, this is being done routinely prior to making any silviculture decision. This model should be tested and validated using an independent data set to evaluate its performance and portability. I f justif ied, i t should be fiirther developed using an expanded data base, including a cl imatically wider range of lodgepole pine ecosystems. Very Dry and Cold Sub-boreal Pine—Spruce subzone (SBPSxc) Soil nutrient regime Figure 4.14. A n edatopic grid showing SBPSxc site series (1, 2, 3, 10, and 13) and lodgepole pine site index isolines calculated from equation [10] and fitted using a distance weighted least squares smoothing algorithm. Symbols for site series, soil moisture regimes, and soil nutrient regimes are defined i n Table 4.2. Moist and Cold Sub—boreal Spruce subzone (SBSmc) Soil nutrient regime Figure 4.15. A n edatopic grid showing S B S m c site series (4, 6, 8, 11, and 14) and lodgepole pine site index isolines calculated from equation [10] and fitted using a distance weighted least squares smoothing algorithm. S3mabols for site series, soil moisture regimes, and soil nutrient regimes are defined i n Table 4.2. Wet and Cool Sub-boreal Spruce subzone (SBSwk) Soil nutrient regime Figure 4.16. A n edatopic grid showing S B S w k site series (5, 7, 9 ,12, and 15) and lodgepole pine site index isolines calculated from equation [10] and fitted using a distance weighted least squares smoothing algorithm. Symbols for site series, soil moisture regimes, and soil nutrient regimes are defined i n Table 4.2. 4.5. C O N C L U S I O N S Regression einalysis demonstrated that several selected measvires of ecological site quahty were strongly related to lodgepole pine site index i n the study area. The most useful categorical variables were vegetation unit , soil moistiire regime, site association, and site series. The most useful analytical variables were potential évapotranspiration, water deficit, and the depth of water table or the gleyed soil horizon. Soi l nutrient variables, although significant, were poorly related to site index. Understory vegetation i n early-seral lodgepole pine stands was found to be a good indicator of ecological site quality, and soil moisture regime was considered to be most strongly related to the variation i n lodgepole pine site index. In order to estimate lodgepole pine productivity on sub-boreal sites, the use of the soil moisture regime, site association, or site series model is reconamended when age and height measurements are not appropriate; however, testing of these models over a wider range of sites is needed. 5. S ITE S P E C I F I C H E I G H T G R O W T H M O D E L S B A S E D O N S T E M ANALYSIS A N D M E A S U R E S O F E C O L O G I C A L SITE Q U A L I T Y 5 .1 I N T R O D U C T I O N The prediction of forest growth and future yields is central to forest science and forest management. This study is centered on the relationship between height growth and ecological site quaKty i n order to establish a strong l i n k between biogeocUmatic ecosystem classification and growth and yield studies. I n B r i t i s h Coltunbia, the biogeoclimatic ecosystem classification system is used to recognize and characterize ecologically different sites for the application of different s i lv icultural treatments. Site index is used as a measure of productivity and to predict height growth of tree species on different sites. A s the ecological quality of a site determines the growth performance or productivity of a particular tree species on that site, i t wotild therefore seem profitable to relate site index to ecological site quality. The presence of strong relationships would mean that (a) there is an ecological basis for estimating site index and height growth, (b) ecological variables could be used to estimate site index and growth more precisely than can be done at present, and (c) the effects of environmental changes, including management practices, on site productivity could be better understood, evaluated, and predicted. In Chapter 4, i t was shown that several selected measiu^es of ecological site quality were strongly related to site index, w i t h soil moisture being the major determinant. This chapter focuses on height growth and addresses the central question: does the pattern of lodgepole pine height growth change w i t h ecological site quality? Height growth of plants can be described by a growth function. As most factors affect height growth randomly, the growth process is also random. The growth of a given species changes as random factors and time change. Random factors i n this case can be defined as site attributes, such as climate, soil moisture, and soil nutrients, which are the pr imary factors that directly affect growth. A s a result, the height growth rate w i l l change wi th changes i n ecological site qual i ty and time. Thus, early growth w i l l be faster and later growth w i l l be slower on some sites than on others (Ha l l 1987,1989). This suggests that the height at an arb i trary age (such as site index) might not give the best measure of site productivity for a given tree species. Therefore, i t is necessary to develop tree species-specific and site-specific height growth models i n order to precisely describe the patterns of height growth over time on different sites. Despite some previous attempts documented i n the l iterature (e.g. Carmean 1970, Monserud 1984), site-specific height growth modelling has not yet been ftdly developed. This may be due to a lack of useful and easily obtainable measures of ecological site quality and a lack of cooperation between biometricians and ecologists. The specific objectives of the research reported i n this chapter are (1) to quantitatively describe height growth of the study stands and (2) to develop site-specific height growth curves for the different sites recognized by biogeoclimatic ecosystem classification. These objectives were accomplished by: (1) selecting a model for describing the height growth of each stand, (2) examining the effect of site index and ecological variables on the performance of the selected model, (3) choosing the most effective concomitant variable(s) for the growth model, (4) computing site-specific curves for describing the height growth of immature sub-boreal lodgepole pine stands, and (5) comparing the site-specific approach to the existing site index approach for height growth modelling. The data and results of the previous chapters were used and extended to address the above objectives. 5.2. L I T E R A T U R E R E V I E W General reviews ofthe methodology of site quality evaluation and height growth modelling were given by Jones (1969), Carmean (1975), Hagg l imd (1981), and Clutter et al. (1983). The idea that height growth varies vnth site and time resulted i n the concept of poljmaorphic growth curves. A nxmiber of attempts have been made to describe the patterns of height grovrth of different tree species, using variables such as stand density, height at a given age (i.e., site index), and/or early growth rate. Site index is commonly used to construct polymorphic height growth curves. One of the asstmiptions underlying the use of site index is that i f tree heights for a given species are the same at index age then they should have the same growth rate at different ages regardless of the ecological quality of the site on which they grow. This has led to site index controlling the shape of height growth ciuves (Beck 1971, Graney and B u r k h a r t 1973, Trousdell et al. 1974, Monserud 1984). However, this assimaption may or may not be true because trees may grow faster or slower i n earlier or later ages on different sites, but they may reach the same height at a certain age. Site index as a single indicator of height growth (one point system; Zeide, 1978) may not t ru ly describe the pattern of height growth, and the site index driven height growth model may overestimate or underestimate height grov^rth before or after the index age for different sites. To deal w i th this problem, vegetation or site variables have been used to modify the height growth curves—a site-specific growth modelling approach. For example, Cajander and Ilvessalo (1921) related major site types to Scots pine growth and stated that the difference i n tree growth rates resulted from the difiference i n productivity potential of site-types. In N o r t h America , Carmean (1956) used soil physical properties to modify Douglas-fir site index curves, and constructed site-specific height growth curves for different soil groups. After working on the relationships between height growth and site properties (soil and topography) for several species, Carmean (1970) concluded that soil and topography were the specific feattires that usually related to polymorphic height growth patterns. B y using habitat types as concomitant variables i n his height growth model for Douglas-fir, Monserud (1984) concluded that the habitat types could determine the shape of both height growth and site index curves. However, he s t i l l used site index as a veiriable to control curve shape wi th in each habitat type i n his model. A s habitat types represent a relatively wide range i n ecological site quality (Pfister and A m o , 1980), the habitat type height growth model might not be able to precisely describe height growth. Goudie (1984) adopted a s imi lar approach for lodgepole pine by stratifying forest sites into two categories: dry (upland) and wet (wetland). This study used his model for comparison. The height growth modelling efforts described above were imable to accurately determine the growth patterns anywhere besides index age due to a lack of appropriate ecological variables and of the knowledge how these variables affect site index. Site index does account for part of the var iat ion i n height growth curves, but a serious bias could occur when they are used for estimating the growth before or after index age. The one point system does not really explain polymorphic growth patterns. In 1978, Zeide proposed a two-point system for approximating height growth cxirves. This system is a method of estimating growth patterns from sequential observations of height and age. The assvmiption of the two-point system is that site index as one-point i n approximating growth curves is not sufficient to determine the curve suitable for a given stand; however, two points are sufficient. The two-point system assimies that i f different stands have the same growth values at any two ages (two points), the values for these stands w i l l be the same at any other age (other points). In other words, gro^rth ciu-ves may intersect only once. M i l n e r (1987a, b) concluded that Zeide's two-point system is an accurate method of approximating height growth curves. H e found that the index of ciu*ve shape, Z, was a useftd attribute i n assessing the applicability ofthe published site curves to a loced population and the shape of the height growth cwcve was not correlated w i t h site index. Although the two-point system addresses the major weakness of the site index system, i t s t i l l remains unreliable as the growth rate i s assumed to be consistent over entire life period of the tree. This may not be the case due to changes i n environmental factors. Strub and Sprinz (1987) developed a piece-wise l inear growth equation that defined the shape and trend of height growth curves to support their c laim that both anamorphic and polymorphic models are not flexible enough to describe the shape of the height-age relationship. Although i t addressed the major weaknesses of anamorphic and polymorphic models, the piece-wise l inear approach brought i n new theoretical difficulties. It is knovm that as age increases, plants consistently reduce their growth rate or growth performance before maximima growth is reached. Therefore, there is no real l inear relationship existing w i t h i n any time interval before the max imum, no matter how many segments are approximated. E i s et al. (1982) used t h i r d degree poljmomials to fit lodgepole pine and white spruce height growth curves using mean grov^h values for each of three vegetation-inferred sites. The i r model i l lustrated a Hnear relationship i n terms of the parameters estimated. As pointed out above, a Unear model may approximate model parameters very wel l statistically, but does not meet the biological assiimption that plant growth w i l l reach its m a x i m u m at infinity. 5 . 3 . M A T E R I A L S A N D M E T H O D S Examinat ion of lodgepole pine height growth was based on 9 5 trees fi-om 4 0 sample plots. Eighteen stemds of the total of 3 6 i n the Bowron River sampHng area (SBSwk subzone) were less than 4 0 years breast height age (b.h.a.), and 1 4 stands i n the A n a h i m L a k e (SBPSxc subzone) and the B u m s Lake (SBSmc subzone) sampling areas were less than 4 0 years b.h.a. These st£mds were too yoxmg to estimate accurately the height at the site index age of 5 0 years b.h.a. (Goudie 1 9 8 4 ) and were excluded fi-om the following stem analysis. The sample plots were located i n even-aged, immature, lodgepole stands w i t h a relatively narrow range i n age (between 4 0 and 7 0 years b.h.a.) and stocking, w i t h a s imi lar history of establishment and development, and without a history of damage. The study plots were chosen to represent the widest possible range of lodgepole pine stsmds i n relation to soil moisture and nutrient gradients wi th in three regional climates i n central B r i t i s h Col imibia , Three well-formed dominant trees, without any evidence of physical damage and disease symptoms, were selected i n each of the 4 0 sample plots for stem analysis. The trees were felled and measured for the total height, and discs were cut at 0 . 3 , 0 . 6 , and 1.3 m and at 1 m intervals thereafl;er. The age of each disc was determined by counting rings i n the laboratory. The study area, and methods of sample plot location, site description, vegetation and soil sampling, site index determination, soil physical and chemical analysis, foliar analysis, soil moisture analysis, vegetation and site classification, and indicator plant analysis were described i n Chapter 3. Ecological analysis (Chapter 3) identified and computed values for a ntunber of variables which were used as independent variables i n regressions against lodgepole pine site index i n Chapter 4. The categorical and continuous variables that showed a strong relationship to site index were adopted as concomitant variables i n models describing lodgepole pine height growth (Table 5.1). Carmean's (1972) method of estimating the true height corresponding to a particular year was used to correct heights at each section, as i t was considered to be the most accurate of the techniques available (Dyer and Bai ley 1987). This procedure is based on the assumption that sectioned points w i l l fa l l i n the middle of the annual leaders. Thus , by adding one-half the estimated length of the annual leader to the sectioned height, the bias can be removed. The formula is expressed as follows: r ^ , , , „ h i + ( h i . l - h i ) (j - l X h , , i • h,) Lo.3.11 M y = + 2(ri - rj+i) rj - rj+i where H y = corrected height at the ith section and t h e / t h r ing , hj = uncorrected total height at the i t h section, r j = the number of growth rings at the i t h section, i = 1,2, ,n , j = 1,2, , r , and n = the number of sections. Since my only interest was the true height at each sectioning point, (i.e., the first r i n g at each section), the term j was gJways equal one and the last term of the formula was zero. Consequently, the formula actually used i n this study was: h i + (hi+i - hi) [5.3.2] H i i = — — — -2(ri - r i^ i ) Table 5.1. Synopsis of the ecological variables used in the height growth models and stratified according to expression (categorical or continuous). C A T E G O R I C A L V A R I A B L E S BGCi - biogeoclimatic subzones from 1 through 3; 1 = SBPSxc, 2 = SBSmc, and 3 = SBSwk SMRs - soil moistiire regimes from ED through W; ED = excessively dry, VD = very dry, MD = moderately dry, SD = slightly dry, F = fresh, M = moist, VM = very moist, W = wet, MD^ = moderately dry to moist, SD^ = slightly dry to very moist, and F^ = fresh to wet SNRs - soil nutrient regimes from VP through VR; VP = very poor, P = poor, M = medivmi, R = rich, and VR = very rich Combination of BGCj, SMRs, and SNRs SAj - site associations from 1 through 11; 1 = Stereocaulon, 2 = Arctostaphylos, 3 = Shepherdia, 4 = Pleurozium, 5 = Vaccinium myrtiloides, 6 = V. membranaceum, 7 = Gymnocarpium, 8 = Aulacomnium, 9 = Equisetum, 10 = Salix, and 11 = Carex SSj - site series from 1 through 15; 1 = SBPSxdStereocaulon, 2 = SBPSxc/Arctostaphylos, 3 = SBPSïdShepherdia, 4 = SBSmc/Pleurozium, 5 = SBSwkA .^ myrtilloides, 6 = SBSmcA .^ membranaceum, 7 =SBSyfls/V.membranaceum, 8 = SBSmc/Gym/iocarjomm, 9 = SBSwk/Gymnocarpium, 10 = SBPSxc/Aulacomnium, 11 = SBSmc/Equisetum, 12 = SBSwk/Equisetum, 13 = SBPSxc/Sa/ùc, 14 = SBSmc/Carex, 15 = SBSwls/Carex C O N T I N U O U S V A R I A B L E S PET - potential évapotranspiration (mm) DGW - the depth of soil water table (W{j) (mm), the depth of soil gleying horizon (G(j) (mm), or soil water deficiency (A )^ (mm) mN - soil mineralizable nitrogen (kg/ha) Combination of PET, DGW, and mN Individual tree height-age curves were plotted and checked for evidence of early suppression or top deunage i n order to avoid the use of abnormal trees i n modelling. Twenty-five trees out of the total of 120 trees in i t ia l ly analyzed were not used i n any fiu-ther analysis because of evidence of early suppression or damage. In order to reduce the potential noise caused by suppression i n very early growth stages, the modelling was based on breast height age. Site index was defined as the average height of three dominant trees on a plot at 50 years b.h.a., calculated for each stand using the heights obtained firom stem analysis. A Hnear extrapolation technique was employed for determining height at 50 years b.h.a. when the age was less than 50. Pa ired height and age were used to compute the average height growth for each stand. The Chapman-Richards growth fimction (Richards, 1959; Chapman, 1961; Pienaar and T u m b u l l , 1973) was chosen to fit the height growth data: [5.3.3] i î = y 3 i ( l - e - M ) ^ 3 + e, where H = total height (m), A = age at breast height (years), e = base of natura l logarithm, e = error of the model, and fii,fi2' sndfi^ = parameters of the model to be estimated. This fimction was in i t ia l ly derived from V o n BertalanflFy's (1951) anabolic-catabolic growth fimction. Most of the other growth fimctions appear to be different forms of the Chapman-Richards equation (Pienaar and T u m b t d l , 1973). The logistic (Verhulst), monomolecular (Mitscherlich), and Gompertz growth fimctions (Richards, 1969) can a l l be considered as special cases of the Chapman-Richards function. Obviously, the Chapman-Richards growth function has a great flexibility i n describing growth of organisms, and parameter chsmges i n the Chapman-Richards equation are not expected to produce greatly different results. The parameter prediction method described by Clutter et al. (1983) was used to develop the parameter prediction equations using selected ecological variables (Table 5.1) and/or site index. To support the use of ecological variables i n the modelling system, a dummy variable approach (Cunia 1973, Habgood 1985) was used to test whether the ecological variables could significantly improve the performance of the parameter prediction equations. Consequently, to derive ecologically based polymorphic height growth models that wotdd precisely describe the shape of the height growth curves, selected measures of ecological site quaUty (Table 5.1) were examined for each stand i n relation to parameters estimated for the model (equation [5.3.3]). F o r comparison, the relationship between site index and the fimction parameters were also examined. The generalized prediction equations were as follows: [5.3.4] Pi, fi2, = / (ecological factors, site index), where ecological factors were either categorical variables or continuous variables (Table 5.1). The variables that showed the highest correlations w i t h the parameters were then substituted into equation [5.3.3] to produce a site-specific height growth model. B y examining the curve shapes, s imi lar ciuves fi-om adjacent sites were combined i n order to simplify the modeling system. Current and mean annual height increments were computed for each site i m i t us ing equation [5.3.3]. Graphical determination and residual analysis were used to verify and vahdate the model performance. The effect of density on height growth was examined by checking for correlation between site index and the nimaber of stems per hectare us ing a graphical method. A s Goudie's (1984) height growth model for lodgepole pine is driven by site index and the model developed i n this study is driven by ecological variables, the performance of the two models was compared. To compare the growth rate i n relation to ecological site quality, physiological growth parameters derived from V o n Bertalanffy's anabolic-catabolic ftmction (1951) were calctdated for different site tmits. A l l data analyses were done by using the Quattro Pro (Borland International Inc. 1989) spreadsheet package and the N L I N (nonlinear) and M G L H (multiple general l inear hypothesis) modules of the S Y S T A T (Wilkinson 1990) statistical package. A l l graphs were drawn using S Y G R A P H module of S Y S T A T . 5.4 R E S U L T S A N D D I S C U S S I O N 5.4.1. Averaging Height Growth Data Average growth curves were constructed for each of the 40 sample plots us ing equation [5.3.3]. The results are stunmarized i n Table 5.2. The mean value of the index of determination (I^) was 0.998 and the standard error of estimate was 0.522 m. Thus , the ftmction appeared to provide an appropriate means to summarize the lodgepole pine height growth data. For ecologically different sites, the asymptotic value (b^) and the growth rate ( b 2 ) , and the shape (hs) w i l l l ikely not be the same. Therefore, there appears to be £m opportunity to relate the model pareimeters to variables representing the ecological quality of forest sites. Table 5,2. A summary of average growth curves for each of the 40 sample plots. Parameter estimated Corrected Plot* b,h.a. b i bg bg P S E E (m) 4 46 22.7 0.04 1,48 1 0.999 0.234 5 46 37.3 0,01 1.02 0,999 0.996 0.379 7 48 40.7 0.01 1.12 1 0.999 0.131 10 48 29,5 0.02 1.07 1 0.999 0.192 11 50 26.8 0.02 1.27 1 0.998 0,254 12 51 26.1 0,02 0.98 0,998 0.990 0.456 13 52 20,9 0.02 1,04 0.998 0.984 0.599 14 53 40.7 0,01 0.98 0.999 0.997 0.337 15 48 40.4 0.01 1.33 1 0.999 0,119 16 52 29.6 0.02 1.19 0.999 0.996 0.403 17 50 28.9 0.02 1.16 0.997 0.997 0,649 19 49 22.0 0,02 1.18 0.999 0.996 0.262 20 48 20.2 0.02 1.15 1 0.997 0.213 21 46 9.52 0,04 1.48 0.999 0.995 0.188 22 49 19.1 0.01 0.91 1 0.998 0.119 23 49 30.5 0.01 1.11 1 0,998 0.178 24 48 30,7 0.01 1.02 1 1 0.109 26 45 32,0 0.01 1.46 1 0.999 0.710 27 48 25.6 0.01 0.95 0.999 0.996 0.217 29 41 21.3 0.02 1.38 0.999 0.997 0.164 31 46 22.3 0,02 1.57 0.999 0.997 0.172 36 40 19.3 0.02 1.10 0.999 0.994 0.238 55 67 25.6 0,03 1.57 0.999 0.996 0.441 56 64 27,3 0.03 1.52 0.997 0.985 0.936 57 70 22.0 0.04 1.45 0.998 0.991 0.652 58 73 22.4 0.04 1.57 0.998 0.987 0.805 59 68 16.7 0.04 1.64 0.998 0.989 0.546 60 68 43,7 0.02 1,23 0.999 0.995 0.609 61 71 19.5 0.03 1.29 0.996 0.978 0.770 62 72 27.7 0.04 1,56 0.998 0.991 0.778 63 73 35.8 0.02 1.08 0.999 0.993 0.694 64 73 23.8 0,03 1,09 0.997 0.984 0.790 65 72 27.3 0.03 1.34 0.997 0.986 0.889 66 73 19.9 0,04 1.57 0.992 0.960 1.235 67 72 31.7 0.03 1.47 0.998 0.992 0.755 68 73 27.2 0.03 1.48 0.997 0.985 0.941 69 46 11.2 0.05 1.83 0.994 0.870 1.387 70 70 19.8 0,04 1.42 0,991 0.949 1.362 71 75 22.0 0.03 1.53 0.997 0.986 0.619 72 71 37.8 0,02 1.34 0.997 0.986 1.003 5.4.2. Height Growth and Steind Density Relationships between site index and the number of stems per hectare were examined to determine the possible effect of stand density on height growth (Figure 5.1). The ntunber of stems per hectare was the only measure of stand density collected i n the study. According to the concept of ecological equivalence, even-aged stands that belong to the same site un i t have the same or s imi lar grovmig conditions and, hence, they are expected to have the same or s imi lar site index, assuming s imilar history of estabUshment and growth. Thus, by comparing the variation i n site index between stands ofthe same site series and s imi lar age, the effect of density on site index can be evaluated. V i s u a l analysis of F igure 5.1 gives no evidence of any consistent relationships between site index and number of stems per hecteu-e for any site imi t . Therefore, density as a factor was not included i n further analysis. Height growth of most tree species is generally considered to be relatively independent of stand density over a wide range of density and amount of foliage, except at extremely narrow spadngs (Oliver and Larson 1990). The height growth of some pines, including lodgepole pine, was found to be affected by stand density at extremes, part icularly by overcrowding (e.g., Alexander et al. 1967, Ol iver 1967, Carmean 1975, Clutter et al. 1983). B y stratifying 20 year-old lodgepole pine stands near Willi£mis Lake i n B . C . into four density classes, Roydhouse et al. (1985) found that stagnation may begin at stemd densities between 20,000 and 50,000 stems per hectare. In contrast, the present max imum density i n the study plots ranged from 3,300 to 8,200 stems per hectare—far below the values reported by Roydhouse et al. (1985). E3 15 10 -1 i q . 1 1 - -1 1 1 0 1700 3400 5100 6B00 8500 Number of stems per ha. i n SBPSxc site series 25 I , r 20 -15 -10 30 25 S 20 B 0) 10 1000 2000 3000 4000 5000 Number of stems per ha. in SBSmc site series 1 1 1 1 1 1 1 r 1 1 1 1 0 500 1000 1500 2000 2500 3000 3500 Number of stems per ha. in SBSwk site series Figure 5.1. Relationships between site index and number of stems per hectare for each stand and site series, according to biogeochmatic subzones. Symbols for site series are defined in Table 5.1. 5.4.3. Height Growth i n Relation to Ecological Variables and Site index U s i n g Cvinia's (1973) method, four l inear regression models were fitted for each of the three parameters using the site units and site index as independent variables (Appendix II). Three hypotheses were tested: (1) both intercepts and slopes together are not significantly different, (2) intercepts are not significantly different, and (3) slopes are not significantly different. The resvdts (Table 5.3) showed that, at the 0.05 level, (1) both intercepts and slopes together were not significantly different i n relation to b^, but significantly different i n relation to bg and h^; (2) intercepts alone were not sigrdficantly different i n relation to any parameters; (3) slopes were not significantly different i n relation to b^, but significantly different i n relation to bg and h^. It was expected that ecological variables would not improve the model performance i n terms of the intercepts because the curves started wi th a s imi lar point i n a l l cases. Ecological variables were highly related to the slopes that control the curve shapes. This relationship indicated that the use of ecological variables i n height growth modelling is necessary and important i n order to precisely describe the curve shapes. Plots of the height growth curves for each site series showed affinities and differences i n curve shapes. Affinities were observed between cl imatically and edaphically closely related site series, the differences were obvious among cl imatically or edaphically contrasting site series, even when the heights at 50 years of b.h.a., were the same (Figure 5.2). The shapes of the height growth curves on very dry sites [Arctostaphylos site series (SS2)] and wet sites [Salix site series (SS13)]) i n the SBSxc subzone were different, yet the value of measured actual site index (11.3 m) was the same for both site series [Figure 5.2(A)]. Consequently, using site index i n a one-point Table 5.3. Testing for site index i n relation to the parameters estimated for the Chapman-Richards growth function using regressions w i t h site units as dummy veuiables. Site units were defined i n Table 5.6. Hypothesis Par£uneter D F Calculated F Cr i t i ca l F (a = 0.05) 1. Bo th Intercepts and b l 15,21 1.26 2.18 slopes are the same b2 15,21 3.11 2.18 b3 15,21 2.27 2.18 2. Intercepts are the same b l 7,21 0.45 2.49 b2 7,21 1.27 2.49 b3 7,21 1.10 2.49 3. Slopes are the same b l 8,21 0.36 2.42 b2 8,21 2.92 2.42 b3 8,21 6.35 2.42 height growth model w i l l introduce bias for either site. It wovdd be reasonable to suggest that us ing site index sdone i n the parameter prediction approach is inappropriate i n situations where height growth curves have the same site index but different shapes. The shapes of the height growth ciu*ves on very moist and nutrient r i ch sites i n the S B P S x c , SBSmc , and S B S w k subzones were different for each site series involved [i.e., SEPSxc/Aulacomnium (SSIO), SBSmc/Equisetum ( S S l l ) , and SBSvfk/Equisetum (SS12)] [Figure 5.2(B)]. This was particularly true for the SSIO site series, whereas the curves for the S S l l and SS12 site series were quite similar. The extent of these differences parallels the pattern i n climatic differences between the subzones (Table 2.1). To determine ecological factors that are highly related to the parameters estimated for the Chapman-Richards growth function, parameter prediction equations were developed using both site index alone and selected measures of ecological site quality (Table 5.1). The coefficients of determination and standard errors of estimation from the parameter prediction models were used to determine which of the ecological variables had the strongest relationships w i t h the parameters (Table 5.4). S i m i l a r to the results obtained i n Chapter 4, the combination of B G C j , S M R s , and S N R s (ecotope), site series, £md the combination of P E T , m N , and D G W , were found to have the strongest relationships to a l l three curve parameters. It was decided to proceed vrith testing site series and ecotopes as concomitant variables i n a site-specific height growth model since the continuous variables (PET , m N , and D G W ) are appropriate for models studying the effect of environmental changes on forest productivity, but may not useful i n practice. This decision recognized the Age at breast height (yr) Figure 5.2 Height growth curves for (A) cl imatically s imi lar and edaphically different site series and (B) cl imatically different £md edaphically s imi lar sites series. Symbols for site series are defined i n Table 5.1. need for ecological strata i n the application of the model. Although useful, the continuous variables can not accommodate this need. B y definition, site series represent relatively uniform, cHmatically and edaphically consistent segments of a regional ecological gradient (Pojar et al. 1987). Comparing the parameter predictions based on site series, ecotopes, and site index showed that only b j had a significant relationship w i t h site index (Table 5.5.). This means that site index is weakly correlated to two of the curve parameters and i t can not be considered as a reliable variable by itsel f i n fitting and describing lodgepole pine height growth patterns. W i t h a l l three parameters significantly correlated to site series and ecotopes, these variables should be more usefiil concomitant variables than site index. 5.4.4 Site-specific and Site Index Dr iven Height Growth Models Subst i tut ing equations [5.4.4], [5.4.5], and [5.4.6] into model [5.3.3], a site series-spedfic model was constructed: [5.4.10] H = h + [15.792 - 6.272(SS1) + 6.456(SS2) + 5.514(SS3) + 6.05(SS5) + 7.710(SS6) + 8.952(SS7) + 16.997(SS8) + 14.897(SS9) + 9.374(SS10) + 14.989(SS11) + 21.972(SS12) + 16.247(SS13) + 24.630(SS14) + 0.000(SS15)]{1 - 6 - - 0 002(SS1) - 0.025(SS2) - 0.023(SS3) - 0.007(SS5) -0.020(SS6) - 0.007(SS7) - 0.022(SS8) - 0.011(SS9) - 0.023(SS10) - 0.017(SS11) - 0.020(SS12) - 0.027(S13) - 0.027(SS14) -0.00(SS15)]A}[1.585 - 0.108(SS1) - 0.433(SS2) - 0.210(SS3) - 0.259(SS5) - 0.577(SS6) - 0.123(SS7) - 0.479(SS8) - 0.180(SS9) -0.490(SS10) - 0.334(SS11) - 0.244(SS12) - 0.127(SS13) - 0.258(SS14) - 0.00(SS15)]^  where 'IT is the totsd height estimated; 'h ' equals corrected average height for the 1.3 meter section for each corresponding site series; 'e', and 'A' are as previously defined; vgiriable names were defined i n Table 5.1. Similgirly, by substituting equations [5.4.7], [5.4.8], and [5.4.9] into model [5.3.3], an ecotope-specific model was constructed: Table 5.4. Coefficients of determination (R2) and standard errors of estimation (SEE) from parameter prediction models for ecological variables ( N = 40). S3mibol£ for ecologicsd variables are defined i n Table 5.1. Variable parameters R2 adjusted R ^ S E E Categorical variables (1) Biogeoclimatic units b l 0.17 0.12 7.396 b2 0.41 0.38 0.009 b3 0.34 0.30 0.193 (2) Soil moisture regimes b l 0.42 0.22 6.95 b2 0.39 0.18 0.01 b3 0.28 0.03 0.229 (3) Soi l nutrient regimes b l 0.30 0.22 6.945 b2 0.19 0.10 0.01 b3 0.22 0.13 0.216 (4) Combination of b l 0.66 0.51 5.386 (1), (2), and (3) b2 0.57 0.39 0.008 ( N = 38) b3 0.52 0.32 0.195 (5) Site associations b l 0.42 0.25 6.834 b2 0.36 0.17 0.01 hi 0.26 0.04 0.227 (6) Site series b l 0.63 0.45 5.868 b2 0.62 0.43 0.008 bg 0.55 0.33 0.189 Continuous variables (7) P E T (mm) b l 0.17 0.12 7.396 b2 0.41 0.38 0.009 b l 0.34 0.30 0.193 (8) D G W (mm) b l 0.40 0.37 6.259 b2 0.04 0.0 0.011 b3 0.05 0.0 0.232 (9) m N (kg/ha) b l 0.19 0.17 7.181 b2 0.01 0.0 0.011 b l 0.07 0.05 0.226 (10) Combination of b l 0.58 0.52 5.489 (7), (8), and (9) b2 0.50 0.43 0.008 b3 0.45 0.37 0.183 Table 5.5. Comparisons of parsmieter predictions for b j , bg, and b3 based on site index, site series, and ecotopes (N = 40). Symbols for ecological variables are defined i n Table 5.1. Site index (SI) [5.4.1] bi = 6.894 + 1.175(SI) R2 = 0.31 SEE = 6.612 [5.4.2] b2 = 0.0196 - 0.00002(81)2 R2 = 0.03 SEE = 0.011 [5.4.3] b3 = 1.942 - 0.087(SI) + 0.0028(81)2 R2 = 0.03 SEE = 0.234 Site series (SSj) [5.4.4] bi = 15.792 - 6.272(SSi) + 6.456(SS2) + 5.514(883) + 6.05(885) + 7.710(885) + 8.952(887) + 16.997(SS8) + 14.897(889) + 9.374(SSio) + 14.989(SSii) + 21.972(SSi2) + 16.247(SSi3) + 24.630(SSi4) + 0.000(SSi5) R2 = 0.63 (adj. R2 = 0.45) SEE = 5.870 [5.4.5] b2 = 0.039 - 0.002(SSi) - 0.025(SS2) - 0.023(883) - 0.007(885) - 0.020(SS6) - 0.007(887) - 0.022(883) - O.OlKSSg) - 0.023(SSio) - 0.017(SSii) - 0.020(SSi2) - 0.027(813) - 0.027(SSi4) - 0.00(8815) R2 = 0.62 (aty. R2 = 0.43) SEE = 0.008 [5.4.6] b3 = 1.585 - 0.108(881) - 0.433(882) - 0.210(883) " 0.259(885) - 0.577(886) - 0.123(887) - 0.479(883) - 0.180(889) - 0.490(SSio) - 0.334(SSii) - 0.244(8812) - 0.127(8813) - 0.258(8Si4) - 0.00(8815) R2 = 0.55 (a(tj. R2 = 0.33) SEE = 0.189 Ecotope (combination of BGCj, SNRs, and SMRs) (N = 38) [5.4.7] bi = 3.742 + 2.640(ED) + 11.415(VD) + 2.568(MDf) + 5.568(80*) + 10.662(MD) + 12.061(SD) + 16.461(F) + 15.360(M) + 12.830(VM) + O.OO(W) + 3.953(SNRs) - 0.814(BGCi) R2 = 0.66 (a4j. R2 = 0.51) SEE = 5.386 [5.4.8] b2 = 0.018 + O.Oll(ED) - 0.009(VD) - 0.004(MDf) - 0.003(80 )^ - 0.009(MD) - 0.008(8D) - 0.014(F) - 0.010(M) - 0.009CVM) - 0.00(W) - 0.002(SNRs) + 0.009(BGCi) R2 = 0.57 (a^j. R2 = 0.39) SEE = 0.008 [5.4.9] b3 = 0.550 + 0.586(ED) + 0.244rVD) + 0.430(MD^ + 0.145(SD )^ - 0.238(MD) - 0.139(SD) - 0.141(F) - 0.198(M) - 0.085(VM) - 0.00(W) + 0.018(SNRs) + 0.323(BGCi) R2 = 0.52 (adj. R2 = 0.32) SEE = 0.195 [5.4.11] H = h + [3.742 + 2.640(ED) + 11.415(VD) + 2.568(MD*) + 5.568(80 )^ + 10.662(MD) + 12.061(SD) + 16.461(F) + 15.360(M) + 12.830(VM) + 0.00(W) + 3.953(SNRs) - 0.814(BGCi)]{l - e -[0.018 + O.Oll(ED) - 0.009(VD) - 0.004(MD1) - 0.003(SDf) - 0.009(MD) - 0.008(SD) - 0.014(F) - 0.010(M) - 0.009(VM) - 0.00(W) -0.002(SNR8) + 0.009(BGCi)A]}[0.550 + 0.586(ED) + 0.244(VD) + 0.430(MD0 + 0.145(SDf) - 0.238(MD) - 0.139(SD) - 0.141(F) -0.198(M) - 0.085(VM) - 0.00(W) + 0.018(SNR8) + 0.323(BGCi)]^ where 'h' equals corrected average height for the 1.3 meter section for each corresponding ecotope; 'IT, 'e', and 'A' are as previously defined; variable names were defined i n Table 5.1. Equations [5.4.10] and [5.4.11] were used to compute lodgepole pine height growth for a l l site series and a l l ecotopes represented i n the study, respectively. U s i n g tabular and graphical data (Appendix III), the height growth curves were compared for similarit ies, differences, consistency, and conformity to a general pattern of relationships by stand, site series, and ecotopes. Consequently, a framework of site units (site series or their groupings), and parameter prediction equations for b j , b2, and b3 based on these site units , were constructed (Table 5.6). For example, SS2 and SS3 were combined as site un i t 2, SS8 and S S l l as site i in i t 5, and SS9 and SS12 as site uni t 8. Comparing the parameter prediction equations for the site series, ecotope, and site unit models (Table 5.7) showed that the relations between height growth curve parameters and ecological variables were slightly improved based on adjusted and S E E by using site units as expressive variables to explain the variation of the height growth parameters. B y substituting equations [5.4.12], [5.4.13], and [5.4.14] into model [5.3.3], the site uni t model was developed: [5.4.15] H = h + [15.792 - 6.272(SU1) + 6.268(SU2) + 9.374(SU3) + 7.710(SU4) + 16.244(SU5) + 6.050(SU6) + 8.952(SU7) + 15.908(SU8) + 0.00(SU9)]{l - e-[oo39-ooo2(SUi)-0.024(SU2) - 0.D23(SU3) - 0.020(SU4) - 0.020(SU5) - 0.007(SU6) - 0.007(SU7) - 0.012(SU8) - 0.00(SU9)]A} [1.585 - 0.108(SU1) -a.388(SU2) - 0.490(SU3) - 0.577(SU4) - 0.425(SU5) - 0.259(SU6) - 0.123(SU7) - 0.189(SU8) - 0.00(SU9)]^  Table 5.6. Parameter prediction equations for b j , b2, and b3 based on site imits (SUj) ( N = 38). [5.4.12] bi = 15.792 - 6.272(SUi) + 6.268(SU2) + 9.374(SU3) + 7.710(SU4) + 16.244(SU5) + e.OSOCSUg) + 8.952(SU7) + 15.908(SU8) + O.OOCSUg) R2 = 0.57 (adj. R2 = 0.45) SEE = 5.713 [5.4.13] b2 = 0.039 - 0.002(SUi) - 0.024(SU2) - 0.023(SU3) - 0.020(SU4) - 0.020(SU5) - 0.007(SU6) - 0.007(SU7) - 0.012(SU8) - 0.00(SU9) R2 = 0.56 (adj. R2 = 0.44) SEE = 0.008 [5.4.14] b3 = 1.585 - 0.108(SUi) - 0.388(SU2) - 0.490(SU3) - 0.577(SU4) . 0.425(SU5) - 0.259(SU6) - 0.123(SU7) - 0.189(SU8) - 0.00(SU9) R2 = 0.51 (adj. R2 = 0.37) SEE = 0.187 where SUj to SUg representing site imits from 1 through 9; 1 = SEPSxc/Stereocauhn, 2 = SBFSxc/Arctostaphylos, 3 = SBPSxc/AMZacomnm/n, 4 = SBSmc/V; membranaceum, 5 = SBSmc/Gymnocarpium, 6 = SBSwkA'l myrtilloides, 7 = SBS-wk/V.membranaceum, 8 = SBSwk/Gymnocarpium, 9 = SBSwk/Carejc Table 5.7. Comparisons of pargmieter prediction equations for site series, ecotope, and site i m i t height growth models. Model R 2 ad j .R2 S E E Site series (SSj) [5.4.4] 0.63 0.45 5.870 [5.4.5] ( N = 40) 0.62 0.43 0.008 [5.4.6] 0.55 0.33 0.189 Ecotope (combination of B G C j , S N R s , and SMRs) [5.4.7] 0.66 0.51 5.386 [5.4.8] (N=38) 0.57 0.39 0.008 [5.4.9] 0.52 0.32 0.195 Site uni t (SUj) [5.4.12] 0.57 0.45 5.713 [5.4.13] (N=38) 0.56 0.44 0.008 [5.4.14] 0.51 0.37 0.187 where 'h ' equals corrected average height for the 1.3 meter section for each corresponding site unit ; 'IT, 'e', and 'A' are as previously defined; site imits were defined i n Table 5.6. Equat ion [5.4.15] was then used for producing site unit height growth tables and curves (Tables 5.8 and 5.9, Figure 5.3). The SBVSxclArctostaphylos, SBSmc /V . membranaceum, and SBSwk/Gymnocarpium site units were selected for comparing performance between the site uni t ctu-ves and their related ecotope curves (Table 5.10, Figure 5.4). It is quite clear that curves developed by these two different approaches are very s imilar . The implication is that the complicated ecotope curves can be satisfactorily represented by the simplified site i m i t curves. E a c h height growth curve has different parameter values (Tables 5.8, 5.11 and 5.12) which are based on site imit , site series or ecotope; thus the curves are site-specific and polymorphic. Once an ecotope and, hence, site series or site unit are identified, then a particular ecotope, site series, or site uni t equation is defined and the site index for that ecotope, site series, or site un i t can be determined at any index age. The reader is reminded that some site series, site units , and, particularly some ecotopes, were not represented by an adequate number of stands. This is a result of l imited sampling, the pattern of sites i n the selected sampling areas, and deleting young stands, or those exhibit ing atypical growth. Due to non-homogeneous VÊuiance i n certain cases, weighted regression should be considered i n future studies. A l l curves generated were extrapolated to 100 years; however, prediction beyond 70 years is not recommended. Table 5.8. Height growth parameters computed for site uni t height growth model [5.4.15] us ing equations [5.4.12], [5.4.13], and [5.4.14]. Site units are defined i n Table 5.6. Site i m i t b j b2 b3 S U i 9.520 0.037 1.477 S U 2 22.060 0.015 1.197 S U 3 25.166 0.016 1.095 S U 4 23.502 0.019 1.008 S U 5 32.036 0.019 1.160 S U g 21.842 0.032 1.326 S U 7 24.744 0.032 1.462 S U g 31.700 0.027 1.396 S U g 15.792 0.039 1.585 Table 5.9. Lodgepole pine height growth by site units based on equation [5.4.15] and parameters given in Table 5.8. Symbols for sites units are given in Table 5.6. B . H . Aga SUI sa2 SU3 SU4 SU5 sn6 SD7 sn8 SU9 0 1.40 1.43 1.46 1.54 1.50 1.56 1.56 1.49 1.42 1 1.47 1.57 1.73 1.97 1.79 1.78 1.72 1.69 1.51 2 1.59 1.76 2.03 2.39 2.18 2.11 1.99 2.01 1.68 3 1.74 1.96 2.34 2.81 2.59 2.48 2.31 2.39 1.90 4 1.91 2.16 2.66 3.22 3.01 2.88 2.68 2.81 2.16 5 2.09 2.38 2.98 3.63 3.45 3.29 3.07 3.25 2.44 6 2.28 2.60 3.30 4.03 3.89 3.72 3.49 3.72 2.74 7 2.47 2.83 3.61 4.42 4.33 4.16 3.93 4.21 3.05 8 2.67 3.05 3.93 4.80 4.77 4.60 4.37 4.71 3.38 9 2.88 3.28 4.25 5.18 5.22 5.04 4.83 5.22 3.71 10 3.08 3.51 4.56 5.55 5.66 5.48 5.29 5.73 4.05 11 3.29 3.75 4.88 5.91 6.10 5.92 5.75 6.25 4.36 12 3.49 3.98 5.19 6.27 6.53 6.36 6.21 6.77 4.74 13 3.70 4.21 5.49 6.62 6.97 6.79 6.68 7.28 5.08 14 3.90 4.44 5.80 6.97 7.40 7.22 7.14 7.80 5.42 15 4.10 4.67 6.10 7.30 7.83 7.64 7.60 8.32 5.76 16 4.30 4.90 6.40 7.64 8.25 8.06 8.06 8.83 6.10 17 4.49 5.13 6.69 7.96 8.67 8.47 8.51 9.35 6.43 IB 4.68 5.36 6.98 8.28 9.08 8.87 8.96 9.85 6.76 19 4.87 5.59 7.27 8.59 9.49 9.26 9.40 10.35 7.08 20 5.05 5.81 7.55 8.90 9.89 9.65 9.83 10.85 7,40 21 5.23 6.04 7.84 9.20 10.29 10.03 10.26 11.34 7.70 22 5.41 6.26 8.11 9.50 10.69 10.40 10.68 11.82 8.01 23 5.58 6.48 8.39 9.79 11.08 10.76 11.10 12.30 8,30 24 5.75 6.70 8.66 10.08 11.46 11.12 11.50 12.77 8.59 25 5.92 6.92 8.93 10.36 11.84 11.46 11.90 13.23 8,88 26 6.08 7.13 9.19 10.63 12.21 11.80 12.29 13.68 9.15 27 6.23 7.35 9.45 10.90 12.57 12.13 12.68 14.13 9.42 28 6.38 7.56 9.71 11.17 12.94 12.45 13.05 14.57 9.68 29 6.53 7.77 9.96 11.43 13.30 12.77 13.42 15.01 9.94 30 6.67 7.98 10.21 11.68 13.65 13.08 13.78 15.43 10.18 31 6.81 8.18 10.46 11.93 13.99 13.38 14.13 15.85 10.42 32 6.95 8.39 10.71 12.18 14.34 13.67 14.47 16.26 10,66 33 7.08 8.59 10.95 12.42 14.68 13.95 14.81 16.66 10.88 34 7.21 8.79 11.18 12.66 15.01 14.23 15.13 17.05 11,10 35 7.33 8.98 11.42 12.89 15.33 14.50 15.45 17.44 11.32 36 7.45 9.18 11.65 13.12 15.65 14.76 15.76 17.82 11.52 37 7.57 9.37 11.88 13.34 15.97 15.02 16.06 18.19 11.72 38 7.68 9.56 12.10 13.56 16.28 15.26 16.36 18.55 11.92 39 7.79 9.75 12.32 13.78 16.59 15.51 16.65 18.91 12.10 40 7.90 9.94 12.54 13.99 16.89 15.74 16.93 19.25 12.29 41 8.00 10.12 12.75 14.20 17.18 15.97 17.20 19.59 12.46 42 8.10 10.31 12.97 14.40 17.48 16.19 17.47 19.93 12.63 43 8.20 10.49 13.18 14.60 17.76 16.41 17.73 20.25 12.80 44 8.29 10.67 13.38 14.80 18.04 16.62 17.98 20.57 12.96 45 8.38 10.84 13.58 14.99 18.32 16.82 18.22 20.88 13.11 46 8.47 11.02 13.78 15.18 18.59 17.02 18.46 21.19 13.26 47 8.56 11.19 13.98 15.36 18.86 17.21 18.70 21.49 13.40 48 8.64 11.36 14.18 15.54 19.12 17.40 18.92 21.78 13.54 49 8.72 11.53 14.37 15.72 19.38 17.58 19.14 22.06 13.67 50 8.79 11.69 14.56 15.90 19.64 17.76 19.35 22.34 13.80 T a b l a 5 .9 . (contlnuad) 51 8.87 11.86 14.74 16.07 19.89 17.93 19.56 22.61 13.93 52 8.94 12.02 14.92 16.24 20.13 18.09 19.76 22.88 14.05 53 9.01 12.18 15.10 16.40 20.38 18.26 19.96 23.14 14.16 54 9.08 12.34 15.28 16.57 20.61 18.41 20.15 23.39 14.28 55 9.14 12.49 15.46 16.72 20.85 18.57 20.34 23.64 14.38 56 9.20 12.65 15.63 16.88 21.08 18.71 20.52 23.88 14.49 57 9.26 12.80 15.80 17.03 21.30 18.86 20.69 34.13 14.59 58 9.32 12.95 15.97 17.18 21.53 18.99 20.86 24.35 14.69 59 9.38 13.10 16.13 17.33 21.74 19.13 21.03 24.57 14.78 60 9.43 13.24 16.29 17.48 21.96 19.26 21.19 24.79 14.87 61 9.49 13.39 16.45 17.62 22.17 19.39 21.34 25.00 14.96 63 9.54 13.53 16.61 17.76 22.37 19.51 21.49 25.21 15.04 63 9.59 13.67 16.77 17.90 22.58 19.63 21.64 25.42 15.12 64 9.63 13.81 16.92 18.03 22.78 19.75 21.78 25.62 15.20 65 9.68 13.95 17.07 18.16 22.97 19.86 21.92 25.81 15.28 66 9.72 14.08 17.22 18.29 23.17 19.97 22.05 25.99 15.35 67 9.77 14.21 17.37 18.42 23.36 20.08 22.18 26.18 15.42 6S 9.81 14.35 17.51 18.54 23.54 20.18 22.31 26.36 15.48 69 9.85 14.48 17.65 18.66 23.72 20.28 22.43 26.54 15.55 70 9.88 14.60 17.79 18.78 23.90 20.37 22.55 26.71 15.61 71 9.92 14.73 17.93 18.90 24.08 20.47 22.67 26.88 15.67 72 9.96 14.86 18.06 19.02 24.25 20.56 22.78 27.04 15.73 73 9.99 14.98 18.20 19.13 24.42 20.65 22.89 27.20 15.79 74 10.02 15.10 18.33 19.24 24.59 20.73 22.99 37.36 15.84 75 10.06 15.22 18.46 19.35 24.75 20.81 23.09 27.51 15.89 76 10.09 15.34 18.59 19.46 24.91 20.90 23.19 37.65 15.94 77 10.12 15.45 18.71 19.56 25.07 20.97 23.29 37.80 15.99 78 10.15 15,57 18.83 19.67 25.23 21.05 23.38 37.94 16.03 79 10.17 15.68 18.96 19.77 25.38 21.12 23.47 38.07 16.08 80 10.20 15.80 19.08 19.87 25.53 21.19 23.56 38.31 16.13 81 10.23 15.91 19.19 19.96 25.68 21.26 33.64 38.34 16.16 82 10.25 16.01 19.31 20.06 25.82 21.33 23.73 38.46 16.30 83 10.28 16.12 19.42 20.15 25.96 21.39 23.81 38.59 16.34 84 10.30 16.23 19.54 20.24 26.10 21.45 23.88 38.71 16.38 85 10.32 16.33 19.65 20.33 26.24 21.52 23.96 38.83 16.31 86 10.34 16.44 19.76 20.42 26.37 21.57 24.03 38.94 16.35 87 10.36 16.54 19.86 20.51 26.51 21.63 24.10 29.05 16.38 88 10.38 16.64 19.97 20.60 26.64 21.69 24.17 39.16 16.41 89 10.40 16.74 20.07 20.68 26.76 21.74 24.24 29.26 16.44 90 10.42 16.83 20.18 20.76 26.89 21.79 24.30 29.36 16.47 91 10.44 16.93 20.28 20.84 27.01 21.84 24.36 29.46 16.50 92 10.46 17.02 20.38 20.92 27.13 21.89 24.42 39.56 16.53 93 10.47 17.12 20.48 20.99 27.25 21.94 24.48 29.66 16.55 94 10.48 17.21 20.57 21.07 27.36 21.98 24.54 29.75 16.58 95 10.51 17.30 20.67 21.15 27.46 22.03 24.59 29.84 16.60 96 10.52 17.39 20.76 21.22 27.59 22.07 24.65 29.93 16.63 97 10.53 17.48 20.85 21.29 27.70 22.11 24.70 30.01 16.65 98 10.55 17.57 20.94 21.36 27.81 22.15 24.75 30.10 16.67 99 10.56 17.65 21.03 21.43 27.91 22.19 24.80 30.18 16.69 100 10.57 17.74 21.12 21.50 28.02 22.23 24.84 30.36 16.71 O SU9 • SU8 > SU7 ^ SU6 O SU5 * SU4 V SU3 • SU2 O SUI 100 Age at breast height (yr) Figure 5.3. Lodgepole pine height growth curves by site imits based on equation [5.4.15] and parameters given i n Table 5.8. Symbols for sites units are given i n Table 5.6. Table 5.10. Comparisons of lodgepole pine height growth predicted by site unit and ecotope models based on equations [5.4.11] and [5.4.15] and parameters given in Tables 5.8 and 5.12. Symbols for site units are given in Table 5.6, and for SMRs and SNRs in Table 5.1. Estimated height SBPSxc SBSmc SBSwk Age SU2 VD*VPVD*M SU4 SD*P SUg F*M M*M M*R VM*E 5 2.38 2.42 2.37 3.63 3.90 3.25 2.88 3.32 3.32 2.90 10 3.51 3.52 3.47 5.55 6.05 5.73 4.91 5.78 5.86 5.08 15 4.67 4.60 4.60 7.30 7.96 8.32 7.11 8.31 8.52 7.48 20 5.81 5.64 5.72 8.90 9.66 10.85 9.29 10.73 11.11 9.86 25 6.92 6.62 6.82 10.36 11.18 13.24 11.39 12.97 13.55 12.15 30 7.98 7.55 7.89 11.68 12.52 15.43 13.36 15.02 15.80 14.28 35 8.98 8.43 8.91 12.89 13.73 17.44 15.18 16.86 17.86 16.24 40 9.94 9.25 9.90 13.99 14.79 19.25 16.86 18.50 19.72 18.02 45 10.84 10.01 10.85 14.99 15.75 20.88 18.38 19.96 21.39 19.62 50 11.69 10.73 11.75 15.90 16.60 22.34 19.77 21.25 22.88 21.05 55 12.49 11.39 12.61 16.72 17.35 23.64 21.01 22.38 24.21 22.32 60 13.24 12.01 13.43 17.48 18.03 24.79 22.13 23.37 25.38 23.45 Figure 5.4. Comparison of site unit and ecotope lodgepole pine height growth curves based on equations [5.4.15] and [5.4.11]. Symbols for sites units are given in Table 5.6, for BGC, SMRs, and SNRs are explained in Table 5.1. Table 5.11. Height growth parameters computed for the site series height growth model using equations [5.4.4], [5.4.5], and [5.4.66]. Symbols for site series are given i n Table 5.1. Site series b^ b2 S S i 9.52 0.037 1.477 SS2 22.25 0.015 1.153 SSg 21.31 0.016 1.375 SSg 21.84 0.032 1.326 SSg 23.50 0.020 1.008 SS7 24.74 0.033 1.462 SSg 32.79 0.017 1.106 SSg 30.69 0.028 1.405 S S i o 25.17 0.016 1.095 S S l l 30.78 0.022 1.251 SS12 37.76 0.019 1.341 SS13 40.42 0.012 1.327 S S i 4 32.04 0.012 1.458 SS15 15.79 0.039 1.585 Table 5.12. Height growth parameters computed for the ecotope height growth model us ing equations [5.4.7], [5.4.8], and [5.4.9]. Symbols for B G C , S M R , and S N R are given i n Table 5.1. B G C S M R S N R b l b2 b3 S B P S x c E D V P 9.522 0.036 1.477 V D V P 18.296 0.016 1.135 V D M 26.202 0.012 1.171 M D ^ R 21.318 0.015 1.375 S D ^ R 24.318 0.016 1.090 S D ^ V R 28.260 0.014 1.108 SBSmc S D P 22.080 0.024 1.093 F M 30.434 0.016 1.109 F R 34.387 0.014 1.127 M R 33.286 0.018 1.090 V M R 30.756 0.019 1,183 V M V R 34.709 0.017 1.210 S B S w k M D P 19.868 0.032 1.317 M D M 23.821 0.030 1.335 S D M 25.220 0.031 1.434 F M 29.620 0.025 1.432 M M 28.519 0,029 1.375 M R 32.472 0.027 1.393 V M R 29.942 0.028 1.506 W M 13.159 0,039 1.573 W V R 21.065 0.035 1.609 U s i n g parameter values calculated from site index equations [5.4.1], [5.4.2], and [5.4.3] (Table 5.1) i n a site index driven height growth model, some serious biases were observed (Figure 5.5). One of the biases was that the site index dr iven curves consistently overestimated height by about 2 m at any site index (Table 5.13). According to Clutter et al. (1983), one of the major problems w i t h using site index i n growth modell ing is that the curve does not pass through that height at index age (Table 5.13, Figure 5.5). The cause of this problem is simply that the relations between site index and the cxirve parameters are too weak to precisely describe height growth patterns. It is s t i l l a common practice to constrain the curves through the height at index age by proportionally adjusting the ciuves. These adjusting procedures could assign too much weight to the curve shape and cause additional noise result ing i n erratic and non-tenable curves. For site-specific height growth curves constructed without site index i n the model, the site index w i l l always be the height at index age without any need for adjustment. Another problem w i t h the site index-driven approach is that site index can not be computed explicitly for a given age and height unless graphical determination or tedious iterative computation are employed following the formulation of a model. This may result i n somewhat erratic estimation of site index and more complex modelling. F ina l l y , w i t h site index i n the parameter prediction equations, choice of index age affects the shape of height growth curves and results i n different curves for different index ages. However, without site index i n the parameter prediction equations for site-specific height growth models, the choice of index age has no effect on curve shapes and results i n the same curves for any index ages. Table 5.13. Comparisons between lodgepole pine site index estimated using equation [5.3.3] w i t h parameters calculated from site index equations [5.4.1], [5.4.2], and [5.4.3], and the height corresponding to the index age of 50 years. Site index (m) Height at index age (m) Difference (m) 5 7.70 -2.70 10 12.12 -2.12 15 17.09 -2.09 20 22.20 -2.20 25 27.29 -2.29 30 32.49 -2.49 50 40 h 30 -20 h ce 10 -0 SI 30 SI 25 SI 20 SI 15 SI 10 SI 5 0 20 40 60 80 Age at breast height (yr) 100 Figure 5.5 Lodgepole pine height growth curves derived by us ing site index i n parameter prediction equations ([5.4.1], [5.4.2], and [5.4.3]). 5,4.5. Increment Characteristics of Height Growth Ctimulative or total height growth for each site un i t was described using equation [5.4.15]. Current annual height increment (CAI) was computed as (Renaar and T u m b u l l 1973): [5.4.16] C A I = b 2 b 3 H [ ( - ^ ) ( l ^ 3 ) . i ] H where H , b^, b2, and b3 are defined i n section 5.4.4, and mean annual height increment (MAI) was computed as (Pienaar and T u m b u l l 1973): [5.4.17] ^^^^ bi( l -e -b2A)b3 M A I = —= , At where b^, b2, b3, and e are as defined i n section 5.4.4, and 'A^.' equals total age i n years, which is breast height age plus age to breast height calculated using Goudie's (1984) equation: [5.4.18] Age to breast height = 8.60 + , S I F imct ion [5.4.17] can be simply expressed as M A I = H/Aj. where H = total height i n meters. Obviously, [5.4.16] and [5.4.17] are derivative functions of [5.4.15]. The estimated values of C A I and M A I for each site i m i t are presented i n Figure 5.6; Figures 5.7 and F igure 5.8 show the pattems of C A I and M A I for site imits stratified by biogeoclimatic subzones; and Table 5.14 gives tabulated data of estimated H , C A I , and M A I for the site units studied. Since C A I and M A I curves were derived fi-om a site-specific model, i t was not surprising that both C A I and M A I curves are site-specific, i.e., the curve shape and, to lesser degree culmination and intersection points vary w i t h ecological site SU3 — SU2 S U l 40 60 80 T o t a l age (yr) 120 SU5 SU4 40 60 60 I b t a l age (yr) 120 SU9 SUB SU7 SU6 40 60 80 T o t a l age (yr) Figure 5.6. The plot of estimated mean annual increments (MAI) for site units stratified according to biogeoclimatic subzone. Symbols for biogeoclimatic subzones and site units are explained in Table 5.1 and 5.6. I " 0.60 054 s 0.48 1 0.42 0-TR a 0.30 1 0J24 a 0J8 a •*> 0J2 î 0.06 5 0.00 •1 1 r -SBPSxc • '/ -•y 1 0.60 0.60 SU3 SU2 SUI 20 40 60 80 T o t a l age (yr) 100 120 40 60 60 T o t a l age (yr) S U 9 SU8 SU7 sue 40 60 80 I b i a l age (yr) 100 120 Figure 5.7. The plot of estimated current annual increments (CAI) for site units stratified according to biogeoclimatic subzones. Sjrmbols for biogeoclimatic subzones and site units are explained in Table 5.1 and 5.6. Current annual increment (solid line) and mean annual increment (dotted line) (m) § § g g § g 8 S S I I I I g g I g g g g g § i g g g i g g g g g g [ • " î e - i ^ ^ — 1 — 1 — I — I — I — 1 — I — I o i-!!»-! I — I — I — 1 — I — 1 — 1 — 1 — 1 ° f « ^ - i — 1 — 1 — 1 — 1 — 1 — 1 — I — I — 1 i § g g g g S g g I i i I g g i g g g g g g g I g g g g g g g g g ° n ! ! = i r — I — I — I — I — I — I — I — I — I ° I— I —1— I —1—1—1—1—1 e — , — , — , — , — , — , — , — , — , Table 5.14. Cumulative growtii (H), current annual increment (CAI), and mean £mnual increment (MAI) for each site imit . Bo ld fonts indicate the total age of max imum mean annual increment and its corresponding growth. Symbols for site units are explained i n Table 5.6. Breast height age is i n parentheses. Total age H C A I M A I H C A I M A I H C A I M A I Site un i t 1 Site unit 2 Site uni t 3 12(00) 1.40 0.20 0.11 1.43 0.23 0.12 1.46 0.32 0.12 22(10) 3.08 0.19 0.13 3.51 0.23 0.16 4.56 0.30 0.21 32(20) 5.05 0.15 0.15 5.81 0.21 0.18 7.55 0.26 0.24 42(30) 6.67 0.10 0.16 7.98 0.19 0.19 10.21 0.23 0.24 52(40) 7.90 0.06 0.15 9.94 0.17 0.19 12.54 0.20 0.24 62(50) 8.79 0.03 0.14 11.69 0.15 0.19 14.56 0.17 0.23 72(60) 9.43 0.003 0.13 13.24 0.13 0.18 16.29 0.14 0.23 82(70) 9.88 0.00 0.12 14.60 0.11 0.18 17.79 0.12 0.22 92(80) 10.20 0.11 15.80 0.09 0.17 19.08 0.10 0.21 102(90) 10.42 0.10 16.83 0.08 0.17 20.18 0.08 0.20 112(100) 10.57 0.09 17.74 0.06 0.16 21.12 0.06 0.19 Site un i t 4 Site uni t 5 Site uni t 6 11(00) 1.54 0.41 0.14 1.50 0.43 0.14 1.56 0.41 0.14 21(10) 5.55 0.34 0.26 5.66 0.43 0.27 5.29 0.46 0.25 31(20) 8.90 0.28 0.29 9.89 0.38 0.32 9.83 0.40 0.32 41(30) 11.68 0.22 0.28 13.65 0.33 0.33 13.78 0.32 0.34 51(40) 13.99 0.18 0.27 16.89 0.27 0.33 16.93 0.23 0.33 61(50) 15.90 0.14 0.26 19.64 0.23 0.32 19.35 0.17 0.32 71(60) 17.48 0.11 0.25 21.96 0.19 0.31 21.19 0.11 0.30 81(70) 18.78 0.09 0.23 23.90 0.15 0.30 22.55 0.07 0.28 91(80) 19.87 0.07 0.22 25.53 0.12 0.28 23.56 0.04 0.26 101(90) 20.76 0.05 0.21 26.89 0.10 0.27 24.30 0.01 0.24 111(100) 21.50 0.04 0.19 28.02 0.08 0.25 24.84 0.00 0.22 Site un i t 7 Site uni t 8 Site uni t 9 11(00) 1.56 0.41 0.14 1.49 0.45 0.14 1.42 0.31 0.12 21(10) 5.29 0.46 0.25 5.73 0.52 0.27 4.05 0.34 0.18 31(20) 9.83 0.40 0.32 10.85 0.47 0.35 7.40 0.28 0.23 41(30) 13.78 0.32 0.34 15.43 0.39 0.38 10.18 0.20 0.24 51(40) 16.93 0.23 0.33 19.25 0.31 0.38 12.29 0.13 0.24 61(50) 19.35 0.17 0.32 22.34 0.24 0.37 13.80 0.08 0.22 71(60) 21.19 0.11 0.30 24.79 0.18 0.35 14.87 0.04 0.21 81(70) 22.55 0.07 0.28 26.71 0.13 0.33 15.61 0.007 0.19 91(80) 23.56 0.04 0.26 28.21 0.09 0.31 16.12 0.00 0.18 101(90) 24.30 0.01 0.24 29.36 0.06 0.29 16.47 0.16 111(100) 24.84 0.00 0.22 30.26 0.04 0.27 16.71 0.15 quality (Table 5.14, Figure 5.6). Changes i n growth rates can be related to climatic, soil moisture, and soil nutrient conditions. Height growth rates were slightly higher i n the S B S w k subzone than i n the S B S m c subzone, and very low i n the S B P S x c subzone. W i t h i n a biogeocHmatic subzone, growth rates increased from water deficient sites to very moist sites and decreased from very moist to wet sites. These trends reflect the climatic and edaphic efFects on height growth which were discussed i n detail i n Chapter 4. The height C A I culminated at or before 11 to 21 years of total age for the study stands, based on the site imi t height growth model (Table 5.14), According to the site un i t height growth model, M A I culminated for the study stands w i t h i n a relatively narrow range—^between 30 and 40 years of total age (Table 5,14). The earlier max imum occurred on drier and nutrient-poorer sites while the later max imum was for wetter and nutrient-richer sites (Table 5.14). 5.4.6. Test of the Site-specific Height Growth Model The plot of measured and estimated heights against breast height age showed that the model fitted the data weU, and there was not any obvious serious bias for any S U , w i t h the exception that the height growth for ages greater than 40 years i n the SBSwk/G^m/iocarpmm S U was slightly over-estimated (Figure 5.9). The results of residual analysis between measured and estimated heights at 5 year intervals at breast height age for each of the 38 stands are summarized i n Table 5.15. Heights i n 87% of stands were correctly estimated w i t h less than 11.01 m error. 12% of the stands were one class off, i.e., w i th in 11.0-1.51 m of measured heights. I f 1.5 m estimation error is considered acceptable for estimating lodgepole pine height, then the heights i n 99% of stands were acceptably estimated. ao 20 10 -T —1 S U B —1 A ' A • • ^ . 1 ' ! ! ' . • X —1 1.... 20 BO 100 40 60 Age a t b r e a s t h e i g h t (yr) 20 40 eO BO 100 30 20 10 h r 1 1 1 SU6 y 1 1 1 20 40 0 0 80 100 Figxire 5.9. Relationships between measured and estimated heights for site units. Symbols for site imits are explained in Table 5.6. UJ Table 5.15. Residual analysis based on equation [5.4.15] at 5-year intervals at breast height age for each stand. Age (yr) Number of stands for each class (proportion i n psirentheses) Correct^ 1 class off 2 classes off Total 5 38 (100) 38 10 35 (92.1) 3 (7.9) 38 15 35 (92.1) 2 (5.3) 1 (2.6) 38 20 32 (84.2) 5 (13.2) 1 (2.6) 38 25 34 (89.5) 3 (7.9) 1 (2.6) 38 30 34 (89.5) 3 (7.9) 1 (2.6) 38 35 33 (86.8) 4 (10.5) 1 (2.6) 38 40 33 (86.8) 4 (10.5) 1 (2.6) 38 45 32 (84.2) 6 (15.8) 38 50 24 (77) 7(23) 31 55 16 (73) 6(27) 22 60 18 (86) 3(14) 21 Average 30.3 (86.8) 3.8(11.9) 0.5(1.3) 34.6 1 Correct: w i t h i n 1 m of measured heights; 1 class off: w i t h i n 1 -1 .5 m; 2 classes off: w i th in 1.6 - 2 m. 5.4.7. Comparison of the Site U n i t Model and Goudie's Models Goudie's site index (SI) driven height growth curves for lodgepole pine are widely used i n B r i t i s h Columbia (Goudie 1984). Goudie constructed his c\u-ves using the Logistic model, stratifying sites into two site classes (dry and wet), and applying a modified Dahms (1975) parameter prediction approach, as did Monserud (1984). (îoudie's curves and the S U curves for this study appeared s imi lar for some S U s such as SBSmc/Gy mnocarpium (SU5) and SBSvfk/Gymnocarpium (SU8) (Figure 5.10, Table 5.16). However, there were some discrepancies that should be noted. F i r s t l y , although Goudie's curves paralleled the S U curves quite well i n some cases, their fit was inferior to that achieved by the S U ciu-ves. The mean difference between the S I calculated from the Goudie's model and that measured i n stem analysis was 0.73 m; the mean difference between the S I calculated fi*om the S U model and that measiu-ed i n stem analysis was 0.43 m, i.e., about 37% improvement i n precision (Table 5.16). Secondly, the S U model estimated SI w i th > 1 m error for two S U s iSBSmdGymnocarpium and SBSy/kJGymnocarpiumi', Goudie's model estimated S I w i t h > 1 m error for 4 S U s [SBPSndStereocaulon ( S U l ) , SBSmc/V. membranaceum (SU4), SBSmc/Gymnocarpium, and S B S w k / V . myrtiloides (SU6)] (Table 5.16). Goudie's model consistently overestimated heights for 5 water-deficient S U s [SBPSxc/StereocaM/on, SBPSxc/Arctostaphylos (SU2), SBSxdAulacomnium (SU3), SBSmcA^. membranaceum, SBS/V. myrtiloides, and S B S w k / V . membranaceum (VU7)] and one waterlogged S U s [SBSwk/Carex (SU9)] (Table 5.16, Figure 5.10). Over estimation was especially severe for extremely dry and wet sites (SBPSxc/StereocoMZon, SBSwk/Carex) . It is evident that biases fi-om Table 5.16. Comparison of site index estimated from the site unit model, Goudie's site index driven model, and measured site index. Site unit Goudie Site unit Actual Errors (38 stands) SI SI SI G-Al S U - A 2 SBPSxdStereocaulon 7.3 8.79 8.70 -1.40 0.09 SBPSxc/Arctostaphylos 12.02 11.69 11.40 0.62 0.29 SBPSxdAulacomnium 13.80 14.56 14.00 -0.20 0.56 SBSmc/Vacc. membranaceum 16.75 15.90 15.75 1.20 0.15 SBSmc/Gymnocarpium 19.80 19.64 18.55 1.25 1.09 SBSyvWVacc. myrtiloides 16,15 17.76 17.60 -1.45 0.16 SBSwk/Vacc. membranaceum 18.77 19.35 19.15 -0.38 0.20 SBSvfk/Gymnocarpium 21.49 22.34 20.97 0.52 1.37 SBSwk/Carex 13.70 13.80 13.57 0.13 0.23 Average (n = 9) 0.73 0.43 Errors between Goudie's site index and actual site index; Errors between site unit-specific site index and actual site index. Age at breast h e i g h t (yr) &'uSs''rœeïS£t.6"^' ' ^ " " ^ '^ - '^^ '^ « " " « d height growth curves. Symbols Goudie's model increase as soil moistm*e increases from very moist to very wet and decreases from fresh to slightly dry, moderately dry, very dry, and excessively dry. Thus, Goudie's curves appeared to be consistently biased for water-deficient sites and waterlogged sites, but for mesic (fresh, moist, and very moist) sites they described lodgepole pine height growth as wel l as the site i m i t height growth model. Third ly , Goudie's model does not solve the three problems inherent i n site index driven modelKng system described by Clutter et al. (1983). These problems are: (1) height growth curves do not pass through the height at index age, (2) height growth curves change when index age changes, and (3) site index can not be solved explicitly for a given age and height. The site-specific models developed i n this study solve these three problems by not using site index i n the model. Site index as a one point system can not possibly accurately explain polymorphic height growth patterns. 5,4.8. Physiological Characteristics of Height Growth The Chapman-Richards growth fimction has a physiological premise. The function assmnes the growth rate to be the residt of two processes: anabolic rate (constructive metabolism such as photosynthesis) and cataboHc rate (destructive metabolism such as respiration), i.e., growth rate = anabolic rate - cataboHc rate. In the case of height growth, the anabolic rate is assumed to be proportionaUy related to the height of trees and raised to a power (aUometric constguit), while the cataboHc rate is assumed to be proportionally related to the height of trees only. These relationships can be expressed i n the foUowing form: [5.4.19] d H / d A = a H " - yffH, where dH/dA is the height growth rate, ' H ' is the height, and 'A' is age of trees; 'a ' is the anaboUc constant; 'j8' is the catabohc constant; 'm' i s the allometric constant. Equat ion [5.4.19] is known as the Chapman-Richards modified V o n Bertalanffy growth function. When this function is solved by using Bernoulli's equation for integration of differential equations wi th the special i n i t i a l condition that H = 0 when A = 0, the resulting fimction is (Pienaar and T u m b u l l 1973): [5.4.20] H = [( - ) ( l - e - A i - m)A)][i/(l - m)] I f (a/y8)[l/(l - = fii, fid - m) = ySg, and 1/(1 - m) = ySg, then the outcome is the three parameter Chapman-Richards fimction (equation [5.3.3]). When fii, and ^3 are estimated, i t then becomes possible to compute the physiological parameters as follows (Pienaar and T u m b u l l 1973): [5.4.21] the allometric constant m = 1 fis [5.4.22] the catabohc constant fi = 1 - m [5.4.23] the anaboUc constant a = [ XSjd - m) or fifii^^ - m) 1 - m Since a l l three physiological parameters were derived from a site-specific model, i t was not surprising that the variat ion i n the values of the computed physiological parameters (metabolic rate) for each site uni t is related to the var iat ion i n climate, soil moisture, and soil nutrients (Table 5.17). Th is was also observed fi"om the analysis of M A I and C A I . Lodgepole pine height growth i n the S B S m c and S B S w k subzones has a higher metabolic rate than i n the S B P S x c subzone. W i t h i n each subzone, the metabolic rate appears to increase w i t h increasing soil moisture fi*om excessively dry to very moist, and decrease wi th increasing soil moisture from very moist to wet. Table 5.17. The physiological parameters derived from the Chapman-Richards function for site tmits stratified according to climate, soil moisture, and soil nutrient. Symbols for soil moisture and soil nutrient regimes are explained in Table 5.1. Site unit a i8 m SMR SNR SB?Sxc/Stereocaulon 0.251 0.055 0.323 ED VP-P SBPSxc/Arctostaphylos 0.238 0.018 0.165 VD-MD VP-M SBPSxc/Aulacomnium 0.333 0.018 0.087 MD-F M-R SBSmcA i^acc. membranaceum 0.439 0.019 0.008 SD P-M SBSmc/Gymnocarpium 0.438 0.022 0.138 F-VM M-VR SBSwkA^acc. myrtiloides 0.434 0.042 0.246 MD VP-M SBSwWVacc. membranaceum 0.420 0.047 0.316 SD P-M SBSwk/Gymnocarpium 0.448 0.038 0.284 F-VM M-VR SBSwUCarex 0.352 0.062 0.369 W M-VR 5.4.9. Potential Application of the Site-specific Height Growth Models The same ecological variables used i n the model recommended to estimate site index (Le., biogeoclimatic subzone, soil moistm*e regime, and soil nutrient regime) £ire required for (1) identification of site series and (2) the application of the site un i t or ecotope height growth model. W i t h biogeoclimatic ecosystem classification i n place and a site-specific height growth model constructed, i t is logical to continue its development as i t offers a very simple and effective tool to assess forest productivity. Knowledge of ecological quahty for a site, regardless of whether i t supports the growth of a particvdar tree species, is i tsel f sufficient to estimate height growth at any point i n time. Grouping site series w i t h i n a zone or group of cl imatically related subzones into site vmits, on the basis of s imilar i ty and coherence i n their height growth curves, should provide an acceptable ntunber of site units for height growth prediction modelling. Evident ly , the model vdl l perform correspondingly to the capabiHty of a user to recognize different sites and to determine basic elements of ecologiced site quality. A s this is being done routinely by practitioners i n the course of preparing prehgirvest s i lv icultural prescriptions, the ski l ls necessary for us ing the model would justify its further development, strengthening linkage between biogeochmatic ecosystem classification and forest growth. 5.5. C O N C L U S I O N S The pattern of height growth i n the immature lodgepole pine stands studied was found to change w i t h ecological site quality. The three-parameter Chapman-Richards growth ftmction was successful i n describing height growth of stands over a wide range of sites. I n contrast to site index, several selected measures of ecological site quality had strong relationships to the function parameters. These were site series, ecotope (combination of biogeoclimatic subzone, soil moisture regime, and soil nutrient regime), and the combination of potential évapotranspiration, water deficit, the depth of water table or gleyed soil horizon, £md mineraUzable soil nitrogen. Two site-specific height growth models were developed us ing categorical ecological variables i n parameter prediction—the site uni t model and the ecotope model, each describing more precisely the shape of height growth curves and site index than Goudie's site index driven model based on the data that the site-specific model derived. However, no independent data were available for testing the site-specific models i n comparison to Goudie's model. As the required ecological veiriables are routinely available fi-om pre-harvest silvicultured prescriptions, i t is logical to recommend that the site-specific models be further developed and tested, and then implemented. 6. S U M M A R Y A N D C O N C L U S I O N S (1) The diagnostic species and tabular analysis distinguished ten vegetation units . B o t h diagnostic species and vegetation units are strongly correlated w i t h , and useful indicators of, relatively narrow segments of regional climatic, soil moisture, and soil nutrient gradients. The imderstory vegetation i n immanaged, mid-seral (30 to 80 year-old) immature lodgepole pine stsmds was sufficiently developed to indicate the ecological site quahty of the study plots. (2) O n the basis of actual/potential évapotranspiration ratio and the depth of growing-season water table or gleyed soil horizon, eleven actual soil moisture regimes, w i t h three regimes being recognized for sites w i t h a strongly fluctuating water table, were successfully stratified. The criteria proposed by K l i n k a et al. (1989b) and the energy/soil-limited model (Spittlehouse and Black 1981) can be used to stratify the study sites into actual soil moisture regimes. (3) F ive soil nutrient regimes were delineated according to soil mineral izable-N and the sum of exchangeable C a , K , and M g . S i m i l a r to severed previous studies, soil mineral izable-N and the sum of exchemgeable C a , K , and M g are the most useful measures for the characterization of a soil nutr ient gradient, and for the delineation of five tradit ionally used soil nutr ient regimes. A complex soil nutrient gradient can be represented, but not replaced by a soil nitrogen gradient, i.e., a one dimensional representation of soil nutrient gradient. (4) Strong relationships exist between understory vegetation and categorical or continuous measures of soil moistvu-e. These ecological measures have a meaning relative to soil moisture conditions experienced by plants. S imi lar ly , there are strong relationships between soil mineraUzable-N w i t h frequency of nitroph3d;ic plants, and w i t h foliar N . Soi l nitrogen is the pr imary determinant of the soil nutrient gradient i n the study eirea, and the criteria and l imits used to stratify the study plots into soil nutrient regimes have meaning relative to the general nutrient supply for plants. (5) Eleven site associations were distinguished based on climate, soil moisture, and soil nutrient regimes i n this study. Site associations can stratify the forest sites into quahtatively and quantitatively distinct, field recognizable, segments of regional gradients of ecological site quahty. (6) T h i r t y regression models were developed to examine the relationships between site index and ecological site quality. The most strongly related ecological variables to lodgepole pine site index are: ecotopes defined either by a combination of categorical variables (biogeoclimatic subzone, soil moisture regime, and soil nutrient regime) (adj. R2 = 0.85) or by a combination of continuous variables (potential évapotranspiration, the depth of water table or gleyed soil horizon, and mineralizable soil nitrogen) (adj. R2 = 0.82), site associations (adj. R2 = 0.81), site series (adj. R2 = 0.84), and vegetation vmits (adj. R2 = 0.83). E i t h e r categorical or continuous S5^optic ecological variables can be used i n describing the var iat ion of lodgepole pine site index w i t h a change i n ecological site quality. Lodgepole pine appears to have a potential to grow on nitrogen-rich sites w i t h p H < 7. The plotting of site index isolines onto edatopic grids represents both effective format and usefiil means for field personnel to estimate lodgepole pine height growth on any given site. The three-parameter Chapman-Richards growth function, fit firom stem gmalysis data, precisely described height growth of immature lodgepole stands over a wide range of sites. Site series and ecotope, defined either by a combination of biogeoclimatic subzone, soil moisture regime, and soil nutrient regime or potential évapotranspiration, the depth of water table or gleyed soil horizon, and mineralizable soil nitrogen, had a stronger relationship w i t h the fimction parameters than site index. The pattern of lodgepole pine height growth i n the study area changes w i t h ecological site quality. There is a strong Hnk between lodgepole pine height growth and measures of ecological site quality derived firom the biogeoclimatic ecosystem classification of the study plots. Categorical or continuous ecological variables can be used i n polymorphic height growth modell ing to precisely predict lodgepole pine height growth so that the efFects of site, environmental changes, inc luding management practices, on forest productivity can be better understood. The site-specific height growth models £u-e more effective and precise i n describing lodgepole pine height growth than site index driven height growth models. R E F E R E N C E S Agriculture Canada Expert Committee on Soi l Siuvey. 1987. The Canadian system of soil classification. Agric . Canada P u b l . 1646. Ottawa, Ontario. 164 pp. Alexander, R.R. , D . Tackle, and W . G . Dahms. 1967. Site index for lodgepole pine, w i t h corrections for stand density: methodology. U S D A For . Ser. Res. Pap. R M - 2 9 , For t CoUms, Colorado. 18 pp. Anonymous. 1976. Technicon Analyzer II methodology: individual/simtdtaneous determination of nitrogen and/or phosphorus i n B D acid digests. Industr ial Method No . 328/74W/A. Technon Corp., Tarrytown, New York. Anonymous. 1982. Canadian climate normals. 1951-1980. Temperature and precipitation. V o l . 6. Environment Canada. Atmospheric Environment Service. Ottawa, Ontario. 276 pp. Assmann, E . 1970. The principles of forest yield study. Pergamon Press, New York. 506 pp. Bakuz i s , E . V . 1969. Forestry viewed i n an ecosystem perspective, pp. 189-258. In G . M . V a n Dyne (ed.). The ecosystem concept i n natura l resource management. Academic Press, New York. B a l l a r d , T . M . and R . E . Csuter. 1986. Eva luat ing forest stand nutrient status. L a n d Manage. Rep. No . 20., B . C . M i n . For. , Victor ia , B . C . 60 pp. Banner , A . , R . N . Green, K K K n k a , D.S. McLennan , D .V . Meidinger, F . C . Nuszdorfer, and J . Pojar. 1990. Site classification for coastal B r i t i s h Coltunbia: a first approximation. B . C . M i n . For. , V ic tor ia B . C. 2 pp. (a coloured pamphlet). Barksley , C E . and J . D . Lancaster. 1965. Sulfiu-. In C A . B lack et a l . (eds.) Methods of soil analysis, Agron. No. 9. A m . Soc. Agron., Inc., Madison, Wisconsin. B . C . M i n i s t r y of Forests, Research Branch . 1988. BiogeocHmatic zones of B r i t i s h Colmnbia (a colorized map). M i n . For . Res. Branch , Vic tor ia , B r i t i s h Colmnbia . Beck, D . E . 1971. Polymorphic site index cm-ves for white pine i n the southern Appalachians. U S D A For . Ser., Res. Pap . SE-80. AsheviUe, N o r t h Carol ina. 8 pp. Becking, R .W. 1957. The Zvuich-Montpellier school of phj^sociology. Bot. Rev. 23: 411-488. Bor land International, Inc. 1989. Quattro Pro. Scotts Val ley , Cal i fornia, Braun-Blanquet , J . 1932. P lant sociology. (Transi, by Fu l l e r , G .D. and H . S . Conard). N e w York. 439 pp. Bremner, J . M . and C.S. Mulvaney. 1982. Ni trogen-Tota l , pp. 595-624. In A . L . Page (ed.) Methods of soil analysis. Agron. No. 9. part 2. A m . Soc. Agron.,Inc. and Soi l Sci . Soc. A m . , Inc. Wisconsin. Bremner, J . M . gmd M . A . Tabatabai. 1971. Use of automated combustion techniques for total carbon, total nitrogen, and toted svdfur analysis, pp. 1-15. In Walsh , L . M . (ed.) Instrumental methods for analysis of soil and plant tissue. Soi l Sci . Soc. A m . , Inc. Wisconsin. Burger, D . 1972. Forest site classification i n Canada. Mit te i l imgen des Vereins fur ForsHche Standortskimde i m d Forstpflanzenzuchtimg 12: 20-36. B u m s , R . M . and B . H . Honka la 1990. Silvics of Nor th America . Agricultm-e Handbook 654 vol 1. U S D A For . Ser., Washington D . C . 675 pp. Cajander, A . K . 1926. The theory of forest types. Acta For. F i n n . 29: 1-208. Cajander, A . K . and Y . Ilvessalo. 1921. Uber waldtypen II. A c t a For. F i n n . 20: 1-77. Cajander, A . K , 1949. Forest types and their significance. Acta For. F i n n . 56: 1-69, 1-71. Campbel l , G.S. 1986. Ext inct ion coefficients for radiat ion i n plant canopies calculated using elUpsoidal incl ination angle distribution. Agrc. and For. Meter. 36: 317-321. Carmean, W . H . 1956. Suggested modifications of the standard Douglas-fir site curves for certain soils i n Southwestern Washington. For . S d . 2: 242-250. Carmean, W . H . 1970. Tree height growth patterns i n relation to soil and site. pp. 499-512. In C.T. Youngberg and C .B . Davey (eds.) Tree growth and forest soils. Proceedings of T h i r d N o r t h American Forest Soils. CÊirmean, W . H . 1972. Site index curves for upland oaks i n the Centred States, For, Sci . 18: 102-120, Carmean, W , H , 1975. Forest site quality evaluation i n the Uni ted States. Advances i n Agronomy 27: 209-269. Carmean, W . H . 1982. Soil-site evaluation for conifers i n the upper great lakes region. In Ar t i f i c ia l regeneration of conifers. Mich igan Technological Univers i ty , Mich igan . Carter , R . E . and K . K l i n k a . 1990. Relationships between grovnng-season soil water-deficit, mineralizable soil nitrogen and site index of coastal Douglas fir. For . Ecol . Manage. 30: 301-311. Carter , R. and K . K l i n k a . 1991. Use of ecological site classification i n the prediction of forest productivity and response to fertil ization, pp. 382-392 In A . P . G . Schonau (ed.) Intensive forestry: the role of eucalypts. l U F R O symposium proceedings. Durban , South Afidca. Carter , R . E , , Q. Wang, J , A , P . Neumann, and K . K l i n k a . 1991, Relationships between leaf area and ecological site quality i n immature lodgepole pine stands of B r i t i s h Coltunbia, Unpublished manuscript. Chambers, J . M . , W.S . Cleveland, B . Kle iner , and P .A . Tvdcey. 1983. Graphical methods for data analysis. Wadsworth & Brooks/Cole Pub . Com. Cali fornia. 395 pp. Chapman, D . G . 1961. Statistical problems i n popvdation dynamics, pp. 147-162 In Proc. F o u r t h Berkerley Symp. M a t h . Stat, and Prob. U n i v . Cal i fornia Press, Berkerley and Los Angeles. Chatterjee, S. and B . Price. 1977. Regression analysis by exemaple. J o h n Wiley & Sons, New York . 228 pp. Clutter , J . L . , J . C . Fortson, L . V . Pienaar, G . H . Brister , and R. Bai ley. 1983. Timber management: a quantitative approach. John Wi l ley & Sons, New York . 331 pp. Cohran, P . H . 1975. Natiu-al regeneration of lodgepole pine i n south-central Oregon. U S D A For . Ser. Res. Notes. PNW-204 . Port land, Oregon, pp 18. Cochran, P . H . 1985. Soils and productivity of lodgepole pine. pp. 89-93. In D .A. Baumgartner et a/.(eds.) Lodgepole pine, the species and its management. Sympositun proc. P u l l m a n , Washington. Corns, I .G.W. and D . J . P l u t h . 1984. Vegetational indicators as independent variables i n forest growth prediction i n west-central Alberta , Canada. For. Ecol . Manage. 9: 13-25. Court in , P . J . , K . K l i n k a , M . C . FeUer, and J . P . Demaerchalk. 1988. A n approach to quemtitative cleissification of nutrient regimes of forest soils. Can. J . Bot. 66: 2640-2653. C i m i a , T. 1973. Dimamy veiriables and some of their uses i n regression analysis. Proc. l U F R O Subject Group S4.02. V o l . 1: 1-146. Curt i s , J . T . 1959. The vegetation of Wisconsin; A n ordination of p lant conmaunities. U n i v . Wisconsin, Madison, Wisconsin. 657 pp. Dahms, W . G . 1975. Gross yield of central Oregon lodgepole pine. pp. 208-232. In D . M . Baumgartner (ed.) Management of lodgepole pine ecosystems. Symposi imi Proc. Wash. State U n i v . , Coop. E x t . Serv., P u l l m a n , Washington. D a h l , E . 1956. Rondane: M o i m t a i n vegetation i n south Norway and its relation to the environment. S k r . norske Vidensk-Akad. M a t . Natvuv. K l . No. 3. 374 pp. Damman, A . W . H . 1979. The role of vegetation i n land classification. For . Chron. 55: 175-182. Danie l , T.W., J . A . Helms, and F .S . Baker . 1979. Principles of silvicvdttu-e. 2nd. ed. M c G r a w - H i l l Book Company, New York. 500 pp. Daubenmire, R . F . 1952. Forest vegetation of northern Idaho and adjacent Washington, and its bearing on concepts of vegetation classification. Ecol . Monogr. 22: 301-330. Daubenmire, R . F . 1968. P lant communities. Harper & Row, Inc., N e w York. 300 pp. Day, P .R. 1965. Particle fi*actionation and particle-size analysis, pp. 545-567. In Black, C A . et al. (eds) Methods of soil analysis, P a r t I. Agron. no 9, A m . Soc. Agron. and Soi l Sci . Soc. A m . Madison, Wisconsin. Decagon Devices. 1987. Sunfleck ceptometer users manual . Decagon Devices, P u l l m a n , Washington. 27 pp. Di l l on , W.R. and M . Goldstein. 1984. Mult ivar iate analysis. Methods and applications. J o h n Wiley & Sons, Inc., New York . 587 pp. Duffy, P . J . B . 1964. Relationships between site factors and grovrth of lodgepole pine (Pinus conforta Dougl. var. latifolia Engelm.) i n the foothill section of Alberta . C a n . Depart. For. , Pub l . 1065. Ottawa, Ontario. 60 pp. Dyer, M . E . and R . L . Bai ley. 1987. A test of six methods for estimating true heights from stem anedysis data. For . Sci . 33: 3-13. E i s , S., D , Craigdalhe, and C, Simmons. 1982. Growth of lodgepole pine and white spruce i n the central interior of B r i t i s h Col imibia. C a n . J . For. Res. 12: 567-575. Emanue l , J . 1987. A vegetation classification progremi (VTAB) . Fac. For . , U n i v . B r i t i s h Columbia, Vancouver, B . C . 26 pp. Etter , H . M . 1969. Growth metabolic components and drought survival of lodgepole pine seedlings at three nitrate levels. C a n . J . P l a n t S d . 49: 393-402. Feol i , E . £md L . O r l 6 d , 1979. Analysis of concentration and detection of underlying factors i n structure tables. Vegetatio 40: 49-54. Fox, D , J , and K . E , Guire . 1976. Documentation of M I D A S , Statistical Research Laboratory, U n i v , Michigan, Il l inois, Michigan, 203 pp. Fr ies , J . 1978. The assessment of growth and yield and the factors influencing i t . S p e d a l paper presented at the V I I I l U F R O World Forestry Congress, J a k a r t a , Indonesia, Gee, G,W, and J , W . Bauder. 1986. Particle-size analysis. In Page, A . L . et al. (eds.) Methods of soil analysis, P a r t I, Phys ica l and Mineralogical Methods. Agron. Monog. no. 9, A m . Soc. Agron and Soi l S d . Soc. A m . Madison, Wisconsin. Gi t t ins , R. 1985. Canonical analysis, Springer-Verlag, N e w York . 351 pp. Goodall , D .W. 1954. Objective methods for the classification of vegetation. III. A n essay i n the use of factor analysis. Aust . J . Bot. 2: 304-324. Goudie, J . W . 1984. Managed stand yield tables for interior lodgepole pine: i n i t i a l and post-spadng density. B . C . M i n . For. , Victor ia , B . C. 14 pp. Graney, D . L . and H . E . Burkhar t . 1973. Polymorphic site index curves for shortleaf pine i n the Ouachita Mountains. U S D A For. Ser., Res. Pap . SO-85. New Orleans, Louis iana. 14 pp. Green, R . N . , P . L . M a r s h a l l , and K . K l i n k a . 1989. Es t imat ing site index of Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco) fi'om ecological variables i n southwestern B r i t i s h Colxunbia. For . Sci . 35: 50-63. Gr ier , C .C . , K M . Lee, N . M . N a d k a m i , G O . Klock, and P . J . Edgerton. 1989. Productivity of forests of the U n i t e d States and its relation to soil and site factors and management practice: a review. U S D A , For . Ser. Gen. Techn. Rep. PNW-222 . Port land, Oregon, pp. 51. Habgood, H . L . 1985. Est imat ion of browse biomass production of Salix spp. and Betula glandulosa us ing multiple l inear regression, M . Sc. thesis. The Univers i ty of B r i t i s h Columbia, Vancouver, B . C . 107 pp. Hagglund, B . 1981. Eva luat ion of forest site productivity. For . Abs. 42: 515-527. Hale , M . E . J r . and W . L . Curberson. 1970, A fourth checkhst of the lichens of the continental U n i t e d States. The Bryologist 73: 499-543. H a l l , F . C . 1987. Growth basal area handbook, U S D A For . Ser. R6-Ecol , 181b-1984, Port land, Oregon. 84 pp. H a l l , F . C . 1989. The concept and application of growth basal area: a forestleind stockability index. U S D A For . Ser., R6-Ecol . Tech. Pap . 007-89. Port land, Oregon. 86 pp. Harr ington, C A . 1986. A method of site quality evaluation for red alder. U S D A For . Ser. Gen. Tech. Rep. PNW-192 . Port land, Oregon. H i l l s , G.A. 1952. The classification emd evaluation of site for forestry. Dept. of Lands and For . , Res. Rep. 24. Toronto, Ontfuio. 41 pp. Hitchcock, C L . and A . Cronquist. 1973. F lora of the pacifie northwest. A n i l lustrated manned. U n i v . of Wash . Press, Seattle, Washington. 730 pp. Hol land, S.S. 1976. Landforms of B r i t i s h Columbia. A physiographic outline. B u l l . No. 8. 2nd ed. B . C . Dept. of Mines and M i n e r a l Resom-ces, Victor ia , B r i t i s h Columbia. 138 pp. Holmes, J . R . B . and D . Tackle. 1962. Height growth of lodgepole pine i n Montana related to soil and stand factors. B i d l . 21. Montana State U n i v . Missoula , Montana, pp. 12. Hosie, R . C . 1979. Nat ive trees of Canada. 8th ed. F i tzhenry & Whiteside L t d . Toronto, Ontario . 380 pp. ni ingworth, K . and J . W . C . Arhdge. 1960. Interim report on some forest site types i n lodgepole pine and spruce-alpine fir stands. Res. Notes 35. M i n . For . Ser., B . C . , V ic tor ia , B r i t i s h Col imibia . 44 pp. Ireland, R.R. , C D . B i r d , G.R. Brassard , W . B . Schofield, and D . H . V i t t . 1980. Checklist of the mosses of Canada. Nat ional M u s e u m of Natured Science pubhcation i n Botany, No. 8. Nat iona l Museums of Canada, Ottawa, Ontario. 75 pp. Jarv i s , P .O . and J . W . Leverenz. 1983. Productivity of temperate, deciduous and evergreen forests, pp. 233-280 In O.L. Lange, P .S . Nobel , C .B . Osmond, and H . Ziegler (eds.). Ecosystem processes: mineral cycHng, productivity and man's influence. Physiological P l a n t Ecology: new series. V o l . 12D. Springer-Verlag , N e w York . Jones, J . R . 1969. Review and comparison of site evaluation methods. U S D A For . Ser., Res. Pap. R M - 5 1 . Fort Col l ins , Colorado. 27 pp. Kabzems, R . D . 1985. Characterization of soil nutrient regimes i n Douglas-fir ecosystems i n the Dr i e r Mar i t ime Coastal Western Hemlock subzone. M . Sc. thesis. Facul ty of Forestry, U n i v . B .C . , Vancouver, B r i t i s h Columbia. Kabzems, R . D . and K . K l i n k a . 1987. Ini t ia l qu£intitative characterization of soil nutr ient regimes. C a n . J . For . Res. 17: 1557-1571. Kennedy, R .W. 1985. Lodgepole pine as a commercial resotu-ce i n Canada, pp. 21-23. In D . M . Baumgartner et al. (eds.) Lodgepole pine - the species and i ts management. Symposium proceedings. Wash. State U n i v . P u l l m a n , Washington. K i m m i n s , J . P . 1977. The need for ecological classification i n B . C . B . C . Forestry 2(1), 2 pp. Assoc. of B . C . Prof. Foresters. Vancouver, B r i t i s h Colmnbia, K l i n k a , K . and M . C . Fel ler . 1984. Principles of tree species selection used i n regenerating forest sites i n southwestern B r i t i s h Columbia. For . Chron. 60: 77-85. K l i n k a , K . and V . J . Kra j ina . 1986. Ecosystems of the Univers i ty of B r i t i s h Columbia Research Forest. Fac. of For. , U n i v . B . C . , Vancouver, B r i t i s h Columbia. 123 pp. K l i n k a , K , Q. Wang, and R . E . Carter . 1990a. Relationships among hxunus forms, forest floor nutrient properties, and understory vegetation. For . Sci . 36: 564-581. K l i n k a , K . , R . N . Green, R . L . Trowbridge, and L . E . Lowe. 1981. Taxonomic classification of humus forms i n ecosystems of B r i t i s h Col iunbia. B . C . M i n . of For. , L a n d . Manag . Rep. No. 8., Victor ia , B r i t i s h Columbia. 54 pp. K l i n k a , K . , R . E . Carter , M . C . Fel ler , and Q. Wang. 1989a. Relations between site index, salal , plant commimities, and sites i n coastal Douglas-fir ecosystems. Northwest Sci , 63: 19-28. K l i n k a , K . and R . E . Carter. 1990. Relationships between site index and synoptic environmental variables i n immature coastal Douglas-fir stands. For . Sci . 36: 815-830. K l i n k a , K , V . J . K r a j i n a , A . Ceska, and A . M , Scagel. 1989b. Indicator plants of coastal B r i t i s h Columbia. U n i v . B . C . Press, Vancouver, B r i t i s h Colimibia. 288 pp. K l i n k a , K . , M . C . Fel ler , R . N . Green, D .V . Meidinger, J . Pojar, and J . Worra l l . 1990b. Ecological principles: appKcations. pp. 55-72 In D . P , Lavander et al (eds.). Regenerating B r i t i s h Columbia's forests. U n i v . B . C . Press, Vancouver, B r i t i s h Columbia. K r a j i n a , V . J . 1933. Die PflEmzengesellschaflen des Mlynica-Tales i n den Vysoke Tatry (Hohe Tatra) mi t besonderer beriicksichtingung okologischen Verhâltnisse. Bot. Centralbl . Abt . 2, 50: 744-956, 51: 1-244. K r a j i n a , V . J . 1965a. Philosophy of ecology. Ecol . West. N . Amer . 1: 102-111. K r a j i n a , V . J . 1965b. Biogeoclimatic zones of B r i t i s h Columbia, Ecol . West. N . Amer . 1: 1-17. K r a j i n a , V . J . 1969. Ecology of forest trees i n B r i t i s h Columbia. Ecol . West. N . Amer . 2: 1-146. K r a j i n a , V . J . 1972. Ecosystem perspectives i n forestry. H . R , M a c M i l l a n Forestry Lecture Series, Faculty of Forestry, U n i v . B . C . , Vancouver, B r i t i s h Columbia. 31pp . L a u s i , D . and P . L . N imis , 1985. Roadside vegetation i n boreal South Y u k o n and adjacent A l a s k a . Phjrtocoenologia 13:103-138. L i - C o r Inc. 1986. Li-cor radiation sensors instruction manual . L i - C o r Inc. Lincoln , Nebraska. 24 pp. Lotsm, J . E . and D.A. Perry . 1983. Ecology and regeneration of lodgepole pine. U S D A For. Ser. Agric . Handbook No. 606. Washington, D . C . 51 pp. Lowe, L . E . and T . F . Guthrie . 1984. A comparison of methods for total sulfur analysis of tree foHage. C a n . J . For. Res. 14: 470-473. Luttmerding, H . A . , D .A . Demarchi , E . G . Lea , D .V . Meidinger, and T. V o i d (eds.). 1990. Describing ecosystems i n the field. 2nd ed., B . C . M i n . For. , Victor ia , B r i t i s h Colmnbia . 213 pp. MacLean , C D . and C L . Bolsinger. 1973. Est imat ing Dmining 's site index fi*om plant indicators. U S D A For . Serv. Res. Note PNW-152 . Port land, Oregon. 18 pp. Major, J . 1963. A climatic index to vascular plant activity. Ecol . 44: 485-498. Mason, R .R . and T . C Tigner. 1972. Forest-site relationships w i t h i n an outbreak of lodgepole pine needle miner i n central Oregon. U S D A For. Ser. Res. Pap. PNW-146 . Port land, Oregon. 18 pp. M c L a i n , D . H . 1974. Drawing contom-s fi*om arbitrary data points. The Computer J o u m . 17: 318-324. Meidinger, D . and J . Pojar (eds.). 1991. Ecosystems of B r i t i s h Columbia. Special Report Series, no. 6. B . C . M i n . For. , Victor ia , B r i t i s h Coltmibia. 330 pp. Mehhch , A . 1978. N e w extractsuit for soil test evaluation of phosphorus, magnesium, calcium, sodium, manganese, and zinc. Comm. Soi l . S d . P l a n t A n a l . 9: 477-492. M i l n e r , K . S . 1987a. The development of site spedfic height growth curves for four conifers i n western Montana. P h . D . Dissertation. U n i v . of Montana , Missoula , Montana. 169 pp. M i l n e r , K . S . 1987b. Constructing site spedfic height growth curves. In E k et a l , (eds) Forest growth modelhng and prediction 1:411-418, Proceedings of the r U F R O Conference, U S D A For . Ser., General Tech. Rep. NC-120 . St. P a u l , Minnesota. Mogren, E .W. and K . P . Dolph. 1972. Prediction of site index of lodgepole pine fi*om selected environmental factors. For . S d . 18: 314-316. Monserud, R .A . 1984. Height growth and site index curves for in land Douglas-fir based on stem anedysis data and forest habitat type. For. Sc i . 30: 943-965. Monserud, R .A . 1988. Var ia t i on on the theme of site index. In Forest growth modehng and prediction. U S D A For . Ser. Gen. Tech. Rep. NC-120 . St. P a u l , Minnesota. Moore, J . J . 1962. The Braun-Blanquet system: a reassessment. J . Ecol . 50: 761-769. Mueller-Dombois, D , and H . EUenberg. 1974. A i m s and methods of vegetation ecology. J o h n Wi l ley & Sons, New York. 547 pp. Nuszdorfer, F . C . 1981. Methods of sampling and analysis. 48-53. I n K l i n k a et a l . Taxonomic classification of himius forms i n ecosystems of B r i t i s h Columbia. L a n d Manage. Rep. no. 8. B . C . M i n . For. , Vic tor ia , B r i t i s h Columbia. 54 pp. Odum, E . P . 1971. Fimdemientals of ecology. 3rd ed. W . B . Saunders Co., Toronto, Ontario. 574 pp. Oliver, C D . and B . C Larson. 1990. Forest stand dynamics. M c G r a w - H i l l , New York. 467 pp. Ol iver , W.W. 1967. Ponderosa pine can stagnate on a good site. J . For . 65: 814-816. Orlôci, L . 1988. Commimity organization: recent advances i n mmaerical methods. C a n . J . Bot. 66: 2626-2633. Page, A . L . (ed.). 1982. Methods of soil analysis. Agron. No. 9. part 2. A m . Soc. Agron., Inc. and Soil Sci . Soc. A m . , Inc. Madison, Wisconsin. Park inson , J . A . and S .E . A l l e n . 1975. A wet oxidation procedure suitable for the determination of nitrogen and mineralizable nitrogen i n biological material . Comm. Soi l . S d . P lant A n a l . 6: 1-11. Peech, M . 1965. Hydrogen-ion activity. 914-926. In C A . Black et al. (eds.). Methods of soil analysis. Agron. no. 9. A m . Soc. Agron. Madison, Wisconsin. Pfister, R . D . and S .F . A m o . 1980. Classi fying forest habitat types based on potential c l imax vegetation. For . Sci . 26: 52-69. Pienaar, L . V . and K . J , T i i m b u l l . 1973. The Chapman-Richards generahzation of V o n Bertalanfiy 's growth model for basal area growth and yield i n even-aged stands. For . S d . 19: 2-22. Pogrebnyak, P .S . 1930. Uber die methodik der standortsimtersuchmigen i n verbindxmg m i t den waldtypen. pp. 455-471 In Verhandlmigen des H . Intemationalen Kongresses Forstl ichen Versuchsanstalten. Stockholm. Pojar, J . 1983. Forest ecology, pp. 221-318 In S .B. Watts (ed.), Forestry handbook for B r i t i s h Coltmibia. The For. Undergraduate S o c , Faculty of For . , U n i v . B . C . Vancouver, B r i t i s h Columbia. Pojar, J . 1985. Ecological classification of lodgepole pine i n Canada, pp. 77-88 In D . M . Baumgartner et al. (eds.), Lodgepole pine: The spedes and its management. Symp. P r o c , Wash. State Un iv . , P u l l m a n , Washington. Pojar, J . , R, Trowbridge, and D . Coates. 1984. Ecosystem classification and interpretation of the Sub-Boreal Spruce zone. Price Rupert Forest Region, B r i t i s h Columbia. L a n d Manage. Rep. 17. B . C . M i n . For . , Vic tor ia , B r i t i s h Columbia. 319 pp. Pojar, J . , K . K l i n k a , and D. Meidinger. 1986. Ecosystem classification by the B r i t i s h Columbia Forest Service, pp. 68-88 In H . van Groenewoud (compiler). Forest site classification method. Proceedings of the workshop of the l U F R O working party on site classification and evaluation. Canadian For . Ser.-Meuitimes. Fredericton, New Brunswick, pp. 182. Pojar, J . , K . K l i n k a , and D.V. Meidinger. 1987. Biogeoclimatic ecosystem classification i n B r i t i s h Columbia. For. Ecol . Manage. 22: 119-154. Poore, M . E . D . 1955, The use of phjrtosodological methods i n ecological investigations. Par t I, II , III, J . Ecol . 43: 226-244, 245-269, 606-651. Poore, M . E . D . 1962. The method of successive approximation i n descriptive ecology. Adv. Ecol . 11: 57-77, Powers, R . F . 1980. Mineral izable soil nitrogen as an index of nitrogen availabi l i ty to forest trees. Soi l S d . Soc. A m . J . 44:1314-1320. Price, W . J , 1978, Analjrtic atomic absorption spectrophotometry, Heyton and Son L t d . , London. 239 pp. Rawhngs, J . O . 1988. Apphed regression analysis: a research tool. Wadsworth, Inc., Cal i fornia, 553 pp, Richards, F . J . 1959. A flexible growth function for empirical use, J . E x p t l , Bot. 10: 290-300. Richards, F , J , 1969, The quantitative analysis of growth, pp. 3-76. In F . C . Steward (ed.) P l a n t physiology, a treatise, vol . 5A. Academic Press, New York. Roydhouse, F . M , , J , L . Crane, and J . H . Bassman. 1985. Biomass distribution i n yoxmg stands of stagnant and non-stagnant lodgepole pine. pp. 379. In Lodgepole pine, the spedes and its management. Symposium proceedings. Wash. State Un iv . , P u l l m a n , Washington. Rose, M . F . and C. Grant . 1976. Remote station climate prediction model. Environment and L a n d Use Conmaittee, Data Service Div is ion , Victor ia , B . C . (mimeo.). Sander, D . H . 1966. Effect of urea and urea-formaldehyde on the growth of lodgepole pine seedlings i n a nursery. Tree Plant , Notes 79: 18-23, S A S Institute Inc, 1985. S A S user's guide: statistics. Ver , 5, S A S Institute Inc, Cary , N o r t h Carol ina . 956 pp. Shimwel l , D.W. 1971. The description and classification of vegetation. U n i v . Washington Press, Seattle, Washington. 322 pp. S m i t h , C . A . B . 1947. Some examples of discrimination. Annals of Eugenics. 13: 272-282. Sneath, P . H . A . and R.R. Sokal . 1973. Niuner ica l taxonomy. Freeman, San Francisco, Cahfomia . Spittlehouse, D . L . and T .A. Black. 1981. A growing-season water balance model applied to two Douglas-fir stands. Water Resotu*. Res. 17:1651-1656. Spurr , S . H . and B . V . Barnes. 1980. Forest ecology. 3rd ed. J o h n Wi ley & Sons, New York. 687 pp. Stottler, R. and B . Grandall-Stottler. 1977. A checklist ofthe liverworts and homworts of N o r t h America . Bryologist 80: 405-428. Strub, M . R . and P .T . Sprinz . 1987. Comparisons of southern pine height growth. In E l k et a l . (eds) Forest growth modelling and prediction 1: 428-434. Proceedings ofthe l U F R O Conference. U S D A For . Ser., General Tech. Rep. NC-120. St. P a u l , Minnesota. Sukachev, V . N , 1964. M a i n concepts of forest biogeocoenology (In Russian). In Osnovy lesn. biogeotsenologii. 5-59. Moscow. Thomthwaite , C.W. 1948. A n approach toward a rational classification of chmate. The geographical review. 38: 55-94. Trewartha, K . W . G . 1968. A n introduction to climate. 4th ed. M c G r a w - H i l l Book Co., New York . 408 pp. Trousdell , K B . , D . E . Beck, and F .T . L loyd . 1974. Site index for loblolly pine i n the Atlgmtic Coastal P l a i n of the Carolinas and V i r g i n i a . U S D A For , Ser., Res. Pap. SE-115. Ashevil le , Nor th Carohna, 11 pp. Valentine, K . W . G . and A . B . Dawson. 1978. The interior plateau, pp. 121-134 In K W . G . Valentine et al. (eds.) The soil landscape of B r i t i s h Colvimbia. M i n . Env i ronm. , Resource A n a l . Branch , Vic tor ia , B r i t i s h Columbia. 197 pp. V a n Dyne, G . M . (ed.) 1969. The ecosystem concept i n natural resource management. Academic Press, New York. 383 pp. Verbyla and F isher 1989. A n alternative approach to conventional soil-site regression modehng. C a n . J . For . Res. 19: 179-184. V i t t , D . H . , J . E . M a r s h , and B . B . Bovey. 1988. Mosses, lichens, and ferns of northwest N o r t h America . A photographic field guide. Lone Pine Publ . , Edmonton, Alberta . 296 pp. V o n Bertalanffy, L . 1951. Theoretiche biologie. Franke , Bern . 403 pp. Walsmley, M . , G . U t z i g , T. Vo id , D . Moon, and J . van B a m v e l d (eds.). 1980. Describing ecosystems i n the field. B . C . M i n . Env . , R A B Tech. Pap . 2, B .C . M i n . For . , L a n d Manage. Rep. No. 7. Victor ia , B r i t i s h Columbia. 225 pp. War ing , S.A. and J . M . Breminer 1964. Ammonitmi production i n soil imder waterlogged conditions as an index of nitrogen availabil ity. Nature 201: 951-952. Wheeler, N . C . and W . B . Critchfield. 1985. The distribution and botanical characteristics of lodgepole pine: biogeographical and management impUcations. pp. 1-12. In D . M . Baumgartner et al. (eds.) Lodgepole pine, the species and its management. Symposium proceedings. Wash. State Univ . , P u l l m a n , Washington. Weetman, G . F . , R . C . Yang , and I .E . Be l la . 1985. Nutr i t i on and ferti l ization of lodgepole pine. pp. 225-232. In D . M . Baumgartner et al. (eds.) Lodgepole pine, the species and its management. Sjnnposium proc. Wash. State Univ . , P u l l m a n , Washington. Whittaker , R . H . 1956. Vegetation of the Great Smoky momitains. Ecol . Monogr. 26: 1-80. Whit taker , R . H . 1967. Gradient analysis of vegetation. B i o l . Rev. 42: 207-264. Whittaker , R . H . (ed.) 1978. Ordination of plant commmiities. J u n k , The Hague, Boston. 388 pp. Wi lk inson , L . 1990. S Y S T A T : The system for statistics. Evanston, lUinois. S Y S T A T Inc. 822 pp. W u , Z h . Y . (ed. i n chief). 1980. Vegetation of C h i n a . Science Press. Bei j ing, China . 1375 pp. (in Chinese). Yoimgberg, C.T. and W . G . Dahms. 1970. Productivity indices of lodgepole pine on pimdce soils. J . For . 68: 90-94. Zeide, B . 1978. Standardization of growth ciuves. J . For . 76: 289-292. A P P E N D I X I L I S T O F P L A N T S P E C I E S F O U N D IN T H E S T U D Y P L O T S Coniferous trees 1 Abies lasiocarpa (Hook.) Nut t . 2 Picea glauca (Moench) Voss 3 P. mariana (Mil l . ) B S P . 4 Pinus contorta Dougl. ex Loud. 5 Thuja plicata Donn ex D . Don 6 Tsuga heterophylla (Raf.) Sarg. Broad-leaved trees 7 Betula papyrifera M a r s h . 8 Populus tremuloides Michx . 9 P. trichocarpa Torr. et Gray ex Hook. 10 Prunus pensylvanica L . f Evergreen shrubs 11 Andromeda polifolia L . 12 Arctostaphylos uva-ursi (L.) Spreng. 13 Chimaphila umbellata (L.) Barton 14 Empetrum nigrum L . 15 Gaultheria hispidula (L.) Muhlenb. ex Bige l . 16 Kalmia microphylla (Hook.) Hel ler 17 Ledum groentandicum Oeder 18 Juniperus sibirica L . Deciduous shrubs 19 Alnus sinuata (Regel) Rydb. 20 Amelanchier alnifolia (Nutt.) Nut t . 21 Betula glandulosa M c h x . 22 Cornus sericea L . 23 Lonicera involucrata (Richards.) Banks ex Spr. 24 Menziesia ferruginea S m . 25 Ribes glandulosum Grauer. 26 R. hudsonianum Richards. 27 R. lacustre (Pers.) Poir . 28 R. oxyacanthoides L . 29 R. triste P a U . 30 Rosa acicularis L i n d l . 31 Rubus idaeus L . 32 R. parviflorus N u t t . 33 Salix barclayi Anderss. 34 S. bebbiana Sarg. 35 S. drummondiana Barra t t 36 S. maccalina Rowlee 37 S. monticola Bebb. ex Coult. 38 S. planifolia Piirsh 39 S. pyrifolia Anderss. 40 S. rigida Mtdi lenb. 41 S. scouleriana Barrat t 42 S. sitchensis Sanson 43 Samhucus racemosa L . 44 Shepherdia canadensis (L.) N u t t . 45 Sorous scopulina Greene 46 Spiraea betulifolia P a l l . 47 S. douglasii Hook. 48 Symphoricarpos albus (L.) B lake 49 V. caespitosum Michx . 50 V. membranaceum Dougl. ex Hook. 51 V. myrtilloides Michx . 52 V. ovalifolia S m . 53 Viburnum edule (Michx.) Raf. Ferns 54 Athyrium filix-femina (L.) Roth 55 Botrychium virginianum (L.) Sw, 56 Dryopteris expansa (Presl) Fraser-Jenkins 57 Equisetum arvense L . 58 E. hyemale L . 59 E. palustre L . 60 E. scirpoides Michx . 61 E. sylvaticum L . 62 Gymnocarpium dryopteris (L.) Newm. 63 Lycopodium annotinum L . 64 L. complanatum L . 65 L. obscurum L . Graminoids 66 Agrostis oregonensis Vasey 67 Agropyron smithii Rydb. 68 Aira praecox L . 69 Calamagrostis canadensis (Michx.) Beauv. 70 Carex concinnoides Mack 71 C. disperma Dew. 72 C. pauciflora Lightf . 73 C. rossii Boott 74 C. sitchensis Prescott 75 Cinna latifolia (Trev. ex Goepp.) Griseb 76 Danthonia intermedia Vasey 77 Elymus glaucus B u c k l . 78 E. hirsutus Pres l 79 Eriophorum scheuchzeri Hoppe 80 Festuca idahoensis E l m e r 81 F. occidentalis Hook. 82 F. subulata T r i n . 83 F. subulifolia Scribn. 84 Hordeum jubatum L . 85 Juncus ensifolius Wiks t r . 86 Luzula parviflora (Ehrh.) Desv. 87 Oryzopsis asperifolia Michx , 88 Stipia richardsonii L i n k . Herbs 89 Achillea millefolium L . 90 Actaea rubra (Ait.) W i l l d . 91 Anaphalis margaritacea (L.) Benth. 92 Anemone multifida Poir . 93 Angelica genuflexa N u t t . 94 Antennaria microphylla Rydb. 95 A neglecta Greene 96 Aquuegia flavescens Wats, 97 A formosa F i s ch , 98 Aralia nudicaulis L . 99 Arnica cordifolia Hook. 100 A latifolia Bong. 101 Aster ciliolatus L i n d l . 102 A conspicuus L i n d l . 103 A foliaceus L i n d l . 104 A subspicatus Nees 105 Calypso bulbosa (L.) Cakes i(?6 Castilleja miniata Dougl. ex Hook. 107 Circaea alpina L . 108 Clintonia uniflora (Schult.) K u n t h 109 Cornus canadensis L . 110 Delphinium glaucum Wats. 111 Disporum trachycarpum (Wats.) Benth , et Hook, 112 Drosera anglica Huds , 113 D. rotundifolia L . 114 Epilobium angustifolium L . 115 E. latifolium L . 116 Erigeron sp. 117 Fragaria vesca L . 118 F. virginiana Duchesne 119 Galium boréale L . 120 G. triflorum Michx . 121 Gentianella amarella (L.) Boerner 122 Geocaulon lividum (Richards.) F e r n . 123 Geum macrophyllum W i l l d . 124 Goodyera oblongifolia Raf. 125 Heracleum lanatum Michx . 126 Hieracium albiflorum Hook. 127 Impatiens noli-tangere L . 128 Lathy rus nevadensis Wats. 129 L. ochroleucus Hook. 130 Leptarrhena pyrolifolia (D. Don) R, B r . ex Ser, 131 Linnaea borealis L . 132 Listera borealis Morong 133 L. cordata (L.) R. B r . 134 Lupinus arcticus Wats. 135 Maianthemum canadense Desf. 136 Melampyrum lineare Desr. 137 Menyanthes trifoliata L . 138 Mertensia paniculata (Ait.) G . Don 139 Mitella nuda L . 140 Nothocalais troximoides (Gray) Greene 141 Orthilia secunda (L.) House 142 Osmorhiza chUensis Hook, et A m . 143 Parnassia fimbriata Koenig 144 Pedicularis sp. 145 Penstemon procerus Dougl . ex G r a h a m 146 Petasites palmatus (Ait.) Gray 147 Phleum alpinum L . 148 Platanthera dUatata (Pursh) L i n d l . ex Beck 149 P. ohtusata (Banks ex Pursh) L i n d l . 150 P. orbiculata (Pursh) L i n d l . 151 Polemonium pulcherrium Hook. 152 Potentilla arguta P u r s h 153 P. gracilis Dougl . ex Hook. 154 P. palustris (L.) Scop. 155 Pyrola asarifolia Michx . 156 P. chlorantha Sw. 157 P. minor L , 158 Ranunculus eschscholtzii Schlecht. 150 R. occidentalis Nut t . 159 Rubus pedatus S m . 160 R. pubescens Raf. 161 Sanguisorba canadensis L , 162 Senecio pauperculus Mi chx . 163 S. pseudaureus Rydb. 164 S. triangularis Hook. 165 Smilacina racemosa (1.) Des f 166 S. stellata (1.) Desf. 167 Solidago canadensis L . 168 S. spathulata D C . 169 Stellaria crispa C h a m , et Schlecht. 170 Streptopus amplexifolius (L.) D C . 171 S. roseus Michx . 172 Taraxacum ceratophorum (Ledeb.) D C . 173 T. officinale Weher 174 Thalictrum occidentale G r a y 175 Tiarella trifoliata L . 176 T unifoliata Hook. 177 T. arctica F i s ch . ex Hook. 178 UrticadioicaL. 179 Vaccinium oxycoccus L . 180 Valeriana sitchensis Bong. 181 Veratrum viride A i t , 182 Vicia americana Muhlenb. ex W i l l d . 183 Viola adunca S m . 184 V. blanda W i l l d , 185 V. canadensis L . 186 V glabella N u t t , 187 V. nephrophylla Greene 188 V. orbiculata Geyer ex Hook. 189 V. palustris L . 190 V. renifolia G r a y Parasites & saprophytes 191 Corallorhiza trifida Chat . Mosses 192 Aulacomnium palustre (Hedw.) Schwaegr. 193 Brachythecium albicans (Hedw.) B .S .G . 194 B. cuHum (Lmdb.) B r i d . 195 B. hylotapetum B . H i g . et N . H i g . 196 B. salebrosum (Web. et Mohr) B . S . G . 197 Bryum caespiticium Hedw. 198 B. pseudotriquetrum (Hedw.) Gaertn. , Meyer et Scherb. 199 Ceratodon purpureus (Hedw.) B r i d . 200 Claopodium crispifolium (Hook.) Ren. et Card . 201 Climacium dendroides (Hedw.) Web. et Mohr . 202 Dicranum acutifolium (Lind. et H .Amel l ) C. Jens. 203 D. fuscescens T u r n . 204 D. polysetum Sw, 205 D. scoparium Hedw. 206 D. undulatum B r i d . 207 Drepanocladus fluitans (Hedw.) W a m s t . 208 D. uncinatus (Hedw.) Weunst. 209 Eurhynchium pulchellum (Hedw.) Jenn . 210 Funaria hygrometrica Hedw. 211 Helodium blandowii (Web. et Mohr.) W a m s t 212 Hylocomium splendens (Hedw.) B . S . G . 213 Hypnum cupressiforme Hedw. 214 Mnium sp. 215 Plagiomnium ellipticum (Brid.) Kop. 216 P. insigne (Mitt.) Kop . 217 P. medium (B. S. G.) Kop. 218 Pleurozium schreberi (Brid.) M i t t . 219 Pohlia cruda (Hedw.) L indb . 220 P. nutans (Hedw.) L indb . 221 Polytrichum commune Hedw. 222 P. juniperinum Hedw. 223 P. piliferum Hedw. 224 Ptilium crista-castrensis (Hedw.) De Not. 225 Rhizomnium glabrescens (Kindb.) Kop. 226 Rh. nudum (Britt . et WilHams) Kop. 227 Rh. punctatum (Hedw.) Kop. 228 Rhytidiadelphus loreus (Hedw.) W a m s t . 229 Rh. squarrosus (Hedw.) Wamst . 230 Rh. triquetrus (Hedw.) Wamst . 231 Sphagnum centrale C. Jens, ex H . A m e l l et C. Jens. 232 S. fuscum (Schimp.) Kl inggr . 233 S. girgensohnii Russ. 234 S. magellanicum B r i d . 235 S. nemoreum Scop. 236 S. squarrosum Crome 237 Tetraplodon mnioides (Hedw.) B .S .G . 238 Tetraphis pellucida Hedw. 239 Thuidium recognitum (Hedw.) L indb . 240 Timmia austriaca Hedw. 241 Tomenthypnum nitens (Hedw.) Loeske Liverworts 242 Barbilophozia barbata (Schmid) Loeske 243 Barbilophozia hatcheri (Eveins) Loeske 244 B. lycopodioides (Wedh-.) Loeske 245 Barbula vinealis B r i d . 246 Blepharostoma trichophyllum (L.) D u m . 247 Cephalozia sp. 248 C. connivens (Dicks.) L indb . 249 Lepidozia reptans (L.) D u m . 250 Lophozia ascendens (Wamst.) Schust. 251 L. guttulata (Lindb. et H . A m e l l ) E v a 252 L. sp. 253 L. ventricosa (Dicks.) D u m . 254 Marchantia polymorpha L . 256 Ptilidium pulcherrimum (G. Web.) Hampe Lichens 257 Cetraria islandica (L.) A c h . 258 Cladina arbuscula (Wallr.) Hale et W. Culb . 259 C. mitis (Sandst.) Ha le et W. Culb 260 C. rangiferina (L.) H a r m . 261 Cladonia carneola (Fr.) F r . 262 C. cenotea (Ach.) Schaerer 263 C. chlorophaea (Florke ex Somm.) Spreng 264 C. cornuta (L.) Hoffin. 265 C. deformis (L.) Hoffin. 266 C. fimbriata (L.) F r . 267 C. furcata (Huds.) Schrad. 268 C. gracilis (L.) mm. 269 C. multiformis M e r r . 270 C. ochrochlora F lorke 271 C. phyllophora E h r h . ex Hoffin. 272 C. veHicillata (Hoffin.) Schaer 273 PeUigera aphthosa (L.) W i l l d . 274 P. canina (L.) W i l l d . 275 P. malacea (Ach.) F u n k 276 Stereocaulon tomentosum F r . 255 MetZi A P P E N D I X I I Cunia 's (1973) method of testing significance of intercepts and slopes was used to test site index and ecological variables i n relation to the parameters estimated for the Chapman-Richards growth function. The procedxu-e was as follows: 1. Regressions without intercepts were fitted for b^, b2, and b3, respectively, using the site units as diunmy variables and site index mult ip l ied by each of the 9 dummy variables as new independent variables. The general model was as follows: [1] b l , bg, bg = S U I + S U 2 + ... + S U 9 + (SU1)(SI) + (SU2)(SI) + ... + (SU9)(SI), 2. To test i f both intercepts and slopes together were not significantly different, equations w i t h single intercept and single slope were fitted for b j , b2, and bg, respectively, using site index alone as independent variable: [2] b j , bg, bg = Co -H Ci(SI), where Cq and c^ are parameters to be estimated. 3. To test i f intercepts were not significantly different, regressions were fitted for b^, b2, and bg, respectively, using site index mult ip l ied by each of the 9 dummy variables, but only one intercept: [3] b l , bg, bs = Co -H (SU1)(SI) + (SU2)(SI) + + (SU9)(SI), 4. To test i f slopes were not significantly different, regressions were fitted for b l , b2, and bg, respectively, using 9 dummy variables, but only one slope coefficient for site index: [4] b l , b2, bg = S U I + S U 2 + + S U 9 + Ci(SI), For each of the 3 parameters (b^, b2, bg), the difference between the residual sum of squares from the step 1 and the residual s imi of squares from steps 2, 3, and 4 (SS(jif) were calculated and divided by the difiference i n the residual degrees of freedom (DFjjif) to obtain the difiference mean squares (MS<jif). Consequently, an F test was carried out for (1) both intercepts and slopes together, (2) intercepts, and (3) slopes as follows: [5] F = MSdif MSres where MS^gg is the mean square of the residual from equation [1]. A P P E N D I X III Table A l . Site series lodgepole pine height growth based on eqiiation [5.4.10] and parameters given in Table 5.11. Symbols for sites series are given in Table 5.1. B . H . A g e 8S1 882 S83 8SS 886 SS7 888 889 8810 8811 8812 8813 881« 8815 0 1.40 1.42 1 1.47 1.58 2 1.S9 1.77 3 1.74 1.98 4 1.90 2.19 5 2.08 2.41 6 2.27 2.64 7 2.47 2.86 8 2.67 3.09 9 2.87 3.32 10 3.08 3.SS 11 3.28 3.78 12 3.49 4.01 13 3.69 4.23 14 3.89 4.46 15 4.09 4.69 16 4.29 4.91 17 4.49 5.14 18 4.68 5.36 19 4.87 5.58 20 5.05 5.80 21 5.23 « . 0 2 22 S.41 6.24 23 5.58 6.45 24 5.75 6.66 25 5.91 6.87 26 6.07 7.08 27 6.33 7.29 28 6.38 7.50 29 6.53 7.70 30 6.67 7.90 1.38 1.57 1.60 1.45 1.79 2.02 1.56 2 .11 2.45 1.69 2.48 2.87 1.84 2.88 3.28 2.00 3.30 3.68 2.17 3.73 4.08 2.35 4.16 4.47 2.53 4.60 4.86 2.72 5.04 5.24 2.91 5.49 5.61 3.11 5.93 5.97 3.31 6.36 6.33 3.51 6.80 6.68 3.72 7.22 7.02 3.92 7.65 7.36 4.13 8.06 7.69 4.34 8.47 8.02 4.55 8.87 8.34 4.76 9.27 8.65 4.97 9.65 8.96 5.17 10.03 9.26 5.38 10.40 9.56 5.59 10.77 9.85 5.80 11.12 10.13 6.01 11.47 10.41 6.22 11.81 10.69 6.42 12.14 10.96 6.63 12.46 11.22 6.83 12.77 11.48 7.03 13.08 11.74 1.55 1.51 1.50 1.70 1.86 1.69 1.97 2.27 2 .01 2.30 2.69 2.39 2.66 3.12 3 .81 3.06 3.SS 3.25 3.48 3.99 3.72 3.91 4.42 4 .21 4.36 4.86 4 .71 4.81 5.29 5.32 S.27 5.72 5.73 5.73 6.14 6.25 6.20 6.56 6.77 6.66 6.98 7.29 7.13 7.40 7.80 7.59 7.81 8.32 8.04 8.21 8.83 8.50 8.61 9.34 8.94 9.01 9.84 9.38 9.40 10.34 9.82 9.79 10.83 10.25 10.17 11.32 10.67 10.55 11.80 11.08 10.92 12.27 11.49 11.29 12.74 11.89 11.65 13.20 12.28 12.01 13.65 12.66 12.36 14.09 13.04 12.71 14.52 13.40 13.05 14.95 13.76 13.39 15.37 1.45 1.46 1.48 1.71 1.71 1.66 2.02 2.06 1.93 2.33 2.44 2.26 2.64 2.85 2.61 2.96 3.27 2.98 3.28 3.71 3.38 3.60 4.15 3.79 3.92 4.60 4.21 4.23 5.05 4.63 4.55 5.50 5.07 4.86 5.95 5.51 5.17 6.41 5.95 5.48 6.86 6.40 5.78 7.30 6.85 6.08 7.75 7.30 6.38 8.19 7.75 6.67 8.63 8.20 6.97 9.06 8.64 7.25 9.49 9.09 7.54 9.91 9.54 7.82 10.33 9.98 8.10 10.74 10.42 8.37 11.15 10.86 8.64 11.55 11.29 8.91 11.95 11.72 9.18 12.34 12.15 9.44 12.72 12.58 9.69 13.10 13.00 9.95 13.48 13.41 10.20 13.85 13.82 1.36 1.40 1.49 1.41 1.51 1.58 1.49 1.68 1.75 1.60 1.87 1.97 1.73 2.09 2.22 1.86 2.32 2.50 2.01 2.57 2. SO 2.17 2.82 3.12 2.34 3.09 3.44 3.51 3.36 3.78 2.69 3.64 4.12 2.88 3.92 4.46 3.07 4.21 4.80 3.36 4.50 5.15 3.46 4.79 5.49 3.67 5.09 5.83 3.87 5.39 6.16 4.08 5.69 6.50 4.29 5.99 6.82 4.51 6.29 7.14 4.72 6.60 7.46 4.94 6.91 7.77 5.16 7.21 8.07 5.38 7.52 8.37 5.61 7.83 8.66 5.83 8.13 8.94 6.05 8.44 9.22 6.28 8.75 9.49 6.50 9.05 9.75 6.73 9.36 10.00 6.96 9.66 10.25 T a b l e A l . (continued) 31 6.81 8.10 7.23 U . 3 8 11.99 14.11 13.72 15.78 10.45 14.21 14.23 7.18 9.96 10.49 32 6.95 8.30 7.43 13.67 12.23 14.46 14.05 16.18 10.69 14.56 14.63 7.41 10.27 10.72 33 7.08 8.49 7.63 13.96 12.48 14.79 14.38 16.58 10.93 14.91 15.03 7.63 10.57 10.95 34 7.21 8.69 7.83 14.23 12.71 15.12 14.70 16.96 11.17 15.26 15.43 7.86 10.87 11.17 3S 7.33 8.88 8.03 14.50 12.95 15.44 15.01 17.34 11.40 15.60 15.81 8.09 11.17 11.38 36 7.45 9.07 8.22 14.77 13.17 15.75 15.32 17.71 11.63 15.93 16.20 8.31 11.46 11.59 37 7.57 9.25 8.41 15.02 13.40 16.05 15.63 18.07 11.86 16.26 16.58 8.54 11.76 11.79 38 7.68 9.44 8.60 15.27 13.62 16.35 15.93 18.43 12.09 16.58 16.95 8.76 12.05 11.98 3» 7.79 9.62 8.79 15.51 13.83 16.63 16.22 18.78 12.31 16.89 17.32 8.99 12.35 12.17 40 7.90 9.80 8.98 15.75 14.04 16.91 16.52 19.12 12.52 17.20 17.69 9.21 12.64 12.35 41 8.00 9.98 9.17 15.97 14.25 17.19 16.80 19.45 12.74 17.51 18.05 9.43 12.93 12.53 42 8.10 10.16 9.35 16.20 14.45 17.45 17.09 19.77 12.95 17.81 18.41 9.65 13.22 12.70 43 8.20 10.33 9.53 16.41 14.65 17.71 17.37 20.09 13.16 18.10 18.76 9.87 13.50 12.86 44 8.29 10.51 9.71 16.62 14.85 17.96 17.64 20.40 13.37 18.39 19.10 10.09 13.79 13.02 45 8.38 10.68 9.89 16.83 15.04 18.21 17.91 20.70 13.57 18.67 19.44 10.31 14.07 13.17 46 8.47 10.85 10.07 17.02 15.23 18.45 18.18 21.00 13.77 18.95 19.78 10.53 14.35 13.32 47 8.55 11.02 10.24 17.22 15.42 18.68 18.44 21.29 13.97 19.22 20.11 10.75 14.63 13.47 48 8.63 11.18 10.42 17.40 15.60 18.91 18.70 21.57 14.16 19.49 20.44 10.97 14.91 13.60 49 8.71 11.34 10.59 17.59 15.78 19.13 18.95 21.84 14.35 19.75 20.76 11.18 15.18 13.74 50 8.79 11.51 10.76 17.76 15.95 19.34 19.20 22 .11 14.54 20.01 21.08 11.40 15.45 13.87 51 8.86 11.67 10.92 17.93 16.12 19.55 19.45 22.37 14.73 20.26 21.39 11.61 15.73 13.99 52 8.94 11.82 11.09 18.10 16.29 19.75 19.69 22.63 14.91 20.51 21.70 11.82 16.00 14.11 53 9.00 11.98 11.25 18.26 16.46 19.95 19.93 22.88 15.09 20.75 22.00 12.03 16.26 14.23 54 9.07 12.13 11.41 18.42 16.62 20.14 20.17 23.12 15.27 20.99 22.30 12.24 16.53 14.34 55 9.14 12.28 11.57 18.57 16.78 20.32 20.40 23.36 15.44 21.22 22.59 13.45 16.79 14.45 56 9.20 12.43 11.73 18.72 16.94 20.50 20.62 23.59 15.61 21.45 22.88 12.66 17.05 14.55 57 9.26 12.58 11.89 18.86 17.09 20.68 20.85 23.82 15.78 21.67 23.17 12.86 17.31 14.65 58 9.32 12.73 12.04 19.00 17.24 20.85 21.07 24.04 15.95 21.89 23.45 13.07 17.57 14.75 59 9.37 12.87 12.20 19.14 17.39 21.01 21.29 24.25 16.12 22.11 23.73 13.27 17.82 14.84 60 9.43 13.02 12.35 19.27 17.53 21.17 21.50 24.46 16.28 22.32 24.00 13.47 18.08 14.94 61 9.48 13.16 12.50 19.39 17.67 21.33 21.71 24.67 16.44 22.53 24.27 13.67 18.33 15.02 62 9.53 13.30 12.64 19.52 17.81 21.48 21.92 34.87 16.60 22.73 24.53 13.87 18.58 15.11 63 9.58 13.44 12.79 19.64 17.95 21.62 22.12 25.06 16.75 22.93 24.79 14.07 18.82 15.19 64 9.63 13.57 12.93 19.75 18.08 21.77 22.32 25.25 16.91 23.13 25.04 14.26 19.07 15.26 65 9.67 13.71 13.07 19.87 18.22 21.90 22.52 25.44 17.06 23.32 25.29 14.46 19.31 15.34 66 9.72 13.84 13.21 19.97 18.35 22.04 22.71 25.62 17.20 23.50 25.54 14.65 19.55 15.41 67 9.76 13.97 13.35 20.08 18.47 22.17 22.90 25.79 17.35 23.69 25.78 14.84 19.79 15.48 68 9.80 14.10 13.49 20.18 18.60 22.29 23.09 25.96 17.49 23.87 26.02 15.03 20.02 15.55 69 9.84 14.23 13.62 20.28 18.72 22.42 23.28 26.13 17.64 24.04 26.26 I S . 22 20.26 15.61 70 9.88 14.35 13.75 20.38 18.84 22.53 23.46 26.29 17.78 24.22 26.49 15.41 20.49 15.68 T a b l a A l . (continued) 71 9.92 14.48 72 9.95 14.60 73 9.99 14.72 74 10.02 14.84 75 10.05 14.96 76 10.08 15.08 77 10.11 15.19 78 10.14 15.31 79 10.17 15.42 80 10.20 15.53 81 10.22 15.64 82 10.35 15.75 83 10.27 15.85 84 10.29 15.96 85 10.32 16.06 86 10.34 16.17 87 10.36 16.27 88 10.38 16.37 89 10.40 16.47 90 10.42 16.56 91 10.43 16.66 92 10.45 16.7 6 93 10.47 16.85 94 10.48 16.94 95 10.50 17.03 96 10.52 17.12 97 10,53 17.21 98 10.54 17.30 99 10.56 17.39 100 10.57 17.47 13.88 20.47 18.96 14.01 20 .56 19.07 14.14 30 .65 19.19 14.27 20.74 19.30 14.39 20.82 19.41 14.51 20.90 19.51 14.64 20.98 19.62 14.75 21.05 19.72 14.87 21.13 19.82 14.99 21.20 19.92 15.10 21.27 20.02 15.22 21.33 20.11 15.33 21.40 20.21 15.44 21.46 20.30 15.55 21.52 20.39 15.65 21.58 20.48 15.76 21.64 20.57 15.86 21.69 20.65 15.96 21.74 20.73 16.07 21.80 20.82 16.17 21.85 20.90 16.26 21.90 20.98 16.36 21.94 21.05 16.46 21.99 21.13 16.55 22.03 21.20 16.64 22.08 21.28 16.73 22.12 21.35 16.82 22 .16 21.42 16.91 22.20 21.49 17.00 22.23 21.56 22.65 23.64 26.45 22.76 23.81 36.60 22.87 23.99 26.75 23.98 24.16 26.90 23.08 24.33 27.04 23.18 24.49 27.18 23.27 24.65 37 .31 23.37 24.81 27.44 23.46 24.97 27.57 23.54 25.12 27.70 23.63 25.28 27.82 23.71 25.43 27.93 23.79 25.57 28.05 23.87 25.72 28.16 23.94 25.86 28.27 24.02 26.00 28.38 24.09 26.14 28.48 24.15 26.27 28.58 24.22 26.41 28.68 24.29 26.54 28.77 24.35 26.67 28.87 24.41 26.79 28.96 24.47 26.92 29.04 24.52 27.04 29.13 24.58 27.16 29.21 24.63 27.28 29.29 24.68 27.40 29.37 24.73 27.51 29.45 24.78 27.63 29.52 24.83 27.74 29.60 17.91 24.39 26.72 18.05 24.55 26.94 18.18 24.71 27.16 18.31 24.87 27.38 18.44 25.03 27.59 18.57 25.18 27.80 18.70 25.33 28.00 18.82 25.48 28.20 18.94 25.62 28.40 19.06 25.76 28.60 19.18 25.90 28.79 19.29 36.03 28.98 19.41 26.17 29.16 19.52 26.29 29.35 19.63 26.42 29.53 19.74 26.55 29.70 19.85 26.67 29.87 19.96 26.79 30.04 20.06 36.90 30.21 20.16 27.02 30.37 20.26 27.13 30.54 20.36 27.24 30.69 20.46 27.34 30.85 20.56 27.45 31.00 20.65 27.55 31.15 20.75 27.65 31.30 30.84 27.75 31.45 20.93 27.84 31.59 21.02 27.94 31.73 21.10 28.03 31.87 15.60 20.72 15.74 15.78 20.95 15.79 15.96 21.17 15.85 16.15 21.40 15.90 16.33 21.62 15.96 16.51 21.84 16.01 16.68 22.06 16.05 16.86 22.27 16.10 17.03 22.49 16.14 17.21 22.70 16.19 17.38 22.91 16.23 17.55 23.11 16.27 17.71 23.32 16.31 17.88 23.52 16.34 18.05 23.73 16.38 18.21 23.92 16.41 18.37 24.12 16.44 18.53 24.32 16.48 18.69 24.51 16.51 18.85 24.70 16.54 19.01 24.89 16.56 19.16 25.08 16.59 19.32 25.27 16.62 19.47 25.45 16.64 19.62 25.63 16.67 19.77 25.81 16.69 19.92 25.99 16.71 20.07 26.17 16.73 20.21 26.35 16.75 20.36 26.52 16.77 •rH CD I—I 20 40 60 80 Age at breast height (yr) 100 <] SS15 V SS14 # SS13 * SS12 O SSll ^ SSIO • SS9 O SS8 • SS7 • SS6 A SS5 A SS3 • SS2 O SSI Figure A l . Site series lodgepole pine height growth ciirves based on equation [5.4.10] and parameters given i n Table 5.11. Symbols for sites series are given i n Table 5.1. Figure A 2 . Site series lodgepole pine height growth ctu-ves for S B P S x c subzone based on equation [5.4.10] and parameters given i n Table 5.11. Symbols for site series are explained i n Table 5.1. Figure A 3 . Site series lodgepole pine height growth curves for S B S m c subzone based on equation [5.4.10] and parameters given i n Table 5.11. Symbols for site series are expledned i n Table 5.1. Figure A4. Site series lodgepole pine height growth curves for S B S w k subzone based on equation [5.4.10] and parameters given i n Table 5.11. Symbols for site series are expjained i n Table 5.1. Table A2. Ecotope lodgepole pine height growth based on equation [5.4.11] and parameters given in Table 5.12. Symbols for BGC, SMRs, and SNRs are given in Table 5.1. B.H.Age Total height BOC SBPlxo . taama -'- SBSwk SMR ID VD VD KDf SDf SDf S D r P K V K V N M D M D S D r M l l V K W W SNR V P V P M K X V R P K R R R V R P X K K M I I R X V R 0 1.43 1.43 1.43 1.43 1.43 1.43 1.47 1.47 1.47 1.47 1.47 1.47 1.50 1.50 1.50 1.50 1 50 1.50 1.50 1 1.50 1.60 1.58 l.SO 1.70 l.<8 1.98 1.71 1.75 1.92 1.75 1.73 1.71 1.72 1.66 1.65 I 71 1.71 1.(3 2 1.12 1.7» 1.76 1.(0 1.99 1.96 2.48 2.13 2.07 2.40 2.10 2.06 2.01 2.04 1.93 1.8» 2 05 2.04 1.87 3 1.76 2.00 1.95 1.72 2.30 2.25 2.97 2.49 2.41 2.8» 2.47 2.41 2.35 2.40 2.25 2.1» 2 44 2.43 2.17 « 1.J2 2.21 2.16 1.8( 2.(0 2.SS 3.44 2.86 2.74 3.3» 2.84 2.7» 2.72 2.80 2.61 2.52 2 8( 2.86 2.52 5 2.0> 2.42 2.37 2.00 2.91 2.8( 3.90 3.24 3.12 3.88 3.27 3.18 3.10 3.21 2.99 2.88 3 32 3.32 2.»0 < 2.28 2.64 2.58 2.1( 3.23 3.17 4.35 3.62 3.4S 4.38 3.(7 3.58 3.50 3.64 3.40 3.26 3 7» 3.80 3.30 7 2.47 2.86 2.80 2.32 3.54 3.47 4.79 3.99 3.85 4.86 4.09 3.»S 3.90 4.08 3.82 3.(( 4 28 4.30 3.73 S 2.tt 3.08 3.02 2.4» 3.85 3.78 S.22 4.37 4.21 5.35 4.50 4.3» 4.30 4.53 4.25 4.07 4 77 4.81 4.17 ) 2.86 3.30 3.25 2.(7 4.15 4.0» 5.64 4.75 4.57 5.83 4.92 4.80 4.70 4.18 4.6» 4.49 5 27 5.33 4.(2 ao 3.06 3.52 3.47 2.85 4.46 4.40 6.05 5.12 4.94 6.30 5.33 5.21 S . l l 5.43 5.14 4.91 5 78 5.86 5.08 11 3.2< 3.74 3.70 3.03 4.74 4.70 (.45 5.50 5.30 (.77 5.74 5.(2 5.51 5.88 5.5» 5.35 ( 29 6.39 5.55 12 3.46 3.9( 3.92 3.21 S.0( 5.00 6.84 5.87 5.67 7.24 (.1( (.03 5.91 (.32 6.04 5.78 ( 80 6.92 (.03 13 3.6< 4.17 4.15 3.40 5.3( 5.31 7.22 6.23 6.03 7.(» (.57 • (.44 (.30 (.77 6.4» (.22 7 30 7.4( (.51 14 3.85 4.39 4.37 3.5» 5.(5 5.61 7.60 6.60 (.39 8.14 (.97 (.85 «.6» 7.21 (.94 (.« 7 81 7.9» (.»» 15 4.05 4.60 4.60 3.78 5.95 5.»1 7.96 6.96 6.74 8.5» 7.38 7.26 7.08 7.64 7.38 7.11 8 31 8.52 7.48 1( 4.24 4.81 4.83 3.98 (.24 6.20 8.32 7.31 7.10 ».03 7.78 7.6( 7.46 8.07 7.83 7.55 8 80 ».05 7.»( 17 4.43 5.02 5.05 4.17 (.52 (.50 8.67 7.67 7.45 ».4( 8.18 8.07 7.83 8.50 8.27 7.9» 9 29 ».57 8.44 18 4.(2 5.23 5.28 4.37 6.80 (.79 9.01 8.02 7.80 ».a» 8.57 8.47 8.20 8.12 8.70 8.42 9 78 10.0» 8.»2 19 4.80 5.43 5.50 4.5( 7.08 7.07 9.34 8.36 8.15 10.31 S.9( 8.87 8.55 9.33 9.13 8.8( 10 25 10.(0 ».3» 20 4.98 5.64 5.72 4.7( 7.36 7.3( ».66 8.71 8.49 10.72 9.35 ».26 8.91 9.73 ».S( ».29 10 73 11.11 9.8( 21 5.16 5.84 5.94 4.95 7.63 7.64 9.98 9.05 8.83 11.13 9.73 9.65 9.25 10.13 9.97 9.72 11 .19 11.(1 10.33 22 5.34 6.04 6.17 5.15 7.90 7.92 10.29 9.38 9.17 11.54 10.10 10.04 9.5» 10.52 10.3» 10.14 11 65 12.11 10.80 23 5.51 6.23 6.39 5.35 8.17 8.20 10.59 9.71 9.51 11.93 10.47 10.42 ».»2 10.90 10.79 10.5( 12 10 12.(0 11.25 24 5.67 (.43 (.60 5.54 8.43 8.48 10.89 10.04 9.84 12.32 10.84 10.80 10.24 11.28 11.1» 10.98 12 .54 13.08 11.70 2S 5.84 (.62 (.82 S.74 8.6» 8.75 11.18 10.3( 10.17 12.70 11.20 11.18 10.56 11.65 11.58 11.39 12 .97 13.55 12.15 2C 5.99 6.81 7.04 5.93 8.94 9.02 11.46 10.68 10.4» 13.08 11.56 11.55 10. a( 12.01 11.»7 11.79 13 40 14.02 12.59 27 6.15 7.00 7.25 (.13 9.20 9.2» 11.73 10.9» 10.82 13.45 11.91 11.92 11.1( 12.36 12.34 12.19 13 .82 14.48 13.02 Tabl« A2. (aontlBUad) 3a 2i 30 31 32 33 34 35 it 37 3S 3» 40 41 42 43 44 45 4< 47 4B 49 50 51 52 53 54 55 S« 57 58 59 <0 81 (2 <3 C4 (.30 (.45 «.5J 4.73 (.a< « .»» 7.12 7.25 7.37 7.4S 7. to 7.71 7.82 7.92 8.02 8.12 8.21 8.30 8.39 8.4S 8.5< 8. (4 8.72 8.80 8.87 8.94 9.01 9.07 9.14 9.20 9.26 9.32 9.37 9.43 9.48 9.53 9.58 7.19 7.37 7.55 7.73 7.91 8.08 8.28 8.43 8.60 8.76 8.93 9.09 9.25 9.40 9.56 9.71 9.86 10.01 10.18 10.30 10.45 10.59 10.73 10.86 11.00 11.13 11.26 11.39 11.52 11.64 11.77 11.89 12.01 12.13 12.24 12.36 12.47 7.46 7.68 7.89 8.09 6.30 8.SI 8.71 8.91 9.11 9.31 9.51 9.71 9.90 10.09 10.28 10.47 10.86 10.85 11.03 11.21 11.39 11.57 11.75 11.92 12.10 12.27 12.44 12.81 12.78 12.94 13.11 13.27 13.43 13.59 13.75 13.90 14.06 6.32 6.51 4.71 6.90 7.09 7.28 7.46 7.85 7.84 8.02 8.20 8.38 8.56 8.74 8.92 9.09 9.27 9.44 9.61 9.78 9.95 10.11 10.28 10.44 10.60 10.78 10.92 11.07 11.33 11.38 11.53 11.68 11.83 11.97 13.12 12.28 12.40 9.44 9.69 9.93 10.17 10.41 10.84 10.87 11.10 11.32 11.54 11.75 11.97 12.18 12.39 12.59 12.79 12.99 13.19 13.38 13.57 13.78 13.94 14.13' 14.30 14.48 14.86 14.83 15.00 15.16 15.33 15.49 15.65 15.80 15.96 16.11 16.28 18.41 9.55 9.81 10.07 10.33 10.58 10.83 11.07 11.32 11.58 11.80 12.03 12.27 12.50 12.72 13.95 13.17 13.39 13.81 13.82 14.03 14.34 14.45 14.65 14.85 15.05 15.34 15.44 15.63 15.82 18.00 18.19 18.37 16.55 18.73 18.90 17.07 17.24 13.00 13.37 13.52 13.78 13.02 13.38 13.50 13.73 13.95 14.17 14.38 14.59 14.79 14.99 15.19 15.38 15.57 15.75 15.93 16.10 18.37 18.44 18.60 16.76 18.91 17.08 17.31 17.35 17.50 17.83 17.77 17.90 18.03 18.15 18.38 18.40 18.51 11.30 11.81 11.91 13.31 13.51 13.80 13.09 13.37 13.65 13.93 14.30 14.48 14.73 14.99 15.35 15.50 15.75 15.99 18.24 18.48 18.71 18.94 17.17 17.40 17.82 17.84 18.08 18.27 18.48 18.69 18.89 19.09 19.29 19.48 19.87 19.86 20.05 11.14 11.45 11.78 12.07 13.38 13.68 12.98 13.28 13.57 13.88 14.15 14.43 14.71 14.99 15.28 15.53 15.80 18.08 18.32 18.58 18.84 17.09 17.34 17.58 17.82 18.06 18.30 18.53 18.76 18.99 19.23 19.44 19.88 19.88 30.0) 30.30 30.51 13.83 14.18 14.53 14.88 15.33 15.58 15.90 16.23 18.54 18.88 17.17 17.47 17.77 18.07 18.38 18.65 18.93 19.30 19.47 19.74 30.00 20.28 20.51 20.76 21.01 21.25 21.49 21.72 21.95 22.17 22.39 23.81 22.83 33.03 33.34 33.44 33.(4 13.38 13.(0 12.94 13.38 13.80 13.93 14.35 14.58 14.87 15.17 15.47 15.77 18.08 18.34 18.83 18.90 17.17 17.44 17.71 17.98 18.22 18.47 18.72 18.96 19.20 19.43 19.66 19.89 20.11 20.33 20.55 30.78 30.97 21.17 21.37 21.57 21.76 12.38 12.85 13.00 13.35 13.70 14.04 14.38 14.73 15.05 15.37 15.70 18.01 18.33 18.64 18.94 17.34 17.54 17.83 18.13 18.41 18.89 18.98 19.34 19.51 19.77 30.03 30.39 30.54 20.79 21.04 21.28 21.52 21.78 31.99 22.22 23.44 33.88 11.46 11.74 13.03 13.39 13.56 13.82 13.07 13.31 13.55 13.78 14.00 14.22 14.44 14.64 14.84 15.04 15.23 15.42 15.59 15.77 15.94 18.10 18.38 16.43 18.57 18.71 18.88 18.99 17.13 17.28 17.38 17.51 17.82 17.74 17.85 17.98 18.06 12.70 13.04 13.37 13.69 14.01 14.31 14.61 14.90 15.19 15.47 15.74 18.00 18.28 18.51 16.76 17.00 17.23 17.48 17.88 17.89 18.10 18.31 18.50 18.70 18.89 19.07 19.25 19.42 19.59 19.75 19.91 30.07 20.23 30.38 20.50 20.64 20.78 12.71 13.08 13.43 13.78 14.13 14.48 14.78 15.10 15.41 15.71 18.01 18.30 18.59 18.88 17.13 17.39 17.85 17.90 18.14 18.38 18.61 18.84 19.08 19.37 19.48 19. (8 19.88 20.08 20.36 20.45 20. (2 30.80 30.9( 21.13 31.39 21.44 31.59 12.59 13.97 13.38 13.73 14.10 14.47 14.83 15.18 15.53 15.87 18.21 18.53 16.88 17.17 17.49 17.79 18.09 18.38 18.67 18.95 19.23 19.50 19.77 20.03 20.28 20.53 20.77 21.01 21.35 21.48 31.70 31.92 32.13 22.34 22.55 22.75 22.95 14.23 14.83 15.03 15.40 15.78 16.15 18.51 18.88 17.30 17.54 17.87 18.19 18.50 18.81 19.\1 19.40 19.(8 19.96 30.33 20.49 20.75 21.00 21.25 21.49 21.72 21.94 33.16 23.38 32.59 22.79 33.99 33.18 23.37 33.55 23.73 33.91 24.08 14.93 15.37 15.80 18.23 It.65 17.08 17.48 17.88 18.25 18.83 19.00 19.38 19.72 20.07 20.41 20.74 21.07 21.39 21.70 23.00 22.30 33.59 23.88 23.18 33.43 23. (9 33.95 24.21 34.45 24. (9 34.93 25.18 35.38 25.60 35.82 28.02 26.33 13.45 13.87 14.28 14.89 15.09 15.48 15.88 16.34 18.81 16.97 17.33 17.48 18.02 18.35 18. (8 19.00 19.31 19. (2 19.92 20.21 30.49 20.77 31.05 21.31 31.57 21.83 32.08 22.33 33.58 33.79 33.01 33.23 33.45 23.88 33.88 24.08 34.25 8.42 8.83 8.83 9.03 9.23 9.42 9.60 9.78 9.95 10.11 10.37 10.43 10.58 10.73 10.87 11.00 11.13 11.38 11.38 11.50 11.62 11.73 11.84 11.94 12.04 13.14 U.33 12.32 U.40 12.49 13.57 12.85 12.73 U.79 13.88 13.93 12.99 11.38 11.71 12.03 12.35 13.68 13.98 13.35 13.54 13.83 14.09 14.35 14.(1 14.86 15.10 15.34 15.56 15.79 18.00 18.31 18.43 18.83 18.81 18.99 17.18 17.35 17.53 17.89 17.84 18.00 18.15 18.39 18.44 18.57 18.70 18.83 18.98 19.08 Tabla X2. (oonclnuad) <S « 67 6S 6t 70 71 72 73 74 75 76 77 7» 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 9.63 9.67 9.72 9.76 9.80 9.84 9.88 9.92 9.95 9.99 10.02 10.05 10.08 10.12 10.14 10.17 10.20 10.23 10.25 10.28 10.30 10.32 10.34 10.37 10.39 10.41 10.42 10.44 10.46 10.48 10.49 10.51 10.53 10.54 10.56 10.57 12.58 12.69 13.80 12.91 13.01 13.12 13.22 13.32 13.42 13.52 13.61 13.71 13.80 13.8» 13.98 14.07 14.16 14.24 14.33 14.41 14.50 14.58 14.66 14.74 14.81 14.89 14.97 15.04 15.11 15.19 15.26 15.33 15.39 15.46 15.53 15.59 14.21 14.36 14.51 14.46 14.80 14.95 15.09 15.23 15.37 15.51 15.65 15.79 15.92 16.06 16.19 16.32 16.45 16.58 16.70 16.83 16.95 17.07 17.19 17.31 17.43 17.55 17.66 17.78 17.89 18.00 18.12 18.23 18.33 18.44 18.55 18.65 12.54 12.68 12.82 12.95 13.08 13.22 13.35 13.47 13.60 13.73 13.85 13.97 14.09 14.21 14.33 14.45 14.56 14.68 14.79 14.90 15.01 15.12 15.22 15.33 15.43 15.53 15.64 15.74 15.83 15.93 16.03 16.U 16.22 16.31 16.40 16.49 16.55 16.70 16.84 16.98 17.11 17.25 17.38 17.51 17.64 17.76 17.89 18.01 18.13 18.25 18.37 18.49 18.60 18.71 18.82 18.93 19.04 19.14 19.24 19.35 19.45 19.55 19.64 19.74 1>.83 1».93 20.02 20.11 20.20 20.28 20.37 20.45 17.41 17.58 17.74 17.90 18.04 18.22 18.38 18.53 18.68 18.83 18.98 19.12 19.27 19.41 19.55 19.69 19.82 19.96 20.09 20.22 20.35 20.48 20.60 20.73 20.85 20.97 21.09 21.21 21.32 21.44 21.55 21.66 21.77 21.88 21.9» 22.0» 18.63 18.74 18.85 18.96 19.06 19.16 19.26 19.36 19.4f 19.55 19.64 19.73 19.82 19.90 19.99 20.07 20.15 20.22 20.30 20.37 20.45 20.52 20.59 20.65 20.72 20.78 20.85 20.91 20.»7 21.03 21.09 21.14 21.20 21.25 21.30 21.35 20.23 20.41 20.59 20.77 20.94 21.11 21.28 21.44 21.61 21.77 21.92 22.08 22.23 22.38 22.53 22.68 22.82 22.96 23.10 23.24 23.37 23.51 23.64 23.77 23.89 24.02 24.14 24.26 24.38 24.50 24.62 24.73 24.84 24.95 25.06 25.17 20.71 20.92 21.12 21.32 21.51 21.71 21.90 22.08 22.27 22.45 22.63 22.81 22.»» 23.16 23.33 23.50 23.67 23.84 24.00 24.16 24.32 24.48 24.63 24.78 24.93 25.08 25.23 25.37 25.52 25.66 25.79 25.93 26.07 26.20 26.33 26.46 23.84 24.03 24.22 24.40 24.58 24.76 24. »4 25.11 25.28 25.45 25.61 25.78 25.93 26.0» 26.24 26.39 26.54 26.69 26.83 26.97 27.11 27.24 27.37 27.51 27.63 27.76 27.88 28.01 28.12 28.24 28.36 28.47 28.58 28.69 28.80 28.90 21.»S 22.14 22.32 22.50 22.48 22.84 23.03 23.1» 23.36 23.53 23.68 23.84 23.9» 24.14 24.29 24.44 24.58 24.72 24.86 25.00 25.13 25.26 25.39 25.51 25.64 25.76 25.88 36.00 26.11 26.23 26.34 26.45 26.55 26.66 26.76 26.86 23.8* 33.0» 33.31 23.51 33.73 23.93 24.13 34.33 34.51 34.70 34.8» 35.07 35.35 35.43 35.60 35.78 35.95 36.11 26.28 26.44 26.60 24.76 26.91 27.06 27.21 27.36 27.51 27.65 27.79 27.93 28.06 28.20 28.33 28.46 38.59 28.71 18.17 18.26 18.36 18.45 18.54 18.63 18.72 18.80 18.88 18.95 19.03 19.10 19.17 19.24 19.31 19.37 19.43 19.49 19.55 19.61 19.66 19.72 19.77 19.82 19.87 19.91 19.96 20.00 20.04 20.09 20.13 20.16 20.20 20.24 20.27 20.31 20.91 21.04 31.16 21.38 21.40 31.51 21.62 31.73 21.83 21.93 22.03 22.13 22.22 22.31 22.40 22.48 22.56 22.64 22.72 22.80 22.87 22.94 33.01 23.08 23.14 23.21 23.27 23.33 23.39 23.44 23.50 23.55 23.60 23.65 23.70 33.75 21.74 31.88 23.03 33.15 33.28 33.41 33.54 33.66 33.77 33.89 33.00 33.10 23.21 33.31 23.41 33.50 23.60 33.6» 23.78 33.86 23. »4 34.03 24.10 34.18 24.25 34.33 24.40 24.46 24.53 24.59 24.65 24.71 24.77 24.83 24.89 24.94 23.14 23.33 23.51 23.69 23.86 24.04 24.20 24.37 24.53 24.68 24.84 24.99 25.13 25.28 25.42 25.55 25.69 25.82 25.94 26.07 26.19 26.31 26.42 26.54 26.65 26.75 26.86 26.96 27.06 27.16 27.26 27.35 27.44 27.53 27.62 27.70 24.24 24.40 24.56 34.71 34.84 35.00 35.14 35.38 35.41 35.54 35.66 35.78 25.90 36.02 26.13 26.24 26.34 26.45 26.55 26.64 26.74 26.83 26.92 27.01 27.09 27.18 27.26 27.33 27.41 27.48 27.55 27.62 27.69 27.76 27.82 27.88 26.43 26.62 26.81 26.99 27.17 27.35 27.52 27.6» 27.85 28.01 28.16 28.31 28.46 28.60 28.74 28.88 2».01 2».14 29.26 2».39 29.51 29.62 29.74 29.85 29.95 30.06 30.16 30.26 30.36 30.45 30.55 30.64 30.72 30.81 30.89 30.97 24.44 24.63 24.81 24.98 25.14 25.33 25.48 35.64 25.80 25.95 26.09 26.24 26.38 26.51 26.64 26.77 26.90 27.02 27.14 27.26 27.37 27.48 27.54 37.69 27.79 37.89 27.98 38.08 28.17 28.26 28.34 28.43 28.51 28.59 28.67 28.74 13.06 13.12 13.17 13.23 13.28 13.33 13.38 13.43 13.48 13.52 13.57 13.61 13.65 13.68 13.72 13.76 13.79 13.82 13.86 13.8» 13.91 13. »4 13.97 14.00 14.02 14.05 14.07 14.0» 14.11 14.13 14.15 14.17 14.1» 14.21 14.23 14.24 l».l» 19.30 19.41 19.52 19.62 19.73 19.81 19. »1 1».»» 30.08 20.16 20.25 20.32 20.40 20.47 20.54 20.61 20.68 20.74 20.80 20.86 20.93 20.98 31.03 21.08 31.13 31.18 31.33 31.37 31.33 31.36 31.40 31.44 31.48 31.53 21.55 40 30 -SBPSxc 10 -0 0 20 40 60 80 Age at breast height (yr) SDf*VR SDf*R MDf*R VD*M VD*VP ED*VP 100 Figure A 5 . Ecotope lodgepole pine height growth cvu-ves for S B P S x c subzone based on equation [5.4.11] and parameters given i n Table 5.12. Symbols for B G C , S M R s , and S N R s are given i n Table 5.1. 40 Figure A 6 . Ecotope lodgepole pine height growth ciu-ves for S B S m c subzone based on equation [5.4.11] and parameters given i n Table 5.12. Symbols for B G C , S M R s , and S N R s are given i n Table 5.1. 40 0 W*VR W*M VM*R M*R M*M F*M SD*M MD*M MD*P 20 40 60 80 Age at breast height (yr) 100 Figure A7 . Ecotope lodgepole pine height growth ctuves for S B S w k subzone based on equation [5.4.11] and parameters given i n Table 5.12. Symbols for B G C , S M R s , and S N R s are given i n Table 5.1. 

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