Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Modeling growth of understory aspen and spruce in western boreal Canada Astrup, Rasmus 2006

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2006-199336.pdf [ 7.5MB ]
Metadata
JSON: 831-1.0075039.json
JSON-LD: 831-1.0075039-ld.json
RDF/XML (Pretty): 831-1.0075039-rdf.xml
RDF/JSON: 831-1.0075039-rdf.json
Turtle: 831-1.0075039-turtle.txt
N-Triples: 831-1.0075039-rdf-ntriples.txt
Original Record: 831-1.0075039-source.json
Full Text
831-1.0075039-fulltext.txt
Citation
831-1.0075039.ris

Full Text

Modeling growth of understory aspen and spruce in western boreal Canada by Rasmus Astrup A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (Forestry) THE UNIVERSITY OF BRITISH C O L U M B I A SEPTEMBER 2006 © Rasmus Astrup, 2006 Abstract For aspen and spruce in western sub-boreal and boreal Canada this study investigated regional variation in: (1) species-specific crown openness for mature trees, and (2) light-growth relationships for juvenile trees. Regional variation in species-specific crown openness was found for both species, but the magnitude of the variation was judged to only cause small variation in understory light levels. Regional variation in the light-growth relationship was found for both species but no indications of shifts in the successional dynamics between the two species were observed. The regional variation in the two investigated quantities did not follow the same regional pattern and their combined effect cannot be expected to strengthen regional differences in understory tree performance. The regional shapes of the light-growth relationship were similar for the two species. The main observed difference between the two species was the initial fast growth of aspen. For spruce in aspen-dominated areas of the boreal mixedwood region, asymptotic light growth relationships were found. In western conifer-dominated regions, approximately linear light-growth relationships were observed. This regional variation was best explained by the different effect of aspen-dominated and conifer-dominated canopies on the light-growth relationship. It is hypothesized that the different effects of canopy-type can be caused by several effects, including nutrient availability, soil temperature, and leaf-off period. The findings of this study were incorporated in the stand level simulation model SORTIE-ND. An evaluation of SORTIE-ND illustrated that the model generally produces realistic predictions and can be considered as a management tool. A comparison of model predictions with permanent plot data for mixed stands in the Sub-Boreal Spruce Zone of British Columbia indicated that the model has problems with prediction of aspen mortality rates and tends to overestimate growth rates especially for spruce. ii Table of Contents Abstract i i Table of Contents i i i Table of Tables v Table of Figures vi Acknowledgements vii Co-Authorship Statement viii Chapter 1: Introduction 1 Mixed aspen-spruce stands in western boreal and sub-boreal Canada 1 Silviculture and management of aspen-spruce mixedwoods 2 Growth modeling in western boreal Canada 4 Predicting understory tree growth 6 Regional variation 7 Problem statement and working hypotheses 9 Dissertation structure 9 Chapter 1 references 11 Chapter 2: Regional Variation of Aspen and Spruce Crown Openness 21 Introduction 21 Methods 23 Results 28 Discussion 31 SORTIE's sensitivity to species-specific crown openness 36 Chapter 2 references 39 Chapter 3: Light Availability and Growth of Understory Aspen and Spruce in Western Boreal Canada 44 Introduction 44 Field methodology and data 45 Results 56 Discussion 63 Chapter 3 references 68 in Chapter 4: Regional Variation in the Light-Growth Response of Understory Trees: Effect of Climate or Canopy Type? 75 Introduction 75 Methods and analysis 76 Results 82 Discussion 92 Chapter 4 references 96 Chapter 5: Evaluation of SORTIE-ND for Growth Prediction in Mixed Stands 103 Introduction 103 General approach to evaluation 104 Development history and description of the evaluated version of SORTIE-ND 106 Methodology and data 112 Results and discussion 118 Recommendations for further model development 140 SORTIE-ND predictive ability and implications for use in management 141 Chapter 5 references 142 Chapter 6: Summarizing Discussion 147 Status of the three working hypotheses 147 Contributions to the field of study 149 Directions for future research 151 Conclusion 152 Chapter 6 references 154 Table of Tables Table 2.1. Summary of site and climatic characteristics 24 Table 2.2. Summary of species-specific crown openness 29 Table 2.3. Summary of the regression estimates for the Full Modeldbh 31 Table 2.4. Species-specific crown openness estimates from related studies 33 Table 3.1. Summary of selected site and climatic characteristics 48 Table 3.2. Sample characteristics 49 Table 3.3. Aspen candidate models 52 Table 3.4. Spruce candidate models 53 Table 3.5. Comparison of local and global models 57 Table 3.6. Parameter estimates for the aspen model 59 Table 3.7. Parameter estimates for the spruce model 60 Table 4.1. Climatic and site information 79 Table 4.2. Models that explain regional variation in the light-growth relationship 80 Table 4.3. Models that explain regional variability in increment obtained at 50% light.. 86 Table 5.1. Stand summary statistics for the 51 permanent sample plots 116 Table 5.2. Ranking of the sensitivity analysis parameters according to R 124 Table 5.3. Combined summary statistics for the 30-year simulation 127 Table 5.4. Species-specific summary statistics for the 30-year simulation of permanent sample plots 131 Table 5.5. Species-specific summary statistics for the 20-year simulation of understory and suppressed trees 134 Table 5.6. Species-specific summary statistics for the 10-year simulation of understory trees 137 V Table of Figures Figure 2.1. Geographic distribution of sampling regions 25 Figure 2.2. Scatter plots of crown openness 30 Figure 2.3. Species-specific crown openness versus longitude and precipitation 35 Figure 3.1. Geographic location of the sampling regions 46 Figure 3.2. Residual plots 58 Figure 3.4. Predicted spruce height and radial increment 62 Figure 3.5. Comparison of aspen and spruce growth patterns 64 Figure 4.1. Plots of Analysis 1 results for growing degree days (GDD5) 84 Figure 4.2. Percentage of maximum increment obtained at 50% light availability 87 Figure 4.3. Height increment regression models from conifer-dominated stands 88 Figure 4.4. Height increment regression models from aspen-dominated stands 89 Figure 4.5. Diameter increment regression models from conifer-dominated stands 90 Figure 4.6. Diameter increment regression models from aspen-dominated stands 91 Figure 5.1. Model flow of SORTIE-ND as configured for this project 108 Figure 5.2. Predictions of single and mixed species stands 120 Figure 5.3. Range of predictions from the sensitivity analysis for aspen and spruce density, DBHq, and basal area 123 Figure 5.4. Plot of predicted values versus observed values from the 30-year simulation. 126 Figure 5.5. Aspen (AT) and spruce (SX) predicted values versus observed values from the 30-year simulation 129 Figure 5.6. Lodgepole pine (PL) and subalpine fir (BL) predicted values versus observed values from the 30-year simulation 130 Figure 5.7. Aspen (AT) and spruce (SX) predicted values versus observed values from the 20-year simulation 135 Figure 5.8. Lodgepole pine (PL) and subalpine fir (BL) predicted values versus observed values from the 20-year simulation 136 Figure 5.9. Aspen (AT) and spruce (SX) predicted values versus observed values from the 10-year simulation 138 Figure 5.10. Lodgepole pine (PL) and subalpine-fir (BL) predicted values versus observed values from the 10-year simulation 139 Acknowledgements I am grateful for the help, support, and advice from Dr. Bruce Larson, Dr. John Barker , Dr. David Coates, and Dr. Peter Marshall. I would like to thank Rebecca Lee for hard work and dedication to the field work. Additionally, I would like to thank Marissa LeBlanc for programming assistance and constructive comments that greatly improved this dissertation. Finally, I am thankful for the funding that made this dissertation a possibility. Funding was provided by the Forest Investment Account, the Mixedwood Management Association, the FRBC Chair of Silviculture (UBC), and the BC Ministry of Forest, Prince George Region. Co-Authorship Statement Chapter 2 is accepted for publication. Chapters 3 and 4 are submitted for publication. Each paper has one co-author that participated in an advisory and editorial role. Rasmus Astrup was responsible for producing the initial draft manuscript before any major activity of the co-authors was initiated. Chapter 1: Introduction Mixed aspen-spruce stands in western boreal and sub-boreal Canada More than 80% of Canada's productive forest area is boreal (CCFM 2000) and within this area the most productive and diverse ecosystems are the boreal mixedwoods (Chen and Popadiouk 2002). The western boreal mixedwood region extends throughout a large portion of northern British Columbia, Alberta, and Saskatchewan (Rowe 1972). It is an important region in terms of timber production, aboriginal interests, recreational value, and biodiversity (e.g. Acton et al. 1998; C C F M 2000; Burton et al. 2003). In the western boreal mixedwood region, mixed stands dominated by aspen (Populus tremuloides Michx) and white spruce (Picea glauca (Moench) Voss) are very common (Rowe 1972). Additionally, mixed aspen-spruce stands are common throughout the sub-boreal part of British Columbia (e.g. DeLong et al. 1990; Meidinger et al. 1991; Banner et al. 1993). In sub-boreal British Columbia, interior spruce (a complex of Engelmann spruce {Picea engelmannii Parry) and white spruce hybrids rather than white spruce is the dominant conifer in mixed aspen-spruce stands (e.g. Banner et al. 1993; Coates et al. 1994). Mixed aspen-spruce stands are generally found on upland mesic sites with medium nutrient availability (e.g. DeLong et al. 1990; Beckingham and Archibald 1996; Beckingham et al. 1996). Aspen is generally regarded as an early successional shade-intolerant species while white spruce and interior spruce are regarded as a mid-successional species of medium shade tolerance (e.g. Krajina et al. 1982; Kobe and Coates 1997). Stand initiation and stand dynamics in mixed aspen-spruce stands occur in several ways (review by Chen and Popadiouk 2002). In the boreal forest, large-scale stand-replacing disturbances such as fire or clear-cut harvesting are common. After a stand-replacing disturbance, the typical stand development pattern is a rapid establishment and growth of shade-intolerant aspen resulting in an initially aspen-dominated stand that over time becomes dominated by the more shade-tolerant spruce (e.g. Dix and Swan 1971; Cogbill 1985; Kabzems et al. 1986; Andison and Kimmins 1999). Aspen generally establishes by vigorous root-suckering, which commonly occurs from shallow roots of small diameter (0.5-2cm) and is stimulated by hormonal changes in 1 the roots caused by removal or destruction of the above-ground stem (e.g. Frey et al. 2003). The availability of roots capable of suckering and the consequent amount of suckers is dependent on an interplay between site and soil attributes, disturbance type, and clone attributes (see review by Frey et al. 2003). Initial sucker densities vary greatly and can reach more than 200,000 stems/ha. During the initial 10 years, aspen stands undergo a rapid self-thinng that generally leads to a convergence of stand density around 20,000-30,000 stems/ha between ages 6-11 (Peterson and Peterson 1992; Comeau et al. 2004a). The abundance of spruce regeneration varies greatly between stands. To obtain large amounts of spruce regeneration, both a nearby seed source and a suitable seedbed are required. Spruce establishment can occur simultaneously with aspen, over a long continous period, or in shorter dominant recruitment periods (Lieffers et al. 1996b; Peters et al. 2002; Kabzems and Garcia 2004). After a stand-replacing disturbance the establishment substrate is normally composed of exposed mineral soil or mineral soil mixed with ashes. If spruce establishment occurs in an existing aspen stand, decaying logs often serve as establishment substrate but establishment can also occurs on patches of suitable forest floor (e.g. Awada et al. 2004). Different timing of spruce establishment leads to different patterns of stand dynamics and stand structure. For example, a study from Fort Nelson, British Columbia found that stand structure of mature aspen-spruce stands is dependent on the timing of spruce establishment (Kabzems and Garcia 2004). In stands where spruce was codominant, establishment had occurred simultaneously, while in stratified stands spruce establishment was associated with a 29 to 59 year time lag (Kabzems and Garcia 2004). For a recent thorough reviews of stand dynamics and succession in boreal mixedwoods see Chen and Popadiouk (2002), Brassard and Chen (2006) and Bergeron (2000). Silviculture and management of aspen-spruce mixedwoods In the past 150 years timber harvesting, management practices, and, most evidently, management intensity of the western boreal mixedwoods have changed dramatically. Until the second half of the 20 t h century, timber harvesting was mainly high-grading of large spruce sawlogs on easily accessible sites (Lieffers and Beck 1994; Andison and 2 Kimmins 1999). This practice was replaced by an agricultural approach to silviculture where mixedwoods were converted to even-aged spruce plantations and aspen generally was considered a weed species (Lieffers and Beck 1994; Andison and Kimmins 1999). A re-evaluation of this conversion strategy started in the late 1970's and was driven by three main reasons: (1) plantation establishment was expensive and often unsuccessful due to intense competition from hardwoods and grass, (2) increase in utilization and value of aspen made mixed aspen-spruce stands much more economically attractive, and (3) environmental concerns over loss of mixedwood sites (Andison and Kimmins 1999). Still, changes in management practices have been relatively slow and many potential mixedwood sites, especially in British Columbia, are still managed as spruce plantations. One reason for the slow change might be lack of experience with many aspects of silviculture of mixed stands. Additionally, there are often legislative obstacles for optimal mixedwood management (e.g. Lieffers et al. 2002). In the last 15 years considerable effort has gone into experimentation with and analysis of silvicultural alternatives to single-species clearcut silvicultural systems (e.g. Brace 1991; Lieffers and Beck 1994; Lieffers et al. 1996a; Man and Lieffers 1999; DeLong 2000; Green et al. 2002; Welham et al. 2002; Comeau et al. 2004b; Man and Greenway 2004; Comeau et al. 2005). Apart from various retention systems (e.g. Mitchell and Beese 2002) two of the alternatives to clearcutting that have greatest potential to become widely used are (1) underplanting of white spruce under aspen canopies, and (2) utilization of existing advanced regeneration (Green et al. 2002; Comeau et al. 2005). These systems are applicable to large portions of the landbase (Green et al. 2002) and are often equal or superior to traditional management in terms economic return and wood production (Green et al. 2002; Comeau et al. 2005). A common component for these silvicultural practices is that crop trees grow for extended periods under shaded conditions. Furthermore, the resulting stands have complex spatial and/or horizontal structure. 3 Growth modeling in western boreal Canada In forestry there is a long tradition of growth and yield modeling (reviews in: Mohren and Burkhart 1994; Vanclay 1995; Peng 2000; Messier et al. 2003). Classic growth and yield models are non-spatial empirical models based on long-term re-measured plots. These models are descriptive and the driving functions are mostly of statistical rather than biological nature (Messier et al. 2003). The advantages of empirical descriptive models are their quantitative accuracy (Kimmins 1993; Vanclay 1995; Landsberg 2001). The largest problem in empirical models is their confinement to environmental conditions and management practices similar to the source of empirical data (Kimmins 1993). Classic growth models are therefore not well-suited to deal with increased heterogeneity of growing conditions, varying initial conditions, and spatial complexity resulting from emerging alternatives to clearcutting. Within the last three decades, more process-based modeling approaches have emerged (Makela 2001). Process-based models predict system behavior from key mechanisms and processes (Korzukhin et al. 1996; Messier et al. 2003). A shift from empirical models to process-based models therefore represents a shift from description to understanding (Bossel 1991). Process-based models are more flexible than empirical models in terms of environmental and management conditions (Kimmins 1993; Korzukhin et al. 1996; Landsberg 2001; Messier et al. 2003). Consequently, process-based models have a greater potential for dealing with new silvicultural systems, with which there is limited experience. On the other hand, from a forest management perspective there are several issues with existing process-based models. Principally there are two main types of models (1) quantitative models designed to provide accurate, quantitative predictions, and (2) models for understanding (Bunnell 1989). Forest managers need quantitative models. Process-based models have primarily been developed as research tools to further our understanding of relationships (Mohren and Burkhart 1994; Korzukhin et al. 1996). However, emphasis on model testing and calibration has often been lacking in process-based model development (Korzukhin et al. 1996). Finally, process-based models have been criticized for lacking (1) the input and output options required by forest managers, and (2) for lacking site specificity (Robinson and Monserud 2003). It is clear that both 4 empirical and process-based models have strengths and weaknesses. Thus, several authors have advocated for models that combine empirical and process-based modeling approaches as the future approach for forest management (e.g. Kimmins 1993; Landsberg 2001) . This combination is desirable to achieve the descriptive accuracy of empirical models with the flexibility of process-based models (Landsberg 2001). For western boreal mixedwood stands, there are only a few models that currently receive attention in terms of development, parameterization, and calibration. The Mixedwood Growth Model (MGM) is an empirical individual-tree non-spatial growth model developed for boreal mixedwoods (Huang and Titus 1994). M G M is the most developed model for western boreal mixedwoods and is calibrated and utilized in British Columbia, Alberta, and Saskatchewan. FORECAST is a non-spatial process-based model that includes empirical data in the calibration process (Kimmins et al. 1999; Seely et al. 1999). FORECAST is the most process-oriented and is the only model with a strong emphasis on nutrient cycling. FORECAST has been utilized to explore implications of the two-pass harvesting system for boreal mixedwoods in Saskatchewan (Welham et al. 2002) . The Tree and Stand Simulator (TASS) is a spatially explicit individual tree growth model (Mitchell 1975). TASS is mainly driven by a detailed representation of tree structure, where individual tree growth mainly is determined by crown size which in turn is determined by the size and location of the surrounding trees. Currently, the operational version of TASS supports simulation of both pure aspen and spruce stands. Aspen-spruce stands are currently not simulated, but this is an area of current research and model development (Harper et al. 2006). SORTIE is a spatially explicit individual tree model that was developed to extrapolate fine-scale/short-term field measurements to large-scale, long-term forest dynamics (Pacala et al. 1996). SORTIE is a descendent from the JABOWA-FORET family of models (Gap models) and the basic structure with growth, mortality, recruitment, and resource submodels is maintained. In recent years, the model has been modified (SORTIE/BC, SORTIE-ND), parameterized for northern mixed forests in western British Columbia, and made more applicable to silvicultural planning (Coates et al. 2004). 5 A model suited for growth prediction and planning of silvicultural regimes, such as underplanting, partial cutting, strip-cuts, and utilization of advanced regeneration should ideally possess the following features: (1) the model must be capable of simulating mixed-species stands, (2) the model has to be partially process-based as there is a lack of long-term data that are relevant to the new types of proposed management, (3) the high degree of spatial heterogeneity makes a spatial-explicitly model desirable, and (4) the reliance on understory trees necessitates a good representation of growth in shaded conditions. The basic structure of SORTIE-ND matches these requirements. This does not necessarily imply that SORTIE-ND is capable of predicting growth of mixed aspen-spruce stands. The model extrapolates short-term measurements into long term stand dynamics and it is uncertain i f the associated uncertainty is acceptable. SORTIE-ND has never been formally evaluated or validated for mixed aspen-spruce stands and the model's predictive ability is not described. Simultaneously, recent evaluation efforts have shown that some models in the Gap model family need significant changes to make satisfactory prediction of local short-term stand development (Linder et al. 1997; Yaussy 2000; Risch et al. 2005). Predicting understory tree growth The high degree of reliance on understory tree growth in many of the emerging mixedwood management regimes necessitates an improved ability to predict their growth. Most management strategies aim to promote understory spruce growth while minimizing competition from young hardwood trees. Thus, to judge the effectiveness of different management practices it is not only necessary to be able to predict understory spruce growth, but also the understory growth of competitors such as aspen. This information is required to make any type of predictions of stand development. One of the main tasks in predicting understory tree growth is selection of predictor variables for the desired model. In the literature there has been a long standing debate over the relative importance of individual growth factors. For understory trees and other vegetation, the debate has mainly focused on belowground resources versus light (e.g. Fricke 1904; Tourney and Kienholz 1931; reviews in Korstian and Coile 1938; Walter and Breckle 1985; Coomes and Grubb 2000). The emerging picture of this debate is that 6 both light and root competition are important for understory tree growth. Below-ground competition seems to be most important on soils with low water or nutrient status while light competition seems most important on highly productive soils (Coomes and Grubb 2000). Accordingly, prediction of understory tree growth has a long list of potential important predictor variables representing both below- and above-ground resources. The model developer is forced to choose a number of predictor variables and an associated level of model complexity. With increasing levels of complexity, a model can represent an increasing number of processes. As most phenomena, including understory tree growth, are dependent on multiple determinants it is often tempting to construct very complex models. Unfortunately, the best model and the most complex model are not necessarily the same, as the best model is dependent on: (1) the model's application and use, (2) representation of the "correct" processes and relationships, and (3) the data available for the model fitting (e.g. Hilborn and Mangel 1997). For models with applications in forest management, it is important that the predictor variables are easily measurable or available, preferably in inventory databases. Spatial and seasonal variations in light availability are easily measurable or can be simulated with spatially explicit light models (e.g. Brunner 1998; Canham et al. 1999; Stadt and Lieffers 2000). Light availability is also the primary driver of photosynthesis and is bound to have an effect on growth. Additionally, in studies from boreal and sub-boreal Canada, light availability has generally shown good correlation with understory tree growth (Lieffers and Stadt 1994; Kayahara et al. 1996; Chen et al. 1996; Wright et al. 1998; Claveau et al. 2002; Comeau and Bedford 2002; Kalischuk 2004; Lajzerowicz et al. 2004; Stadt et al. 2005; Claveau et al. 2005). Thus, light availability is a potentially good predictor variable for understory tree growth. Regional variation In the boreal mixedwood region, local inter-stand variation in stand structure, growth, and dynamics is common (e.g. Chen and Popadiouk 2002), but broader-scale regional variation also exists (e.g. Kabzems and Garcia 2004). An example of broad scale variation is between the eastern Canadian and western Canadian boreal forest. In the 7 eastern Canadian boreal forest, fire frequencies are lower (Johnson 1992), precipitation is generally higher (Environment Canada 2004), the understory is more developed (Messier et al. 1999), and balsam fir {Abies balsamea (L.) Mill) is more common than spruce in the understory of aspen stands (Messier et al. 1999). This generally leads to older stands, larger trees, higher occurrence of non-stand replacing disturbances such as wind-throw and eastern spruce budworm outbreaks, and more frequent occurrence of stands with gap dynamics (e.g. Kneeshaw and Bergeron 1998; Bergeron 2000; Johnson et al. 2003). Regional variation is partly caused by a climate gradient, but there are also gradual (clinal) inter-specific genetic differences (Morgenstern 1996). Regional variations in tree growth rates and growing conditions are also present within the western boreal mixedwood region. For example, aspen stands near Fort Nelson (British Columbia) achieve greater heights, exhibits higher productivity and longevity, and have less internal decay than those observed in other areas of the western boreal mixedwood (Kabzems and Garcia 2004). For juvenile spruce, there are indications that the light-growth relationship exhibits regional variability. Approximately linear light-growth relationships have been observed in several geographic regions of northern British Columbia (Wright et al. 1998; Coates and Burton 1999; Lajzerowicz et al. 2004). On the other hand, studies from Alberta have indicated that white spruce height increment does not increase significantly above 40-50% light availability (Lieffers and Stadt 1994; Lieffers et al. 1996b; Stadt et al. 2005). A comparison of regional species-specific crown openness estimates (fraction of sky that can be seen through the crown of an individual tree) also reveals regional variation. Both aspen and spruce crown openness estimates from Alberta (Stadt and Lieffers 2000) are approximately double the estimates from British Columbia (Canham et al. 1999). Regional variation in the light-growth relationship combined with regional variation in understory light availability can have considerable impact on: (1) silvicultural systems that rely on understory spruce growth, and (2) on local management targets for overstory densities and resulting understory light levels. Simultaneously, it is necessary to understand regional variability in order to assess stand dynamics and portability of regionalized knowledge. Without knowledge of regional variability it is, for example, 8 impossible to judge how localized a light-growth relationship needs to be or i f the same light-growth relationship can be used under different canopy-types. Problem statement and working hypotheses The objectives of this dissertation are to increase knowledge of: (1) the light-growth relationship for understory spruce and aspen, and (2) to explore regional variability in understory light levels and light-growth relationships in western boreal and sub-boreal Canada. In order to integrate this work with existing research and make it available for forest management, the described studies were designed to be incorporated into the ongoing development of the simulation model SORTIE-ND. To meet these objectives the following three working hypotheses were explored: (A) There is regional variation in the performance of understory aspen and spruce within western boreal and sub-boreal Canada. This can be caused by two main effects; differences in light transmission through overstory canopies between regions, and/or regional variability in light-growth relationship for understory trees. (B) The regional difference in the performance of understory spruce can be related to climatic variables and other variables such as overstory canopy-type. (C) It is possible to incorporate short term measurements into a process-oriented model and obtain reasonable growth predictions that can be used for stand-level silvicultural planning. Dissertation structure Chapters 2-5 are designed to explore the three working hypothesis for aspen and spruce in western boreal and sub-boreal Canada. Chapter 2 investigates and quantifies regional differences in species-specific crown openness (fraction of sky that can be seen through the crown of an individual tree). Additionally, Chapter 2 assesses if regional variation in species-specific crown openness is sufficient to cause regional differences in understory light availability. Chapter 3 investigates regional differences in the light-growth relationship for understory trees. Thus, in combination Chapter 2 and Chapter 3 9 corresponds to Working Hypothesis (A). Chapter 4 investigates the possible causes for regional variation in the light-growth relationship for understory spruce. Thus, Chapter 4 is designed to correspond to Working Hypothesis (B). Chapter 5 incorporates the findings from Chapter 2 and Chapter 3 into the stand-level simulation model SORTIE-ND. SORTIE-ND is then evaluated as a predictive tool for stand-level growth prediction and silviclutural planning. Thus, Chapter 5 corresponds to Working Hypothesis (C). The conclusions of this work are described in Chapter 6, which briefly discusses and summarizes the main findings. 10 Chapter 1 references Acton, D.F., Padbury, G.A. and Stushnoff, C.T. 1998. The ecoregions of Saskatchewan. Saskatchewan Environment and Resource Management, Canadian Plains Research Centre, University of Regina. 205 p. Andison, D.W. and Kimmins, J.P. 1999. Scaling up to understand British Columbia's boreal mixedwoods. Environ. Rev. 7: 19-30. Awada, T., Henebry, G .M. , Redmann, R.E. and Sulistiyowati, H . 2004. Picea Glauca dynamics and spatial pattern of seedlings regeneration along a chronosequence in the mixedwood section of the boreal forest. Ann. For. Sci. 61: 789-794. Banner, A. , MacKenzie, W., Haeussler, S., Thomson, S., Pojar, J. and Trowbridge, R. 1993. A field guide to site identification and interpretation for the Prince Rupert Forest Region. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Land Management Handbook No. 26. Beckingham, J.D. and Archibald, J.H. 1996. Field guide to ecosites of northern Alberta. Canadian Forest Service, Northwest Region, Northern Forestry Centre, Edmonton, Alberta. Spec. Rep. 5. Beckingham, J.D., Nielsen, D.G. and Futoransky, V . A . 1996. Field guide to ecosites of the mid-boreal ecoregions of Saskatchewan. Canadian Forest Service, Northwest Region, Northern Forestry Centre, Edmonton, Alberta. Spec. Rep. 6. Bergeron, Y . 2000. Species and stand dynamics in the mixed woods of Quebec's southern boreal forest. Ecology 81: 1500-1516. Bossel, H . 1991. Modelling forest dynamics: moving from description to explanation. For. Ecol. Manage. 42: 129-142. Brace, L .G. 1991. Protecting understory white spruce when harvesting aspen. In Shorthreid, A. , editor Northern Mixedwood '89: Proceedings of a symposium. 11 Fort St, Johns, B.C. For. Can., Pacific Forestry Centre, Victoria, B.C. FRDA report 164. p 116-128. Brassard, B.W. and Chen, H . Y . H . 2006. Stand structural dynamics of North American boreal forests. Critical Reviews in Plant Science 25: 37-59. Brunner, A . 1998. A light model for spatially explicit forest stand models. For. Ecol. Manage. 107: 19-46. Bunnell, F.L. 1989. Alchemy and uncertainty: what are good models? U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, Portland, Gen. Tech. Rep. PNW-GTR-232. Burton, P.J., Messier, C , Smith, D.W. and Adamowicz, W.L., editors. 2003. Towards sustainable management of the boreal forest: National Research Council of Canada. N R C Research Press, Ottawa. 1039 p. Canadian Council of Forest Ministers (CCFM). 2000. Criteria and indicators of sustainable forest management in Canada. Natural Resources Canada, Canadian Forest Service, Ottawa, Ontario. 122 p. Canham, C D . , Coates, K.D. , Bartemucci, P. and Quaglia, S. 1999. Measurement and modeling of spatially-explicit variation in light transmission through interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1775-1783. Chen, H.Y.H. , Klinka, K . and Kayahara, G.J. 1996. Effects of light on growth, crown architecture, and specific leaf area for naturally established Pinus contorta var. latifolia and Pseudotsuga menziesii var. glauca saplings. Can. J. For. Res. 26: 1149-1157. Chen, H .Y.H. and Popadiouk, R.V. 2002. Dynamics of North American boreal mixedwoods. Environ. Rev. 10: 137-166. 12 Claveau, Y . , Messier, C. and Comeau, P.G. 2005. Interacting influence of light and size on aboveground biomass distribution in sub-boreal conifer saplings with contrasting shade tolerance. Tree Phys. 25: 373-384. Claveau, Y . , Messier, C , Comeau, P.G. and Coates, K .D. 2002. Growth and crown morphological responses of boreal conifer seedlings and saplings with contrasting shade tolerance to a gradient of light and height. Can. J. For. Res. 32: 458-468. Coates, K . D . and Burton, P.J. 1999. Growth of planted tree seedlings in response to ambient light levels in northwestern interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1374-1382. Coates, K .D. , Canham, C D . , Beaudet, M . , Sachs, D.L. and Messier, C. 2004. Use of a spatially explicit individual-tree model (SORTIE-BC) to explore the implications of patchiness in structurally complex forests. For. Ecol. Manage. 186: 297-310. Coates, K.D. , Haeussler, S., Lindenbourgh, S., Pojar, J. and Stock, A.J . 1994. Ecology and silviculture of interior spruce in British Columbia. Canada/B.C. Economic and Regional Development, Canadian Forest Service, Victoria, FRDA report II. Cogbill, C.V. 1985. Dynamics of the boreal forests of the Laurentian Highlands, Canada. Can. J. For. Res. 15: 252-261. Comeau, P.G. and Bedford, L. 2002. Light under and adjacent to aspen stands and implications for growing spruce. In: Frochot, H. , Collet, C. and Balandier, P., (editors). Popular summaries from the fourth international conference on forest vegetation management. 17-21 June 2002, Nancy, France. Institut National de la Recherche Agronomique. p 177-179. Comeau, P.G., Bokalo, M . and Titus, S. 2004a. Early dynamics of tended mixedwood stands. Centre for Enhanced Forest Management, Department of Renewable Resources, University of Alberta. E F M research note 06/2004. 13 Comeau, P.G., Filipescu, C.N., Kabzems, R. and DeLong, C. 2004b. Early growth of white spruce underplanted beneath spaced and unspaced aspen stands in northeastern British Columbia. Can. J. For. Res. 34: 2277-2283. Comeau, P.G., Kabzems, R., McClarnon, J. and Heineman, J. 2005. Implications of selected approaches for regenerating and managing western boreal mixedwoods. For. Chron. 81: 559-574. Coomes, D.A. and Grubb, P.J. 2000. Impact of root competition in forests and woodlands: a theoretical framework and review of experiments. Ecol. Mon. 70: 171 -207. DeLong, C. 2000. Planting white spruce under trembling aspen, 7-year results of seedling condition and performance. Research Branch, B.C. Ministry of Forests. Working Paper 54. DeLong, C , MacKinnon, A . and Jang, L. 1990. A field guide for site identification and interpretation of ecosystems of the northeast portion of Prince George Forest Region. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Land Management Handbook No. 22. Dix, R.L. and Swan, J.A. 1971. The role of disturbance and succession in upland forest at Candle Lake, Saskatchewan. Can. J. Bot. 49: 657-676. Environment Canada. 2004. Climate normals and averages. Available at: http://www.climate.weatheroffice.ec.gc.ca/climate_normals/index_e.html. Last accessed: March 8, 2005. Frey, B.R., Lieffers, V.J . , Landhausser, S.M., Comeau, P.G. and Greenway, K.J . 2003. An analysis of sucker regeneration of trembling aspen. Can. J. For. Res. 33: 1169-1179. Fricke, K . 1904. Licht- und Schattenholzarten, ein wissenschaftlige nicht begriidetes Dogma. Centralblatt fur das gesamte Forstwesen 30: 315-325. 14 Green, D.F., Kneeshaw, D.D., Messier, C , Lieffers, V. , Cormier, D., Doucet, R., Coates, K.D. , Groot, A. , Grover, G. and Calogeropoulos, C. 2002. Modelling silvicultural alternatives for conifer regeneration in boreal mixedwood stands (aspen/white spruce/balsam fir). For. Chron. 78: 281-295. Harper, G.J., Astrup, R. and Simpson, D. 2006. TASS III boreal mixedwood modelling: light and understory tree growth. B.C. Ministry of Forest and Range. Forest Sciences Program, Poster 077. Available at: http://www.for.gov.bc.ca/hfd/pubs/Docs/P/P077.htm. Hilborn, R. and Mangel, M . 1997. The ecological detective: confronting models with data. Princeton University Press, Princeton, New Jersey. 309 p. Huang, S. and Titus, S. 1994. An age-dependent individual tree height prediction model for boreal spruce-aspen stands in Alberta. Can. J. For. Res. 24: 1295-1301. Johnson, E.A. 1992. Fire and vegetation dynamics: studies from the North American boreal forest. Cambridge University Press, Cambridge, U K . 129 p. Johnson, E.A., Morin, H. , Miyanishi, K. , Gagnon, R. and Green, D.F. 2003. A process approach to understanding disturbance and forest dynamics for sustainable forestry. In: Burton, P.J., Messier, C , Smith, D.W.and Adamowicz, W.L., (editors). Towards sustainable management of the boreal forest. National Research Council of Canada. N R C Research Press, Ottawa, p 261-306. Kabzems, A. , Kosowan, A . L . and Harris, W.C. 1986. Mixedwood section in an ecological perspective, Saskatchewan. Saskatchewan Parks and Renewable Resources, Forestry Division, Regina, and Canadian Forestry Service, Ottawa. 122 p. Kabzems, R. and Garcia, O. 2004. Structure and dynamics of trembling aspen - white spruce mixed stands near Fort Nelson, B.C. Can. J. For. Res. 34: 384-395. 15 Kalischuk, M . L . 2004. Influence of site quality and overstory age on the growth of understory white spruce in boreal mixedwood stands [M.Sc. Thesis]: University of Alberta, Edmonton. 117 p. Kayahara, G.J., Chen, H .Y.H. , Klinka, K. and Coates, K.D. 1996. Relations of terminal growth and specific leaf area to available light in naturally regenerated seedlings of logdepole pine and interior spruce in central British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Research Report 09. Kimmins, J.P. 1993. Scientific foundation for the simulation of ecosystem function and management in FORCYTE-11. Information report NOR-X-328. Forestry Canada, Northwest Region, Northern Forestry Centre. Kimmins, J.P., Mailly, D. and Seely, B. 1999. Modelling forest ecosystems net primary production: the hybrid simulation approach used in FORECAST. Ecol. Model. 122: 195-224. Kneeshaw, D.D. and Bergeron, Y . 1998. Canopy gap characteristics and tree replacement in the southeastern boreal forest. Ecology 79: 783-794. Kobe, R.K. and Coates, K .D. 1997. Models of sapling mortality as a function of growth to characterize interspecific variation in shade tolerance of eight tree species of northwestern British Columbia. Can. J. For. Res. 27: 227-236. Korstian, C. and Coile, C. 1938. Plant competition in forest stands. Duke University Forestry Bulletin 3: 1-125. Korzukhin, M.D. , Ter-Mikaelian, M.T. and Wagner, R.G. 1996. Process versus empirical models: which approach for forest ecosystem management? Can. J. For. Res. 26: 879-887. Krajina, V.J . , Klinka, K . and Worrall, J. 1982. Distribution and ecological characteristics of trees and shrubs of British Columbia. Faculty of Forestry, University of British Columbia, Vancouver. 131 p. 16 Lajzerowicz, C.C., Walters, M.B. , Krasowski, M . and Massicotte, H.B. 2004. Light and temperature differentially colimit subalpine fir and Engelmann spruce seedling growth in partial-cut subalpine forests. Can. J. For. Res. 34: 249-260. Landsberg, J. 2001. Modelling forest ecosystems: state-of-the-art, challenges and future directions. In LeMay, V.and Marshall, P., (editors). Proceedings of forest modelling for ecosystem among, forest certification, and sustainable management conference. 12-17 August 2001, Vancouver, B.C., UBC. p 3-21. Lieffers, V.J . and Beck, J.A., Jr. 1994. A semi-natural approach to mixedwood management in the Prairie Provinces. For. Chron. 70: 260-264. Lieffers, V.J . , Macmillan, R.B., MacPherson, D., Branter, K. and Stewart, J.D. 1996a. Semi-natural and intensive silvicultural systems for the boreal mixedwood forest. For. Chron. 72: 286-292. Lieffers, V.J . , Pinno, B.D. and Stadt, K.J . 2002. Light dynamics and free-to-grow standards in aspen-dominated mixedwood forests. For. Chron. 78: 137-145. Lieffers, V.J . and Stadt, K.J . 1994. Growth of understory Picea glauca, Calamagrostis canadensis, and Epilobium angustifolium in relation to overstory light transmission. Can. J. For. Res. 24: 1193-1198. Lieffers, V.J . , Stadt, K.J . and Navratil, S. 1996b. Age structure and growth of understory white spruce under aspen. Can. J. For. Res. 26: 1002-1007. Linder, M . , Sievanen, R. and Pretzsch, H. 1997. Improving the simulation of stand structure in a forest gap model. For. Ecol. Manage. 95: 183-295. Makela, A . 2001. Modelling tree and stand growth: towards a hierarchical treatment of multi-scale processes. In LeMay, V.and Marshall, P., (editors). Proceedings of forest modelling for ecosystem among, forest certification, and sustainable management conference. 12-17 August 2001, Vancouver, B.C., UBC. p 27-44. 17 Man, R. and Greenway, K.J . 2004. Meta-analysis of understory white spruce response to release from overstory aspen. For. Chron. 80: 694-704. Man, R. and Lieffers, V.J . 1999. Effects of shelterwood and site preparation on microclimate and establishment of white spruce seedlings in a boreal mixedwood forest. For. Chron. 75: 837-844. Meidinger, D., Pojar, J. and Harper, W.L. 1991. Sub-Boreal Spruce Zone. In: Meidinger, D. and Pojar, J. (editors and compilers). Ecosystems of British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Special Report Series No. 6. p 209-221. Messier, C , Doucet, R., Ruel, J . -C, Claveau, Y . , Kelly, C. and Lechowicz, M.J . 1999. Functional ecology of advanced regeneration in relation to light in boreal forests. Can. J. For. Res. 29: 812 - 823. Messier, C , Fortin, M.-J. , Schmiegelow, F., Doyon, F., Cumming, S., Kimmins, J.P., Seely, B., Welham, C. and Nelson, J. 2003. Modelling tools to assess the sustainability of forest management scenarios. In: Burton, P.J., Messier, C , Smith, D.W. and Adamowicz, W.L. (editors). Towards sustainable management of the boreal forest. National Research Council of Canada. N R C Research Press, Ottawa, p 531-580. Mitchell, K.J . 1975. Dynamics and simulated yield of Douglas-fir. For. Sci. Monogr. 17: 1-39. Mitchell, S.J. and Beese, W.J. 2002. The retention system: reconciling variable retention with the principles of silvicultural systems. For. Chron. 78: 397-403. Mohren, G.M.J, and Burkhart, H.E. 1994. Contrasts between biologically-based process models and management-oriented growth and yield models. For. Ecol. Manage. 69: 1-5. Morgenstern, E.K. 1996. Geographic variation in forest trees: genetic basis and application of knowledge in silviculture. U B C Press, Vancouver. 214 p. 18 Pacala, S.W., Canham, C D . , Saponara, J., Silander, J.A., Jr., Kobe, R.K. and Ribbens, E. 1996. Forest models defined by field measurements: II. Estimation, error analysis, and dynamics. Ecol. Mon. 66: 1-43. Peng, C. 2000. Growth and yield models for uneven-aged stands: past, present and future. For. Ecol. Manage. 132: 259-279. Peters, V.S., MacDonald, E.S. and Dale, M.R.T. 2002. Aging discrepancies of white spruce affect the interpretation of static age structure in boreal mixedwoods. Can. J. For. Res. 32: 1496-1501. Peterson, E.B. and Peterson, N . M . 1992. Ecology, management, and use of aspen and balsam poplar in the Prairie Provinces, Canada. Northern Forestry Centre, Edmonton. Special report 1. Risch, A . C , Heiri, C. and Bugmann, H. 2005. Simulating structural patterns with a forest gap model: a model evaluation. Ecol. Model. 181: 161-172. Robinson, A.P. and Monserud, R.A. 2003. Criteria for the comparing adaptability of forest growth models. For. Ecol. Manage. 172: 53-67. Rowe, J.S. 1972. Forest regions of Canada. Department of Environment, Canadian Forest Service, Ottawa. Publication No. 1300. 172 p. Seely, B., Welham, C , Kimmins, J.P. and Scoullar, K . 1999. Defining stand-level sustainability, exploring stand-level stewardship. J. For. 97: 4-11. Stadt, K.J . and Lieffers, V.J . 2000. MIXLIGHT: a flexible light transmission model for mixed-species forest stands. Agric. For. Meteorol. 102: 235-252. Stadt, K.J . , Lieffers, V.J . , Hall, R.J. and Messier, C. 2005. Spatially explicit modeling of PAR transmission and growth of Picea glauca and Abies balsamea in the boreal forests of Alberta and Quebec. Can. J. For. Res. 35: 1-12. 19 Toumey, J.W. and Kienholz, R. 1931. Trenched plots under forest canopies. Yale Sch. For. Bull. 30: 1-31. Vanclay, J.K. 1995. Growth models for tropical forests: a synthesis of models and methods. For. Sci. 41: 7-42. Walter, H . and Breckle, S.W. 1985. Ecological systems of the biosphere. I. Ecological principles in global perspective. Springer-Verlag, GmbH & Co. K G , Berlin, Germany. Welham, C , Seely, B. and Kimmins, H. 2002. The utility of the two-pass harvesting system: an analysis using the ecosystem simulation model FORECAST. Can. J. For. Res. 32: 1071-1079. Wright, E.F., Coates, K.D. , Canham, C D . and Bartemucci, P. 1998. Species variability in growth response to light across climatic regions in northwestern British Columbia. Can. J. For. Res. 28: 871-886. Yaussy, D.A. 2000. Comparison of an empirical forest growth and yield model and a forest gap simulator using actual 30-year growth from two even-aged forests in Kentucky. For. Ecol. Manage. 126: 385-398. 20 Chapter 2: Regional Variation of Aspen and Spruce Crown Openness1 Introduction There is a large body of literature regarding the complex mechanisms of light transmission through forest canopies (e.g. Norman and Jarvis 1975; Canham 1988; Chazdon 1988) and related methods to predict light transmission (reviewed in: Larsen and Kershaw 1996; Brunner 1998; Lieffers et al. 1999). Monsi and Saeki (1953) were the first to apply the Beer-Lambert law to light extinction in plant canopies. This law has since been the most frequently used method for predicting light levels under forest canopies. Application of the Beer-Lambert law in its original form produces an average light intensity, which is subject to several crude assumptions regarding canopy structure (Monsi and Saeki 1953; Larsen and Kershaw 1996). As reviewed by Brunner (1998) and Lieffers et al. (1999), several complex models have dealt with some of the short-comings of the original canopy structure assumptions by accounting for non-random foliage distribution, inclination angles, foliage clumping, and reflection and transmission from foliage. A problem with these complex models is that they require extensive input data regarding canopy structure and have often proven difficult and costly to calibrate (Brunner 1998; Canham et al. 1999; Stadt and Lieffers 2000). Thus from a management perspective there is a need for a light model which can be applied with readily available inventory data (Lieffers et al. 1999; Stadt and Lieffers 2000). SORTIE is a spatially explicit individual tree model where tree growth mainly is driven by light availability and neighborhood composition. The model was initially developed for modeling successional dynamics in northern hardwood forests by Pacala et al. (1993, 1996). Since then, the model has been further developed (SORTIE-BC and SORTIE-ND) and made more suitable for application to forest management issues in boreal Canada (Coates et al. 2004). Canham et al. (1994) parameterized and tested the light submodel in SORTIE and showed that spatial variability in understory light levels can be predicted with relatively simple input data. Additionally, the results indicated that understory light 1 A version of Chapter 2 is in press with Forest Ecology and Management. Dr. Bruce C. Larson is co-author on this paper. 21 levels can be predicted with a simple model where light transmission is equally extinguished by each encountered crown of a given species independent of size and angle of view. This type of model was termed an "absolute hits model" and in this terminology each tree can be referred to as a hit. Additionally, it was shown that the majority of spatial heterogeneity in understory light levels can be explained from the position and crown allometry of neighborhood trees (Canham et al. 1994). Most light models are not absolute hits models (e.g. Brunner 1998; Stadt and Lieffers 2000) and light extinction is dependent on the path length through the individual crowns. Although an absolute hits model cannot predict the light environment within individual crowns, it can be advantageous in the prediction of understory light levels because of its simplicity (Canham et al. 1994). Canham et al. (1999) further developed the absolute hits version of SORTIE's light submodel and achieved good test results for sub-boreal sites in British Columbia. In this paper, species-specific crown openness is defined as the fraction of sky that, on average, can be seen through the crown of an individual tree of a given species. The species-specific crown openness is assumed to be independent of tree size and angle of view. In the latest version of SORTIE's light submodel (Canham et al. 1999), species-specific crown openness is the only input factor that is not available from the literature or from reanalysis of permanent sample plots. The initial method used to determine species-specific crown openness was complex and included a three-dimensional reconstruction of a stand in conjunction with fisheye photos (Canham et al. 1994). This initial method was replaced by a simplified and direct method introduced by Canham et al. (1999). In this revised method, species-specific crown openness is determined directly from fisheye photos. The difference in canopy and crown openness among species has received attention due to the effects of shading and shade tolerance on forest stand dynamics and succession (e.g. Horn 1971; Oliver and Larson 1996; Canham et al. 1994, 1999). Intraspecific variability between regions has received less attention but is interesting from several perspectives. From a modeling perspective, it is necessary to determine transferability of species-specific crown openness among regions in order to judge when light models 22 should be re-parameterized. From a silvicultural standpoint, geographic variation in species-specific crown openness might influence understory light levels. In this case, the performance of understory trees and the success and transferability of various silvicultural systems are likely influenced. Several studies have shown that leaf area index varies with climate (e.g. Gholz et al. 1976; Grier and Running 1977) and it is also likely that species-specific crown openness varies with climate. The main objective of this chapter was to investigate the intraspecific variability of species-specific crown openness for both aspen {Populus tremuloides Michx) and spruce (Picea glauca (Moench) Voss) within western boreal Canada. This was done by comparing mean species-specific crown openness estimates from five different regions in western boreal Canada. To ensure a robust comparison, the assumptions that species-specific crown openness is independent of (1) tree size and (2) angle of view were tested. The secondary objective of this study was to compare regional variation in species-specific crown openness to SORTIE's sensitivity to this parameter. This was done to evaluate possible regional differences in understory light environments caused by regional differences in species-specific crown openness. Methods Sampling and measurements Five sampling regions located in northern British Columbia (BC), Alberta (AB) and Saskatchewan (SK) were selected. A sampling region was defined as an area 40 km in radius with relatively uniform climatic conditions. The sampling regions were selected to capture the range of climatic conditions in areas dominated by mixed stands of aspen and spruce throughout western boreal and sub-boreal Canada. The selected sampling regions were located in the vicinity of Smithers (BC), Fort Nelson (BC), Peace River (AB), Calling Lake (AB) and Porcupine Hills (SK). The geographic distribution of the sampling regions is illustrated in Figure 2.1. In all five regions, both aspen and spruce were sampled. In the Smithers region, interior spruce (P. glauca x engelmannii) was sampled because it is the most common spruce on mesic sites (e.g. Banner et al. 1993). In the remaining regions white spruce was sampled. A short summary of climatic characteristics and sample site characteristics of each region is presented in Table 2.1. 23 Table 2,1, Summary of site and climatic characteristics. General location Ecosystem classification Latitude range of sampling region (N) Longitude range of sampling region (W) Elevation range of sampling region (m) No. of sampling sites within sampling region Mean annual precipitation (mm) Mean May-September precipitation (mm) Mean annual temperature (°C Mean temperature of warmest month (°C) Mean temperature of coldest month (°C) Growing degree days > 5"C Average wind (May-September) speed (km/h) Smithers (BC) SBSdk* Ola-Sxw-Spirea -Purple peavine Fort Nelson (BC) BWBSmw2** 01-SwAt-Step moss Peace River (AB) Calling Lake (AB) Boreal Mixedwood*** Boreal Mixedwood*** BM-d low brush BM-d low brush cranberry cranberry 54"35"-54°.39' 126"51" -127*0 T 561 - 665 21 509.5 164 3.8 14.9 1 164 7.3 59°06 ' -59°18' 123"H'- 123"28' 279-412 27 448.5 259 -1.1 16.7 -22 1289 8.3 56"24' - 56"48' 116"57"- 1 I 7 ° I 4 -561 - 721 28 387.6 0.7 15.9 -17.5 1276 13.3 55"05' - 55n3 I' 112°53 ' - 1 13"27' 6 0 6 - 775 22 501.4 295 1.8 16.3 -15.6 1366 N.A. Porcupine Hills (SK) Mid-boreal Highlands**** D low-brush cranberry 5 2 ° 2 2 ' - 5 2 ° 3 0 ' 102°49 ' - 103"08' 512-620 26 479.5 224.6 0.6 17.3 -19.5 1472 N.A. Fine textured soils. Fine textured soils. Mainly Fine textured soils. Mainly Fine textured soils. Mainly Fine textured soils. Mainly Gray Mainly Gray Luvisols. Gray Luvisols. Gray Luvisols. Gray Luvisols. Luvisols. N.A. N.A. 18.2 18.2 20 17.8 15 16.8 16.8 19.7 •Banner et al. (1993), **DeLong et al. (1990), ***Beckingham and Archibald (1996), ****Beckingham et al. (1996). The climatic data are environment Canada's 1990 climatic normals from the nearest weather station (Environment Canada 2004). The following stations are used in the table: Smithers A ( 5 4 ' W - N . 127"l I -W. Altitude 523m). Dease Lake ( 5 8 ° 2 5 ' - N . 130"00'-W, Altitude 816m), Foil Nelson A (58"50'-N. I22"35'-W, Altitude 382m), Peace River A (56"14'-N, I 17"26'-W, Altitude 571m), Athabasca 2 (54"49"-N, 113°32"-W, Altitude 626) and. Kuroki (52"00-N, I03"27-W, Altitude 585). Alberta site indexes are from Beckingham and Archibald (1996). British Columbia site indexes are from (BC Ministry of Forests 2003), Saskatchewan site indexes are from Beckingham el al. (1996). Not Available, (N.A.). 4^  Soil characteristics of sampled sites Aspen site index Spruce site index Figure 2.1. Geographic distribution of sampling regions. Sampling was performed from late June until mid August 2003. Within a sampling region, between 10 and 12 stands located on zonal sites were sampled. In this paper, the term zonal is used for a site that best reflects the regional climate rather than edaphic or topographic factors2. An observed difference between sampling regions will thus be an effect of local climate rather than edaphic or topographic factors. In this project, the focus is on zonal sites classified to site series in BC and of ecosite in A B and SK. The actual site types are given in Table 2.1. The sampled stands were mature (30 years) aspen and spruce mixtures that ranged from aspen- to spruce-dominated. In each stand, between one and seven overstory trees of each species were sampled. In stands where multiple trees were sampled, an effort was made to maximize the range of sampled tree sizes. For each sampled tree, the general methodology of Canham et al. (1999) was used to determine species-specific crown openness. For each sampled tree one fisheye photo was taken. For each photo, the camera was placed in a location where the crown of the selected tree could clearly be distinguished against the sky without any other trees blocking the view. 2 This use of zonal site is equivalent to the use for classification in B C (Pojar et al. 1991) and equivalent to the term reference site used for classification in A B (Beckingham and Archibald 1996) and SK (Beckingham et al. 1996). 25 Locating an appropriate camera position often required testing several camera positions until a satisfactory photo was obtained. Consequently, variable distance from the tree to the camera was necessary. Additionally, in each stand, a conscious effort was made to use variable distances between the camera and the sampled trees. For each sampled tree, distance from the camera and diameter at breast height (dbh) were measured. A l l photos were taken with a tripod-mounted digital Nikon Coolpix 950 with a Nikon true fisheye lens. Photos were taken under uniform sky conditions either early in the morning, late in the afternoon, or on uniform overcast days. The crown openness of an individual tree was determined through a three-step procedure with the computer program G L A version 2 software (Frazer et al. 1999, 2000). First, the crown outline was digitized. Second, the picture went through a manual thresholding procedure in which the tree components were distinguished from the background sky. Third, crown openness was calculated by dividing the number of pixels determined to be sky within the digitized crown by the total number of pixels within the same crown. The photos had a resolution of 2048x1536 pixels and the digitizing was performed at the same resolution. Analysis The analysis was performed with SAS Version 8.2 (SAS Institute Inc., Cary, NC) and all statistical tests were performed with a = 0.05. Prior to analysis, the regionalized data were assessed for normality by means of descriptive statistics, histograms, normal probability plots, and boxplots. The sparse outlaying data points were investigated, but only removed i f they positively were caused by specific methodological errors. In this paper, angle of view was considered to be the estimated angle from the camera to the top of the sampled tree. The angle of view was estimated in two steps. First, the height of the sampled tree was estimated with nonlinear dbh to height regression. This was done with the equation from Huang et al. (1992) for aspen and with the equation from Huang et al. (2000) for spruce. Secondly, the angle of view was estimated using the tangent trigonometric formula for a right triangle. The initial analysis examined the assumption that species-specific crown openness is independent from both dbh and angle of view. This was done by assessing plots of 26 openness versus dbh and angle of view. Additionally, the effect of distance between the camera and the tree (distance) was assessed. This was done because in a photo the number of pixels contained in a crown decreases with distance and can consequently influence the crown openness estimates. For each predictor variable (dbh, distance, and angle of view), two models were constructed: (1) (Full Model): Opnj = 130 + BiXj + B 2 R i 2 + B 3 R i 3 + B 4 R i 4 + B 5 R i 5 + B 6 XiR l 2 + B y X j R j 3 + 6gXjRj4 + B 9 X J R 1 5 + £j (2) (Regional Model): Opni = B 0 + B,R i 2+ B 2 R i 3 + B 3 R i 4 + B 4 R i 5 + £j where Opnj = the openness of tree i , Bo = the intercept, Xj = the predictor variable of tree i (dbh, distance, or angle of view), Rj 2 - Ri5 are indicator variables such that Rjj is 1 i f tree i is from region j and 0 otherwise, and Sj is the associated error term. These models will be referred to as: Full M o d e l s and Regional Modeldbh when Xj = dbh;, Full Model dj s t and Regional M o d e l s when Xj = distance;, and Full Model a n g i e and Regional Model a n gie when Xj = angle of viewj. Partial F-tests (Neter et al. 1996) were performed for each species between the Full Modeldbh and the Regional Modeldbh to test whether one or more parameters related to dbh were different from zero. The same procedure was repeated for distance and angle of view, using the appropriate Full Model and Regional Model. The partial F-test builds on the principle of extra sum of squares (ESS) where ESS = [(SSER-SSEF)/(dfR-dfF )] /(SSEp/dfp), where SSEp and dfF are the error sum of squares and the degrees of freedom for the Full Model, and SSE R and dfR are the error sum of squares and the degrees of freedom for the Regional Model. ESS is distributed as an F-statistic with (dfR-dfF ,dfF) degrees of freedom (Neter et al. 1996). Following this analysis, under the assumption that species-specific crown openness is independent of dbh, distance, and angle of view, a one-way analysis of variance of species-specific crown openness was performed to test for regional differences, and Tukey's pairwise t-test was performed between the regional means. 27 Results Assumptions of species-specific crown openness The mean and the range of observations for dbh, distance, and angle of view are listed in Table 2.2. Scatter plots of species-specific crown openness versus distance, dbh and angle of view are illustrated in Figure 2.2. Generally, no obvious trends emerge from these plots. The partial F-tests with distance and angle of view gave no significant results, indicating that the parameters related to distance or angle of view do not significantly differ from zero. For aspen, this was also true for the partial F-test with dbh. For spruce, the partial F-test with dbh indicated that one or more parameters related to dbh were significantly different from zero. Table 2.3 outlines the species-specific regionalized parameters from the Full Modeld bh . The majority of the slope parameters in Table 2.3 are negative but non-significant. The only significant slope parameters are found for spruce in the Fort Nelson and Porcupine Hills. These two parameters indicate that spruce crown openness decreases with dbh. Simultaneously, it should be noted that the remaining non-significant parameters only are slightly negative and some are even positive. In summary, there is weak indication in the dataset that spruce crown openness is slightly negatively correlated with dbh. Regional differences in species-specific crown openness The mean species-specific crown openness estimates for each region are shown in Table 2.2. A /-test indicated that aspen had a significantly (P <0.001) higher mean species-specific crown openness than spruce in all regions. Both species had high variability in crown openness and the data points for the two species were overlapping within all regions and between all regions (Figure 2.2). The results from the one-way analysis of variance indicated a significant (P <0.001) difference in mean regional aspen crown openness. Tukey's pairwiset-test showed significant differences between most combinations of means. For aspen, all comparisons were significantly different except between Smithers-Fort Nelson and Calling Lake-Peace River. One-way analysis of variance of the spruce data indicated a significant (P <0.001) difference in mean regional species-specific crown openness. The pairwise t-test illustrated that there were significant 28 differences between all combinations of means except for between Smithers-Peace River, Fort Nelson-Peace River, and Fort Nelson-Calling Lake. Table 2.2. Summary of species-specific crown openness, n = number of samples, Std. Dev. = standard deviation, Min = minimum observation, Max = maximum observation, C L = confidence limit. Region abbreviations are: Smithers (Sm), Fort Nelson (FN), Peace River (PR), Calling Lake (CL), and Porcupine Hills (PH). Region n Mean Std. 95% C L for Mean Mean Mean angle of openness Dev. mean dbh distance view (degrees) ( M i n - openness (cm) (m) (Min - (Min - Max) Max) ( M i n -Max) Max) Aspen C L 71 0.187 (0.12-0.27) 0.0341 0.179-0.195 28 ( 1 5 -45) 3.9 (1.3-20.0) 80 (49 - 87) FN 69 0.206 (0.10-0.33) 0.0429 0.195-0.216 35 ( 2 0 -60) 3.7 (0.8-16.1) 82 (59-88) PH 65 0.147 (0.08-0.24) 0.0375 0.138-0.157 30 ( 1 9 -44) 4.3 (0.6-12.9) 79 (57 - 89) PR 72 0.174 (0.09-0.28) 0.0351 0.166-0.183 30 ( 2 0 -58) 3.8 (0.4-10.2) 81 (67 - 89) Sm 50 0.207 (0.13-0.37) 0.0522 0.192-0.222 34 ( 2 4 -53) 4.3 (1.7-11.8) 80 (66 - 86) Pooled 327 0.183 (0.08-0.37) 0.0453 0.178-0.188 31 ( 1 5 -60) 4.0 (0.4 - 20.0) 80 (49 - 89) Spruce C L 68 0.123 (0.05-0.22) 0.0338 0.115-0.131 33 ( 2 0 -52) 4.7 (0.3-15.1) 79 (62 - 89) FN 71 0.137 (0.04-0.27) 0.0401 0.128-0.147 40 ( 2 2 -66) 5.4 (0.2-17.0) 79 (61-89) PH 66 0.098 (0.05-0.16) 0.0260 0.091-0.104 35 ( 1 6 -55) 3.9 (0.3-10.6) 81 (64 - 89) PR 67 0.142 (0.07-0.22) 0.0309 0.135-0.150 36 ( 2 0 -55) 5.7 (2.2-12.0) 77 (67 - 84) Sm 49 0.157 (0.08-0.26) 0.0390 0.146-0.168 37 (16 -52) 5.5 (2 .0- 10.8) 78 (68 - 85) Pooled 321 0.130 (0.04-0.27) 0.0392 0.126-0.134 36 ( 1 6 -66) 5.0 (0.2-17.0) 79 (61-89) 29 % 0.15 200 400 600 800 1000 1200 1400 1600 1800 Distance from camera (cm) 60 65 70 75 Angle of view (degrees) Figure 2.2. Scatter plots of crown openness. Region abbreviations are: Smithers (Sm), Fort Nelson (FN), Peace River (PR), Calling Lake (CL), and Porcupine Hills (PH). 30 Table 2.3. Summary of the regression estimates for the Full Modeldbh-Region Bo/ ' ' Standard flu" Standard P-value r v ' Error (BQJ) Error (flij) for Bij Spruce Smithers 0.147 0.024 0.00026 0.00066 0.6994 0.0032 Fort Nelson 0.188 0.0187 -0.00127 0.000455 0.0068 0.1015 Peace River 0.129 0.0147 0.000372 0.000395 0.3500 0.0134 Calling Lake 0.123 0.0180 -0.0000015 0.000531 0.9978 0.0000 Porcupine 0.130 0.0127 -0.000919 0.000358 0.0125 0.0936 Hills Aspen Smithers 0.212 0.0354 -0.000148 0.00102 0.8856 0.0004 Fort Nelson 0.199 0.0228 0.000200 0.000636 0.7541 0.0015 Peace River 0.183 0.0174 -0.000289 0.000568 0.6045 0.0039 Calling Lake 0.197 0.0191 -0.000344 0.000660 0.6042 0.0039 Porcupine 0.161 0.0247 -0.000479 0.000821 0.5622 0.005 Hills (*) The Full Model Opn, = B 0 + J 3 i X j + 62Ri2 + 6 3R 13 + l34Ri4+135R s+BeXiRa + BTXjRo+BgXiRa + 6 9 X ^ 5 + £j can be rewritten for a particular region. For instance, for Region 2 the Full Model can be written as: Opn; = B 0 + BiXj+ B 2 + 8 6Xj This can be simplified to: Opn j 2 = B0>2+ B i J 2 X j + s i j2, where Opn j 2 denotes the species-specific crown openness for tree i in region j , B0>2 = B 0 + B 2 > 6,>2= B, + B 6 , and e i i 2is the associated error term. In general, Opny = B0j + ByXy + Ey, for Region j . (**) r 2 was calculated separately for each region with the regional simple linear regression. Discussion Independence of angle of view and dbh The initial method of Canham et al. (1994) for determining species-specific openness provided all the necessary data to test the independence of light extinction from calculated path length. The method used here does not directly address this possibility because each crown is treated as a two-dimensional entity with a specific openness. From casual observation of individual crowns, there appears to be areas of high openness and areas of low openness in an individual crown. It seems reasonable to assume that this variability in openness is caused by: (1) the path length through the crown and (2) the crown architecture including branch and leaf morphology (see review in Messier et al. 1999). The tests for the influence of dbh and angle of view on crown openness relate to whether the proportion of the crown with high openness changes with dbh or angle of view. It has been shown that light extinction is correlated with a calculated path length through an individual crown (e.g. Stadt and Lieffers 2000). This is not inconsistent with the assumptions of species-specific crown openness because the central part of a crown 31 can be less open than the outer part of the crown. The main assumption for use of species-specific crown openness is that the proportion of high and low openness areas (a function of path length and foliage distribution) within a crown is independent of dbh and angle of view. The performed tests showed no significant effect of dbh, distance or angle of view on openness for aspen. This indicates that use of a species-specific value for aspen meets the necessary assumptions. For spruce, a small but significant effect of dbh on openness was found in two out of five regions. Thus, use of species-specific crown openness might cause a biased estimate in stands with low or high average dbh. It must be noted that the inclusion of dbh only explains a small portion of the overall variation (revalues <0.14 in Table 2.3) and only had a significant effect in two out of five regions. Accordingly, within the range of data collected in this study, species-specific crown openness appears to be a relatively robust measure. Regional variability in species-specific crown openness The results indicate that there are differences in species-specific crown openness between regions. Table 2.4 outlines openness results from other regions and studies. A comparison between Tables 2.2 and 2.4 reveals several interesting points. The Alberta openness estimates from Table 2.4 (Stadt and Lieffers 2000) are from the same geographic area as the Calling Lake region in this study. The estimates from the Calling Lake area of this study and the estimates from Table 2.4 are not within the same range. There are several possible explanations for this disagreement. The sample size of Stadt and Lieffers (2000) is small and some of the difference might be sampling related. Stadt and Lieffers (2000) used a different methodology, in which the actual light level in the shadow of an individual tree was measured. Their method indirectly included beam enrichment, which is not included in the fisheye photo method used in this study. Beam enrichment might explain some of the higher openness found by Stadt and Lieffers (2000) but should not result in a two-fold difference. The method used to determine crown openness in this study has three potential associated errors that might explain some of the difference. Firstly, there is the issue of lack of objectivity and problems in the manual thresholding procedure. These issues are discussed in detail by Wagner (1998, 2001). It is possible that the thresholding method has lead to some bias in the estimates presented here, but it is unlikely that the bias amounts to a value close to 100%. Secondly, some concerns about 32 the use of digital cameras for fisheye photos of forest canopy have been raised (Frazer et al. 2001). In very dense canopies, canopy openness estimates obtained from digital fisheye photos have been shown to overestimate the openness compared to estimates obtained with a traditional film camera (Frazer et al. 2001). This error is less important in more open canopies, and this error biases towards higher openness estimates. Consequently, this error should result in over-estimation of openness with the utilized methodology, which is the opposite of the observed difference. Thirdly, analyses for openness using fisheye photos are not very accurate at low openness levels. Machado and Reich (1999) found problems with estimation of light transmission of less than 6% above canopy photosynthetic photon flux density. Consequently, it is likely that the low crown openness estimates of spruce have slightly higher uncertainty than the higher aspen crown openness estimates. The reported mean crown openness estimates from this study are all above 12% and this problem should consequently not be large. The large difference in openness estimates between this study and that of Stadt and Lieffers (2000) is likely caused by unidentified methodological differences and possibly the small sample size in the study of Stadt and Lieffers (2000). Table 2.4. Species-specific crown openness estimates from related studies. Region Openness 95% Confidence limits Sample size Aspen Hazelton (BC) 0.21 0.167-24.5 20 Calling Lake (AB) 0.36 N . A . 11 Quebec 0.16 0.015-0.18 38 Spruce Hazelton (BC) 0.11 0.08-0.147 20 Calling Lake (AB) 0.19 N.A. 5 Quebec 0.11 0.094-0.12 37 British Columbia (BC) data from Canham et al. (1999); Alberta (AB) data from Stadt and Lieffers (2000); Quebec data from Coates (unpublished) pers. comm.; Not Available (N.A.) . 33 Regional variability of species-specific crown openness can be caused by both variations in crown architecture, including branch and leaf morphology, or path length. The results of this study do not give any possibility for teasing apart these effects. The observed geographic variability can therefore be attributed to one or both of those factors. Figure 2.3A illustrates a plot of species-specific crown openness versus longitude. Visual inspection of this plot indicates that species-specific crown openness estimates seem to decrease directionally from west to east. This is consistent with stand level understory light observations by Messier et al. (1998) who compared their results from Quebec with results from northern Alberta (Lieffers and Stadt 1994; Constabel and Lieffers 1996). This comparison indicated that understory light levels were lower in Quebec than in Alberta for similar deciduous and mixed stands. It is likely that this is caused by the systematic variation of several climatic factors. The challenge is to determine which combination of factors influences species-specific crown openness because no individual factor seems to exhibit the observed pattern. Messier et al. (1998) speculated that the difference in understory light levels in Quebec and Alberta might be caused by higher precipitation in Quebec. Figure 2.3B illustrates a plot of species-specific crown openness versus May-September precipitation. For spruce Figure 2.3B seems to indicate a slight drop in species-specific crown openness as the May-September precipitation increases. For aspen, this relationship is not apparent. A simple linear regression in which species-specific crown openness was predicted as a function of May-September precipitation gave non-significant results for both species (spruce: P = 0.41, aspen: P = 0.92). These non-significant results are probably due to the many factors influencing species-specific crown openness and the small sample size. 34 o c c o a o c i o o 1 a CA 0.25 0.2 0.15 0.1 8 0.05 a CO A aspen • spruce A AA 60 70 80 90 100 110 120 130 Longitude (degrees W) 140 B 0.25 8 a c c <D a o c 3 2 o o o <]> a. in 0.2 0.15 0.1 0.05 A aspen • spruce 0 50 100 150 200 250 300 350 May-September precipitation (mm) Figure 2.3. Species-specific crown openness versus longitude and precipitation. (A) From east the data points are: Quebec, Porcupine Hills, Calling Lake, Peace River, Fort Nelson, Smithers, and Hazelton. Quebec data from Coates (unpublished, pers. comm.) and Hazelton data from Canham et al. (1999)). (B) Data from this study only, see Table 2.1 for sources of precipitation data and additional climatic information. 35 Crown transparency (also referred to as crown density) is an alternative measure of the amount of sky visible through an individual crown that is often used for forest health assessment (e.g. Innes 1993; USDA Forest Service 2002; Redfern and Boswell 2004). Crown transparency is normally visually estimated by comparison to a reference illustration (e.g. Innes 1990; U S D A Forest Service 2002). The reference used for estimation often varies between countries or regions and this results in different measurement scales. Regional variations in crown transparency should fundamentally be consistent with regional variations in species-specific crown openness. Unfortunately, regional comparisons of crown transparency are problematic due to biases created by the estimation methods (e.g. Innes 1993; De Vries et al. 2000). Still, several studies have shown regional variation in crown transparency (e.g. Innes and Boswell 1988; Innes 1993; Klap et al. 2000). The magnitude of this variation is very similar to the geographic variation of species-specific crown openness shown in this paper. As for species-specific crown openness, it is generally difficult to determine which factors are responsible for regional variation in crown transparency as the determinants are plentiful and often correlated (Innes and Boswell 1988). SORTIE's sensitivity to species-specific crown openness This study shows that mean species-specific crown openness does vary between regions. Furthermore, it was found that dbh might influence the crown openness of spruce and thus potentially bias understory light predictions. The impact of the geographic intraspecific variability of species-specific crown openness and the possible effect of dbh on light predictions can only be assessed through a sensitivity analysis using the model. Beaudet et al. (2002) performed a validation and sensitivity analysis of the light submodel of SORTIE for the northern hardwoods in eastern Canada. This sensitivity analysis showed that the understory light predictions were relatively insensitive to changes in species-specific crown openness while being more sensitive to changes in crown dimensions. Despite this relative insensitivity, the range of species-specific crown openness estimates found in the literature from western boreal Canada would still be sufficient to cause significant differences in understory light levels. 36 SORTIE predicts understory light levels with the Gap Light Index (GLI) which is 100% in full light and 0% in full shade. Beaudet et al. (2002) investigated the effect on GLI from doubling the estimate of species-specific crown openness from 0.2 to 0.4. Under a closed canopy this was found to change the predicted GLI from approximately 6 to 9%. South of a 400 m gap the change was larger and the predicted GLI changed from 19 to 27%. North of a 400 m2 gap the predicted GLI changed from 50 to 57%. The literature indicated regional variations in species-specific crown openness close to 100% in western boreal Canada (Table 2.4). If this regional variability is true, regional variation of understory light levels would be suspected to vary in a similarly magnitude to the predictions from the sensitivity analysis of Beaudet et al. (2002). This study indicated that the actual regional variability of species-specific crown openness in the investigated part of western boreal Canada is less than indicated by the literature for the same area (Table 2.4). Dbh was found to cause species-specific crown openness estimate to change by less than 30% while regional differences cause the species-specific crown openness estimate to vary by less than 50%. The variation of understory light levels caused by regional variations in species-specific crown openness can thus be expected to be approximately half of the outlined numbers from the sensitivity analysis. The importance of such regional variations in understory light levels is dependent on the process in question. In terms of quantifying annual growth of understory trees (e.g. Wright et al. 1998) the differences in predicted growth from such variations in light levels are small. The differences are more likely to be important for processes with a threshold value or a very steep response related to understory light level. Thus, the observed regional variability could potentially have a larger impact on a process such as understory tree mortality. In relation to most management issues the above outlined variations in understory light levels caused by the regional variability of species-specific crown openness are small. Thus, for most management purposes the light model is portable between regions without remeasurement of local species-specific crown openness. It should be noted that the climatic variation investigated in this study is relatively narrow compared to the climatic 37 ranges of the two species. Thus, it is unknown i f similar conclusions would hold under more extreme climatic conditions. Species-specific crown openness is the only parameter in SORTIE's light model that cannot be obtained from published equations, or reanalysis of permanent sample plots. Accordingly, the results presented here must be seen as an asset for the model, because they facilitate application of the model without the large associated cost of re-parameterization. 38 Chapter 2 references Banner, A. , MacKenzie, W., Haeussler, S., Thomson, S., Pojar, J. and Trowbridge, R. 1993. A field guide to site identification and interpretation for the Prince Rupert Forest Region. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Land Management Handbook No. 26. BC Ministry of Forests 2003. Site Index Estimates by Site Series: Report by Region (2003 approximation). Available at: http://www.for.gov.bc.ca/hre/sibec/reports/sisu2003ByRegion.pdf. Last accessed: December 7, 2004. Beckingham, J.D. and Archibald, J.H. 1996. Field guide to ecosites of northern Alberta. Canadian Forest Service, Northwest Region, Northern Forestry Centre, Edmonton, Alberta. Spec. Rep. 5. Beckingham, J.D., Nielsen, D.G. and Futoransky, V . A . 1996. Field guide to ecosites of the mid-boreal ecoregions of Saskatchewan. Canadian Forest Service, Northwest Region, Northern Forestry Centre, Edmonton, Alberta. Spec. Rep. 6. Beaudet, M . , Messier, C. and Canham, C D . 2002. Predictions of understory light conditions in northern hardwood forests following parameterization, sensitivity analysis, and test of the SORTIE light model. For. Ecol. Manage. 165: 235-248. Brunner, A . 1998. A light model for spatially explicit forest stand models. For. Ecol. Manage. 107: 19-46. Canham, C D . 1988. An index for understory light levels in and around canopy gaps. Ecology 69: 1634-1638. Canham, C D . , Finzi, A . C , Pacala, S.W. and Burbank, D.H. 1994. Causes and consequences of resource heterogeneity in forests: interspecific variation in light transmission by canopy trees. Can. J. For. Res. 24: 337-349. 39 Canham, C D . , Coates, K.D. , Bartemucci, P. and Quaglia, S. 1999. Measurement and modeling of spatially explicit variation in light transmission through interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1775-1783. Chazdon, R.L. 1988. Sunflecks and their importance to forest understory plants. Adv. Ecol. Res. 18: 1-63. Coates, K.D. , Canham, C D . , Beaudet, M . , Sachs, D.L. and Messier, C. 2004. Use of a spatially explicit individual-tree model (SORTIE-BC) to explore the implications of patchiness in structurally complex forests. For. Ecol. Manage. 186: 297-310. Constabel, A.J . and Lieffers, V.J . 1996. Seasonal patterns of light transmission through boreal mixedwood canopies. Can. J. For. Res. 26: 1008-1014. DeLong, C , MacKinnon, A . and Jang, L . 1990. A field guide for site identification and interpretation of ecosystems of the northeast portion of Prince George Forest Region. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Land Management Handbook No. 22. De Vries, W., Klap, J .M. and Erisman, J.W. 2000. Effects of environmental stress on forest crown condition in Europe. Part I. Hypotheses and approach to the study. Water Air Soil Pollut. 119: 317-333. Frazer, G.W., Canham, C D . and Lertzman, K.P. 1999. Gap Light Analyzer (GLA), version 2: imaging software to extract canopy structure and gap light indices from true-colour fisheye photographs. Simon Fraser University, Burnaby, B C , and the Institute of Ecosystem Studies, Mill-brook, N Y . Frazer, G.W., Trofymow, J.A. and Lertzman, K.P. 2000. Canopy openness and leaf area in chronosequences of coastal temperate rainforests. Can. J. For. Res. 30: 239-256. Frazer, G.W., Fournier, R.A., Trofymow, J.A. and Hall, R.J. 2001. A comparison of digital and film fisheye photography for analysis of forest canopy structure and gap light transmission. Agric. For. Meteorol. 109: 249-263. 40 Gholz, H.L., Fitz, F.K. and Waring, R.H. 1976. Leaf area differences associated with old-growth forest communities in the western Oregon Cascades. Can. J. For. Res. 6: 49-57. Grier, C.G. and Running, S.W. 1977. Leaf area of mature northwestern coniferous forests; relation to site water balance. Ecology 58: 893-899. Horn, H.S. 1971. The adaptive geometry of trees. Princeton University Press, Princeton, NJ, 144 p. Huang, S., Price, D. and Titus, S.J. 2000. Development of ecoregion-based height-diameter models for white spruce in boreal forests. For. Ecol. Manage. 129: 125-141. Huang, S., Titus, S.J. and Wiens, D.P. 1992. Comparison of nonlinear height-diameter functions for major Alberta tree species. Can. J. For. Res. 22: 1297-1304. Innes, J.L. 1990. Assessment of tree condition. Forestry Commission Field-book 12. HMSO, London. Innes, J.L. 1993. Forest health: its assessment and status. C A B International, Wallingford, U K , 667 p. Innes, J.L. and Boswell, R.C. 1988. Forest health surveys 1987. Part 2: analysis and interpretation. Forestry Commission Bulletin 79. HMSO, London. Klap, J .M., Voshaar, J.H.O., De Vries, W. and Erisman, J.W. 2000. Effects of environmental stress on forest crown condition in Europe. Part IV. Statistical analysis of relationships. Water Air Soil Pollut. 119: 387^420. Larsen, D.R. and Kershaw Jr., J.A. 1996. Influence of canopy structure assumptions on predictions from Beer's law. A comparison of deterministic and stochastic simulations. Agric. For. Meteorol. 81: 61-77. 41 Lieffers, V.J . , Messier, C , Stadt, K.J . , Gendron, F. and Comeau, P.G. 1999. Predicting and managing light in the understory of boreal forests. Can. J. For. Res. 29: 769-811. Lieffers, V.J . and Stadt, K. 1994. Growth of understory Picea glauca, Calamagrostis canadensis, and Epilobium angustifolium in relation to overstory light. Can. J. For. Res. 24: 1193-1198. Machado, J.-L. and Reich, P.B. 1999. Evaluation of several measures of canopy openness as predictors of photosynthetic photon flux density in deeply shaded conifer-dominated forest understory. Can. J. For. Res. 29: 1438-1444. Messier, C , Parent, S. and Bergeron, Y . 1998. Effects of overstory and understory vegetation on the understory light environment in mixed boreal forests. J. Veg. Sci. 9: 511-520. Messier, C , Doucet, R., Ruel, J . -C, Claveau, Y . , Kelly, C. and Lechowicz, M.J . 1999. Functional ecology of advanced regeneration in relation to light in boreal forests. Can. J. For. Res. 29:812-823. Monsi, M . and Saeki, T. 1953. Uber den lichtfakctor in den pflanzengesellschaften und seine bedetung fur die stoffproduktion. Jpn. J. Bot. 14: 22-52. Neter, J., Kunter, M.H. , Nachtsheim, C.J. and Wasserman, W. 1996. Applied linear statistical models, fourth edition. The McGraw-Hill Companies Inc., Boston, 1408 P-Norman, J .M. and Jarvis, P.G. 1975. Photosynthesis in sitka spruce (Picea sitchensis (Bong.) Carr.). V . Radiation penetration theory and a test case. J. Appl. Ecol. 12: 839-878. Oliver, C D . and Larson, B.C. 1996. Forest stand dynamics, update edition. John Wiley & Sons, Inc, New York. 544 p. 42 Pacala, S.W., Canham, C D . and Silander Jr., J.A. 1993. Forest models defined by field measurements. I. The design of a northeastern forest simulator. Can. J. For. Res. 23:1980-1988. Pacala, S.W., Canham, C D . , Saponara, J., Silander Jr., J.A., Kobe, R.K. and Ribbens, E. 1996. Forest models defined by field measurements: estimation, error analysis, and dynamics. Ecol. Monogr. 66: 1-43. Pojar, J., Meidingerm, D. and Klinka, K . 1991. Concepts. In: Meidinger, D. and Pojar, J. (editors and compilers). Ecosystems of British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Special Report Series No. 6, p. 9-37. Redfern, D.B. and Boswell, R . C 2004. Assessment of crown conditions in forest trees: comparison of methods, sources of variation and observer bias. For. Ecol. Manage. 188: 146-160. Stadt, K.J . and Lieffers, V.J . 2000. MIXLIGHT: a flexible light transmission model for mixed-species forest stands. Agric. For. Meteorol. 102: 235-252. U S D A Forest Service. 2002. Phase 3 field guide - crowns: measurements and sampling. Available at: http://fia.fs.fed.us/library.htm%20manuals. Last accessed: December 7, 2004. Wagner, S. 1998. Calibration of gray values of hemispherical photographs for image analysis. Agric. For. Meteorol. 90: 103-117. Wagner, S. 2001. Relative radiance measurements and zenith angle dependent segmentation in hemispherical photography. Agric. For. Meteorol. 107: 103-115. Wright, E.F., Coates, K.D. , Canham, C D . and Bartemucci, P. 1998. Species variability in growth response to light across climatic regions in north-western British Columbia. Can. J. For. Res. 28: 871-886. 43 Chapter 3: Light Availability and Growth of Understory Aspen and Spruce in Western Boreal Canada3 Introduction Mixedwood forests of trembling aspen (Populus tremuloides Michx) and spruce (Picea spp.) are widespread on upland sites across western Canada's boreal and sub-boreal forests (Rowe 1972; DeLong et al. 1990; Beckingham and Archibald 1996; Beckingham et al. 1996). The general successional dynamics of the boreal mixedwoods are well understood (e.g. Dix and Swan 1971; Andison and Kimmins 1999; Chen and Popadiouk 2002; Brassard and Chen 2006) with a general tendency for spruce to replace aspen over time since major disturbance. Historical forest management practices have been designed to promote the dominance of either aspen or spruce after logging. There has, however, been renewed interest in management practices that result in mixed-species stands with both horizontal and vertically complex structure (e.g. Lieffers and Beck 1994; Man and Lieffers 1999; Green et al. 2002; Welham et al. 2002; Comeau et al. 2005). The success of complex stand management will depend on our ability to understand and predict stand dynamics, especially the performance of understory aspen and spruce trees (e.g. Kimmins 1996; Oliver and Larson 1996; Chen and Popadiouk 2002). Quantification of understory tree growth under different stand structural conditions involves a complex suite of factors. The primary driver of photosynthesis is light availability which is limited in the understory. Thus, much attention has been focused on quantifying the relationship between light availability and growth (e.g. Gustafson 1943; Logan 1969; Chen 1997; Wright et al. 1998). Clearly, light is not the sole factor that influences growth (e.g. Fricke 1904; Korstian and Coile 1938; Coomes and Grubb 2000), but light availability is an appealing predictor of understory growth because it is relatively easy to measure (e.g. Gendron et al. 1998) and predict (e.g. Larsen and Kershaw 1996; Stadt and Lieffers 2000). 3 A version of Chapter 3 is submitted to Canadian Journal of Forest Research. Dr. David Coates is co-author on this paper. 44 The relationship between light availability and growth has been shown to exhibit regional variability (e.g. Carter and Klinka 1992; Wright et al. 1998; Drever and Lertzman 2001; Pritchard 2003). For juvenile understory spruce in western boreal and sub-boreal Canada, there are several models that predict growth of individual trees as a function of light availability (e.g. Kayahara et al. 1996; Wright et al. 1998; Comeau and Bedford 2002; Pritchard 2003; Stadt et al. 2005). Comparison of these models is difficult due to different functional forms, tree sizes, light availability, and overstory canopy-type. For aspen, a literature search revealed only a single study (Wright et al. 1998) that has quantified juvenile aspen growth as a function of light availability. Considering how widespread the mixedwood aspen-spruce forest type is across boreal Canada, it is surprising there has been no paired sampling of the two species at different sites to provide data on growth dynamics of the two species. In this study the objectives were to: (1) develop models of juvenile aspen and spruce height and diameter increment as a function of light availability and tree size, and (2) explore the magnitude of regional inter-specific and intra-specific differences in these relationships across western boreal Canada. Field methodology and data Sampling regions and sites Sampling was performed in six Sampling Regions located in northern British Columbia (BC), Alberta (AB), and Saskatchewan (SK). A Sampling Region was defined as a circular area with a radius of 40 kilometers and with relatively uniform climatic conditions. The Sampling Regions were selected to capture a large portion of climatic conditions in areas dominated by mixed aspen-spruce stands in the western boreal Canada. The selected sampling regions were located in the vicinity of Smithers (BC), Fort Nelson (BC), Dease Lake (BC), Peace River (AB), Calling Lake (AB) and Porcupine Hills (SK) (Figure 3.1). Each Sampling Region contained 12-28 sampling sites (stands) where individual trees were sampled. A l l sampling sites were located on zonal sites to minimize confounding between the influence of site and regional climate. A zonal site best reflects the regional 45 climate rather than local edaphic factors. This use of zonal site is equivalent to its use for classification in B C (Pojar et al. 1991) and equivalent to the reference site used for classification in A B (Beckingham and Archibald 1996) and SK (Beckingham et al. 1996). An observed difference between sampling regions was assumed to be an effect of local macro climate rather than edaphic factors. The climatic characteristics of each region are presented in Table 3.1. Figure 3.1. Geographic location of the sampling regions. Sampled trees A l l sampling was performed in the summer of 2001 and followed a methodology similar to that of Wright et al. (1998). Sample sites were mainly aspen dominated mixed stands, but varied from nearly pure aspen stands to even aspen-spruce mixtures. Sampling was performed on sites without indications of recent disturbance (e.g. logging or windthrow). Sites were selected to capture the full light gradient experienced by juvenile trees within a sampling region. Only healthy trees with no signs of biotic or abiotic damage were sampled. Trees were sampled where the light level was determined mainly by older 46 canopy trees rather than similar-sized competitors. Individual trees were selected to ensure that the sample population was evenly stratified across light levels and tree sizes. Between 51-120 trees were sampled per species and sample region. Sample tree characteristics are found in Table 3.2. 47 Table 3.1. Summary of selected site and climatic characteristics. General Location Smithers (B.C.) Dease Lake (B.C.) Fort Nelson (B.C.) Peace River (Ab) Calling Lake (Ab) Porcupine Hills (SK) SBSdk* B W B S d k l * BWBSmw2** Boreal Mixedwood*** Boreal Mixedwood*** Mid-boreal Ecosystem classification Ola-Sxw-Spirea - 01 -Sw-Knight's plume - Step moss 01-SwAt-Step moss BM-d low brush BM-d low brush Highlands**** Purple peavine cranberry cranberry D low-brush cranberry Latitude range of 5 4 " 3 5 ' - 5 4 ° . 3 9 ' 59"43'-60"0I' 59"06' -59"! 8' 5 6 ° 2 4 ' - 56°48 ' 55*05' -55*31' 52*22' - 52*30' sampling region (N) Longitude range of ! 26"51' - I27"0r 129"00" - 129"09' 123"! 1" - 123"28' 116**57' - 117"l4' 112"53' - 113*27' 102°49" - 103"08 sampling region (W) Elevation range of . 561-665 700- 861 279-412 561 - 721 6 0 6 - 775 512-620 sampling region No. of sampling sites 21 12 27 28 22 26 within sampling region Mean annual 510 422 449 388 501 480 precipitation (mm) Mean May-September 164 187 259 208 295 225 precipitation (mm) Mean annual 4 -1 -1 1 2 1 temperature (C") Mean temperature of 15 13 17 16 16 17 wannest month (C°) Mean temperature of -9 -18 -22 -18 -16 -20 coldest month (C°) Growing degree days > 5" 1 164 734 1289 1276 1366 1472 Average wind (May- 7 8 8 13 N.A. N.A. September) speed (km/h) Soil characteristics of Fine textured soils. Coarser soil texture than remaining Fine textured soils. Fine textured soils. Fine textured soils. Fine textured soils. sampled sites Mainly Gray regions. Maninly Gray Luvisols and Mainly Gray Luvisols. Mainly Gray Luvisols. Mainly Gray Luvisols. Mainly Gray Luvisols. Luvisols. Brunisols. Aspen siteindex N A N A N A 18 18 20 Spruce siteindex 18 14.0 15.0 17 17 20 •Banner et al. (1993), **DeLong et al. (1990), ***Beckingham and Archibald (1996), ****Beckingham et al. (1996). The climatic data are environment Canada's 1990 climatic normals from the nearest weather station (Environment Canada 2004). Utilized weather stations: Smithers A (54°49'-N, 127°1 l ' - W , Altitude 523m), Dease Lake (58°25'-N, 1 3 0 W - W , Altitude 816m), Fort Nelson A (58°50'-N, 122°35'-W, Altitude 382m), Peace River A (56°14'-N, 117°26'-W, Altitude 571m), Athabasca 2 (54°49'-N, 113°32'-W, Altitude 626) and, Kuroki (52°00-N, 103°27-W, Altitude 585). Not Available (N.A.). Alberta site indexes are from Beckingham and Archibald (1996), British Columbia site indexes are from B.C. Ministry of Forests Research Branch (2005), and Saskatchewan site indexes are from Beckingham et al. (1996) oo Table 3.2. Sample characteristics. Mean (minimum - maximum). Species Region Age (years) Height (cm) Diameter (cm) Sample size Aspen Smithers 13 ( 6 - 35) 462 (114- 971) 3.00 (0.60 - 8.90) 88 Spruce Smithers 21 ( 9 - 48) 289 (130- 954) 2.91 (0.45 - 8.95) 91 Aspen Dease Lake 13 ( 5 - 34) 380 (150- 693) 1.95 (0.35 -4.55) 57 Aspen Fort Nelson 12(5- 24) 421 (158- 821) 2.75 (0.40 -7.10) 63 Spruce Fort Nelson 30 ( 9 - 80) 351 (147 - 718) 4.13 (0.50 - 9.90) 51 Aspen Peace River 15 ( 5 - 30) 441 (188 - 702) 3.31 (0.60 -7.10) 87 Spruce Peace River 28 (10 -63) 353 (152 - 776) 4.15 (0.70 -9.7) 119 Aspen Calling Lake 13 ( 5 - 22) 448 (184 - 732) 3.25 (0.60 -6.95) 75 Spruce Calling Lake 63 (13 - 100) 383 (131 - 682) 4.77 (0.50 -9.80) 82 Aspen Porcupine Hills 11 ( 5 - 40) 413 (212 - 722) 3.18 (1.0- 6.35) 84 Spruce Porcupine Hills 25 (10 -52) 369 (136- 662) 4.91 (0.60 - 10.25) 98 Aspen A l l Regions 13 ( 5 - 40) 430 (128- 971) 2.97 (0.35 -8.9) 454 Spruce A l l Regions 33 ( 9 - 100) 352 (130- 954) 4.25 (0.45 -10.25) 441 Diameter at breast height (dbh) and height were measured for all sampled trees. For white spruce, the annual height increments for the previous five years were also measured. A disk was taken 10 centimetres above the root collar for measurement of past radial increment. Radial increment was measured with a 40X stereo microscope and a Parker Instruments digital readout (resolution: 0.01 mm) connected to a computer with the Nutricom A G R M M Ring Width Analyzer Program (Version 1.1, R E A Engineering Services, 1988). For each disk, ring counts and measurements were performed for the 49 longest and shortest radii. The average of the two measurements was used as an estimator of radial increment. This method was used as it effectively gives a good and consistent estimate of radial increment (Astrup and Larson in prep.). Light measurements To obtain estimates of growing season light availability, a fisheye photo was taken between 1.1-1.4 meters above the stump of each sampled tree. In stands with sparse understory and canopy height greater than 6 meters, it has been shown that the light levels do not change dramatically between 1 - 5 meters (e.g. Beaudet et al. 2002). Thus, one photo was assumed to be sufficient to characterize the light received throughout the full height of the tree. A l l photographs were taken with a tripod-mounted digital Nikon Coolpix 950 with a Nikon true fish-eye lens. Photographs were taken under uniform sky-conditions either early in the morning or late in the afternoon, but mainly on uniform overcast days. The photographs were analysed for growing season light availability with the G L A version 2 software (Frazer et al. 1999; Frazer et al. 2000). This software produces a Gap Light Index (GLI) which expresses the percent growing season light availability. GLI integrates the seasonal and diurnal distribution of solar radiation transmitted through the canopy into a simple index (Canham 1988). Additional data Spruce data from four regions of BC sampled by Wright et al. (1998) were also reanalyzed. These datasets were collected with a similar methodology to the current study except that sampling was mainly performed under conifer-dominated canopies rather than aspen-dominated canopies. The data from Wright et al. (1998) were collected in the following biogeoclimatic zones (Meidinger and Pojar 1991; Banner et al. 1993): BWBSdkl (Boreal White and Black Spruce dry cool subzone, Stikine variant); BWBSdk2 (Boreal White and Black Spruce dry cool subzone); ESSFmc (Engelmann spruce - Subalpine fir, moist cold subzone; SBSmc2 (Sub-boreal Spruce, moist cold subzone, Babine variant). Seven observations were deleted from this dataset as they were well outside the range of tree sizes sampled in this study. The data were reanalyzed because: (1) the analysis of Wright et al. (1998) did not include tree size as a predictor 50 variable, (2) reanalysis of the data created directly comparable results, and (3) inclusion of the additional data provided a combined spruce dataset that covers a wide climatic gradient. Model selection and data analysis A set of candidate models (Table 3.3 and Table 3.4) of radial (mm/5-year) and height increment (cm/5-year) as a function of light availability (GLI, 0-100% full sunlight) and initial tree diameter, measured (in cm) under the bark 10 cm above root collar (Dio) were developed. The candidate models were developed by incorporating different subsets of these two factors in different functional forms. The candidate models were developed prior to model fitting and selection to avoid problems with over fitting data. After model development, the candidate models were compared with a model selection criterion. The majority of existing regression models that predict juvenile tree growth as a function of light availability use a transformed dependent variable (e.g. Chen 1997; Wright et al. 1998; Comeau and Bedford 2002; Pritchard 2003). These transformations are most commonly used to linearize nonlinear responses, to eliminate unequal error variance, or to normalize the residuals. Transformation of the dependent variable can be problematic due to: (1) altered meaning of "biological meaningful" parameters (i.e. the meaning of an asymptote of logarithmically transformed data), (2) create overconfidence in the selected model due to increase in R or adjusted - R , and (3) create problems with bias in prediction caused by backtransformation of both estimates and confidence limits (e.g. Finney 1941; Baskerville 1972; Lee 1982). With increased computer power and accessibility it is possible to fit nonlinear models and deal with divergence from the standard assumptions of regression analysis. Consequently, untransformed dependent variables were modeled. The candidate models can be divided into two broad groups. The first group (Light models) consists of models that predict height and diameter increment as a function of light, independent of tree size. The second group of models (Size-Shade Models) consists of models which utilize both tree diameter and light availability as predictor variables. A n effort was made to utilize models with biologically meaningful parameters. 51 Table 3.3. Aspen candidate models. Radial increment (Y) (mm/5-years), GLI (0-100%) is light availability, and Dio is diameter 10cm above root collar (cm). Probability density functions: Normal (N), Normal with variance increasing proportional to the predicted value (NI), and Lognormal (LN). AICc was calculated for each sampling region and the summed. AAICc is the models AICc minus the lowest AICp No Model Y = a + bGLI Y = a + b4GLI Y = a/(\ + exp(b - cGLI) Y = aGLI /((a I b) + GLI) Y = a((GLJ -\0)/\00)b Y = (a + bDw) /(l + exp(c - dGLI)) Y = (a + bD]0)(GLI/100)c Y = (a + bD]0)(GLI - 5 /95) c Y = (a + bDw){GLI -10/90) c N : L N : NI: NI: AICc AICc A I C C Rank (AAICc) (AAICc) ( A A I C C ) 2320 .8 2288 .5 2277.1 9 (100.6) (68 .3) (56.9) 2309.8 2278.8 2261.1 8 (89.6) (58 .6) (40.9) 2282.1 2250 .6 2220 .2 1 (61 .9) (30 .4) (0.0) 2304.1 2289 .3 2260 .7 5 (83.9) (69 .1 ) (40 .5) 2304 .6 2291 .4 2261 6 (84.4) (71 .2) (40.8) 2284 .2 2252 .3 2220 .3 2 (64.0) (32 .1 ) (0 .1 ) 2308 .4 2087 .2 2262 .7 7 (88.2) (133) (42.5) 2304 .9 2283 .5 2257 .6 4 (84.7) (63 .3) (37.4) 2301 .7 2288.8 2256.8 3 (81 .5) (68.6) (36.6) The aspen Light models are represented by models 1-5 in Table 3.3. The spruce Light models are represented by models 1-4 in Table 3.4. The Light model functional forms are; two simple linear functions, a logistic function, and a Michaelis-Menten function. These functional forms have previously been used to model diameter or height increment as a function of light availability (Lieffers and Stadt 1994; Kayahara et al. 1996; Chen 1997; Wright et al. 1998; Coates and Burton 1999). 5 2 Table 3.4. Spruce candidate models. Radial Increment (RI) (mm/5-years), Height Increment (HI) (cm/5-years), GLI (0-100%) is light availability, and Dio is diameter 10cm above root collar (cm). Probability density functions: Normal (N), Normal with variance increasing proportional to the predicted value (NI), and Lognormal (LN). AICc was calculated for each region and then summed. AAICc is the models AICc minus the lowest A I C C . No Y Model N : L N : NI: NI: AICc AICc A I C C Rank (AAIC C ) (AAICc) (AAICc) 4299 4167.5 4238.2 (561.3) (429.8) (500.5) 12 8278.1 8291.6 8282.3 (459.2) (472.7) (463.4) 12 4291.5 4160.8 4225.9 (553.8) (423.1) (488.2) 11 8225.8 8206.8 8223.6 (406.9) (387.9) (404.7) 9 4296.9 4217 4216.7 (559.2) (479.3) (479) 10 8240.3 8209.7 8226.3 (421.4) (390.8) (407.4) 10 4295.1 4158.5 4220.9 (557.4) (420.8) (483.2) 9 8254.5 8267.5 8234.5 (435.6) (448.6) (415.6) 11 3879.8 3784.2 3749 (142.1) (46.5) (11.3) 4 7862.6 7857.6 7849.8 (43.7) (38.7) (30.9) 4 3872.8 3791.5 3745.9 (135.1) (53.8) (8.2) 2 7896.9 7885.6 7846.9 (78) (66.7) (28) 2 3961.5 3842.9 3840.1 (223.8) (105.2) (102.4) 8 7975.9 7949.1 7924.3 (157) (130.2) (105.4) 8 3887.6 3746.6 3737.7 (149.9) (8.9) (0.0) 1 7912.7 7836.4 7818.9 (131.1) (17.5) (0.0) 1 3920.7 3790.4 3783 (183) (52.7) (45.3) 6 7950 7919.2 7889.6 (131.1) (100.3) (70.7) 7 3915.5 3798.9 3781 (177.8) (61.2) (43.3) 5 7941.9 7904.8 7879.4 (123) (85.9) (60.5) 5 3963.6 3793.8 3746.6 (225.9) (56.1) (8.9) 3 7894.8 7894.2 7848.1 (75.9) (75.3) (29.2) 3 3965.6 3849.9 3811.6 (227.9) (112.2) (73.9) 7 7976.5 7936.7 7916.3 (157.6) (117.8) (97.4) 6 1 RI. HI 2 RI HI 3 RI HI 4 RI HI 5 RI HI 6 RI HI 7 RI HI 8 RI HI 9 RI HI 10 RI HI 11 RI HI 12 RI HI Y = a + bGLI Y = a + bJGLI Y = a /(l + exp(b - cGLI) Y = aGLI /((a I b) + GLI) Y = a exp((-0.5(ln(D,0 / 36) / b)2 )(GLI 1100)c Y = aexp((-0.5(ln(£> 1 0 /36)/b)2)(GLI - 5 /95 ) ' Y = exp(a - bDi0 )(GLI 1100)c Y = (a + bDw) /(l + exp(c - dGLI)) Y = (a + bDi0)(GLI/\00)c Y = (a+ bDl0)(GLI-5/95)c Y = a[(l - exp(-£>1 0 / b))(\ - exp(-GL/ / c))] Y = a + bGLI + cD, 10 53 The Size-Shade Models were developed with an approach where a potential increment (function of tree diameter) is reduced according to the light availability (degree of shading). This type of model can be formulated as additive or multiplicative. In an additive model, the shade induced reduction of the potential growth will be identical for trees of different sizes. Additive models have been utilized by several authors for both juvenile and mature trees (e.g. Comeau and Bedford 2002; Pritchard 2003; Canham et al. 2004). For conifers, in the range of tree sizes represented in this study, it is has been shown that: (1) trees grown under very low light conditions will grow slowly and at similar rates independently of tree size, and (2) in more open conditions larger trees have larger height and diameter increments (Williams et al. 1999; Claveau et al. 2002). This is in better agreement with a multiplicative model than an additive model. Consequently, the Size-Light models were formulated as multiplicative models rather than additive models. To model the potential increment as a function of diameter, a lognormal, an exponential, and a linear function were tested. These functional forms were chosen because they have been shown to describe the increase in growth with size well for many different plants (e.g. Hunt 1982; Stroll et al. 1994; Canham et al. 2004). Aspen suckers grow quickly in their initial years after suckering. The exponential and the lognormal function have very low initial growth rates and they were consequently not used to model aspen increment. For spruce all three functions were tested. To describe the shade induced reductions in radial or height increment, an exponential and a logistic function were tested. These functions are simple and flexible. One regular additive multiple linear model was included for spruce to provide a basis for comparison. When model fitting is performed with maximum likelihood methods, different formulations of the probability density function (PDF) can be evaluated just as different formulations of the functional form can be evaluated (Hilborn and Mangel 1997). Many biological phenomena are either normally or log-normally distributed. A l l candidate models were fitted with both distributions. In natural phenomena, like growth, the variance often increases with the observed/predicted entity. It is not unusual to observe an increasing variance in larger faster growing individuals compared to slow growing 54 individuals. This information was incorporated into the analysis by testing a normal PDF where the variance increases proportionally to the predicted value. A l l analysis were preformed with SAS Version 8.2 (SAS Institute Inc., Cary, N.C.). The parameters for the candidate models were estimated using maximum likelihood. Model functional forms were compared with Akaike's Information Criteria (AICc) appropriate for small sample sizes (Hurvich and Tsai 1989; Burnham and Anderson 2002). AICc was used for model selection because it allows comparison of non-nested models and penalizes models for increasing numbers of parameters. Three general rules can be used to compare support for individual models: (1) i f AAICc is between 0-2 the support for the compared models is similar, (2) i f AAICc is between 4-7, this indicates less support for a model, and (3) i f AAICc > 10, this indicates that a substantial variation in the data is not explained by the model (Burnham and Anderson 2002). The first part of the analysis was to select the best approximating candidate model. Initially, all candidate models were fitted to the data from each individual sampling region. Then, the AICc for each model was summed over all regions and an overall AICc for each model was obtained. The best approximating model was then selected as the model with the lowest overall AICc-The analysis for spruce included data collected specifically for this study and data from Wright et al. (1998). Consequently, the model selection was performed for: (1) the data from this study, (2) the data from Wright et al. (1998), and (3) data from both sources combined. Results from these three datasets did not differ in any noteworthy way and only results for the combined dataset are reported. The second part of the analysis was to determine the appropriate number of local parameters for the selected models. This was done by fitting three model types. The first model type had only global parameters and allowed no local variation in growth pattern. The global parameters model type was fitted by pooling all data into one dataset. The second model type allowed local variation in growth patterns by allowing all parameters to be estimated from local datasets. The final model type allowed a mixture of global parameters estimated from the pooled data and local parameters estimated from local 55 datasets. The appropriate number of local parameters was determined by selection of the model with the lowest AICc. The actual fitting of the local and global parameters were performed by inclusion of 0-1 indicator variables. Other considerations and diagnostics than AICc were also allowed to enter into the model selection process, especially issues of model stability and possibility for biological interpretation of the parameter values. Visual inspection of residual plots and normality plots were also used as complementary model selection guides. Results Model selection The lowest AICc for both species was achieved with the normal PDF where variance increased proportionally to the predicted value (Table 3.3 and Table 3.4). Spruce models that included tree diameter (Dio) as predictor variable were considerably better (AAICc>400) than the Light-Models (Table 3.4). This was not the case for aspen where there was no apparent benefit from the inclusion of diameter as a predictor variable (Table 3.3). Aspen models 3 and 6 had equal support and were the best approximating models (lowest AICc) (Table 3.3). Aspen model 3 is the logistic function, while Aspen model 6 is a logistic function where the asymptote increases linearly with tree size. For Aspen model 6, the parameter that described the change in increment with tree size was small and varied between positive and negative in the different regional datasets. Thus, Aspen model 3 was selected for further analysis. Compared to Aspen model 3, all other candidate models had associated AAICc > 35 and can be considered to fail in explaining a substantial amount of the variation. Spruce model 8 was the best approximating model for both radial and height increment (Table 3.4). Spruce model 8 is a logistic function where the asymptote increases linearly with tree diameter. Spruce models 6 and 11 were ranked as second and third with AAICc for diameter increment of 8.2 and 8.9 and for height increment of 28 and 29.2 (Table 3.4). Spruce model 8 was selected as for further analysis. 56 The second part of the model selection process examined if Aspen model 6 and Spruce model 8 with local parameters better represent the data than a global model where parameters were fitted to the combined dataset across all regions. Strong support for local models was found for both species (Table 3.5). Table 3.5. Comparison of local and global models. A local parameter is fitted from a local dataset while a global parameter is fitted from the combined data. The spruce model: Y = (a + b D, 0 ) / (1+ exp(c-d GLI)) (Spruce 8, Table 3.6). The aspen model: Y = a/(l+ exp(b-c GLI)) (Aspen 3, Table 3.3). The models are fitted with a normal probability density function where the variance is proportional to the predicted value. Model Local parameters Global parameters AICc (AAICc) Rank Spruce diameter increment (mm/5-years) (8A) Local A l l None 3737.7 (1.1) 3 (8B) Global None A l l 4342.1 ( 605.5) 6 (8C) Local light c, d a, b 3740.9 (4.3) 4 (8D) Local asymptotes a, b c,d 3774.4 (37.8) 5 (8E) Mix 1 a, d b,c 3737.5 (0.9) 2 (8F) Mix 2 b ,d a, c 3736.6 (0) 1 Spruce height increment (cm/5-years) (8A) Local A l l None 7818.9 (0) 1 (8B) Global None A l l 8352 (533.1) 6 (8C) Local light c,d a, b 7855.1 (36.2) 4 (8D) Local asymptotes a, b c, d 7867.9 (49) 5 (8E) Mix 1 a, d b,c 7853.5 (34.6) 3 (8F) Mix 2 b ,d a, c 7824.4 (5.5) 2 Aspen diameter increment (mm/5-years) (3 A) Local A l l None 2220.2(0) 1 (3B) Global None A l l 2301(80.8) 6 (3C) Local light b, c a, p 2223(2.8) 2 (3D) Local asymptotes A b, c 2241.4(21.2) 4 (3E) Mix 1 a, c B 2232.2(12) 3 (3F) Mix 2 a, b C 2242.1(21.9) 5 For aspen, the local model had the lowest AICc while the global model had the highest AICc (Table 3.5). Even though the local model had the lowest AICc, it was decided to select aspen model 3E (Table 3.5) where parameters a and c are estimated from local data while parameter b is estimated from the combined data. Aspen model 3E was ranked third (AAICc = 12), but was chosen due to tighter confidence intervals for parameters, and because the model predictions did not differ in any noteworthy way from the 57 predictions from the local model. The R2-values for Aspen model 3E varied between 0.36 in Smithers to 0.69 in Fort Nelson, while the remaining regions had R2-values close to 0.5 (Table 3.6). A residual plot (Figure 3.2A) illustrates the model fit and the increasing variance. (A) Aspen residuals •• . •V j iv:*s .,1V 0 2 4 6 8 10 12 14 16 Predicted increment (mm/5-years) (C) Spruce HI (B) Spruce RI .0. . ' • * * 0 5 10 15 20 25 Predicted value (mm/5-years) - B W B S d k l o BWBSdk2 • CL » ESSFmc . FN ° PH • PR o S B S m c » Sm Predicted (cm/5-years) Figure 3.2. Residual plots. Residual is calculated as predicted value - observed value. Spruce predictions are made with parameters from Table 3.7. Aspen predictions are made with the parameters from Table 3.6. Geographic regions: Calling Lake (CL), Fort Nelson (FN), Porcupine Hills (PH), Peace River (PR), and Smithers (Sm). Remaining abbreviations refer to BC biogeoclimatic zones 58 Table 3.6. Parameter estimates for the aspen model. Predicted radial increment (rnm/5-years) = a/(l+ exp(b-c GLI)). GLI (0 - 100%) is light availability. Parameter b is estimated from the combined data while parameters a and c are estimated from the local data. The model is fitted with a normal probability density function where the variance increases proportionally to the predicted value. Parameter estimate (95% approximate confidence interval). Region A B c R 2 Calling Lake 11.64 2.71 0.090 0.46 (10.19 - 13.10) (2.36--3.05) (0.072 --0.107) Dease lake 10.16 2.71 0.056 0.43 (3.90 - 16.42) (2.36--3.05) (0.023 -0.088) Fort Nelson 15.54 2.71 0.064 0.69 (10.66 - 20.42) (2.36--3.05) (0.041 - 0.087) Porcupine Hills 11.77 2.71 0.089 0.51 (9.74 - 13.79) (2.36--3.05) (0.071 -0.107) Peace River 10.16 2.71 0.108 0.44 (8.41 - 11.94) (2.36--3.05) (0.086 -0.130) Smithers 10.36 2.71 0.084 0.36 (8.36 - 12.36) (2.36--3.05) (0.063 -0.104) For spruce, the global model was found to be the poorest approximating model (DI AAICc - 606, HI AAICc = 533). For radial increment, the best approximating model was spruce model 8F (Table 3.5), where parameters b and d are estimated from the local data, while parameters a and c are estimated from the combined data. For height increment Spruce model 8F was ranked second (AAICc = 5.5). Spruce model 8F was selected as the most appropriate and parsimonious model to predict radial and height growth for spruce. For radial increment, the R -values for Spruce model 8F varied between 0.47 and 0.81. For height increment the R -values varied between 0.39 and 0.88 (Table 3.7). A residual plot (Figure 3.2B & 3.2C) illustrates the model fit and the increasing variance. 59 Table 3.7. Parameter estimates for the spruce model. The model: Y = ((a+ b D to)/(l+ exp(c - d GLI))). GLI (0 -100%) is light availability and Din is diameter 10 cm above root collar (cm). Parameters a and b are estimated from the combined data while parameters b and d are estimated from local data. The models are fitted with a normal probability distribution where the variance increases proportionally to the predicted value. Parameter estimate (95% approximate confidence interval). Region A B C d R^ Spruce radial increment (mm/5-years) Calling Lake 8.19 3.14 2.23 0.088 0.69 (7.30 - 9.08) (2.54- 3.75) (2.07- 2.39) (0.075 --0.101) Fort Nelson 8.19 2.75 2.23 0.068 0.63 (7.30-9.08) (1.53 - 3.98) (2.07- 2.39) (0.047 - 0.089) Porcupine Hills 8.19 2.75 2.23 0.082 0.73 (7.30-9.08) (2.04 - 3.45) (2.07- 2.39) (0.067 - 0.097) Peace River 8.19 3.39 2.23 0.055 0.76 (7.30-9.08) (2.28- 4.50) (2.07- 2.39) (0.039 - 0.071) Smithers 8.19 3.71 2.23 0.062 0.81 (7.30-9.08) (2.88 - 4.54) (2.07- 2.39) (0.048 - 0.077) BWBSdkl 8.19 2.00 2.23 0.043 0.50 (7.30-9.08) (0.45 - 3.55) (2.07- 2.39) (0.023 - 0.063) BWBSdk2 8.19 2.93 2.23 0.032 0.47 (7.30-9.08) (0.29 - 5.58) (2.07 - 2.39) (0.012- 0.052) ESSFmc 8.19 3.63 2.23 0.024 0.61 (7.30-9.08) (2.27 - 4.98) (2.07- 2.39) (0.001 - 0.039) SBSmc2 8.19 9.82 2.23 0.018 0.63 (7.30-9.08) (5.46- 14.17) (2.07 - 2.39) (0.002 - 0.034) Spruce height increment (cm/5-years) Calling Lake 111.55 25.92 1.67 0.1024 0.59 (103.00- 120.10) (20.55 -31.30) (1.49- 1.85) (0.082 --0.123) Fort Nelson 111.55 16.74 1.67 0.081 0.68 (103.00- 120.10) (7.82- 25.67) (1.49- 1.85) (0.053 - 0.108) Porcupine Hills 111.55 16.98 1.67 0.094 0.64 (103.00- 120.10) (10.90 -23.07) (1.49- 1.85) (0.072 - 0.117) Peace River 111.55 21.18 1.67 0.078 0.63 (103.00- 120.10) (14.56 - 27.79) (1.49- 1.85) (0.056 - 0.100) Smithers 111.55 32.33 1.67 0.075 0.77 (103.00- 120.10) (24.91 - 39.75) (1.49- 1.85) (0.053 - 0.097) BWBSdk l 111.55 28.23 1.67 0.035 0.49 (103.00- 120.10) (10.01 - 46.45) (1.49- 1.85) (0.010- 0.059) BWBSdk2 111.55 46.27 1.67 0.024 0.39 (103.00- 120.10) (16.10 - 76.44) (1.49- 1.85) (0.001 - 0.047) ESSFmc 111.55 37.49 1.67 0.018 0.48 (103.00- 120.10) (24.52 - 50.47) (1.49- 1.85) (-0.002 - 0.039) SBSmc2 111.55 92.05 1.67 0.016 0.59 (103.00- 120.10) (52.52 - 131.59) (1.49- 1.85) (-0.006 -0.038) 60 Model predictions For aspen, predicted radial growth for Calling Lake, Peace River, Porcupine Hills and Smithers have similar magnitude and asymptotic shapes (Figure 3.3). The graphs for Fort Nelson and Dease Lake are less asymptotic and the predicted increment increased throughout the full range of light levels (Figure 3.3). Predicted growth rates of aspen in the Dease Lake region were considerable lower at all light levels than in all other regions. At high light levels (60-100%), the highest growth rates were predicted for Fort Nelson while at low light levels all regions, except Dease Lake, had similar predictions. \ co CD i in E CD E CD i _ O c T3 CD on 16 14 12 10 • CL o DL T FN v PH • PR • Sm 100 GLI (%) Figure 3.3. Predicted aspen radial increment. GLI (0-100%) is light availability. The model and parameters are given in Table 3.5. Geographic regions: Calling Lake (CL), Dease Lake (DL), Fort Nelson (FN), Porcupine Hills (PH), Peace River (PR), and Smithers (Sm). 61 Figure 3.4. Predicted spruce height and radial increment. GLI (0-100%) is light availability. The model and parameters are given in Table 3.7. (A) Radial increment for spruce with diameter (D| 0) = 1cm. (B) Radial increment for spruce with diameter (Dio) = 3cm. (C) Height increment for spruce with diameter (Dio) = 1cm. (C) Height increment for spruce with diameter (Dio) = 3cm. Geographic regions: Calling Lake (CL), Fort Nelson (FN), Porcupine Hills (PH), Peace River (PR), and Smithers (Sm). Remaining abbreviations refer to BC biogeoclimatic zones. Based on curve shape, the spruce light-growth relationship can be divided into two distinctive groups with either approximately linear or asymptotic growth patterns (Figure 3.4). The approximately linear pattern was found in the data collected by Wright et al. (1998) (BWBSdkl, BWBSdk2, ESSFmc and SBSmc2), while predictions for all other regions exhibits a more asymptotic pattern. The regions with approximately linear relationships also exhibit the lowest growth rates. The five asymptotic relationships have both similar shape and actual predicted increments at full light. They exhibit a rapid increase in height increment until approximately 50% light above which the effect of extra light is small. For radial increment the relationships increase rapidly until approximately 75% light and then levels off. The difference in shape of the radial and 62 height growth relationships results in low heightdiameter ratios at high light levels and high height: diameter ratios at low light levels. The main difference between the selected aspen and spruce model is the inclusion of tree diameter as predictor variable. As a consequence, predicted radial increment of small aspen is larger than the predicted increment of a small spruce, whereas a larger spruce has equal or greater radial increment than an aspen of any size (Figure 3.5A). Another difference between aspen and spruce is in their heightdiameter ratios (Figure 3.5B). Aspen has a higher heightdiameter ratio at all light levels. Both tree species had similar patterns of growth (linear or asymptotic) in the same region (Figure 3.5C). A comparison of the two species illustrates more regional variance in the growth at full sunlight than in the actual shape of the light-growth relationship (Figure 3.5D). In Fort Nelson exceptional aspen growth was observed while spruce growth was at the lower end for the boreal mixedwood regions. Contrary to this, aspen growth at full light in Smithers and Peace River was on the lower end of the mixedwood regions while spruce growth was high. Discussion Regional variability of growth pattern The rank order of juvenile aspen and spruce light-growth relationships was found not to change across regions (Figure 3.3, Figure 3.4). Thus, the results give no reason to expect a change in successional dynamics between these two species in western sub-boreal and boreal forests. The observed regional variability in growth at full light can potentially result in slightly different rates of mixed stand development and inter-specific competitive strengths. Most obvious was the exceptional aspen growth in Fort Nelson which is likely to give aspen a greater competitive advantage over spruce at full light. On the other hand, spruce in Smithers or Peace River may require a smaller head start to successfully compete with aspen. 63 Geographic region |j Geographic region Figure 3.5. Comparison of aspen and spruce growth patterns. (A) Predicted aspen and spruce radial increment in Porcupine Hills. (B) Observed ratios of height (cm) over diameter (Dio) (cm). (C) Inflection points for the radial increment graphs. (D) Predicted radial increment at GLI = 100% for aspen and spruce with diameter Dio=2 cm. Geographic regions: Calling Lake (CL), Fort Nelson (FN), Porcupine Hills (PH), Peace River (PR), Smithers (Sm).BWBSdkl (Dease Lake) Regional variability in both the shape of the light-increment relationship and the maximum increment at full light has been observed for spruce (e.g. Wright et al. 1998; Pritchard 2003; Kalischuk 2004). The broad regional data supports this observation. Little variability was found in the typical boreal mixedwood regions, but when compared with the conifer-dominated regions of north-western B C (ESSFmc, B W B S d k l , BWBSdk2, SBSmc) striking differences were observed. Thus, this analysis provides further support that there is not one general species-specific shape of the light-growth relationship across significant environmental gradients. For spruce, approximately linear relationships with lower growth rates were found in the data from Wright et al. (1998) 64 (conifer-dominated regions of north-western BC) while more asymptotic relationships were found in the remaining data. The difference in the shape of the light-increment relationship can have considerable effect on the performance of understory spruce. For example, assume an asymptotic light-increment relationship as observed in Calling Lake, Porcupine Hills or Smithers. Understory spruce with 50-60% light availability will realize approximately 75% of the potential diameter increment and approximately 90% of the potential height growth. Secondly, assume an approximately linear light-increment relationship (BWBSdkl , BWBSdk2, ESSFmc, and SBSmc). At 50% light availability, understory spruce will only realize approximately 50% of their potential diameter and height increment. The Wright et al. (1998) dataset and the current dataset were sampled with similar methodology and there is no indication that the observed differences in the shape of the light-growth relationship was due to methodology. One possible explanation is that climatic conditions result in the observed divergence in the shape of the light-increment relationship. Another possible explanation relates to the fact that Wright et al. (1998) sampled in stands with conifer-dominated overstories while the data from the current study was sampled in aspen-dominated stands. Chapter 4 explores these alternate hypotheses for factors controlling the shape of the light-growth relationships. Aspen in Fort Nelson had the largest radial increments, while aspen in Dease Lake had the lowest radial increments. This generally fits well with expectations, as aspen in Fort Nelson typically exhibits higher growth rates than aspen in other western boreal mixedwood regions (Kabzems and Garcia 2004). Aspen growth is quite sensitive to low soil temperatures (Landhausser et al. 2001) and it is generally accepted that a short growing season will lead to slower growth. These two observations most likely explain the slow growth rates of aspen observed in the harsh climate of Dease Lake (Table 3.1). 65 Comparison of aspen and spruce models The main difference between the selected aspen and spruce models is the inclusion of diameter as a predictor variable. The literature (e.g. Assmann 1970; Comeau et al. 1993; Lieffers et al. 1996; Williams et al. 1999; Claveau et al. 2002; Comeau and Bedford 2002; Pritchard 2003) and this study provide substantial support for the large effect of tree size on annual radial increment of conifer species in both full light and shaded conditions. However no effect of tree size on aspen radial increment was found. The reason for this difference is the high initial growth rates that characterize aspen suckers. In the model predictions, small aspen had higher radial increment than small spruce while a larger spruce had the same or higher radial increments than an equal sized aspen (Figure 3.5A). This initial fast growth of aspen suckers, the slow growth of small spruce, and the difference in allocation patterns (Figure 3.5B) are the drivers of successional dynamics of a mixedwood stand after a major disturbance. Several studies have tried to quantify shade tolerance by measuring and comparing growth rates at low light levels or by illustrating trade-offs between growth at low light and growth at high light (e.g. Carter and Klinka 1992; Pacala et al. 1994; Walters and Reich 1996). In this study aspen and spruce were found to have very similar radial growth rates at low light levels and no clear trade-offs between growth at low light and growth at high light were found. Rather this study indicates that it is the initial fast growth of aspen and the allocation pattern that differentiate the two species. Figure 3.5B illustrated the difference in allocation pattern between the two species. As expected for an early successional species, aspen had higher height: diameter ratios at all light levels. Management implications At full light, aspen and spruce growth were found to vary between regions. Consequently, it is likely that regions such as Fort Nelson compared with Smithers or Peace River require more intensive vegetation management to promote growth of spruce regeneration on a mixedwood sites. Across the western boreal mixedwood region, juvenile spruce was found to respond very similarly to light environments. Thus, across this region 66 management practices that promote understory spruce can be expected to have similar outcomes. The data from the conifer-dominated forests of north-western BC illustrated very different light-growth patterns that have considerable impact on the growth rates of understory spruce. Such difference in growth rates can have considerable effects on the success of understory spruce management and on targets for optimal understory light levels. This study indicate that in the conifer-dominated forests of north-western BC understory spruce requires higher light levels to perform as well as understory spruce in the boreal mixedwood region. In conclusion, caution should be taken when transferring management practices and experiences across significant environmental gradients. 67 Chapter 3 references Andison, D.W. and Kimmins, J.P. 1999. Scaling up to understand British Columbia's boreal mixedwoods. Environ. Rev. 7: 19-30. Assmann, E. 1970. The Principles of Forest Yield Study. Pergamon Press, Oxford. 506 p. B.C. Ministry of Forests Research Branch (2005). Site index estimates by site series (SIBEC) - second approximation. Available at: http://www.for.gov.be/hre/sibec. Last accessed: November 25, 2005. Banner, A. , MacKenzie, W., Haeussler, S., Thomson, S., Pojar, J. and Trowbridge, R. 1993. A field guide to site identification and interpretation for the Prince Rupert Forest Region. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Land Management Handbook No. 26. Baskerville, G.L. 1972. Use of logarithmic regression in the estimation of plant biomass. Can. J. For. Res. 2: 49-53. Beaudet, M . , Messier, C. and Canham, C D . 2002. Predictions of understory light conditions in northern hardwood forests^ following parameterization, sensitivity analysis, and test of the SORTIE light model. For. Ecol. Manage. 165: 235-248. Beckingham, J.D. and Archibald, J.H. 1996. Field guide to ecosites of northern Alberta. Canadian Forest Service, Northwest Region, Northern Forestry Centre, Edmonton, Alberta. Spec. Rep. 5. Beckingham, J.D., Nielsen, D.G. and Futoransky, V . A . 1996. Field guide to ecosites of the mid-boreal ecoregions of Saskatchewan. Canadian Forest Service, Northwest Region, Northern Forestry Centre, Edmonton, Alberta. Spec. Rep. 6. Brassard, B.W. and Chen, H .Y .H . 2006. Stand structural dynamics of North American boreal forests. Critical Reviews in Plant Science 25: 37-59. 68 Burnham, K.P. and Anderson, D.R. 2002. Model selection and multimodel inference, a practical information-theoretic approach. Second edition. Springer-Verlag New York, Inc. 488 p. Canham, C D . 1988. An index of understory light levels in and around canopy gaps. Ecology 69: 1634-1638. Canham, C D . , LePage, P. and Coates, K . D . 2004. A neighborhood analysis of canopy tree competition: effects of shading versus crowding. Can. J. For. Res. 34: 778-787. Carter, R.E. and Klinka, K. 1992. Variation in shade tolerance of Douglas fir, western hemlock, and western red cedar in costal British Columbia. For. Ecol. Manage. 55: 87-105. Chen, H .Y.H. 1997. Interspecific responses of planted seedlings to light availability in interior British Columbia: survival, growth, allometric patterns, and specific leaf area. Can. J. For. Res. 27: 1383-1393. Chen, H .Y.H. and Popadiouk, R.V. 2002. Dynamics of North American boreal mixedwoods. Environ. Rev. 10: 137-166. Claveau, Y . , Messier, C , Comeau, P.G. and Coates, K.D. 2002. Growth and crown morphological responses of boreal conifer seedlings and saplings with contrasting shade tolerance to a gradient of light and height. Can. J. For. Res. 32: 458-468. Coates, K.D. and Burton, P.J. 1999. Growth of planted tree seedlings in response to ambient light levels in northwestern interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1374-1382. Comeau, P.G. and Bedford, L. 2002. Light under and adjacent to aspen stands and implications for growing spruce. In: Frochot, H. , Collet, C. and Balandier, P., (editors). Popular summaries from the fourth international conference on forest vegetation management. 17-21 June 2002, Nancy, France. Institut National de la Recherche Agronomique. p 177-179. 69 Comeau, P.G., Braumandl, T.F. and Xie, C.Y. 1993. Effects of overtopping vegetation on light availability and growth of Engelmann spruce (Picea engelmannii) seedlings. Can. J. For. Res. 23: 2044-2048. Comeau, P.G., Kabzems, R., McClarnon, J. and Heineman, J. 2005. Implications of selected approaches for regenerating and managing western boreal mixedwoods. For. Chron. 81: 559-574. Coomes, D.A. and Grubb, P.J. 2000. Impact of root competition in forests and woodlands: a theoretical framework and review of experiments. Ecol. Mon. 70: 171 -207. DeLong, C , MacKinnon, A . and Jang, L. 1990. A field guide for site identification and interpretation of ecosystems of the northeast portion of Prince George Forest Region. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Land Management Handbook No. 22. Dix, R.L. and Swan, J. A . 1971. The role of disturbance and succession in upland forest at Candle Lake, Saskatchewan. Can. J. Bot. 49: 657-676. Drever, C.R. and Lertzman, K.P. 2001. Light-growth response of costal Douglas-fir and western redcedar saplings under different regimes of soil moisture and nutrients. Can. J. For. Res. 31: 2124-2133. Environment Canada. 2004. Climate normals and averages. Available at: http://www.climate.weatheroffice.ec.gc.ca/climate_normals/index_e.html. Last accessed: March 8, 2005. Finney, D.J. 1941. On the distribution of a variate whose logarithm is normally distributed. Supplement to the Journal of the Royal Statistical Society 7: 155-161. Frazer, G.W., Canham, C D . and Lertzman, K.P. 1999. Gap light analyzer (GLA), version 2: imaging software to extract canopy structure and gap light indices from true-colour fisheye photographs. Simon Fraser University, Burnaby, B.C., and the Institute of Ecosystem Studies, Millbrook, N . Y . 70 Frazer, G.W., Lertzman, K.P. and Trofymow, J.A. 2000. Canopy openness and leaf area in chronosequences of coastal temperate rainforests. Can. J. For. Res. 30: 239-256. Fricke, K . 1904. Licht- und Schattenholzarten, ein wissenschaftlige nicht begriidetes Dogma. Centralblatt fur das gesamte Forstwesen 30: 315-325. Gendron, F., Messier, C. and Comeau, P.G. 1998. Comparison of various methods for estimating mean growing season percent photosynthetic photon flux density in forest. Agric. For. Meteorol. 92: 55-70. Green, D.F., Kneeshaw, D.D., Messier, C , Lieffers, V. , Cormier, D., Doucet, R., Coates, K.D. , Groot, A. , Grover, G. and Calogeropoulos, C. 2002. Modelling silvicultural alternatives for conifer regeneration in boreal mixedwood stands (aspen/white spruce/balsam fir). For. Chron. 78: 281-295. Gustafson, F.G. 1943. Influence of light upon tree growth. J. For. 41: 212-213. Hilborn, R. and Mangel, M . 1997. The ecological detective: confronting models with data. Princeton University Press, Princeton, New Jersey. 309 p. Hunt, R. 1982. Plant growth curves: the functional approach to plant growth analysis. Edward Arnold, London. 248 p. Hurvich, C M . and Tsai, C.-L. 1989. Regression and time series model selection in small samples. Biometrika 76: 297-307. Kabzems, R. and Garcia, O. 2004. Structure and dynamics of trembling aspen - white spruce mixed stands near Fort Nelson, B.C. Can. J. For. Res. 34: 384-395. Kalischuk, M . L . 2004. Influence of site quality and overstory age on the growth of understory white spruce in boreal mixedwood stands [M.Sc. Thesis]: University of Alberta, Edmonton. 117 p. 71 Kayahara, G.J., Chen, H.Y.H. , Klinka, K . and Coates, K .D. 1996. Relations of terminal growth and specific leaf area to available light in naturally regenerated seedlings of logdepole pine and interior spruce in central British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Research Report 09. Kimmins, J.P. 1996. Forest ecology, a foundation for sustainable management. Prentice Hall. 596 p. Korstian, C. and Coile, C. 1938. Plant competition in forest stands. Duke University Forestry Bulletin 3: 1-125. Landhausser, S.M., Desrochers, A . and Lieffers, V.J . 2001. A comparison of growth and physiology in Picea glauca and Populus tremuloides at different soil temperatures. Can. J. For. Res. 31: 1922-1929. Larsen, D.R. and Kershaw, J.A., Jr. 1996. Influence of canopy structure assumptions on predictions from Beer's law. A comparison of deterministic and stochastic simulations. Agric. For. Meteorol. 81: 61 - 77. Lee, C.Y. 1982. Comparison of two correction methods for the bias due to the logarithmic transformation in the estimation of biomass. Can. J. For. Res. 12: 326-331. Lieffers, V.J . and Beck, J.A., Jr. 1994. A semi-natural approach to mixedwood management in the Prairie Provinces. For. Chron. 70: 260-264. Lieffers, V.J . and Stadt, K. 1994. Growth of understory Picea gluca, Calamagrostis Canadensis, and Epilobium angustifolium in relation to overstory light transmission. Can. J. For. Res. 24: 1193-1198. Lieffers, V.J . , Stadt, K.J . and Navratil, S. 1996. Age structure and growth of understory white spruce under aspen. Can. J. For. Res. 26: 1002-1007. 72 Logan, K.T. 1969. Growth of tree seedlings as affected by light intensity. IV. black spruce, white spruce, balsam fir, and eastern white cedar. Canadian Forestry Service. Publication No. 1256. Man, R. and Lieffers, V.J . 1999. Effects of shelterwood and site preparation on microclimate and establishment of white spruce seedlings in a boreal mixedwood forest. For. Chron. 75: 837-844. Meidinger, D. and Pojar, J. 1991. (compilers and editors). Ecosystems of British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Special Report Series No. 6. Oliver, C D . and Larson, B.C. 1996. Forest stand dynamics, update edition. John Wiley & Sons, Inc, New York. 544 p. Pacala, S.W., Canham, C D . , Silander, J.A., Jr. and Kobe, R.K. 1994. Sapling growth as a function of resources in a north temperate forest. Can. J. For. Res. 24: 2172-2183. Pojar, J., Meidingerm, D. and Klinka, K . 1991. Concepts. In: Meidinger, D. and Pojar, J. (editors and compilers). Ecosystems of British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Special Report Series No. 6, p. 9-37. Pritchard, J .M. 2003. The effect of opening size on light, temperature and growth of white spruce under a trembling aspen canopy. [M.Sc. Thesis]: University of Alberta, Edmonton. 144 p. Rowe, J.S. 1972. Forest regions of Canada. Department of Environment, Canadian Forest Service, Ottawa. Publication No. 1300. 172 p. Stadt, K.J . and Lieffers, V.J . 2000. MIXLIGHT: a flexible light transmission model for mixed-species forest stands. Agric. For. Meteorol. 102: 235-252. Stadt, K.J. , Lieffers, V.J . , Hall, R.J. and Messier, C. 2005. Spatially explicit modeling of PAR transmission and growth of Picea glauca and Abies balsamea in the boreal forests of Alberta and Quebec. Can. J. For. Res. 35: 1-12. 73 Stroll, P., Weiner, J. and Schmid, B. 1994. Growth variation in a naturally established population oiPinus sylvestris. Ecology 75: 660-670. Walters, M.B. and Reich, P.B. 1996. Are shade tolerance, survival, and growth linked? Low light and nitrogen effects on hardwood seedlings. Ecology 77: 841-853. Welham, C , Seely, B. and Kimmins, H. 2002. The utility of the two-pass harvesting system: an analysis using the ecosystem simulation model FORECAST. Can. J. For. Res. 32: 1071-1079. Williams, H. , Messier, C. and Kneeshaw, D.D. 1999. Effects of light availability and sapling size on the growth and crown morphology of understory Douglas-fir and lodgepole pine. Can. J. For. Res. 29: 222-231. Wright, E.F., Coates, K.D. , Canham, C D . and Bartemucci, P. 1998. Species variability in growth response to light across climatic regions in northwestern British Columbia. Can. J. For. Res. 28: 871-886. 74 Chapter 4: Regional Variation in the Light-Growth Response of Understory Trees: Effect of Climate or Canopy Type?4 Introduction The relationship between light availability and growth has been shown to exhibit regional variability for species with wide geographic and climatic ranges (e.g. Carter and Klinka 1992; Wright et al. 1998; Drever and Lertzman 2001; Pritchard 2003). In Chapter 3, the growth-light relationship for white spruce ((Picea glauca [Moench] Voss)) and interior spruce ((Picea glauca x engelmannii) in western Canada, was found to be approximately linear in four out of nine geographic regions. Strongly asymptotic relationships were observed in the other five regions. Regional variability in growth responses may affect successional dynamics in forests and they clearly need to be understood to enable successful management of understory spruce. It is also central to understand the mechanisms controlling regional variability in order to assess the portability of regionalized knowledge. In this Chapter, two hypotheses regarding regional variation in the light-growth relationship for understory spruce in northern-interior western Canada are explored. The first hypothesis (Climate Hypothesis) is that macro-climatic variables explain the regional variability. It is generally accepted that macro climate determines the ranges, composition, and competition of vegetation, and that the limits of a vegetation type or a species often are determined by an extreme climatic variable, such as growing season length, temperature, or precipitation (e.g. Woodward 1992; Kimmins 1996). Radial increment of mature trees along climatic gradients is correlated to macro-climatic variables (e.g. Peterson and Peterson 2001; Peterson et al. 2002; Bunn et al. 2005; Littell and Peterson 2005). Macro-climatic variables have also been shown to be important for the abundance and vigor of understory species. For example, Adams and Loucks (1971) found that the amount of understory eastern hemlock (Tsuga canadensis L. (Carriere)) 4 A version of Chapter 4 is submitted to Journal of Ecology. Dr. David Coates is co-author on this paper. 75 regeneration was correlated to summer air temperatures in southwestern Wisconsin. In summary, there is convincing information to support the Climate Hypothesis. The second hypothesis (Canopy-Type Hypothesis) is that different canopy-types control the regional variation in light-growth relationships. Specifically, this study tests the hypothesis that aspen-dominated and conifer-dominated canopies influence understory tree growth differently. This hypothesis is a widely held belief among many boreal foresters and ecologists but has never been formally tested. The leaf-off period in boreal mixedwood stands may account for increased carbon gain of understory spruce compared to spruce under conifer-doniinated canopies (Constabel and Lieffers 1996). There are also differences in light quality beneath aspen-dominated and conifer-dominated canopies. Messier et al. (1998) found that diffuse light accounted for a much higher proportion of the total light availability under aspen and birch canopies than under mixed conifers, while under mixed-conifer canopies large sunfleck events around midday made up much larger amounts of the total light availability. It is also clear that forest floor composition and nutrient availability under aspen-dominated canopies and coniferous-dominated canopies differ (e.g. Peterson and Peterson 1992; Hannam et al. 2004; Jerabkova et al. 2006). In summary, there are numerous factors that support the Canopy-Type Hypothesis. The objective of this paper is to explore the relative strengths of the Climate Hypothesis and the Canopy-Type Hypothesis using a model selection approach. Two analyses (Analysis 1 & Analysis 2) were undertaken. Each analysis was associated with a dataset that consisted of a collection of published light-growth relationships which exhibit variation in curve shape. Methods and analysis Analysis approach The dataset associated with Analysis 1 (Dataset 1) consisted of nine light-growth relationships developed in Chapter 3. The dataset associated with Analysis 2 (Dataset 2) consisted of a larger collection of published light-growth relationships from the northern part of western Canada. Both analyses were performed in a framework of multiple working hypotheses where each hypothesis was represented by one or more mathematical 76 models and the support for each model was determined with a model selection criterion. A l l models were fitted with a normal probability density function and maximum likelihood in SAS Version 8.2 (SAS Institute Inc., Cary, N.C.). After all models were fitted, the best approximating model was selected using the AICc model selection criterion (Hurvich and Tsai 1989). AICc was utilized because it was developed for model selection in small samples, allows comparison of non-nested models, and penalizes models for increasing numbers of parameters (Hurvich and Tsai 1989; Burnham and Anderson 2002). When model selection is performed with AICc the best approximating model will have the lowest AICc- The remainder of the Methods and Analysis section is structured to match the analysis and consists of four sections, one for each dataset and one for each analysis. These data come from the study of light availability and growth of understory spruce undertaken in Chapter 3. The regression models in Chapter 3 were parameterized with data collected in 9 geographic regions in western sub-boreal and boreal Canada. The regression models have the following form: where the predicted increment is either height (cm/5-years) or radial (mm/5-years), GLI is a Gap Light Index which represents the growing season light availability expressed as percent full sunlight and A o is the initial tree diameter measured 10 cm above the root collar. Parameters a and c were estimated with data from all 9 geographic regions while parameters b and d are regional estimates. Analysis 1 Analysis 1 investigated how well the Canopy-Type Hypothesis and the Climate Hypothesis were supported by Dataset 1. Additionally, Analysis 1 tested how well the Climate Hypothesis explains the variation in the predicted increment in full light. As dependent variables Analysis 1 utilized predicted increment (height and diameter) at full Dataset 1 Y = a + b x D 10 [1] 77 light availability for a tree with Z)io=2.5cm and two measures of curve shape: parameter c which is responsible for the regional variation in curve shape and percentage of maximum increment obtained at 50% light availability. Consequently, a total of 6 dependent variables were utilized. The climatic predictor variables were: Growing Degree Days above 5° (GDD 5), May-September precipitation (mm/year) (precipitation), and May-September Moisture Deficit (MD) calculated according to Thornthwaite and Mather (1955) and Thornthwaite and Mather (1957). These climatic variables were chosen because they have been shown to exhibit correlation with tree growth (e.g. Peterson et al. 2002; Gustafson et al. 2003; Littell and Peterson 2005) and because they were available for all locations. Detailed site and climatic information can be found in Table 4.1. Ten models representing the Climate Hypothesis, one Null model, and one model representing the Canopy-Type Hypothesis were fitted to Dataset 1 (Table 4.2). These 12 models were developed prior to analysis. Models 1-3 are simple linear regressions with zero intercept and GDD5, precipitation, or M D as individual predictor variables. Models 4-6 are the same as models 1-3 but allow for non-zero intercepts. Models 7-10 are multiple linear regression models with zero or non-zero intercept and GDD5 and precipitation or GDD5 and M D as predictor variables. These initial 10 models represent different formulations of the Climate Hypothesis. Model 11 is the Null model which represents an overall mean. Model 11 represents the possibility that the variation is sampling related or related to factors not included in the analysis. Model 12 represents the Canopy-Type Hypothesis. Model 12 was fitted with 0-1 indicator variables and simply represents two means, one for aspen-dominated canopies and one for conifer-dominated canopies. Models 1-11 (Climate Hypothesis and Null Model) were fitted to all 6 dependent variables. As there is, by definition, no influence of canopy-type in full light, Model 12 (Canopy-Type Hypothesis) was only fitted to the two dependent variables relating to the curve shape. 78 Table 4.1. Climatic and site information. The climatic data is climatic normals (1971-2000) (Environment Canada 2004). Growing Degree Days > 5° ( G D D 5 ) , Moisture Deficit ( M P ) , growing season (May-September). Ecosystem Sampling Site type Precipitation Growing season Mean annual G D D 5 G D D 5 M D classification Location classification (mm) precipitation temperature full growing growing (mm) (C°) year season season (mm) B H ( , j 52°30 'N d (mesic) 509 321 1 1400 1324 -155 B M ( 2 ) 102°80'W 56°40 'N d (mesic) 402 269 1 1307 1230 -196 B M ( 2 ) 116°80 'W 55°20 'N d (mesic) 479 337 2 1302 1222 -127 B W B S d k l ( 3 ) 112°90 'W 59°40 'N 01 (mesic) 419 218 0 645 630 -189 B W B S d k 2 ( 3 ) 128°70 'W 58°10 'N 129°10 'W 01 (mesic) 419 192 -1 942 908 -208 B W B S m w 2 ( 4 ) 59°10 'N 01 (mesic) 452 311 -1 1320 1210 -161 E S S F m c ( 3 ) 123°20 'W 54°50 'N 01 (mesic) 656 293 1 655 635 -113 S B S d k ( 3 ) 126°70 'W 54°40 'N 01 (mesic) 513 224 4 1194 1122 -225 SBSmc2 ( 3 ) 126°80'W 54°30 'N 127°70'W 01 (mesic) 555 240 3 1063 1009 56 (1) Beckingham et al. (1996), (2) Beckingham and Archibald (1996), (3) Banner et al. (1993), and (4) DeLong et al. (1990). - 0 Table 4.2. Models that explain regional variation in the light-growth relationship. Radial Increment (RI), Height Increment (HI), Growing Degree Days >5° (GDD 5), May-September Precipitation (Precip), May-September Moisture Deficit (MD), and Not Applicable (NA). The highest ranking model has the lowest A I C C . Numbers are Rank (AICc, AAIC C ) . Model, Dependent variable Parameter c Parameter c %RI at • %HIat Full Light RI Full Light HI (Y) (RI) (HI) 50%light 50%light (100% light) (100% light) (1) Y=bxGDD 5 2 (-43.7, 1.04) 3 (-38.6, 9.4) 2 (70.3, 1.2) 5 (69.1 , 16.7) 3 ( 4 2 . 2 , 3 . 9 ) 7 ( 9 5 . 2 , 9 ) (2) Y=bxMD 11 (-34.1, 10.6) 10 (-29.9, 18.2) 12 (94, 24.9) 12 ( 9 5 . 8 , 4 3 . 4 ) 11 ( 6 4 . 9 , 2 6 . 6 ) 1 1 (109 .3 , 23 .1 ) (3) Y=bx Precip 4 (-39.7, 5) 7 (-33, 15.1) 6 (74 .3 ,5 .2 ) 8 ( 7 8 . 2 , 2 5 . 7 ) 8 (50.4, 12.1) 8 ( 9 5 . 6 , 9 . 3 ) (4) Y=a+bxGDD5 5 (-39.6, 5.1) 4 ( -38 .1 ,9 .9 ) 4 (72 .7 ,3 .7 ) 6 (69.3, 16.9) 1 ( 3 8 . 3 , 0 ) 2 (87.8, 1.6) (5) Y=a+bxMD 12 (-33.3, 11.4) 12 (-27.2, 20.8) 11 (85, 15.9) 1 1 ( 8 5 . 8 , 3 3 . 4 ) 9 (51.8, 13.5) 5 ( 9 0 . 8 , 4 . 5 ) (6) Y=a+b* Precip 8 (-36.2, 8.5) 11 (-29.8, 18.2) 9 ( 7 9 , 9 . 9 ) 10 ( 8 2 . 8 , 3 0 . 4 ) 10 (52.2, 13.9) 4 ( 9 0 . 6 , 4 . 3 ) (V) Y=bxGDD 5+ bxMS 3 (-41.1, 3.6) 5 (-34.9, 13.1) 5 (72 .9 ,3 .9 ) 2 (64.5, 12.1) 5 ( 4 2 . 8 , 4 . 5 ) 10 (98.4, 12.2) (8) Y=bxGDD 5+bxPrecip 6 (-38.9, 5.8) 6 (-34.8, 13.3) 1 ( 6 9 . 1 , 0 ) 4 (68.3, 15.9) 6 ( 4 5 . 4 , 7 . 1 ) 9 (97.7 , 11.4) (9) Y=a+bxGDD5+bxMS 7 (-37.3, 7.4) 2 (-39, 9) 8 ( 7 8 . 8 , 9 . 8 ) 3 (67.7, 15.3) 4 (42.4, 4) 6 (94.8 , 8.5) (10) Y=a+bxGDD5+bxPrecip 10 (-34.5, 10.2) 8 (-32.4, 15.7) 7 ( 7 5 . 9 , 6 . 8 ) 7 ( 7 5 . 2 , 2 2 . 8 ) 2 ( 4 0 . 7 , 2 . 3 ) 3 (88 .1 , 1.8) (11) Y=a 9 (-36, 8.7) 9 (-30.1, 17.9) 10 (80.6, 11.6) 9 ( 8 2 . 2 , 2 9 . 8 ) 7 (47.9, 9.5) 1 ( 8 6 . 2 , 0 ) (12) N A N A Y=a(aspen)+a( conifers) 1 (-44.7, 0) 1 (-48, 0) 3 (71 .6 ,2 .6 ) 1 ( 5 2 . 4 , 0 ) Dataset 2 This dataset was created through a literature review on spruce in northwestern interior Canada. The review included white spruce (Picea glauca [Moench] Voss), black spruce (Picea mariana (Mill.) BSP), Engelmann spruce (Picea engelmannii Parry), interior spruce (a complex of Engelmann spruce and white spruce hybrids), and hybrid spruce (a complex of hybrids between interior spruce and Sitka spruce (Picea sitchensis (Bong.) Carr). Dataset 2 contains a compilation of all the regression models that predict height or diameter increment of an individual tree as a function of light availability. No distinctions were made between different methods of light measurement, even though it is acknowledged that different methodologies can create some divergence in light availability estimates (e.g. Comeau et al. 1998). To facilitate comparison, the units of the height increment models were transformed to cm/year and diameter increments were transformed to mm/year. For diameter increment, a total of 20 regional models from 7 studies were included. The included studies and their associated number of models were: This dissertation 9, Chen (1997) 1, Coates and Burton (1999) 1, Comeau and Bedford (2002) 1, Groot (1999) 3, Pritchard (2003) 2, Wright et al. (1998) 3. For height increment, a total of 25 regional models from 10 studies were included. The included studies and their associated number of models were: This dissertation 9, Chen (1997) 1, Coates and Burton (1999) 1, Comeau and Bedford (2002) 1, Groot (1999) 3, Kayahara et al. (1996) 3, Pritchard (2003) 2, Stadt et al. (2005) 1, Wang et al. (2000) 1,Wright et al. (1998) 3. A l l included studies were from approximately mesic sites where site conditions, to a large extend, should be determined by macro-climate rather than topographic factors. Where available the climatic variables were obtained directly in the publications, otherwise climatic normals from the nearest Environment Canada Weather Station were used (Environment Canada 2004). Two regional models from Wright et al. (1998) had to be excluded because insufficient climatic data was available. Regression models from Kalischuk (2004) and Lieffers and Stadt (1994) had to be excluded because only trees at low light levels were measured. 81 Analysis 2 Analysis 2 investigated how well the Canopy-Type Hypothesis and the Climate Hypothesis were supported. Analysis 2 utilized the same approach as Analysis 1 but the number of models was reduced from 12 to 4. Models 1-2 represent the Climate Hypothesis and are simple linear regressions with G D D 5 . Model 3 (Null model) represented the possibility that the variation is sampling related or related to factors not included in the analysis. Model 4 represented the Canopy-Type Hypothesis. The regression models in Dataset 2 have different functional forms and originate from trees of different sizes. Thus, percentage of increment (height and diameter) obtained at 50% light availability were the only two dependent variables used. To ensure that the results of Analysis 2 were not solely driven by findings from an individual study, the analysis was performed on three subsets of Dataset 2: (1) the complete dataset, (2) the dataset without the findings of Groot (1999) (excluded because growth in open conditions were largely determined by frost damage), and (3) the dataset without the models from Chapter 3. Results Analysis 1 For diameter increment, the variation in parameter c (determining curve shape) was best approximated by Model 12 and Model 1 (Table 4.2). AAICc for these two models is 1.2 which indicates that the support for these two models is similar (Burnham and Anderson 2002). Model 12 represents the Canopy-Type Hypothesis, while Model 1 explains the variation with GDD5 (Figure 4.1 A). For height increment, the variation in parameter c was best approximated with Model 12 and the remaining models have AAICc-values greater than 9 which indicate that they fail to explain a substantial part of the variation displayed in the data. Nevertheless, it should be noted that G D D 5 was the best climatic predictor variable. The percentage of diameter increment obtained at 50% light availability was best explained by Model 8, but Model 1 and Model 12 had similar AICc-values and the support for these three models were similar. Model 8 includes GDD5 and precipitation, Model 1 includes G D D 5 , and Model 12 includes canopy-type. The variation in the percentage of height increment obtained at 50% light availability was best 82 approximated with Model 12 while the remaining models had AAICc-values greater than 12. Thus, the variation in the percentage of potential height increment obtained at 50% light was best explained by the Canopy-Type Hypothesis. For diameter and height increment in full light there is, by definition, no effect of canopy-type. Diameter increment in full light is best explained by G D D 5 by Model 4. Model 10, which in addition to G D D 5 includes precipitation as a predictor variable, had a AAICc of 2.3. Thus, it is plausible that precipitation has an effect on diameter increment. The variation in height increment at full light was best explained by the Null model (Model 11), which is the mean of all the values. This implies that the remaining relationships are weak. The best climatic models were Model 4 with G D D 5 and Model 10 with G D D 5 and precipitation. These results were relatively robust in term of initial tree diameter and did not change substantially for other values of initial tree diameter (e.g. Di 0 =l or D]0=3). Analysis 1 illustrates that canopy-type best explains the variation in the shape of light-growth relationships. Simultaneously, the variation in the shape of the light-growth relationship was also well correlated to the number of growing degree days. This is illustrated in Figure 4.1. This dataset did not allow us to fully tease these two effects apart because there was a correlation between the growing degree days and the canopy-type. This can be seen in Figure 4.1, where all the observations with number of growing degree days below 1100 have coniferous-dominated canopies and all the studies above 1100 growing degree days have aspen-dominated canopies. 83 Figure 4.1. Plots of Analysis 1 results for growing degree days (GDD5). A : Radial increment parameter c, regression line: RI parameter c = 0.00004987><GDD5 (PO.0001, r2= 0.58); B: Height increment parameter c, regression line: HI parameter c = -0.04804 + 0.00009894xGDD5 (P=0.0023, r2=0.76); C: % Radial increment obtained at 50% light availability, regression line: %RI at 50% light = 0.06052xGDD5 (PO.0001, r2=0.68); D: %HI obtained at 50% light availability, regression line: %HI at 50% light = 0.0714xGDD5 (PO.0001, r2=0.77); E: Maximum Radial increment (100% light), regression line: Maximum RI = 5.529 + 0.00772xGDD5 (PO.0012, r2=0.80); F: Maximum HI (100% light), regression line Maximum HI = 115.25 + 0.040xGDD5 (PO.1257,r2=0.30). 84 Analysis 2 For height increment, the four models (Table 4.3) were fitted to three datasets: (1) the complete dataset (Dataset 2), (2) Dataset 2 without the study of Groot 1999, and (3) Dataset 2 without Chapter 3 results. For all three height-increment datasets, the variation in percentage of potential height increment obtained at 50% light is best approximated with the canopy-type model (Model 4). The remaining models have AAICc in excess of 10, which indicates that they fail to explain a substantial amount of the variation in the data (Burnham and Anderson 2002). The difference between the two canopy-types is illustrated in Figure 4.2. In the two datasets that include the findings of Chapter 3, Model 1 and Model 2 generally have slightly better AICc than the overall mean (Model 3). In the smaller dataset the overall mean (Model 3) and the best model with G D D 5 (Model 1 or Model 2) have similar support. Thus, the correlation with G D D 5 that was observed in Analysis 1 is not strongly supported in Analysis 2. Consequently, the results of Analysis 2 downplay the effect of G D D 5 and mainly favors the Canopy-Type Hypothesis. For diameter increment, the four models (Table 4.3) were fitted to two datasets. The first dataset is the complete Dataset 2, while the second dataset excludes the findings from Chapter 3. In the complete Dataset 2 the percentage of diameter increment obtained at 50% light is best explained by the canopy-type model (Model 4) (Table 4.3). In the reduced dataset there is equal support for the Null model (Model 3) and the canopy-type model (Model 4). Thus, without the findings from Chapter 3 the Canopy-Type Hypothesis is less supported. On the other hand, the reduced dataset is not in disagreement with the Canopy-Type Hypothesis and the lower support can likely be attributed to a smaller sample size. In conclusion, Analysis 2 indicates that the percentage of potential diameter increment obtained at 50% light availability is best explained by the Canopy-Type Hypothesis. It should be noted that none of the results from Analysis 2 change substantially i f the dependent variable is altered slightly (e.g., percentage increment obtained at 30% light or 60% light). 85 Table 4.3. Models that explain regional variability in increment obtained at 50% light. Radial Increment (RI), Height Increment (HI), Growing Degree Days >5° (GDD S). The highest ranking model has the lowest A I C C . Numbers are Rank (AIC C , AAIC C ) . Model, Dependent variable %RI at 50%light (All data, n=20) %HI at 50%light (All data, n=25) %HI at 50%light (data except Groot 1999 n=22) %RI at 50%light (Data except Chapter3 n=ll) %HI at 50%light (Data except Chapter3 n=16) 0 ) Y=bxGDD 5 4 (-14, 14.3) 4 (-11.3, 31.9) 4 (-6.5, 27.7) 4 (-1.1, 8.9) 4 (-4.2, 18.2) (2) Y=a+bxGDD 5 2 (-20, 7.2) 2 (-20.6, 22.7) 2 (-15, 19.2) 3 (-6.3, 3.7) 3 (-10.5, 11.9) (3) Y=a 3 (-17.6, 10.7) 3 (-17.1, 26.1) 3 (-13.7, 20.6) 1(-10, 0) 2 (-12.2, 10.2) (4) Y=a(aspen)+a(conifers) 1 (-27.1, 0) 1 (-43.3, 0) 1 (-34.2, 0) 2 (-9.6, 0.4) 1 (-22.4, 0) 100 90 g> 5> 80 A o m CD "O CD C CO -•—» . Q O 70 60 50 H 40 A. Diameter increment • Aspen-dominated canopies o Conifer-dominated canopies O cP 600 O O 800 O o 1000 1200 GDDC o o 1400 1600 O) o m 100 90 80 CD -a 70 o c s s £ 60 X 50 40 B. Height increment o • • • o • o ° o o o o o o o o 400 600 800 1000 1200 GDDC 1400 1600 1800 2000 Figure 4.2. Percentage of maximum diameter (DI) and height (HI) increment obtained at 50% light availability. The points represent the studies included in Dataset 2. Growing Degree Days > 5°C (GDD 5). 87 CD CD .>. E c CD E 0 i o c £ CD .c 15 CZ < 60 50 40 30 A 20 10 A. Absolute growth conifer-dominated canopies 100 Light (%) Coates and Burton (1999) Chen (1997) • Kayahara et al. (1996) MD v Kayahara et al. (1996) SD — Kayahara et al. (1996) FM • Wright et al. (1998) ESSFwv Wright et al. (1998) ICHwc Wright etal. (1998) ICHvc Wright etal. (1998) ICHmc2 Wright et al. (1998) Sb BWBSdk2 Astrup and Coates BWBSdkl O — Astrup and Coates BWBSdk2 • Astrup and Coates ESSFmc Astrup and Coates SBSmc2 100 Light (%) Figure 4.3. Height increment regression models from conifer-dominated stands. The graphs in (A) represents published models of individual tree increment as a function of light. To obtain same units of the predicted values some models had to be transformed (e.g. from cm/5-years to cm/year). The graphs in (B) are transformations of the graphs in (A), where relative increment was calculated as the increment at a given light level divided by the maximum increment. Values of other predictor variables than light; Astrup and Coates (in review) = Chapter 3 (Diameter = 2.5cm). 88 A. Absolute growth aspen-dominated canopies Lieffers and Stadt (1994) Pritchard (2003) Slave Lake Pritchard (2003) Siphon Creek Groot (1999) Halsey Groot (1999) Hellyer bare-root Groot (1999) Hellyer plugs Kalischuk (2004) 01 Kalischuk (2004) 03 Kalischuk (2004) 06 Stadt et al. (2005) Wang et al. (2000) Comeau and Bedford (2002) Astrup and Coates BM (CL) Astrup and Coates BWBSmw2 Astrup and Coates BH Astrup and Coates BM (PR) Astrup and Coates SBSdk 20 40 60 80 100 Light (%) Pritchard (2003) Slave Lake Pritchard (2003) Siphon Creek Groot (1999) Halsey Groot (1999) Hellyer bare-root Groot (1999) Hellyer plugs Stadt et al. (2005) Wang et al. (2000) Comeau and Bedford (2002) Astrup and Coates BM (CL) Astrup and Coates BWBSmw2 Astrup and Coates BH Astrup and Coates BM (PR) Astrup and Coates SBSdk Light (%) Figure 4.4. Height increment regression models from aspen-dominated stands. The graphs in (A) represents published models of individual tree increment as a function of light. To obtain same units of the predicted values some models had to be transformed (e.g. from cm/5-years to cm/year). The graphs in (B) are transformations of the graphs in (A), where relative increment was calculated as the increment at a given light level divided by the maximum increment. Values of other predictor variables than light; Pritchard (2003) Slave Lake CSA=10000cm2, Pritchard (2003) Siphon creek (CSA=25000 cm2), Stadt et al. (2005) (height = 1.5m), Comeau and Bedford (2002) (height = 1.5). Astrup and Coates (in review) = Chapter 3 (Diameter = 2.5cm). 89 10 <D 8 | 6 E CO CO £ 2 A. Absolute growth conifer-dominated canopies Light (%) 1.0 & 0.8 E £ 0.6 d) E ro ro 0.4 c ro CD ro 5> 0.2 0.0 B. Relative growth 20 40 60 Light (%) 80 100 - • Coates and Burton (1999) O Chen (1997) Wright et al. (1998) ESSFvw v Wright et al. (1998) ICHwc Wright eta l . (1998)ICHvc - • Wright eta l . (1998) ICHmc2 Wright et al. (1998) Sb BWBSdk2 - O Astrup and Coates B W B S d k l A Astrup and Coates BWBSdk2 Astrup and Coates E S S F m c • Astrup and Coates SBSmc2 100 Figure 4.5. Diameter increment regression models from conifer-dominated stands. The graphs in (A) represents published models of individual tree increment as a function of light. To obtain same units of the predicted values some models had to be transformed (e.g. from mm/5-years to mm/year). The graphs in (B) are transformations of the graphs in (A), where relative increment was calculated as the increment at a given light level divided by the maximum observed increment. Values of other predictor variables than light; Astrup and Coates (in review) = Chapter 3 (Diameter = 2.5cm). 90 A. Absolute growth aspen-dominated canopies , y 20 40 60 Light (%) 80 100 B. Relative growth aspen-dominated canopies Pritchard (2003) Slave Lake O Pritchard (2003) Siphon Creek Groot (1999) Halsey Groot (1999) Hellyer bare-root Groot (1999) Hellyer plugs — • Comeau and Bedford (2002) Astrup and Coates B M (CL) Astrup and Coates BWBSmw2 Astrup and Coates BH Astrup and Coates B M (PR) Astrup and Coates SBSdk 20 40 60 Light (%) 80 100 Figure 4.6. Diameter increment regression models from aspen-dominated stands. The graphs in (A) represents published models of individual tree increment as a function of light. To obtain same units of the predicted values some models had to be transformed (e.g. from mm/5-years to mm/year). The graphs in (B) are transformations of the graphs in (A), where relative increment was calculated as the increment at a given light level divided by the maximum increment. Values of other predictor variables than light; Pritchard (2003) Slave Lake CSA=10000cm2, Pritchard (2003) Siphon creek (CSA=25000 cm2), Astrup and Coates (in review) — Chapter 3 (Diameter = 2.5cm). 91 A comparison of all regression models included in Dataset 2 plus the models from Kalischuk (2004), Lieffers and Stadt (1994), and Wright et al. (1998) (ESSFwv, ICHvc) illustrates that there is great variation in both: (1) the increment observed at a given light level (horizontal distribution of graphs), and (2) the general shape of the light-growth response curve (non-parallel graphs) (Figure 4.3-4.6). To facilitate an easier comparison of the curve shapes the increment relative to the maximum predicted increment is graphed in Figure 4.3B, 4.4B, 4.5B and 4.6B. Discussion The model selection process indicated that the light-growth relationship of juvenile spruce trees across broad geographic and climatic ranges was most influenced by canopy-type and growing degrees days above 5° C (GDD5). Canopy-type best explained the observed variability in shape of the light-increment relationship. G D D 5 appeared to strongly influence the growth rate of spruce trees in full sunlight. The fact that the Canopy-Type Hypothesis better explains the variation in curve shape indicates that the local effect of canopy-type is stronger than the broad-scale climatic variation. There is no doubt that macro-climate influences understory tree growth, but this study illustrates that the mediating effects of canopy-type on micro-climate is more important than the macro-climatic variation within the investigated climatic gradient. The finding that deciduous-dominated and conifer-dominated canopies influence the shape of the light-increment relationship for understory spruce trees can be explained in several ways. Much higher light availability has been observed in the understory of aspen stands in the spring and fall leaf-off periods compared to summer and this could account for a large carbon gain by understory spruce in boreal mixedwood stands compared to spruce under conifer-dominated canopies (Constabel and Lieffers 1996). Simultaneously, white spruce have been shown to be relatively tolerant towards low soil temperatures (Landhausser et al. 2001) and can thus take advantage of increased light availability during the leaf-off period even when the soil temperature is low (Lieffers et al. 2004). A linear light-growth relationship indicates that growth at lower light levels is relatively more limited than in an asymptotic light-growth relationship. This suggests that 92 availability of below ground resources might influence the light-growth relationship of understory spruce. Shadehouse experiments (Gustafson 1943; Shirley 1945; Logan 1969) where there is no leaf-off period have resulted in light-increment (diameter and height) relationships with a similar asymptotic shape as observed for spruce grown under aspen-canopies (e.g. Lieffers et al. 1996; Man and Lieffers 1999; Stadt et al. 2005; Chapter 3) (Figure 4.4). In shadehouse experiments, belowground competition is generally low while nutrient and moisture availability are high. In boreal mixedwood forests, it is well established that the forest floor and soil characteristics differ between deciduous-dominated and conifer-dominated stands. Aspen and birch litter have been shown to have lower C/N ratios and a generally higher nutrient concentration than spruce litter (e.g. Flanagan and Van Cleve 1983; Pastor et al. 1987; Jerabkova et al. 2006). Compared to conifer-dominated stands, deciduous-dominated stands generally have forest-floor organic matter of a higher quality, less organic matter accumulation (Flanagan and Van Cleve 1983; Pare and Bergeron 1996; Hannam et al. 2004), and higher nitrogen availability (Cote et al. 2000; Jerabkova et al. 2006). Seedling growth, nitrogen uptake, and nitrogen tissue concentrations have been found to decrease with increased C/N ratio of the forest floor substrate (Flanagan and Van Cleve 1983). Additionally, it has been shown that leaf-level photosynthesis for spruce grown at low light levels increases with leaf nitrogen content (Reich et al. 1998). Thus, increased nutrient availability in aspen-dominated stands can also be hypothesized to positively influence understory spruce growth and consequently make the relationship between light availability and growth more asymptotic. After observing a linear relationship between light availability and growth of high elevation juvenile Engelmann spruce under conifer canopies, Lajzerowicz et al. (2004) hypothesized that the non-asymptotic shape of the light-growth relationship might be caused by additionally positive effects caused by increased soil temperature in more open conditions. This hypothesis is related to the effect of G D D 5 and to differences between deciduous and coniferous canopies. In boreal mixedwoods soil temperatures under aspen-dominated canopies are generally higher than under conifer-dominated canopies (Amacher et al. 2001). This is mainly for two reasons. First, canopy spruce trees allow less radiation to reach the forest floor and intercept more snow than aspen canopy trees 93 (Canham et al. 1999; Amacher et al. 2001). Second, conifer-dominated stands generally have thicker forest floors that keep the soil cooler (Flanagan and Van Cleve 1983). Even though it is well established that low soil temperatures inhibits tree growth (e.g. Tryon and Chapin 1983; Landhausser et al. 2001), it has also been shown that white spruce is relatively tolerant of low soil temperatures (Landhausser et al. 2001). Under the same low light availability, Picea and Abies species growing under aspen canopies in eastern Canada have been found to have larger live crown ratios than those grown under coniferous-dominated canopies in western Canada (Claveau et al. 2002). A larger live crown ratio is generally indicative of better tree growth. Thus, the finding of Claveau et al. (2002) support the notion that understory spruce grow better under an aspen-dominated canopy than under a conifer-dominated canopy which again leads to a more asymptotic light-increment relationship. The capacity to carry higher live crown ratios can both be related to light quality differences (e.g. Messier et al. 1998) or nutrient and water availability. The analysis of data from the nine regions studied in Chapter 3 indicated that regional variation in diameter increment at full sunlight (100% light availability) was best explained by growing season length (GDD 5). Regional variation in height increment at full light was less strongly related to climatic variables than was the diameter increment. The correlation to climatic variables is not surprising as it is well established that site productivity measured by site index is correlated with macro-climatic variables and site conditions (e.g. Xu et al. 2000; Chen et al. 2002; Gustafson et al. 2003). Consequently, in the reviewed studies of the relationship between light availability and increment, it must be assumed that the increment at full light is determined by site conditions and macroclimate. On the other hand, the shape of the relationship appears to be more strongly determined by canopy-type rather than climatic variables. Additionally, it must be emphasized that there are genetic differences between populations that influence both the performance in full light and in the understory. Analysis 2 investigated the shapes of light-growth relationships in Dataset 2 but did not investigate the horizontal distribution (difference in growth rates at a given light level) of 94 graphs at full light (Figure 4.3-4.6). Analysis 1 indicates that some of the horizontal variation at full light can be explained with macro-climatic variability. For Dataset 2, another possible explanation for the observed horizontal variation (Figure 4.3-4.6) is the effect of tree size. In Figure 4.2 and 4.3 the range of tree heights is approximately 0 .1 -7 meters. Except at very low light levels, conifers in this size range generally exhibit faster growth (at a given light level) as tree size increases (e.g. Comeau et al. 1993; Williams et al. 1999; Claveau et al. 2002; Pritchard 2003;Chapter 3). Consequently, a large portion of the horizontal variation may be attributed to difference in sampled tree sizes. The majority of the reviewed regression models do not explicitly take tree size into account (Lieffers and Stadt 1994; Kayahara et al. 1996; Chen 1997; Wright et al. 1998; Groot 1999; Coates and Burton 1999) and the lowest height and diameter increment predictions generally originate from studies of small trees (<5 years) (e.g. Chen 1997; Groot 1999). For the regression models that do utilize tree size as a predictor variable, the predicted increments increase substantially with tree size (Wang et al. 2000; Comeau and Bedford 2002; Pritchard 2003; Kalischuk 2004; Chapter 3). This analysis showed that the light-growth relationship for understory spruce differs between aspen-dominated and coniferous-dominated canopies. Under aspen-dominated canopies the relationship between light availability and growth follows an asymptotic pattern where height increment increases rapidly between 0 and 50% light and then further gains in height increment are small. Diameter increment increases are less asymptotic than height increment, but the majority of diameter increment occurs below 75% light and the increase in diameter increment between 75% and 100% light is small. Contrary to this, the relationship between light and diameter or height increment for spruce grown under conifer-dominated canopies is approximately linear (slightly exponential or slightly asymptotic). While the shape of the relationship appears to be mostly influenced by the canopy-type, the maximum increment observed at full light is likely determined by site conditions and macro-climatic variables. This analysis indicated that the growing season length ( G D D 5 ) best explained this variation. 95 Chapter 4 references Adams, M.S. and Loucks, O.L. 1971. Summer air temperatures as a factor affecting net photosynthesis and distribution of eastern hemlock (Tsuga canadensis L. (Carriere) in southwestern Wisconsin. Amer. Midi . Nat. 85: 1-10. Amacher, M.C. , Johnson, A.D. , Kutterer, D.E. and Bartos, D.L. 2001. First-year postfire and postharvest soil temperature in aspen and conifer stands. USDA Forest Service Res. Pap. RMRS-RP-27-WWW. Banner, A. , MacKenzie, W., Haeussler, S., Thomson, S., Pojar, J. and Trowbridge, R. 1993. A field guide to site identification and interpretation for the Prince Rupert Forest Region. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Land Management Handbook No. 26. Beckingham, J.D. and Archibald, J.H. 1996. Field guide to ecosites of northern Alberta. Canadian Forest Service, Northwest Region, Northern Forestry Centre, Edmonton, Alberta. Spec. Rep 5. Beckingham, J.D., Nielsen, D.G. and Futoransky, V . A . 1996. Field guide to ecosites of the mid-boreal ecoregions of Saskatchewan. Canadian Forest Service, Northwest Region, Northern Forestry Centre, Edmonton, Alberta. Spec. Rep 6. Bunn, A .G . , Waggoner, L .A. and Graumlich, L.J. 2005. Topographic mediation of growth in high elevation foxtail pine (Pinus balfouriana Grev. et Balf.) forests in the Sierra Nevada, USA. Global Ecol. Biogeogr. 14: 103 - 114. Burnham, K.P. and Anderson, D.R. 2002. Model selection and multimodel inference, a practical information-theoretic approach. Second edition. Springer-Verlag New York, Inc. 488 p. 96 Canham, C D . , Coates, K .D. , Bartemucci, P. and Quaglia, S. 1999. Measurement and modeling of spatially-explicit variation in light transmission through interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1775-1783. Carter, R.E. and Klinka, K . 1992. Variation in shade tolerance of Douglas fir, western hemlock, and western red cedar in costal British Columbia. For. Ecol. Manage. 55: 87 - 105. Chen, H . Y . H . 1997. Interspecific responses of planted seedlings to light availability in interior British Columbia: survival, growth, allometric patterns, and specific leaf area. Can. J. For. Res. 27: 1383-1393. Chen, H .Y.H. , Krestov, P.V. and Klinka, K . 2002. Trembling aspen site index in relation to environmental measures of site quality at two spatial scales. Can. J. For. Res. 32: 112-119. Claveau, Y . , Messier, C , Comeau, P.G. and Coates, K .D. 2002. Growth and crown morphological responses of boreal conifer seedlings and saplings with contrasting shade tolerance to a gradient of light and height. Can. J. For. Res. 32: 458-468. Coates, K . D . and Burton, P.J. 1999. Growth of planted tree seedlings in response to ambient light levels in northwestern interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1374-1382. Comeau, P.G. and Bedford, L. 2002. Light under and adjacent to aspen stands and implications for growing spruce. In: Frochot, H. , Collet, C. and Balandier, P. (editors). Popular summaries from the fourth international conference on forest vegetation management. Nancy, France 17-21 June 2002. Institut National de la Recherche Agronomique. p 177-179. 97 Comeau, P.G., Braumandl, T.F. and Xie, C.Y. 1993. Effects of overtopping vegetation on light availability and growth of Engelmann spruce (Picea engelmannii) seedlings. Can. J. For. Res. 23: 2044-2048. Comeau, P.G., Gendron, F. and Letchford, T. 1998. A comparison of several methods for estimating light under a paper birch mixedwood stand. Can. J. For. Res. 28: 1843-1850. Constabel, A.J . and Lieffers, V.J . 1996. Seasonal patterns of light transmission through boreal mixedwood canopies. Can. J. For. Res. 26: 1008-1014. Cote, L., Brown, S., Pare, D., Fyles, J. and Bauhus, J. 2000. Dynamics of carbon and nitrogen mineralization in relation to stand type, stand age and soil texture in the boreal mixedwood. Soil Biology & Biochemistry 32: 1079-1090. DeLong, C , MacKinnon, A . and Jang, L. 1990. A field guide for site identification and interpretation of ecosystems of the northeast portion of Prince George Forest Region. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Land Management Handbook No. 22. Drever, C.R. and Lertzman, K.P. 2001. Light-growth response of costal Douglas-fir and western redcedar saplings under different regimes of soil moisture and nutrients. Can. J. For. Res. 31:2124-2133. Environment Canada. 2004. Climate normals and averages. Available at: http://www.climate.weatheroffice.ec.gc.ca/climate_normals/index_e.html. Last accessed: March 8, 2005. Flanagan, P.W. and Van Cleve, K. 1983. Nutrient cycling in relation to decomposition and organic-matter quality in taiga ecosystems. Can. J. For. Res. 13: 795-817. Groot, A . 1999. Effects of shelter and competition on the early growth of planted white spruce (Picea glauca). Can. J. For. Res. 29: 1002-1014. 98 Gustafson, E.J., Lietz, S.M. and Wright, J.L. 2003. Predicting the spatial distribution of aspen growth potential in the Upper Great Lakes Region. For. Sci. 49: 499-508. Gustafson, F.G. 1943. Influence of light upon tree growth. J. For. 41: 212-213. Hannam, K.D. , Quideau, S.A., Oh, S.W., Kishchuk, B.E. and Wasylishen, R.E. 2004. Forest floor composition in aspen- and spruce- dominated stands of the boreal mixedwood forest. Soil Sci. Soc. Am. J. 68: 1735-1743. Hurvich, C M . and Tsai, C.-L. 1989. Regression and time series model selection in small samples. Biometrika 76: 297-307. Jerabkova, L. , Prescott, C E . and Kishchuk, B.E. 2006. Nitrogen availability in soil and forest floor of contrasting types of boreal mixedwood forests. Can. J. For. Res. 36: 112-122. Kalischuk, M . L . 2004. Influence of site quality and overstory age on the growth of understory white spruce in boreal mixedwood stands [M.Sc. Thesis]: University of Alberta, Edmonton. 117 p. Kayahara, G.J., Chen, H.Y.H. , Klinka, K. and Coates, K .D. 1996. Relations of terminal growth and specific leaf area to available light in naturally regenerated seedlings of logdepole pine and interior spruce in central British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Research Report 09. Kimmins, J.P. 1996. Forest ecology, a foundation for sustainable management. Prentice Hall. 596 p. Lajzerowicz, C.C., Walters, M.B. , Krasowski, M . and Massicotte, H.B. 2004. Light and temperature differentially colimit subalpine fir and Engelmann spruce seedling growth in partial-cut subalpine forests. Can. J. For. Res. 34: 249-260. 99 Landhausser, S.M., Desrochers, A . and Lieffers, V.J . 2001. A comparison of growth and physiology in Picea glauca and Populus tremuloides at different soil temperatures. Can. J. For. Res. 31: 1922-1929. Lieffers, V . , Landhausser, S.M. and Man, R. 2004. White spruce is a specialist for low temperatures. Centre for Enhanced Forest Management, Department of Renewable Resources, University of Alberta. E F M research note 05/2004. Lieffers, V.J . and Stadt, K.J . 1994. Growth of understory Picea glauca, Calamagrostis canadensis, and Epilobium angustifolium in relation to overstory light transmission. Can. J. For. Res. 24: 1193-1198. Lieffers, V.J . , Stadt, K.J . and Navratil, S. 1996. Age structure and growth of understory white spruce under aspen. Can. J. For. Res. 26: 1002-1007. Littell, J.S. and Peterson, D.L. 2005. A method for estimating vulnerability of Douglas-fir growth to climate change in the northwestern U.S. For. Chron. 81: 369-374. Logan, K.T. 1969. Growth of tree seedlings as affected by light intensity. IV. black spruce, white spruce, balsam fir, and eastern white cedar. Canadian Forestry Service. Publication No. 1256. Man, R. and Lieffers, V.J . 1999. Effects of shelterwood and site preparation on microclimate and establishment of white spruce seedlings in a boreal mixedwood forest. For. Chron. 75: 837-844. Messier, C , Parent, S. and Bergeron, Y . 1998. Effects of overstory and understory vegetation on the understory light environment in mixed boreal forests. J. Veg. Sci. 9: 511-520. Pare, D. and Bergeron, Y . 1996. Effect of colonizing tree species on soil nutrient availability in a clay soil of the boreal mixedwood. Can. J. For. Res. 26: 1022-1031. 100 Pastor, J., Gardner, R.H., Dale, V . H . and Post, W.V. 1987. Successional changes in nitrogen availability as a potential factor contributing to spruce declines in boreal North America. Can. J. For. Res. 17: 1394-1400. Peterson, D.W. and Peterson, D.L. 2001. Mountain hemlock growth responds to climatic variability at annual and decadal time scales. Ecology 82: 3330-3345. Peterson, D.W., Peterson, D.L. and Ettl, G.J. 2002. Growth responses of subalpine fir to climatic variability in the Pacific Northwest. Can. J. For. Res. 32: 1503-1517. Peterson, E.B. and Peterson, N . M . 1992. Ecology, management, and use of aspen and balsam poplar in the Prairie Provinces, Canada. Northern Forestry Centre, Edmonton. Special report 1. Pritchard, J .M. 2003. The effect of opening size on light, temperature and growth of white spruce under a trembling aspen canopy. [M.Sc. Thesis]: University of Alberta, Edmonton. 144 p. Reich, P.B., Walters, M.B. , Tjoelker, M.G . , Vanderklein, D. and Buschena, C. 1998. Photosynthesis and respiration rates depend on leaf and root morphology and nitrogen concentration in nine boreal tree species differing in relative growth rate. Functional Ecology 12: 395-405. Shirley, H.L. 1945. Reproduction of upland conifers in the lake states as affected by root competition and light. Amer. Midi . Nat. 33: 537-612. Stadt, K.J . , Lieffers, V.J . , Hall, R.J. and Messier, C. 2005. Spatially explicit modeling of PAR transmission and growth of Picea glauca and Abies balsamea in the boreal forests of Alberta and Quebec. Can. J. For. Res. 35: 1-12. Thornthwaite, C.W. and Mather, J.R. 1955. The water balance. Drexel institute of technology. 104 p. 101 Thornthwaite, C.W. and Mather, J.R. 1957. Instructions and tables for computing potential evapotranspiration and the water balance. Drexel institute of technology, Laboratory of climatology. Tryon, P.R. and Chapin, F.S. 1983. Temperature control over root growth and biomass in taiga forest trees. Can. J. For. Res. 13: 827-833. Wang, G.G., Su, J. and Wang, J.R. 2000. Height growth of planted black spruce seedlings in response to interspecific vegetation competition: a comparison of four competition measures at two measuring positions. Can. J. For. Res. 30: 573-579. Williams, H. , Messier, C. and Kneeshaw, D.D. 1999. Effects of light availability and sapling size on the growth and crown morphology of understory Douglas-fir and lodgepole pine. Can. J. For. Res. 29:222-231. Woodward, F.I. 1992. A review of the effects of climate on vegetation: ranges, composition, and composition. In: Peters, R.L.and Lovejoy, T.E. (editors). Global warming and biological diversity. Yale University Press, New Haven & London, p 105 - 121. Wright, E.F., Coates, K.D. , Canham, C D . and Bartemucci, P. 1998. Species variability in growth response to light across climatic regions in northwestern British Columbia. Can. J. For. Res. 28: 871-886. Xu, P., Ying, C.C. and El-Kassaby, Y . A . 2000. Multivariate analysis of casual correlation between growth and climate in Sitka spruce. Silvae Genetica 249: 257-263. 102 Chapter 5: Evaluation of SORTIE-ND for Growth Prediction in Mixed Stands Introduction If truth is defined as reality, models, including computer simulation models, can by definition never be true (Popper 1963; Vanclay and Skovsgaard 1997; Oreskes et al. 1994). Nevertheless, the main objective of most models used in forest management is to make predictions about the behavior of the system they represent. Since all models are abstractions, both model developers and models users require information on how well a particular model conforms to the expectations and observations from the simulated system. As a consequence, the literature relating to concepts and methods for model validation, verification, and evaluation is plentiful. The bibliography of Balci and Sargent (1984) listed 308 references on the topic and several new methods and reviews have been published since (reviews in: e.g. Robinson and Monserud, 2003; Rykiel 1996; Kleijnen 1999; Sargent 1999; Pretzsch et al. 2002; Huang et al. 2003). There does seem to be broad agreement that these topics are complicated and form some of the most controversial issues in modeling (e.g. Raykiel 1996; Huang et al. 2003; Robinson and Monserud 2003). On the other hand, there does not seem to be any general widely accepted procedures for validation, verification, or evaluation (Haung et al. 2003; Robinson and Monserud 2003; Yang et al. 2004). There even appear to be controversies on the general meaning, philosophic implication, and correct semantic use of the terms validation and verification (Oreskes et al. 1994; Soares et al. 1995; Rykiel 1996). One point of broad agreement is that a model can only be assessed in regard to a specified objective (e.g. Goulding 1979; Buchman and Shifley 1983; Bunnell 1989; Sores et al. 1995; Rykiel 1996; Vanclay and Skovsgaard 1997; Sargent 1999). Model assessment is consequently problem-dependent (Sores et al. 1995; Yang et al. 2004), and this is likely the reason for the lack of one generally accepted procedure. As suggested by Sores et al. (1995) and Vanclay and Skovsgaard (1997), the use of validation and verification is replaced here by the term evaluation as it is less value-loaded. In this dissertation, evaluation is defined as a process in which a model's 103 conceptual structure and predictions are described and assessed with regard to a specific purpose. Consequently, this definition encompasses what is often referred to as validation and verification. There are three general stages in the lifecycle of a model: "initial model objectives drive the structure of the model; model objectives drift and expand; and, eventually, the initial model structure must be revamped or abandoned to address substantially different objectives" (Monserud 2003). The small scale disturbance model SORTIE is a spatially explicit individual tree model developed and tested in the mid 1990's for transitional oak-northern hardwood forests in the northeastern US (Pacala et al. 1993; Pacala et al. 1996). SORTIE was designed to extrapolate fine-scale/short-term field measurements to large-scale, long-term forest dynamics (Pacala et al. 1996). In recent years the model has been modified (SORTIE/BC) and parameterized for northern mixed forests in western British Columbia (Kobe and Coates 1997; Wright et al. 1998, 2000; Canham et al. 1999; LePage et al. 2000; Coates et al. 2004; Canham et al. 2004). Simultaneously the model has become more suited for silvicultural planning (Coates et al. 2004). SORTIE/BC has recently been restructured into SORTIE-ND (for details see the section: Development history and description of the evaluated version of SORTIE-ND). SORTIE-ND possesses the required features for simulating spatially complex silvicultural systems in mixed-species stands. Consequently, there has been considerable interest in the use of SORTIE-N D for simulating the effects of alternative silvicultural systems on stand structure and growth for boreal and subboreal mixedwood stands. However, neither SORTIE/BC nor SORTIE-ND have been formally evaluated as predictive models for growth and stand dynamics in mixed boreal and subboreal stands. Consequently, the main objective of this chapter is to perform such an evaluation of SORTIE-ND. The evaluation will be limited to the components of SORTIE-ND that directly influence growth. Consequently, the regeneration component of the model is not evaluated. General approach to evaluation The purpose of this evaluation is to investigate the capabilities of SORTIE-ND as a predictive model for growth and stand dynamics in mixed boreal and subboreal stands. This is done to provide users with information on model performance, and model 104 developers with knowledge on where to concentrate further model development. The evaluation will not result in a simple "yes or no" answer as this requires a set range of tolerance which inevitably will depend on the individual user (Brand and Holdaway 1983). Furthermore, as all models are incomplete, model evaluation should rather be thought of a relative process through which different models can be compared (Buchman and Shifley 1983). This point also leads to concerns about the role of statistical tests in the evaluation. There are numerous available tests designed for model validation (e.g. Freese 1960; Reynolds et al. 1981; Kleijnen 1999; Yang et al. 2004). The majority of these tests are designed to compare model predictions with independent observations. We know a priori that a model is incomplete, thus it does not make sense to test that it matches reality (Reynolds and Chung 1986). Consequently, use of a test requires that an acceptable level of divergence between the predictions and observations is set. As this divergence level is user-dependent, the level of divergence should be set by the model user rather than the model developer. Additionally, it has recently been shown that different tests can yield conflicting results and thus can lead to confusion rather than increased knowledge from the evaluation process (Yang et al. 2004). In the evaluation performed here, statistical tests will consequently have a very limited role. The alternative to statistical tests is statistical estimation and description (Reynolds and Chung 1986). Statistical description can be more informative than statistical tests and it leaves the choice of acceptability up to the individual user. Consequently, different forms of statistical description will be utilized to characterize how the model predictions conform to independent data. Sensitivity analysis is an important part of model evaluation (e.g. Fossett et al. 1991; Vanclay and Skovsgaard 1997; Kleijnen 1998, 1999). There are essentially two basic methods of sensitivity analysis: (i) where each investigated parameter is varied individually, or (ii) where Monte Carlo techniques are used to vary all parameters simultaneously and the parameter value for each model run is determined by a random draw from a distribution (Lexer and Honninger 2004). The Monte Carlo approach where parameters are drawn from their error distribution is often referred to as the study of error propagation (e.g. Pacala et al. 1996). Varying one parameter at a time is simple, but does not detect interactions between different factors (e.g. Kleijnen 1999; Frey and Patil 105 2002). This type of sensitivity analysis is often used to rank the importance of factors, but for nonlinear models it is not certain that a reliable rank ordering of factors is provided (Frey and Patil 2002). In the majority of cases there is a superior approach to varying one factor at the time (Montgomery 1997). The span of predicted values following a Monte Carlo style sensitivity analysis gives an indication of the error in the model predictions created due to uncertainty about the input parameters. On the other hand this result does not directly yield a ranking of the importance of input parameters. To get at this issue, regression analysis can be employed to identify and rank the most important parameters following a Monte Carlo type sensitivity analysis (e.g. Neter et al. 1996; Frey and Patil 2002). The evaluation presented here has three main components. Initially, the model was evaluated in terms of its conceptual structure. This was done to identify obvious structural limitations of the model. Secondly, a sensitivity analysis of the model was performed. Sensitivity analysis provided information on the model's sensitivity to uncertainty about the parameter estimates and indicates the parameters with greatest influence on predictions. Third, model predictions were compared to independent observations of growth from permanent sample plots. This provided information on ranges of accuracy and precision of stand level predictions. Development history and description of the evaluated version of SORTIE-ND SORTIE is a descendent from the JABOWA-FORET (e.g. Botkin et al. 1972; Shugart 1984; Botkin 1993) family of models and the basic structure of growth, mortality, recruitment, and resource submodels is maintained. The main points that differentiate SORTIE from the majority of the JABOWA-FORET models are: (1) the tight link between field measurements and parameterization of relationships, (2) the spatially-explicit light submodel, and (3) the absence of other nutrient and water submodels (Pacala et al. 1996). A version of the model (SORTIE/BC) was further developed and adapted to forests of northern British Columbia (Coates et al. 2004). The development of SORTIE/BC maintained the basic structure of SORTIE, but made the model more suited 106 to deal with management issues (Coates et al. 2004). During the past two years the model has been restructured and reprogrammed in C++. The result is SORTIE-ND where ND signifies the model's focus on neighborhood dynamics. The new structure has amalgamated the original SORTIE with SORTIE/BC and added several new features and a very high degree of flexibility. In SORTIE-ND, each equation that affects a tree is called a behavior. Examples of behaviors are a growth behavior which determines the growth of an individual tree given its available resources or a mortality behavior which assigns a probability of mortality to an individual tree given its current growth rate. In SORTIE-ND the user has to specify which behaviors (processes) to apply to a population of trees. Each behavior can be specific for a combination of species and life-cycle stage (seed, seedling, saplings, adult trees, snags, woody debris). The number of available behaviors is large and SORTIE-ND can consequently be configured to do different types of simulations with very different objectives and outcomes. The new C++ code structure allows for new behaviors to be incorporated into the model with relative ease. In SORTIE-ND a behavior is represented as an equation with a number of parameters. The parameters do not have default values and have to be specified by the user in a parameter file that can be accessed through the model's user interface. Thus, SORTIE-ND simulations performed by different users can be very different and are dependent on the specified setup of the model. The following section outlines the model setup used for simulations presented in this chapter. Figure 5.1 outlines the general flow of the model. In the model, trees are stratified into seedlings, saplings, and adults. Seedlings are trees less than 1.35 m tall. Spruce saplings are trees with a dbh of less than 3 cm, while aspen, logdepole pine (Pinus contorta Dougl. ex Loud, var . latifolia Engelm.), and subalpine fir {Abies lasiocarpa (Hook.) Nutt.) saplings are trees with a dbh of less than 5 cm. Adults are all trees with a dbh greater than saplings. A simulation is initialized by specifying a starting condition (input box in Figure 5.1). The input data can consist of a stem mapped stand with dbh and (x,y) coordinates for all trees. Alternatively, the input can consist of user specified initial tree densities (stems/ha) stratified by species and dbh classes. The model will then randomly position the trees in a plot of a specified size. 107 Seedling and sapling diameter increment: DI = f(light, diameter) Probability of mortality (Pm) for seedling and saplings: Random mortality: Pm = Random B C mortality: Pm = f(DI) Density self-thinning Pm = f(neigbourhood density, mean dbh) Light Behavior: Predicts light at any required position and height in the plot with following input: (1) Position and allometry of trees (2) Species-specific crown openness (3) Sky brightness distribution Allometry/Tree population: Height = f(dbh) Crown depth = f(dbh) Crown width = f(dbh) Dbh = f(diameter (a). 10 cm) Input and tree list: Plot information: size and location Years to simulate For each tree: species (x,y) coordinates, dbh. Analysis/output: Volume calculations: Volume = f (dbh, height) Stand and stock tables, basal area etc. by species by dbh class Adult diameter Increment (DI): DI = f(light, crowding, dbh) Probability of mortality (Pm) for adults: Random mortality: Pm = Random Competition mortality: Pm=f(DI) Senescence: Pm = f(dbh) Figure 5.1. Model flow of SORTIE-ND as configured for this project. Tree growth is modeled as diameter growth, while tree height and crown dimensions are regressed from dbh. The allometry equations (Allometry/Tree population box in Figure 5.1) assign height and crown dimensions to each tree and update these during a simulation. Seedling height is regressed from diameter at 10 cm above ground (diameterio) with equation [1 A] , where a is a user specified parameter. For seedlings and saplings, diameterio is converted to dbh with equation [2A], where / and R are user specified parameters. Sapling and adult tree height is regressed with the equation [3A], where MaxHeight and b are user specified parameters. In SORTIE-ND, sapling and adult tree crowns are represented as cylinders with a radius and a depth while seedlings do not have a crown. Crown radius is regressed with equation [4A] where i, a, b and c are user-108 specified parameters. Crown depth is regressed with equation [5A], where i, a, b and c are user specified parameters. [ 1 A] Height = 0.1 + 3 0 x [l - e'axdiame,er"> J [2 A] dbh = I + diameterX OxR [3 A] Height = 1.35 + (MaxHeight -1.35) x [l - e-bxdbh J [4A] CrownRadius = i + a[l - e'bxdbh f [5A] CrownDepth = i + a[\ - e ' M e i g h t f Light is the main resource in SORTIE-ND and all trees must have a light level assigned to them (Light behavior box in Figure 1). Light levels are predicted with the Gap Light Index (GLI) (Canham 1988) which is 100 in full light and 0 in darkness. The light level at a given location is calculated using the position and allometry of the neighborhood trees, the sky brightness distribution, and species-specific crown openness. Species-specific crown openness is defined as the fraction of sky that on average can be seen through the crown of an individual tree of a given species. Species-specific crown openness is the only parameter from the light calculations that will be considered here. For a more detailed description of the light calculations see Canham et al. (1999). Seedling and sapling diameter increment are predicted from light availability and tree size (seedling and sapling increment box in Figure 1). The utilized models are from Chapter 3. Aspen diameter^ increment is predicted with equation [1JG], where a, b, and c are user-defined parameters. Spruce and subalpine fir diameterio increment is predicted with equation [2JG], where a, b, c, and d are user-specified parameters. Logdepole pine diameterio increment is predicted with [3JG], where a, b, and c are user-defined parameters. [1JG] diameter.Jncrement = , f „,„ 109 a + bx. diameter^ [2Jul diameter,^increment = —7 -—„,„ \— 10 Jj + e ( c - r f x C I / ) j [3 JG] diameterwincrement = (a + bx diameter^ ) x (GL/ /100) c Adult dbh increment is predicted from the target tree size, light availability, and crowding received from neighborhood trees. The utilized model (Coates et al. in prep.) is a multiplicative version of the additive model presented by Canham et al. (2004). An individual tree's dbh increment is calculated according to equation [1AG]: [ 1 AG] dbhincrement = MaxGrowth x SizeEffect x ShadingEffect x Crowdingeffect where MaxGrowth is a user specified parameter. The SizeEffect is calculated with equation [2AG] where Xo and Xb are user-specified parameters. The ShadingEffect is calculated with [3AG] where shading is the shade cast by neighbors (0 = no shade, 1 = full shade) and m is a user-defined parameter. The CrowdingEjfect is calculated with [4AG] where c is a user-specified parameter and NCI is the neighborhood crowding index which is calculated with [5AG]. In equation [5AG] dist is the distance to a given neighbor; a and P are user specified parameters and; A. is a user-defined competition intensity factor of the neighbor species relative to the target tree. [2AG] SizeEffect = e y x" ] [3AG] ShadingEffect = e-mxslmdi"s [4AG] CrowdingEjfect = e'cxNCI A mortality behavior assigns a probability of mortality [Vr(Mortality)] to a given tree and a random number draw from a uniform distribution determines i f the tree actually dies. Seedlings and saplings both have three mortality behaviors assigned to them. Random 110 juvenile mortality is predicted with equation [1JM] where a is a user-specified annual probability of mortality parameter. Mortality due to low growth (caused by shading) is predicted with equation [2JM], where m is a user-defined parameter, and diameter)oincrement is the number predicted by the juvenile growth equations. The third mortality behavior is only applied to aspen and is responsible for the density dependent self-thinning. The probability of mortality due to density dependent processes is predicted with equation [3JM]. In this equation A, C, and S are user-defined parameters, while meandiameter is the mean diameter of all juvenile trees within 5 meters of the target tree, and density is the density of juvenile trees (stems/ha) within a radius of 5 meters. [1JM] Yr(Mortality) = a [2JM] ?r(Mortality) = £ _ - mxdiameter] ^increment [3JM] Vr(Mortality) = (A + (C x meandiameter)) x density (A + (Cx meandiameter)) — + density Adult trees have three mortality behaviors assigned to them. Random adult mortality is predicted with equation [1AM], where a is a user-specified annual probability of mortality parameter. Mortality due to low growth rate (caused by crowding and shading) is predicted with equation [2AM], where z and Max are user defined parameters. Relativelncrement is calculated with equation [3AM], where the PredictedGrowth is the prediction from equation [1 AG] and MaxGrowth and SizeEffect have the same meaning as in [1 AG] . Mortality due to old age (large dbh) is predicted with the senescence equation [4AM]. In this equation dbh is the diameter at breast height for the target tree while a, b, and c are user-defined parameters. [1AM] Vr(Mortality) = a [2AM] Pr(Mortality) = Z^lativelncrement/Max 111 ,.„.,„,„, . T PredictedGrowth [3AJV1J Relativelncrement = [4AM] Vr(Mortality) MaxGrowth x SizeEffect e(a+b(dbl,-c)) lW (a+b(dbh-c)) SORTIE-ND has a wide variety of output options (Figure 5.1). As the model contains a tree map that is saved at each time-step there are few limits to the possibility for calculating summary statistics. Volume estimates are one of these options. In SORTIE-N D volume estimates are not part of the driving functions. Rather volume is estimated from dbh and height of each tree by a specified equation. For these simulations, the latest version of Kozaks's variable exponent taper equations (Kozak 2004) was incorporated into the model and was utilized to estimate volume. Methodology and data Evaluation of model logic and conceptual model structure This initial step of the evaluation explored the conceptual structure of the model for gaps in realistic representations of forest stands. This was done by identifying model structures that resulted in counterintuitive growth patterns. Additionally, model predictions were compared to general expectations of stand development. Initially, predictions for even-aged single species stands with variable densities were investigated. Secondly, mixed-species even-aged stand development was investigated. Sensitivity analysis The sensitivity analysis was performed on a 100-year simulation of a 115x115 m plot of a mixed aspen-spruce stand. The initial conditions were set to simulate stand development starting from a 7 year old stand, of suckering aspen and planted spruce. The aspen density was set to 7000 stems/ha with a mean dbh of 2cm. The spruce density was set to 1000 stems/ha with individual heights ranging between 35 - 50 cm. The sensitivity analysis was performed using a Monte Carlo approach that included 2000 simulations (approximately 15 minutes of computer-time/simulation). In each simulation the trees were randomly positioned and each parameter to be investigated was randomly 112 drawn from a uniform distribution. Sixty-four parameters were included in the sensitivity analysis. In an individual simulation, each of the 64 parameters was randomly drawn from a uniform distribution. This distribution was characterized by a mean (u) which was set as the best estimate for the parameter and upper and lower bounds set at u±10%. This approach likely overestimates the uncertainty about parameter estimates as it assumes that all parameters are independent. In most of the equations in the model (e.g. juvenile and adult growth) the value of one parameter is clearly dependent on the other. Consequently, the sampling space from which the parameters were drawn was likely overestimated. The output from the sensitivity analysis was assessed in two steps. The first step assessed the amplitude of variability caused by uncertainty in parameter estimates. This was performed through visual assessment of species-specific plots of basal area, stems/ha, and quadratic mean diameter (DBHq). The second step ranked the relative influence of parameters on final basal area, stems/ha, and DBHq. This was done with regression analysis where each of the output variables was regressed against the individual predictor variables and the parameters were ranked according to R 2 . Comparison to permanent sample plots The British Columbia Ministry of Forests database of permanent sample plots was searched to find independent, repeatedly-measured plots to compare to SORTIE-ND predictions. The plots were selected using the following criteria: either aspen or spruce had the highest or second highest crown cover; a plot was located on a mesic site in the Subboreal Spruce (SBS) zone5; data were available for at least 25-years; and tree species other than aspen, spruce, subalpine fir and logdepole pine comprised a maximum of 4% of the crown cover in the initial year of measurement. This search yielded a total of 51 permanent sample plots that were measured over a 30 year period. The selected plots were either 0.1 or 0.08 ha in size and were established in either 1970 or 1971. Since establishment they were re-measured three times at 10 year intervals for a total of 30 years (M0-M3). Table 5.1 provides stand-level information about the individual plots. 5 It was the aim to only use sites classified to site series 01 (Meidinger and Pojar 1991). However, to increase the number of plots, 4 plots classified as site series 03 and 5 plots classified as 05 were included in the analysis. 113 Geographically, the plots were distributed throughout the SBS zone in five different biogeoclimatic subzones (Table 5.1). 18 plots were located in the SBSmw subzone, which mainly occurs in the Quesnel Highland (Meidinger et al. 1991). 23 plots were located in SBSmkl and SBSmk2 subzones, which extend from Prince George - Fort St. James to Nation Lakes - Williston Reservoir (Meidinger et al. 1991). 9 plots were located in the SBSwk2 subzone which in the west occurs around Tatla Lake and in the east between the Peace Arm of Williston Reservoir to the upper Quesnel River (Meidinger et al. 1991). 1 plot was located in the SBSdwl subzone which extends in a band from Stuart Lake to Canim Lake on the Interior Plateau (Meidinger et al. 1991). The utilized parameter estimates for SORTIE-ND mainly originates from the SBSmc, which occurs from the Blackwater - Ootsa Lake area to Babine Lake and River (Meidinger et al. 1991). There is some variation between the productivity of the SBS subzones. The most readily available measure of this variation is the SIBEC system (Ministry of Forests and Range 2006) which associates a site index to a site type (site series) in each subzone. Site index estimates are available for spruce (SX), lodgepole pine (PL), and subalpine fir (BL) but generally not for aspen. The estimated site indices for mesic sites with medium nutrient availability (site series 01) are: SBSmc2 (SX = 18.7, PL = 17.9, B L = 15.4), SBSmkl (SX = 19.1, PL = 20.1, B L = 17.6), SBSmw (SX = 20.0, PL = 22.4, B L = 15.0), SBSwk2 (SX = 18.0, PL = 18.0, B L - 12.0), SBSmk2 (SX = 18.0, PL = 21.0, B L = 15), and SBSdwl (SX = 21.0, PL = 24.0, B L = not available) (Ministry of Forests and Range 2006). Generally the site indices are similar. If anything, site indices from the SBSmc2 indicate that the SORTIE-ND SBSmc2 parameter estimates should slightly underestimate growth of the majority of plots which are located in slightly more productive subzones (SBSmw and SBSmkl). This underestimation should be most evident for pine. In the initial measurement (M0) of the permanent sample plots, only trees with a dbh larger than 9.1 cm were measured, while all trees with a dbh > 2 cm were measured in the three re-measurements (M1-M3). To take full advantage of all the information in the data, three types of SORTIE-ND simulations were run for each permanent plot. The first simulation covered 30 years (M0-M3) and only included trees larger than 9.1 cm. This 114 simulation was used to investigate how well SORTIE-ND predicted the growth of overstory trees. The second simulation covered twenty years (M1-M3) and included all trees with dbh > 2cm. This simulation type was used to investigate how well SORTIE-N D predicted growth of understory and suppressed trees. In this analysis only trees that were not included in the initial thirty-year simulation were investigated. The final simulation was a ten-year simulation (M2-M3) and included all trees with dbh>2. This simulation was used to investigate how well SORTIE-ND predicted growth of in-growth understory trees. In analysis of the ten-year simulation, only trees that were not included in the 30 year and 20 year simulations were investigated. Thus, the trees investigated in the ten-year simulation are mainly in-growth that reached 2 cm between measurement 1 (Ml) and measurement 2 (M2). To simulate the plots in SORTIE-ND, the tree list from the initial plot measurement was repeated 89 or 111 times to create a 9 ha stemmap-file for input into SORTIE-ND. In the stemmap-files, the individual trees were assigned random (x,y) locations. Minor portions of birch (Betula papyrifera Marsh.), cottonwood (Populus balsamifera ssp. tricocarpa (Torr. & Gray)), alder (Alnus spp.), and Douglas-fir (Pseudaotsuga menziesii var. glauca (Bessin.) Franco) were present in the plots (less than 4% of crown cover). Parameter estimates were not available for these species. Birch, cottonwood and alder were simulated as aspen, but with different allometric relationships. Douglas-fir was simulated as lodgepole pine. These species were only included to make the simulated densities correspond to the actual densities in the permanent sample plots. They were not included in any analysis of the results. 115 Table 5.1. Stand summary statistics for the 51 permanent sample plots. The species codes are: aspen (At), logdepole pine (PI), spruce (SX), subalpine fir (BL), birch (Ep), cottonwood (Ac), Douglas-fir (Fd). Site index is estimated for the leading species at 50 years of age at dbh. Plot B E C classification Plot Size (ha) Year Est. Species Composition (Species code %cover) Age Site Index Volume (nrVha) Basal Area (m2/ha) Density (stems/ha) 1 SBS mwOl 0.081 70 At 44 PI 42 SX 14 30 18.2 110 17.9 1383 2 SBS mw 03 0.081 70 PI 52 At 45 SX 03 30 20.6 83 13.0 716 3 SBS mk 1 05 0.101 71 At 53 PI 47 32 19.2 85 13.0 515 4 SBS mk 1 01 0.101 71 At 71 PI 16 SX 13 39 20 211 29.8 1228 5 SBS mk 1 01 0.101 71 At 45 PI 37 SX 18 31 20.6 152 21.2 733 6 SBSmk 1 01 0.101 71 At 96 SX 02 PI 01 EpOl 40 18.9 119 18.3 1109 7 SBS mk 1 5 0.101 71 PI 75 At 25 32 17.4 84 13.5 911 8 SBS mk 1 01 0.101 71 At 53 PI 29 SX 18 41 16.9 129 19.7 1099 9 SBS mk 1 01 0.101 71 At 70 PI 21 S X 0 7 E p 0 2 37 18.2 125 18.5 1010 10 SBS mk 1 01 0.101 71 PI 53 At 30 SX 14Ep03 37 18.4 134 19.8 970 11 SBS mk 1 01 0.081 71 At 46 S X 4 2 E p 10 PI 02 37 16.2 104 20.8 1556 12 SBS mk 1 01 0.101 71 At 38 PI 31 SX 31 36 18.9 159 24.3 1040 13 SBS mk 1 05 0.101 71 At 43 SX 29 PI 24 Ep 02 Bl 02 32 19 149 25.4 1-525 14 SBS mk 1 01 0.101 71 At 65 PI 21 S X 0 8 E p 0 6 37 17 169 26.6 1248 15 SBSmw 01 0.101 71 PI 77 At 20 SX 03 23 17 66 11.1 733 16 SBSmw 01 0.101 71 At 61 PI 39 35 22.2 154 22.8 1188 17 SBSmw 01 0.101 71 PI 54 At 40 SX 06 37 17.5 141 20.7 1287 18 SBSmw 01 0.101 71 At 58 SX 42 37 19.8 101 17.2 1089 19 SBSmw 01 0.101 71 At 77 SX 19 PI 04 19 20.6 103 19.5 1010 20 SBS wk2 01 0.101 71 At 54 PI 46 41 20.4 248 29.4 1337 21 SBS mk 1 01 0.101 71 PI 63 At 32 Ac 05 28 19.7 58 10.7 851 22 SBS mk 1 01 0.101 71 PI 54 At 44 Bl 02 30 22.4 92 14.0 941 23 SBS mk2 01 0.101 71 At 62 PI 36 Ep 02 41 23.1 238 29.3 1832 24 SBS wk2 01 0.101 71 At 74 PI 25 SX01 44 18.3 301 40.3 2297 25 SBS wk2 01 0.101 71 At 39 SX 27 B l 22 PI 07 Ac 05 38 18.7 151 24.1 1762 26 SBS wk2 01 0.101 71 At 49 PI 43 SX 08 53 17.9 257 31.5 1891 27 SBS wk2 01 0.081 71 At 86 SX 08 PI 06 49 23.4 329 40.8 1667 28 SBS wk2 01 0.081 71 At 76 SX 24 49 23.7 294 39.9 1728 29 SBS mk 2 03 0.081 71 At 49 PI 31 SX 17 Ep 01 Ac02 61 17.5 366 47.4 1605 30 SBS mk 1 01 0.101 71 At 86 Ep 10 PI 03 SX 01 37 22.7 128 20.4 1505 31 SBS mk 1 03 0.101 71 PI 95 At 05 34 15.2 25 3.8 277 Table 5.1 Continued. Plot BEC classification Plot size (ha) Year-Est. Species Composition (Species code % cover) Age Site Index Volume (m3/ha) Basal Area (m2/ha) Density (stems/ha) 32 SBS mwOl 0.081 71 SX 58 PI 38 B l 04 79 17.3 245 37.2 2235 33 SBS mwOl 0.101 71 SX 67 PI 16 At 13 Ep04 65 24.9 120 16.5 347 34 SBS dwl 01 0.081 71 SX 85 B l 10 PI 05 74 21.3 274 36.8 1802 35 SBS mwOl 0.081 70 SX 49 PI 34 At 14Fd03 59 21.7 147 22.8 852 36 SBS mwOl 0.081 70 SX 56 At 26 PI 18 59 21.3 152 25.7 1321 37 SBS mwOl 0.081 70 SX 46 PI 30 At 24 58 22.3 122 17.4 519 38 SBS mk 1 01 0.101 71 SX 41 PI 37 At 22 63 20.1 169 26.4 1069 39 SBS mk 1 01 0.101 71 SX 42 PI 36 At 17 B l 05 57 18.2 114 20.4 1416 40 SBS mk 1 01 0.081 71 SX 54 PI 26 At 13 Bl 05 Fd 02 72 20 210 31.6 1370 41 SBS mk 1 05 0.081 71 SX 45 PI 39 A t l 2 B 1 0 2 F d 0 2 72 17.9 186 29.5 1284 42 SBS mk 1 05 0.101 71 SX 60 PI 30 At 07 Fd 03 Bl 69 20.5 188 26.4 881 43 SBS mwOl 0.101 71 SX 90 At 06 PI 04 67 18.5 102 23.4 1168 44 SBS mwOl 0.101 71 SX 56 PI 23 At 21 65 21.1 130 21.9 1238 45 SBS mwOl 0.101 71 SX 50 PI 47 Fd 02 EpOl 66 22.9 218 30.8 1267 46 SBS mwOl 0.101 71 SX 90 PI 06 Fd 03 At 01 60 21.9 138 27.1 1030 47 SBS mwOl 0.101 71 SX 82 At 17 Fd 01 60 20.7 121 22.4 1079 48 SBS mwOl 0.101 71 SX 64 At 25 PI 07 Fd 04 70 20.9 160 25.2 1218 59 SBS wk2 01 0.081 71 SX 59 At 24 PI 11 B105 EpOl 68 18.7 245 38.5 2136 50 SBS wk2 01 0.101 71 SX 45 Ep 26 At 24 Bl 05 79 18.8 294 40.6 1287 51 SBS wk 2 03 0.101 71 SX 46 At 32 PI 22 69 19.4 236 38.1 2139 The predicted values of species-specific basal area, densities and quadratic mean dbh (DBHq) were compared to the actual values from the permanent sample plots. Initially, this was done using visual assessment of plots of predicted versus actual values. The accuracy of the predictions for each re-measurement was described by mean actual residual (bias) calculated with formula {1}. The precision was described by calculating the mean absolute residual calculated with formula {2}. {1} Meanactualresidual = ^  (y — y) I n {2} Meanabsoluteresidual = y j j ) — y\ln where y is the observed value and y is the predicted value. Results and discussion Evaluation of model logic and conceptual model structure Any model will have limitations that are inherent in the model structure and SORTIE-ND is no exception. Two such structural limitations are worthy of mention. As do many other models, SORTIE-ND utilizes a fixed diameter-height relationship. In actual stands, tree diameter-height ratios vary with stand density. Due to the fixed diameter-height relationship SORTIE-ND is not capable of predicting such variations. This also results in a fixed volume for each tree of a given diameter. This is not a major problem in most situations, where stand densities are within the natural range for which the diameter-height relationships were parameterized. It does become a problem i f the model is used to investigate stem dimensions resulting from different density management regimes. In such a case, SORTIE-ND should be used with stand-specific allometric relationships or a more appropriate model should be selected. Secondly, SORTIE-ND utilizes fixed crown dimensions and allows individual crowns to overlap. In actual stands individual crowns in the same canopy layer do not overlap due to crown shyness caused by physical abrasion (e.g. Oliver and Larson 1996). Consequently, crown size is highly density dependent. One of greatest challenges in modeling aspen is the great variation in densities and thus in crown sizes. A non-density dependent crown relationship will likely cause inconsistent understory light predictions. More specifically, the model will likely 118 underestimate understory light levels under high density overstory and overestimate the light levels at low densities. This point is much less of an issue in most stand types where the ranges of densities are less extreme. For prediction of aspen-spruce dynamics where densities are highly variable SORTIE-ND would become a more robust model i f the crown dimensions were density dependent. Predicted even-aged single-species development of basal area and density at different initial densities for aspen and spruce are illustrated in Figures 5.2 A - D . Both species show believable patterns of self-thinning and have between 500 - 800 stems/ha at year 100. At very high initial densities, aspen had a tendency to thin too rapidly at young ages. This is caused by the growth dependent mortality function [2 JM]. This mortality function is necessary to create the appropriate mortality patterns in understory conditions but also affect early aspen self-thinning6. Thus, to improve the aspen early self-thinning pattern it is recommended that [2 JM] is reprogrammed so that it only applies to trees in the understory. The predicted basal areas also appear plausible and ranges between 35 and 60 m2/ha (Figure 5.2). In agreement with expectations, spruce basal area reached higher values than aspen basal area. The predicted initial growth of spruce stands was faster than is most often observed. This was due to the absence of any type of competing vegetation or damaging agents in the simulation. The model also predicted the expected mixed-species development pattern (Figure 5.2) where aspen initially outgrows spruce, but the surviving spruce trees outgrow aspen in the long term. As expected, the mortality rate of spruce was negatively correlated to the aspen density. At very high initial aspen densities hardly any spruce survived, while low initial densities of aspen result in mixed-species stands where spruce made up the majority of the basal area after 100 years. In conclusion, SORTIE-ND conformed to the general expectations for stand development of both single-species and mixed-species stands of aspen and spruce. This should increase the general level of belief in the model. On the other hand, no suggestions about the accuracy and precision of the predictions can be drawn from these observations. Such information must come from comparison to actual field measurements. 6 This effect can also be observed when simulating young dense logdepole pine stands. Generally, it will likely be a problem for all shade-intolerant species with high initial densities. 119 Figure 5.2. Predictions of single and mixed species stands. Single species scenarios: (A) aspen density over time, (B) spruce basal area over time, (C) spruce density over time, and (D) spruce basal area over time. Mixed aspen-spruce scenarios: (E) aspen density over time, (F) spruce density over time, (G) aspen basal area over time, and (H) spruce basal area. A l l aspen had an initial dbh of 2cm. A l l spruce had an initial height of between 30 -45 cm 120 Sensitivity analysis The sensitivity analysis illustrates that with the large number of parameters in the model, relatively small levels of uncertainty about parameter estimates can lead to very large levels of variation in the predictions (Figure 5.3). Even with very large levels of variation, the model always predicted a stand development pattern that was in reasonable agreement with generally observed patterns of stand growth and tree sizes (e.g. Peterson and Peterson 1992). To illustrate this, the following points can be considered. For the first 50 years, aspen basal area and density were always larger than spruce basal area and density. The final DBHq range for aspen was between 22 and 32 cm, which is in the correct range. For spruce the final DBHq range was between 5 and 40 cm, which is a very large variation but still plausible. For all measures except spruce density (Figure 5.3B), the variation in predicted outcome increased gradually over time. This gradual increase illustrates that no individual parameter acts as a "threshold value" that fundamentally changes the prediction. For spruce density, the variation in predictions was created rapidly in the initial 20-years of the simulation. This illustrated that the initial 20-30 years seems to be the pivotal period for obtaining correct predictions of spruce understory survival and in turn, aspen-spruce stand dynamics. Consequently, when modeling aspen-spruce stands with SORTIE-ND, great care should be given to obtaining correct understory light levels in the initial 30 years (understory light levels are responsible for growth and thus survival of juvenile spruce). The parameters that had the greatest influence on the sensitivity analysis outcomes are listed in Table 5.2. A high R -value indicates that the model is sensitive to small variations in a given parameter. The R -values were produced by the simple linear equation illustrates in equation {3}. {3} Response Variable = Po + Pi x Parameter Table 5.2 only lists parameters for which equation {3} produced R -values greater than or equal to 0.05. For each of the response variables, four to six parameters fulfilled these criteria. Generally, the response variables were most sensitive to parameters included in the adult NCI growth equations. A l l the selected response variables were sensitive to 121 small variations in the ct parameter from equation [5AG]. This parameter is responsible for determining the size dependent competitive effect of neighborhood trees (Canham et al. 2004). The strength of the analysis approach developed by Canham et al. (2004) is that this parameter actually is directly estimated from data rather than arbitrarily determined. A concern might be that this parameter is assumed to be the same for all species, and thus likely have a wide range of associated variance. 122 BOOO 1200 40 60 Year 80 100 120 100 120 40 60 Figure 5.3. Range of predictions from the sensitivity analysis for aspen and spruce density, DBHq, and basal area. At each 10-year interval there are 2000 points which each illustrates a simulation with a unique set of parameters. 123 Table 5.2. Ranking of the sensitivity analysis parameters according to R 2 . The Parameter and Function columns refer to the equations listed in the text. The parameters are ranked according to the R 2 - value resulting from the linear equation: Response Variable = (30 + pi x Parameter. Only parameters with an R 2 - value equal to or higher than 0.05 are included. Response Parameter Function Rank R 2 Variable Aspen a (alpha) Aspen 5AG 1 0.30 Density NCI crowding radius Aspen N A 2 0.18 Max Aspen 2 A M 3 0.13 c (crowding-effect slope) Aspen 4AG 4 0.06 X-Aspen Aspen 5AG 5 0.05 Spruce c (shape parameter 1) Spruce 2JG 1 0.31 Density MaxHeight Aspen 3A 2 0.17 a (seedling height diameter) Aspen 1A 3 0.11 a (alpha) Aspen 5AG 4 0.07 a (asymptote) Aspen 1JG 5 0.06 d (shape parameter 2) Spruce 2JG 6 0.05 Aspen B A a (alpha) Aspen 5AG 1 0.39 NCI crowding radius Aspen N A 2 0.23 c (crowding-effect slope) Aspen 4AG 3 0.08 X-Aspen Aspen 5AG 4 0.07 Spruce B A a (alpha) Aspen 5AG 1 0.18 a (alpha) Spruce 5AG 2 0.11 c (shape parameter 1) Spruce 2JG 3 0.10 MaxHeight Aspen 3A 4 0.07 NCI crowding radius Aspen N A 5 0.05 NCI crowding radius Spruce N A 6 0.05 Aspen Mean MaxGrowth Aspen 1AG 1 0.27 D B H a (alpha) Aspen 5AG 2 0.23 Max Aspen 2 A M 3 0.12 NCI crowding radius Aspen N A 4 0.12 Xo (size effect mode) Aspen 2AG 5 0.06 Spruce Mean a (alpha) Spruce 5AG 1 0.27 D B H a (alpha) Aspen 5AG 2 0.18 NCI crowding radius Spruce N A 3 0.13 NCI crowding radius Aspen N A 4 0.09 The variation in spruce density was created in the first 20-years of the simulation (Figure 2.2). The regression analysis indicated that the shape parameter c from the juvenile spruce growth equation [2JG] explained most of this variation (Table 5.3). This parameter controls the growth rate at low light levels, thus it is logical that this parameter 124 is pivotal to the prediction of spruce density. The MaxHeight parameter from the diameter height regression was an important parameter for both spruce density and basal area. This is due to the relationship between tree height and crown dimensions and thus understory light levels. The large sensitivity to this parameter illustrates the importance of obtaining correct crown dimensions and correct understory light levels. One of the main problems with evaluating process-oriented models is that it is hard to know whether the discrepancy between observations and model predictions is caused by inadequacy of the entire model, inadequacy of a submodel, or by uncertainty about parameter estimates (Makela et al. 2000). The performed sensitivity analysis yielded information on the effect of uncertainty about parameter estimates. Consequently, this is valuable information when trying to improve and understand why model predictions do not conform to expectations or independent data. Additionally, this information can guide new projects working on parameterization of SORTIE-ND in different geographic regions or under different site conditions. The thirty-year simulation of permanent sample plots The combined predictions for aspen, spruce, lodgepole pine, and subalpine fir in the initial 30 year simulation illustrated a good match with permanent sample plot data (Figure 5.4, Table 5.3). For stand density, the predictions followed the observations well at all densities (Figure 5.4). This is confirmed by the summary statistics where the mean actual residual was between -9 and -24 trees/ha (Table 5.3). This indicates that there was a small tendency to overestimate the mortality rates. For basal area, the mean actual residual was approximately 4 m2/ha at year 30. This illustrates that SORTIE-ND overestimated the basal area. The mean absolute residual was approximately 6 m2/ha which indicates that the basal area was not overestimated for all stands. A closer inspection indicated that basal areas were overestimated for younger stands with low initial basal areas (Figure 5.4). As the density was underestimated and the basal area was overestimated, DBHq generally followed the same pattern as basal area (Table 5.3, Figure 5.4). The volume predictions also followed the same pattern, with a tendency for overestimation in younger stands. The correspondence between the observed and predicted volume at the initial measurement (M0) illustrates how well the observed dbh-125 height relationships corresponds to the SORTIE-ND dbh-height relationships. Generally there was not a pattern of over or underestimation in this initial measurement. The general underestimations of the highest volumes are likely caused by a combination of the dbh-height relationship and slight underestimation of density in these stands. Generally, caution should be taken when interpreting the volume predictions, as non-localized dbh-height relationships were used. 15 20 25 30 35 40 0 100 300 500 Observed DBHq (cm) Observed Total Volume (m3) Figure 5.4. Plot of predicted values versus observed values from the 30-year simulation. A circle indicates an observation. The four observations from each sample plots are connected with a line. 126 Table 5.3. Combined summary statistics for the 30-year simulation. Included species are aspen, spruce, lodgepole pine and subalpine-fir. A negative Mean Actual Residual indicates that the SORTIE-ND predictions on average were lower than the plot values. The Mean Actual Residual value illustrates the average difference between the predicted values and the observed values. Response Year Mean Observed No. of Plots Mean Actual Mean Absolute variable Value Residual Residual Aspen, lodgepole pine, subalpine -fir, and spruce B A 10 30.09 51 1.51 2.78 B A 20 34.36 51 3.27 4.64 B A 30 38.34 51 3.96 5.71 Density 10 1126.32 51 -8.66 56.78 Density 20 1032.25 51 -14.00 71.77 Density 30 941.01 51 -23.63 83.14 DBHq 10 18.44 51 0.61 0.82 DBHq 20 20.59 51 1.20 1.45 DBHq 30 22.78 51 1.57 1.92 127 The species-specific summary statistics illustrate that the divergence between the 30 year simulation and the plot data was not evenly distributed among the species (Table 5.4, Figure 5.5 & 5.6). Aspen caused the majority of the divergence in density with mean actual and absolute residuals that are very similar to the combined values. The overestimation of basal area was mainly driven by spruce (Table 5.4, Figure 5.5). Aspen also contributed to this overestimation of basal area. For lodgepole pine, the density, basal area, and DBHq were all slightly underestimated, while for subalpine-fir these measures were slightly overestimated (Table 5.4, Figure 5.6). The vast majority of species-specific graphs (Figure 5.5 & 5.6) appeared to be on correct trajectories. An exception was four plots where simulated aspen basal area was decreasing while it was increasing in the actual plots (plot 27, 28, 49, 51). These plots were all dense, with a high density and basal area of both aspen and spruce. Under these conditions, SORTIE-ND underestimated aspen growth and overestimated aspen mortality. This was related to the parameterization of the adult aspen growth function, where aspen's sensitivity to spruce competition appeared to be overestimated. This can also be realized from the initial evaluation (Figure 5.2), where aspen basal area was strongly influenced by the spruce density. Another exception was plot 31 (lowest basal area in Figure 5.4) where the growth was greatly overestimated. The reason for this overestimation was that plot 31 is on a poorer site (03 site series) that exhibited poor growth. 128 0 10 20 30 40 AT Observed B A (m2/ha) 0 10 30 50 S X Observed BA (m2/ha) o o in o o ID •o H CO x: "55 E. S CO T3 £ o D l o o in o o in o -4 1500 0 500 1500 A T Observed Stems/ha S X Observed Stems/ha AT Observed D B H q (cm) S X Observed DBHq (cm) Figure 5.5. Aspen (AT) and spruce (SX) predicted values versus observed values from the 30-year simulation. A circle indicates an observation. The four observations from a single plot are connected with a line. 129 T — i — r 0 5 10 20 J 0 r 5 "T~ 10 15 PL Observed BA (m2/ha) BL Observed BA (m2/ha) (0 E in ~a a) .*—< o CL o o CD O O CM O -4 I I I 0 200 600 03 XT: is O E O -CO © CO T3 0) O o XJ o -CD i_ CL o -0 100 300 PL Observed Stems/ha BL Observed Stems/ha E cr X CO Q 1 3 <D O T3 CD O o CO o CM . 10 T — I I I I 20 30 40 tr X CO Q •a S o TJ CD O O CO o CM O i r i i r n r 10 20 30 40 PL Observed DBHq (cm) BL Observed DBHq (cm) Figure 5.6. Lodgepole pine (PL) and subalpine fir (BL) predicted values versus observed values from the 30-year simulation. A circle indicates an observation. Each four observations from each of the 51 sample plots are connected with a line. 130 Table 5.4. Species-specific summary statistics for the 30-year simulation of permanent sample plots. A negative Mean Actual Residual indicates that the SORTIE-ND predictions on average were lower than the plot values. The Mean Actual Residual value illustrates the average difference between the predicted values and the observed values. Response Year Mean Observed No. of Plots Mean Actual Mean Absolute variable Value Residual Residual Aspen B A 10 12.82 48 1.34 2.39 B A 20 13.99 48 1.78 3.76 B A 30 14.79 48 1.68 4.93 Density 10 581.82 48 -9.42 53.69 Density 20 509.58 48 -16.36 71.23 Density 30 441.49 48 -23.15 77.71 D B H q 10 16.75 48 1.02 1.37 D B H q 20 18.70 48 1.41 2.17 D B H q 30 20.66 48 1.57 2.86 Spruce B A 10 11.88 48 0.66 0.88 B A 20 14.35 48 2.37 2.42 B A 30 16.72 48 3.77 3.89 Density 10 447.75 48 -3.74 8.09 Density 20 428.70 48 0.71 13.50 Density 30 410.37 48 0.96 25.00 D B H q 10 18.38 48 0.65 0.93 D B H q 20 20.65 48 1.47 1.77 D B H q 30 22.78 48 2.19 2.64 Lodgepole pine B A 10 6.97 47 -0.45 0.79 B A 20 7.80 47 -0.82 1.44 B A 30 8.60 47 -1.51 2.18 Density 10 152.81 47 4.06 11.14 Density 20 145.13 47 -0.10 16.51 Density 30 136.39 47 -5.56 22.86 D B H q 10 24.09 47 -1.30 1.63 DBHq 20 26.16 47 -1.87 2.34 DBHq 30 28.33 47 -2.62 3.14 Subalpine fir B A 10 1.66 14 0.16 0.18 B A 20 1.96 14 0.43 0.46 B A 30 2.16 14 0.80 0.83 Density 10 64.65 14 -0.04 1.46 Density 20 59.99 14 2.97 3.98 Density 30 59.12 14 8.68 10.02 Dbhq 10 18.07 14 1.60 1.93 Dbhq 20 20.38 14 2.73 3.17 Dbhq 30 21.55 14 3.63 4.08 131 In summary the 30 year simulation generally followed the development of the permanent sample plots well. SORTIE-ND had a tendency to overestimate basal area which was mainly caused by over predicted spruce growth. The overestimation of growth could be caused by the lack of competition from understory trees in the simulations compared to the actual plots. On the other hand, the geographic distribution of the permanent plots was expected to lead to underestimation of growth. Stand density was generally well-predicted, the main divergence was caused by aspen where SORTIE-ND did the poorest job of estimating mortality rates. One important divergence was that predicted aspen growth seemed to be too strongly influenced by high densities of large spruce. The 20 year and 10 year simulations of understory and suppressed trees The species-specific summary statistics for the twenty-year simulation of understory and suppressed trees showed slightly different trends than the initial 30 year simulation (Table 5.4). Generally, SORTIE-ND underestimated the mortality of the understory and suppressed trees investigated in the 20 year simulation. This was especially the case for aspen (Table 5.5, Figure 5.7). For spruce, lodgepole pine, and subalpine fir, the mortality rates were slightly underestimated and an overestimation of mortality was observed for a significant portion of the simulations (Table 5.5, Figure 5.7 & 5.8). From the summary statistics (Table 5.5), basal area and DBHq of all species (especially aspen) were overestimated. Unfortunately, the summary statistics on basal area and DBHq were not very informative, as they were driven by the difference in mortality rates. For aspen and pine, the summary statistics were especially influenced by the low-density plots where these species disappear in the permanent plots, while a few trees survive in the simulations. These simulations are represented by the horizontal lines for aspen and lodgepole pine DBHq in Figures 5.7-5.10. The main reason that aspen or pine never disappeared in the simulations, while they did so repeatedly in the plot data (Figure 5.7 & 5.8), was the size difference between the permanent plots and the simulated plots. The permanent plots were approximately 0.1 ha in size while the simulated plots were 9 hectares. Thus, existence of 1 aspen or pine in a plot represents approximately 10 trees/ha and approximately 90 trees in a simulation. In a low density plot with one or two understory aspen or pine these species will often die off in the 20 year period. On the 132 other hand, it is likely that some of the 90 or 180 trees in the simulation will be randomly assigned a favorable position in the canopy and will survive for the 20 year period. The species-specific summary statistics for the 10 year simulation of in-growth showed similar trends to the 20 year simulation (Table 5.6, Figure 5.9 & 5.10). Aspen mortality was clearly underestimated, while the coniferous species exhibited a slight tendency for underestimation of mortality rates. However, for the conifer species, the predicted density development patterns were quite similar to the permanent sample plots. The predicted growth rates of the three conifer species were very similar to the observed growth rates (Figure 5.9 & 5.10). For aspen, the growth was hard to assess due to the difference in mortality rates. 133 Table 5.5. Species-specific summary statistics for the 20-year simulation of understory and suppressed trees. A negative Mean Actual Residual indicates that the SORTIE-ND predictions on average were lower than the plot values. The Mean Actual Residual value illustrates the average difference between the predicted values and the observed values. Response Year Mean Observed No. of Plots Mean Actual Mean Absolute variable Value Residual Residual Aspen B A 20 36 1.29 0.87 0.87 B A 30 36 0.96 1.67 1.68 Density 20 36 178.57 44.19 53.69 Density 30 36 103.65 77.47 78.32 D B H q 20 36 9.60 3.00 3.00 DBHq 30 36 10.87 6.37 6.37 Spruce B A 20 49 2.12 0.49 0.54 B A 30 49 2.69 1.05 1.21 Density 20 49 258.60 24.85 29.98 Density 30 49 234.46 32.03 42.64 DBHq 20 49 10.21 0.61 0.84 DBHq 30 49 12.10 1.27 1.91 Lodgepole pine B A 20 19 0.28 0.04 0.08 B A 30 19 0.29 0.10 0.13 Density 20 19 32.04 1.17 9.19 Density 30 19 22.66 5.30 9.73 DBHq 20 19 10.49 2.37 2.48 DBHq 30 19 12.76 3.95 4.10 Subalpine fir B A 20 21 0.31 0.03 0.06 B A 30 21 0.44 0.10 0.16 Density 20 21 40.52 1.70 2.44 Density 30 21 38.40 3.35 4.57 DBHq 20 21 9.90 0.10 1.19 DBHq 30 21 12.08 0.51 2.25 134 ea. sz 'PS E "o OS si o H < •Q 1 i s H o Q. AT Observed BA (m2/ha) 0 SX 5 10 15 BA (m2/ha) E to u as a CM Q 0 200 800 AT Observed Stems/ha m E M CO T3 .2 o £ el o o CM o o C O o "3-i — i — r n — i — i — r .0 400 800 1200 SX Observed Stems/ha CD Q. M <D i— a C M 10 15 AT Observed DBHq (cm) 5X Observed DBHq (cm) Figure 5.7. Aspen (AT) and spruce (SX) predicted values versus observed values from the 20-year simulation. A circle indicates an observation. The three observations from each plot are connected with a line. 135 0 1 2 3 4 PL Observed BA (m2/ha) T — i 1 r — r 0 50 100 200 PL Observed Stems/ha i r — i 1 r 0 5 10 15 20 PL Observed DBHq (cm) BL Observed BA (m2/ha) 0 50 150 250 BL Observed.Stems/ha 0 5 10 15 20 BL Observed DBHq (cm) Figure 5.8. Lodgepole pine (PL) and subalpine fir (BL) predicted values versus observed values from the 20-year simulation. A circle indicates an observation. The three observations from each plot are connected with a line. 136 The mortality rates in the 30 year simulation of overstory trees were slightly overestimated, while the mortality rates in the 10 and 20 year simulations of the understory were underestimated. For both the understory and overstory, the divergence from the observed mortality rates was mainly driven by the aspen density. One explanation for this divergence pertains to the agents of mortality. It is likely that a larger portion of understory tree mortality, especially for aspen, is driven by agents other than competition. For example, moose browse is very common on understory aspen in the SBS zone. In SORTIE-ND such mortality is covered by the random mortality function, which is independent of position in the canopy. Thus, to better represent non-density dependent mortality, the random mortality should be made dependent on canopy position and tree size. Table 5.6. Species-specific summary statistics for the 10-year simulation of understory trees. A negative Mean Actual Residual indicates that the SORTIE-ND predictions on average were lower than the plot values. The Mean Actual Residual value illustrates the average difference between the predicted values and the observed values. Response variable Year Mean Observed Value No. of Plots Mean Actual Residual Mean Absolute Residual Aspen B A 30 0.40 19 0.53 0.55 Density 30 77.64 19 48.78 50.62 DBHq 30 8.07 19 4.68 5.22 Spruce B A 30 0.67 44 0.16 0.20 Density 30 150.61 44 13.03 20.13 DBHq 30 7.52 44 0.42 0.88 Lodgepole pine B A 30 0.11 10 0.03 0.03 Density 30 23.02 10 0.22 4.18 DBHq 30 7.64 10 3.08 3.08 Subalpine fir B A 30 0.30 36 0.04 0.07 Density 30 66.25 36 2.30 3.14 DBHq 30 7.65 36 0.04 1.12 137 i — i — i — i — i — r 0 2 4 6 8 10 1 — i — i — i — i — r 0 1 2 3 4 5 A T Observed B A (rn2/ha) S X Observed BA (m2/ha) 1 I I " I — 1—1—I—I—I— 0 5 10 15 2 4 6 8 10 A T Observed DBHq (cm) S X Observed D B H q (cm) Figure 5.9. Aspen (AT) and spruce (SX) predicted values versus observed values from the 10-year simulation. A circle indicates an observation. The two observations from each plot are connected with a line. 138 0.0 0.5 1.0 1.5 0.0 1.0 2.0 PL Observed BA(m2/ha) BL Observed BA (m2/ha) w .£• CO "Q _ T 3 CD CL O O o o L O T 1 "I T 0 50 100 150 PL Observed Stems/ha P •T i T 3 CL i i i i—i—r 0 2 4 6 8 12 PL Observed DBHq (cm) ~<J> E w T3 CL 8 J o Lf) t 1 — n — t 0 50 150 BL Observed Stems/ha c w CO 0) t5 _ I I II—i—i—r 0 2 4 6 8 12 BL Observed DBHq (cm) Figure 5.10. Lodgepole pine (PL) and subalpine-fir (BL) predicted values versus observed values from the 10-year simulation. A circle indicates an observation. The two observations from each plot are connected with a line. 139 In summary, the 20 and 10 year simulations of understory and suppressed trees illustrate that SORTIE-ND has problems predicting aspen mortality. The mortality and growth rates for the three conifer species seem quite well-predicted. Nevertheless, for the three conifer species there was a small tendency for underestimating mortality rates in the understory. Recommendations for further model development One of the objectives of this evaluation was to guide future model development. As such this evaluation has highlighted four areas. (1) To make the model understory light predictions robust across different stand densities, the crown sizes of individual trees should be made density dependent and crown shyness should be incorporated into the model. (2) Changes are required to make early self-thinning of shade-intolerant species, such as aspen and lodgepole pine, more realistic. These changes would entail reprogramming the growth-dependent juvenile mortality function so it only applies to trees in the understory. (3) Mature aspen growth rates, especially in the presence of spruce, require further research. As the current aspen data set used for parameterization of the adult aspen growth function is small, this would likely entail collecting additional data. (4) It is recommended that the random mortality should be made dependent on canopy position and tree size. This would allow higher random mortality rates for understory trees than young trees in a clear-cut or overstory trees. Currently SORTIE-ND is parameterized, but not calibrated. Parameterization is the process in which the parameters in an equation are fitted to a dataset. Calibration is the processes in which the predictions from a model are compared with observations and afterwards one or more parameters in the model are changed to produce predictions that match the observations. Most growth models have some kind of calibration performed in order to make the predictions realistic. There is no doubt that SORTIE-ND could conform better with the permanent plot data i f the model were calibrated. On the other hand, this is generally against the basic ideas from which the model was developed. As a research tool used to understand basic ecological questions such as successional dynamics, calibration is not appropriate as is does not necessarily allocate the changes to the correct processes. For a model used in management, a calibration is more appealing 140 as it, for example, might reduce biases in volume predictions. An obvious example where SORTIE-ND could be calibrated is spruce growth rates. The comparison to the permanent sample plots illustrated that spruce growth was slightly overestimated in young stands. Comparison to other single-species stand level models also indicates that SORTIE-ND slightly overestimates spruce growth. Thus, it is tempting to calibrate the parameter that determines the maximum increment of spruce radial growth. SORTIE-ND predictive ability and implications for use in management The evaluation shows that SORTIE-ND produces biologically believable predictions of stand development patterns for mixed-species stands in the SBS zone. For overstory trees, the comparison to permanent sample plots illustrated that the model generally predicted the growth and mortality rates well. The largest problem with prediction of overstory development was aspen mortality rate and a tendency for overestimating spruce growth. For understory and suppressed spruce, lodgepole pine, and subalpine fir, growth and mortality rates were generally well predicted, with a slight tendency for overestimating growth rates. For understory aspen, mortality rates were underestimated. There is currently interest in using SORTIE-ND as a decision support tool for growth prediction in complex stands, such as underplanted, partially-cut, and mountain pine beetle infected stands. Thus, the obvious question is whether SORTIE-ND is appropriate for such use. In line with the general approach to this evaluation, a simple yes or no answer to this question is not supplied. This evaluation was designed to provide a basis for comparison to other models and to describe the predictive ability of SORTIE-ND so that uncertainty associated with the model predictions is better understood. It must be emphasized that a model can be appropriate for one purpose but not for another. For example, for stand level silvicultural planning and decision making, the most important feature of a growth model is that it can correctly rank different scenarios and produce approximately correct stand structures. This evaluation implies that in most cases the predictive ability of SORTIE-ND is sufficient to make such rankings of silvicultural alternatives. This does not necessarily make SORTIE-ND the most appropriate model for such use, but it means a potential user should consider the model for this application. 141 Chapter 5 references Balci, O. and Sargent, R.G. 1984. A bibliography on the credibility assessment and validation of simulation and mathematical models. Simuletter 15: 15-27. Botkin, D.B. 1993. Forest dynamics: an ecological model. Oxford University Press, Oxford. 328 P-Botkin , D.B., Janak, J.F. and Wallis, J.R. 1972. Rationale, limitations, and assumptions of a northeastern forest simulator. International Business Machine Journal of Research and Development 16: 106-116. Brand G.J. and Holdaway, M.R. 1983. Users need performance information to evaluate models. J. For. 81: 235-237, 254. Buchman, R.G. and Shifley, S.R. 1983. Guide to evaluating forest growth projection systems. J. For. 81: 231-234. Bunnell, F.L. 1989. Alchemy and uncertainty: what are good models?. US Forest Service, General Technical Report, PNW-GTR-232. Canham, C D . 1988. An index of understory light levels in and around canopy gaps. Ecology 69: 1634-1638. Canham, C D . , Coates, K .D. , Bartemucci, P. and Quaglia, S. 1999. Measurement and modeling of spatially explicit variation in light transmission through interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1775-1783. Canham, C D . , LePage, P.T., and Coates, K.D. 2004. A neighborhood analysis of canopy tree competition: effects of shading versus crowding. Can. J. For. Res. 34: 778-787. 142 Coates, K.D. , Canham, C D . , Beaudet, M . , Sachs, D.L. and Messier, C. 2004. Use of a spatially explicit individual-tree model (SORTIE-BC) to explore the implications of patchiness in structurally complex forests. For. Ecol. Manage. 186: 297-310. Freese, F. 1960. Testing accuracy. For. Sci. 6: 139-145. Fossett, C.A., Harrison, D., Weintrob, H. and Gass, S.I. 1991. An assessment procedure for simulation models: a case study. Operations Research 39: 710 - 723. Frey, H . C and Patil, S.R. 2002. Identification and review of sensitivity analysis methods. Risk Analysis 22: 553-578. Goulding, C.J. 1979. Validation of growth models used in forest management. N.Z. J. For. 24: 108-124. Huang, S., Yang, Y . and Wang, Y . 2003. A critical look at procedures for validating growth and yield models. In: Amaro, A. , Reed, D. and Soares, P. (editors). Modelling Forest Systems. C A B International, p. 271-293. Kleijnen, J.P.C. 1998. Experimental design for sensitivity analysis, optimization, and validation of simulation models. In: Banks, J. (editor). Handbook of simulation. Wiley, New York. P. 173-224. Kleijnen, J.P.C. 1999. Validation of models: statistical techniques and availability. In: Farrington, P.A., Nembhard, H.B., Sturrock, D.T. and Evans, G.W. (editors). Proceedings of the 1999 Winter Simulation Conference, p.647-654. Kobe, R.K. and Coates, K .D. 1997. Models of sapling mortality as a function of growth to characterize interspecific variation in shade tolerance of eight tree species of northwestern British Columbia. Can. J. For. Res. 27: 227-236. Kozak, A . 2004. M y last words on taper equations. For. Chron. 80: 507-515. 143 LePage, P.T., Canham, C D . , Coates, K .D. and Bartemucci, P. 2000. Seed sources versus substrate limitations of seedling recruitment in interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 30: 415-427. Lexer, M.J. and Honninger, K . 2004. Effects of error in model input: experiments with a forest patch model. Ecol. Model. 173: 159-176. Makela, A. , Landsberg, J., Ek, A.R., Burk, T.E., Ter-Mikaelian, M . , Agren, G.I., Oliver, C D . and Puttonen, P. 2000. Process-based models for forest ecosystem management: current state of the art and challenges for practical implementation. Tree Phys. 20: 289-298. Meidinger, D. and Pojar, J. 1991. (compilers and editors). Ecosystems of British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Special Report Series No. 6. Meidinger, D., Pojar, J. and Harper, W.L. 1991. Sub-Boreal Spruce Zone. In: Meidinger, D. and Pojar, J. (editors and compilers). Ecosystems of British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Special Report Series No. 6. p 209-221. Ministry of Forests and Range 2006. Site index estimates by site series: report by region (2006 approximation). Available at: http://www.for.gov.bc.ca/hre/sibec/sisuByRegion.pdf. Last accessed: July 10, 2006. Monserud, R.A. 2003. Evaluating forest models in a sustainable forest management context. FBMIS 1: 35-47. Montgomery, D.C. 1997. Design and Analysis of Experiments, 4 t h Edition. John Wiley and Sons Inc. 704 p. Neter, J., Wasserman, W. and Kutner, M . H . 1989. Applied Linear Regression Models, 2 n d Edition, Irwin. 667 p. 144 Oliver, C D . and Larson, B.C. 1996. Forest stand dynamics, update edition. John Wiley & Sons, Inc, New York. 544 p. Oreskes, N . , Shrader-Frechette, K. , and Belitz, K. 1994. Verification, validation, and confirmation of numerical models in the earth sciences. Science 263: 641-646. Pacala, S. W., Canham, C. D., and Silander, J. A. , Jr. 1993. Forest models defined by field measurements: I. The design of a northeastern forest simulator. Can. J. For. Res. 23: 1980-1988. Pacala, S. W., Canham, C. D., Saponara, J., Silander, J. A. , Jr., Kobe, R. K. and Ribbens, E. 1996. Forest models defined by field measurements: II Estimation, error analysis, and dynamics. Ecol. Mon. 66: 1-43. Peterson, E.B. and Peterson, N . M . 1992. Ecology, management, and use of aspen and balsam poplar in the Prairie Provinces, Canada. Northern Forestry Centre, Edmonton. Special report 1. Popper, K.R. (1963) Conjectures and refutations: the growth of scientific knowledge. Routledge and K. Poul, London. 412 p. Pretzsch, H. , Biber, P. Dursky, J., von Gadow, K. , Hasenauer, PL, Kandler, G., Kenk, G., Kublin, E., Nagel, J., Pukkala, T., Skovsgaard, J.P., Sodtke, R. and Sterba, H . 2002. Recommendations for standardized documentation and further development of forest growth simulators. Forstwissenschftliches Centralblatt 121: 138-151. Reynolds, M.R. and Chung J. 1986. Regression methodology for estimating model prediction error. Can. J. For. Res. 16: 931-938. Reynolds, M.R., Jr., Bukhart, H.E. and Daniels, R.F. 1981. Procedures for statistical validation of stochastic simulation models. For. Sci. 27: 349-364. 145 Robinson, A.P. and Monserud, R.A. 2003. Criteria for the comparing adaptability of forest growth models. For. Ecol. Manage. 172: 53-67. Rykiel, E.J. Jr. 1996. Testing ecological models: the meaning of validation. Ecol. Model. 90: 229-244. Sargent, R.G. 1999. Validation and verification of simulation models. In: Farrington, P.A., Nembhard, H.B., Sturrock, D.T. and Evans G.W. (editors). Proceedings of the 1999 Winter Simulation Conference, p. 39-48. Shugart, H.H. 1984. A theory of forest dynamics: the ecological implications of forest succession models. Springer-Verlag, New York. 278 p. Sores, P., Tome, M . , Skovsgaard J.P. and Vanclay J.K. 1995. Evaluating a growth model for forest management using continuous forest inventory data. For. Ecol. Manage. 71: 251-265. Vanclay, J.K. and Skovsgaard J.P. 1997. Evaluating forest growth models. For. Ecol. Manage. 98: 1-12. Wright, E.F., Coates, K.D. , Canham, C D . and Bartemucci, P. 1998. Species variability in growth response to light across a climatic gradient in northwestern British Columbia. Can. J. For. Res. 28:871-886. Wright, E.F., Canham, C D . , Coates, K .D. 2000. Effects of suppression and release on sapling growth for eleven tree species of northern interior British Columbia. Can. J. For. Res. 30: 1571-1580. Yang, Y . , Monseurd, R.A. and Huang, S. 2004. An evaluation of diagnostic tests and their roles in validating forest biometric models. Can. J. For. Res. 34: 619-629. 146 Chapter 6: Summarizing Discussion Status of the three working hypotheses The initial working hypothesis stated that regional variation in the growth performance of understory aspen and spruce within western boreal and sub-boreal Canada exists and that this variation can be caused by two main effects. Either light transmission through overstory canopies differs between regions, and/or the light-growth relationship for understory trees exhibits regional variation. Regional variation in both aspen and spruce crown openness was found. However, within the western boreal mixedwood region the observed variation was too small to create major regional differences in understory light levels (Chapter 2). Regional variation in the light-growth relationship for understory aspen and spruce within western boreal and sub-boreal Canada was also observed. However, within aspen-dominated stands in the western boreal mixedwood region the observed species-specific light-growth relationship had a similar shape and magnitude (Chapter 3). In combination, the findings of Chapters 2 and 3 gave no indication of general changes in successional dynamics between aspen and spruce in western sub-boreal and boreal forests. Nevertheless, the observed regional variability resulted in regional variation in inter-specific competitive strengths that might influence the rate of mixed species stand development. In Fort Nelson, exceptionally good growth of aspen was observed and this provided aspen with a competitive advantage. On the other hand, the findings indicated that juvenile spruce in Smithers or Peace River required a smaller head start to successfully compete with aspen. Regional variation in light transmission and light-growth relationships were investigated simultaneously because their combined effects could strengthen regional variation in understory tree performance. If this were the case, rapid juvenile growth would be expected to be associated with low crown openness. However, a comparison of the results illustrated little correlation between the two. For example, in Fort Nelson where the observed juvenile aspen growth was highest, the second highest aspen crown openness was observed. In Smithers where the observed juvenile aspen growth was moderate to low, the highest aspen crown openness was observed. Thus, the observed regional variation in species-specific crown openness did not strengthen the observed 147 regional variation in light-growth relationships. This warrants the question of which factors determine the observed regional variation. Generally, the light-growth relationships and species-specific crown openness were not found to follow the same regional pattern. Thus, it is likely that they are not determined by the same factors or alternatively not equally influenced by these determinants. No obvious correlations between macro-climatic data and the variation in species-specific crown openness were observed (Chapter 2). It could be argued that a wider climatic gradient should have been sampled. A wider climatic gradient would likely have resulted in more pronounced relationships between climate and crown openness. Unfortunately, a wider climatic gradient would contain regions where aspen mainly is found on non-mesic sites and topographic factors influence tree growth more than macro-climatic variables. Thus, sampling along a wider climatic gradient would produce a very different dataset with factors other than macro-climate having increased importance. By including the data from Wright et al. (1998) the data for spruce light-growth relationships originated from a wider climatic gradient than the species-specific crown openness data. These data also exhibited a greater degree of regional variation. The second working hypothesis explored the causes of this variation and stated that the regional difference in the performance of understory spruce can be related to climatic variables and other variables such as overstory canopy-type. It was found that canopy-type best explained the observed variation in the shape of the light-growth relationship (Chapter 4). Under aspen-dominated mixedwood canopies, the light-growth relationship was found to be asymptotic. Under conifer-dominated canopies in colder climates, the light-growth relationship was found to be approximately linear. On the other hand, growth in full light was found to be correlated with macro-climate variables, especially growing season length measured as growing degree days (Chapter 4). The weakness of this analysis was that the data contained a partial correlation between canopy-type and growing season length. To confirm the findings, it would be necessary to have studies in one region over a range of different canopy-types. This would provide a better opportunity to separate the effects of different factors on understory spruce growth. However, the correlation between growing season length and canopy-type is an inherent 148 phenomenon in western boreal and sub-boreal Canada. Thus, for describing regional variation in understory spruce performance it might not be essential to identify the effects of different factors. The third and final working hypothesis stated that it is possible to incorporate short term measurement into a process-oriented model and obtain reasonable growth predictions for stand-level silvicultural planning. This hypothesis was included to integrate this study with existing research and to make the findings available to management. Chapter 5 illustrated how the findings from the previous chapters were incorporated into the stand level simulation model SORTIE-ND. The evaluation of SORTIE-ND illustrated that the model is capable of making reasonable predictions of mixed-species stand development (Chapter 5). Compared to permanent sample plot data, it was found that stand density patterns generally were well predicted, but that there were problems with the predicted aspen mortality rates. SORTIE-ND tended to overestimate growth rates, especially for spruce. Overall, the evaluation illustrated that it was possible to obtain reasonable prediction of growth and stand development with SORTIE-ND and that the model can be used as a decision support tool for management in complex stands. Contributions to the field of study Quantification of the relationship between growth and light availability for juvenile trees in general or in the western sub-boreal and boreal Canada is not unique (e.g. Gustafson 1943; Cayford 1957; Logan 1969; Comeau etal. 1993; Lord etal. 1993; Lieffers and Stadt 1994; Jobidon 1994; Pacala etal. 1994; Constabel and Lieffers 1996; Kayahara et al. 1996; Chen et al. 1996; Man and Lieffers 1997; Chen 1997a; Groot et al. 1997; Chen 1997b; Wright et al. 1998; Groot 1999; Coates and Burton 1999; Wang et al. 2000; Bedford et al. 2000; KiiBner et al. 2000; Coates 2000; Wang and Su 2002; Claveau et al. 2002; Burton 2002; Pothier and Prevost 2002; Comeau et al. 2003; Pritchard 2003; Kalischuk 2004; Lajzerowicz et al. 2004; Stadt et al. 2005; Green and Hawkins 2005; Claveau et al. 2005; Voicu and Comeau 2006). Studies of light transmission through mature overstory canopies are also plentiful in general and in western boreal and sub-boreal Canada (e.g. Monsi and Saeki 1953; Canham 1988; Chazdon 1988; Oker-Blom et al. 1991; Constabel and Lieffers 1996; Messier 1996; Ter-Mikaelian and Wagner 1997; 149 Man and Lieffers 1999; Lieffers et al. 1999; Stadt et al. 1999; Canham et al. 1999; Stadt and Lieffers 2000; Pinno et al. 2001; Beaudet et al. 2002; Comeau 2003; Pritchard 2003; Stadt et al. 2005). The novel part of this project was the paired sampling of both understory growth and overstory species-specific crown openness of aspen and spruce across a significant part of western boreal and sub-boreal Canada. In this respect, this study is unique and has expanded knowledge of regional variation in the relationship between light availability and understory tree growth. Chapter 4 summarized existing knowledge and utilized it to test hypotheses of what determines regional variation of understory tree growth. Thus, Chapters 2-4 have provided quantification and partial explanation of regional variation of understory tree growth and overstory light transmission in western boreal and sub-boreal Canada. Most studies are localized and limited to given regions by societal constraints, so studies of broad scale variation are pivotal for development of general theory. For example, many people would claim that the light-growth relationship for understory trees always follows an asymptotic pattern. As shown here, this is often true but not a general law. In forestry, there is a long tradition for growth and yield modeling (reviews in: Mohren and Burkhart 1994; Vanclay 1995; Peng 2000; Messier et al. 2003). In this study, SORTIE-ND was evaluated as a growth model and decision tool for forest management in complex stands (Chapter 5). SORTIE-ND utilizes a very different approach to growth prediction than other growth models in western boreal and sub-boreal Canada. This modeling approach stems from forest ecology rather than forest management. Rather than utilizing relationships derived from analysis of long-term permanent-plot measurements, as do most traditional growth models, the modeling approach of SORTIE-ND utilizes key processes and short term field measurements to make long term predictions. To many established growth modelers, this modeling approach is controversial and questionable. By performing an evaluation of SORTIE-ND as a growth model, Chapter 5 provides part of the basis for a more informed discussion on approaches to growth modeling. Chapter 5 utilized an ecological modeling approach in a traditional growth model setting. In this sense, Chapter 5 acted as a bridge between an ecological modeling tradition and the growth modeling tradition dominant in forest management. If nothing else, it is my hope that this work will contribute to a diversification of modeling approaches utilized in 150 western boreal Canada. In the field of modeling, it is important to have a variety of approaches as one approach never will be best for all purposes. Directions for future research This dissertation provided ideas for several future research topics. The most obvious topic is a further investigation of the difference between understory spruce growth under aspen-dominated and conifer-dominated canopies. In this case, a localized study with both canopy-types in same geographic location would be appropriate. Detailed measurements on resource availability and tree growth could provide a foundation for better teasing apart the determinants of understory spruce growth. The evaluation of SORTIE-ND illustrated several topics for further model development. Four of the obvious topics include: (I) creating a dynamic crown allocation model (behavior) that produces better crown allometry predictions for a wide range of stand densities (including development of crown shyness functions); (II) improving the adult aspen growth predictions, especially in dense stands and in the presence of spruce; (III) parameterizing the model to a wider range of sites types would be appropriate as it is currently only parameterized for mesic sites; (IV) improving the mortality functions, especially for aspen. Topics I-III all require substantial amounts of spatially explicit data. Obtaining such data is both expensive and labor intensive. Thus, development of more efficient approaches of data collection is an also an important research topic. The model evaluation (Chapter 5) illustrated that there were substantial levels of uncertainty associated with growth predictions in complex stands. Monte Carlo approaches to sensitivity analysis, as in Chapter 5, provide an approach for assessment of this uncertainty. Generally, decision making and planning in forest management do not 151 take this uncertainty into account. However, approaches for incorporating uncertainty into decision making are relatively well developed. Thus, an obvious research topic is to combine the knowledge of uncertainty of growth in complex stands with the approaches for incorporating uncertainty into decision making. Generally, this study has dealt with data from different geographic locations and has attempted to identify the causes of regional variation. Chapter 4 illustrated the large amounts of regionalized knowledge that exists on a topic such as the light-growth relationship. This topic is not a unique example and many topics have a wealth of regional data. Most widely used analysis approaches do not allow for incorporation of such different data sources. Give the limited research resources, this can be seen as an unfortunate loss of valuable information. Thus, development of approaches for combining different data sources is an interesting area for further research. Conclusion For aspen and spruce in western sub-boreal and boreal Canada this study investigated regional variation in: (1) species-specific crown openness for mature trees, and (2) light-growth relationships for juvenile trees. Regional variation in species-specific crown openness was found for both species, but the magnitude of the variation was judged to only cause small variation in understory light levels. Regional variation in the light-growth relationship was found for both species but no indications of shifts in the successional dynamics between the two species were observed. The regional variation in the two investigated quantities did not follow the same pattern and their combined effect cannot be expected to strengthen regional differences in understory tree performance. The regional shapes of the light-growth relationship were similar for the two species. The main observed difference between the two species was the initial fast growth of aspen. For spruce in aspen-dominated areas of the boreal mixedwood region, asymptotic light growth relationships were found. In western conifer-dominated regions, approximately linear light-growth relationships were observed. This regional variation was best explained by the different effect of aspen-dominated and conifer-dominated canopies on 152 the light-growth relationship. It is hypothesized that the different effects of canopy-type can be caused by several effects, including nutrient availability, soil temperature, and leaf-off period. The fact that the variations in the light-growth relationships were better explained by canopy-type than macro-climatic variables indicates that the mediating effect of canopy-type on micro-climate is stronger than the effect of macro-climatic variation. Finally, the findings of this study were incorporated in the stand level simulation model SORTIE-ND. An evaluation of SORTIE-ND illustrated that the model generally produces realistic predictions and can be used as a management tool. Compared to permanent sample plot data for mixed stands the model had problems predicting aspen mortality rates and tended to overestimate growth rates especially for spruce. Several structural changes were suggested to improve the model predictions. 153 Chapter 6 references Beaudet, M . , Messier, C. and Canham, C D . 2002. Predictions of understory light conditions in northern hardwood forests following parameterization, sensitivity analysis, and test of the SORTIE light model. For. Ecol. Manage. 165: 235-248. Bedford, L. , Sutton, R.F., Stordeur, L. and Grismer, M . 2000. Establishing white spruce in the boreal white and black spruce zone. New Forests 20: 213-233. Burton, P.J. 2002. Effects of clearcut edges on trees in the sub-boreal spruce zone of northwest-central British Columbia. Silva Fennica 36: 329-352. Canham, C D . 1988. An index of understory light levels in and around canopy gaps. Ecology 69: 1634-1638. Canham, C D . , Coates, K.D. , Bartemucci, P. and Quaglia, S. 1999. Measurement and modeling of spatially explicit variation in light transmission through interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1775-1783. Cayford, J.H. 1957. Influence of the aspen overstory on white spruce growth in Saskatchewan. Department of Northern Affairs and National Resources. Forestry Branch. Technical Note No. 58. Chazdon, R.L. 1988. Sunflecks and their importance to forest understory plants. Advances in Ecological Research 18: 1-63. Chen, H . Y . H . 1997a. Interspecific responses of planted seedlings to light availability in interior British Columbia: survival, growth, allometric patterns, and specific leaf area. Can. J. For. Res. 27: 1383-1393. Chen, H.Y.H. , Klinka, K. and Kayahara, G.J. 1996. Effects of light on growth, crown architecture, and specific leaf area for naturally established Pinus contorta var. latifolia and Pseudotsuga menziesii var. glauca saplings. Can. J. For. Res. 26: 1149-1157. 154 Chen, Y.H.C. 1997b. Interspecific responses of planted seedlings to light availability in interior British Columbia: survival, growth, allometric patterns, and specific leaf area. Can. J. For. Res. 27: 1383-1393. Claveau, Y . , Messier, C. and Comeau, P.G. 2005. Interacting influence of light and size on aboveground biomass distribution in sub-boreal conifer saplings with contrasting shade tolerance. Tree Phys. 25: 373-384. Claveau, Y . , Messier, C , Comeau, P.G. and Coates, K .D. 2002. Growth and crown morphological responses of boreal conifer seedlings and saplings with contrasting shade tolerance to a gradient of light and height. Can. J. For. Res. 32: 458-468. Coates, K .D. 2000. Conifer seedling response to northern temperate forest gaps. For. Ecol. Manage. 127: 249-269. Coates, K.D. and Burton, P.J. 1999. Growth of planted tree seedlings in response to ambient light levels in northwestern interior cedar-hemlock forests of British Columbia. Can. J. For. Res. 29: 1374-1382. Comeau, P.G. 2003. Estimating and managing understory light using aspen density and diameter in central and north-eastern B.C. Centre for Enhanced Forest Management, Department of Renewable Resources, University of Alberta. E F M research note 02/2003. Comeau, P.G., Braumandl, T.F. and Xie, C.Y. 1993. Effects of overtopping vegetation on light availability and growth of Engelmann spruce {Picea engelmannii) seedlings. Can. J. For. Res. 23: 2044-2048. Comeau, P.G., Wang, J.R. and Letchford, T. 2003. Influences of paper birch competition on growth of understory white spruce and subalpine fir following spacing. Can. J. For. Res. 33: 1962-1973. Constabel, A.J . and Lieffers, V.J . 1996. Seasonal patterns of light transmission through boreal mixedwood canopies. Can. J. For. Res. 26: 1008-1014. 155 Green, D.S. and Hawkins, C.D.B. 2005. Competitive interactions in sub-boreal birch-spruce forests differ on opposing slope aspects. For. Ecol. Manage. 214: 1-10. Groot, A . 1999. Effects of shelter and competition on the early growth of planted white spruce (Picea glauca). Can. J. For. Res. 29: 1002-1014. Groot, A . , Carlson, D.W., Fleming, R.L. and Wood, J.E. 1997. Small openings in trembling aspen forest: microclimate and regeneration of white spruce and trembling aspen. Natural Resources Canada, Canadian Forest Service, Great Lake Forestry Centre, Sault Ste. Marie, Ontario. NODA/NFP Technical Report TR-47. Gustafson, F.G. 1943. Influence of light upon tree growth. J. For. 41: 212-213. Jobidon, R. 1994. Light threshold for optimal black spruce (Picea mariana) seedling growth and development under brush competition. Can. J. For. Res. 24: 1629-1635. Kalischuk, M . L . 2004. Influence of site quality and overstory age on the growth of understory white spruce in boreal mixedwood stands [M.Sc. Thesis]: University of Alberta, Edmonton. 117 p. Kayahara, G.J., Chen, H .Y.H. , Klinka, K. and Coates, K.D. 1996. Relations of terminal growth and specific leaf area to available light in naturally regenerated seedlings of logdepole pine and interior spruce in central British Columbia. B.C. Ministry of Forests, Research Branch, Victoria, B.C. Research Report 09. KuBner, R., Reynolds, P.E. and Bell, F.W. 2000. Growth response of Picea mariana seedlings to competition for radiation. Scand. J. For. Res. 15: 334-342. Lajzerowicz, C.C., Walters, M.B. , Krasowski, M . and Massicotte, H.B. 2004. Light and temperature differentially colimit subalpine fir and Engelmann spruce seedling growth in partial-cut subalpine forests. Can. J. For. Res. 34: 249-260. 156 Lieffers, V.J . , Messier, C , Stadt, K.J . , Gendron, F. and Comeau, P.G. 1999. Predicting and managing light in the understory of boreal forests. Can. J. For. Res. 29: 796-811. Lieffers, V.J . and Stadt, K.J . 1994. Growth of understory Picea glauca, Calamagrostis canadensis, and Epilobium angustifolium in relation to overstory light transmission. Can. J. For. Res. 24: 1193-1198. Logan, K.T. 1969. Growth of tree seedlings as affected by light intensity. IV. Black spruce, white spruce, balsam fir, and eastern white cedar. Canadian Forestry Service. Publication No. 1256. Lord, D., Morissette, S. and Allaire, J. 1993. Influence of light intensity, night air temperature and CO2 concentration on the growth of containerized black spruce (Picea mariana) seedlings in greenhouses. Can. J. For. Res. 23: 101-110. Man, R. and Lieffers, V.J . 1997. Seasonal photosynthetic responses to light and temperature in white spruce (Picea glauca) seedlings planted under an aspen (Populus tremuloides) canopy and in the open. Tree Physiol. 17: 437-444. Man, R. and Lieffers, V.J . 1999. Effects of shelterwood and site preparation on microclimate and establishment of white spruce seedlings in a boreal mixedwood forest. For. Chron. 75: 837-844. Messier, C. 1996. Managing light and understory vegetation in boreal and temperate broadleaf-conifer forests. In: Comeau, P.G. and Thomas, K.D. , (editors). Silviculture of temperate and boreal broadleaf-conifer mixtures. B.C. Ministry of Forests. Land Management Handbook 36. p. 59-81. Messier, C , Fortin, M.-J., Schmiegelow, F., Doyon, F., Cumming, S., Kimmins, J.P., Seely, B., Welham, C. and Nelson, J. 2003. Modelling tools to assess the sustainability of forest management scenarios. In: Burton, P.J., Messier, C , Smith, D.W. and Adamowicz, W.L. (editors). Towards sustainable management 157 of the boreal forest. National Research Council of Canada. N R C Research Press, Ottawa, p 531-580. Mohren, G.M.J, and Burkhart, H.E. 1994. Contrasts between biologically-based process models and management-oriented growth and yield models. For. Ecol. Manage. 69: 1-5. Monsi, M . and Saeki, T. 1953. Uber den lichtfakctor in den pflsnzengesellschaften und seine bedetung fur die stoffproduction. Jpn. J. Bot. 14: 22-52. Oker-Blom, P., Kaufmann, M . and Ryan, M . G . 1991. Performance of a canopy light interception model for conifer shoots, trees and stands. Tree Physiol. 9: 227-243. Pacala, S.W., Canham, C D . , Silander, J.A.J, and Kobe, R.K. 1994. Sapling growth as a function of resources in a north temperate forest. Can. J. For. Res. 24: 2172-2183. Peng, C. 2000. Growth and yield models for uneven-aged stands: past, present and future. For. Ecol. Manage. 132: 259-279. Pinno, B.D., Lieffers, V.J . and Stadt, K.J . 2001. Measuring and modelling the crown and light transmission characteristics of juvenile aspen. Can. J. For. Res. 31: 1930-1939. Pothier, D. and Prevost, M . 2002. Photosynthetic light response and growth analysis of competitive regeneration after partial cutting in a boreal mixedwood stand. Trees 16: 365-373. Pritchard, J .M. 2003. The effect of opening size on light, temperature and growth of white spruce under a trembling aspen canopy. [M.Sc. Thesis]: University of Alberta, Edmonton. 144 p. Stadt, K.J . , Lieffers, S.M. and Stewart, J.D. 1999. Crown characteristics of boreal conifers and application of the light model MIXLIGHT. Final report. Funded by Manning Diversified Forest Products Research Trust Fund MDFP 1/98. University of Alberta, Department of Renewable Resources, Edmonton. 158 Stadt, K.J . and Lieffers, V.J . 2000. MIXLIGHT: a flexible light transmission model for mixed-species forest stands. Agric. For. Meteorol. 102: 235-252. Stadt, K.J . , Lieffers, V.J . , Hall, R.J. and Messier, C. 2005. Spatially explicit modeling of PAR transmission and growth of Picea glauca and Abies balsamea in the boreal forests of Alberta and Quebec. Can. J. For. Res. 35: 1-12. Ter-Mikaelian, M.T. and Wagner, R.G. 1997. Distance-independent models for predicting photosynthetically active radiation transmission through young forest plant canopies. Can. J. For. Res. 27: 127-130. Vanclay, J.K. 1995. Growth models for tropical forests: a synthesis of models and methods. For. Sci. 41: 7-42. Voicu, M.F. and Comeau, P.G. 2006. Microclimate and spruce growth gradients adjacent to young aspen stands. For. Ecol. Manage. 221: 13-26. Wang, G.G. and Su, J. 2002. Growth of black spruce seedlings planted in burned, logged and undisturbed boreal mixedwood stands of southeastern Manitoba. For. Chron. 78: 275-280. Wang, G.G., Su, J. and Wang, J.R. 2000. Height growth of planted black spruce seedlings in response to interspecific vegetation competition: a comparison of four competition measures at two measuring positions. Can. J. For. Res. 30: 573-579. Wright, E.F., Coates, K.D. , Canham, C D . and Bartemucci, P. 1998. Species variability in growth response to light across climatic regions in northwestern British Columbia. Can. J. For. Res. 28: 871-886. 159 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0075039/manifest

Comment

Related Items