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Interspecific interactions in mixed stands of paper birch (Betula papyrifera) and interior Douglas-fir… Louw, Deon 2015

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      Interspecific interactions in mixed stands of paper birch (Betula papyrifera) and interior Douglas-fir (Pseudotsuga mensiezii, var. glauca)  by Deon Louw B.A. Athabasca University, 2007  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF   MASTER OF SCIENCE  in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  July 2015 © Deon Louw, 2015 ii  Abstract Growing mixed conifer-broadleaf forests instead of monoculture coniferous forests could reduce problems with seedling regeneration, disease and volume loss, all of which are expected to increase with warmer climates and more frequent droughts.  Understanding mixed forest dynamics, as well as their quickly evolving mycorrhizal symbionts, could reveal key management strategies for adapting to climate change.  This study is a long-term analysis of two field experiments established in 1992 in the southern interior of British Columbia, Canada, where I sought to gain insight into the outcomes and mechanisms of interspecific interactions in mixtures of broadleaves and conifers.  The broader experiment examined interactions within mixed stands of Douglas-fir and paper birch in an extensive response surface design, while a second experiment isolated rooting areas of individual trees within two density pairings embedded in the larger experiment.  The treatments were replicated across three geographically distinct sites within the same BEC subzone (ICHmw). Twenty-one years after the experiments were established, I found strong evidence of reduced Armillaria root disease and increased foliar nutrition in interior Douglas-fir with increasing density of paper birch neighbours, but no negative effect of paper birch competition on interior Douglas-fir growth.  This last result may be due in part to the comparatively weak status of the planted paper birch, which never overcame early poor performance.  The mechanisms by which the struggling paper birch interacted with interior Douglas-fir were revealed in the trenching experiment, where ability to form mycorrhizal networks resulted in cumulative benefits to paper birch over time, with significantly less growth loss in untrenched than trenched treatments.  This benefit was consistent across densities and regardless of climatic stress, pointing to a pattern of constant benefits of belowground interactions for subordinate tree species.  This finding points towards belowground interactions as a medium for balancing species inequalities and, by extension, of maintaining ecosystem diversity and stability.  Taken as a whole, these results illustrate the possible benefits of maintaining broadleaves in commercially valuable conifer plantations, both in terms of direct health benefits to conifers, and in the broader sense of providing negative feedback mechanisms to species loss and ecosystem instability.      iii  Preface This thesis is an original, unpublished product of the author, Deon Louw.  The identification of the research topic was done by supervisor Dr. Suzanne Simard and modified by Deon Louw and Suzanne Simard with input from committee members Dr. Gary Bradfield and Dr. Melanie Jones.  The performance of all parts of the research were lead by Deon Louw with the exception of the foliar and soil mineral analysis, which were sent to the British Columbia Ministry of Forests, Lands and Natural Resource Operations.  The tree-ring analysis (Chapter 2) was undertaken with the help of Dr. Lori Daniels and her lab at the University of British Columbia.  The analysis of the research data was done by Deon Louw with suggestions from PhD candidate Pascale Gibeau, Simon Fraser University and Dr. Amy Angert, University of British Columbia.   iv  Table of contents Abstract ......................................................................................................................................................... ii Preface ......................................................................................................................................................... iii Table of contents .......................................................................................................................................... iv List of tables ................................................................................................................................................. vi List of figures ............................................................................................................................................. viii Acknowledgements .....................................................................................................................................xiii Chapter 1 Introduction .................................................................................................................................. 1 Mixedwoods .............................................................................................................................................. 1 Mycorrhizal networks ............................................................................................................................... 2 Armillaria root disease .............................................................................................................................. 3 Understory composition ............................................................................................................................ 4 Overview of thesis .................................................................................................................................... 4 Chapter 2 Effects of root trenching on long-term stand dynamics in mixtures of Douglas-fir and paper birch .............................................................................................................................................................. 6 Introduction ............................................................................................................................................... 6 Methods .................................................................................................................................................. 12 Study sites ........................................................................................................................................... 12 Field data collection ............................................................................................................................ 13 Soil and foliar nutrients ....................................................................................................................... 14 Dendrochronology .............................................................................................................................. 15 Statistical analysis ............................................................................................................................... 15 Results ..................................................................................................................................................... 18 Growth ................................................................................................................................................ 18 Growth over time ................................................................................................................................ 18 Foliar nutrients .................................................................................................................................... 19 Soil nutrients ....................................................................................................................................... 19 Armillaria root disease incidence ........................................................................................................ 20 Discussion ............................................................................................................................................... 20 Growth ................................................................................................................................................ 21 Growth over time ................................................................................................................................ 21 v  Foliar nutrients .................................................................................................................................... 24 Armillaria root disease ........................................................................................................................ 25 Conclusion .............................................................................................................................................. 26 Recommendations for forest practice.................................................................................................. 27 Chapter 3 Long-term growth dynamics in experimental stands of planted interior Douglas-fir, paper birch and admixtures ............................................................................................................................................ 53 Introduction ............................................................................................................................................. 53 Methods .................................................................................................................................................. 58 Study sites ........................................................................................................................................... 58 Field data collection ............................................................................................................................ 59 Statistical analysis ............................................................................................................................... 60 Results ..................................................................................................................................................... 62 Growth ................................................................................................................................................ 62 Foliar nutrients .................................................................................................................................... 63 Armillaria root disease ........................................................................................................................ 63 Understory plant community .............................................................................................................. 64 Discussion ............................................................................................................................................... 65 Growth dynamics in response to competition ..................................................................................... 65 Foliar nutrients .................................................................................................................................... 66 Armillaria root disease ........................................................................................................................ 67 Understory diversity ............................................................................................................................ 69 Conclusions ............................................................................................................................................. 71 Management Implications ................................................................................................................... 71 Chapter 4 Summary and conclusions .......................................................................................................... 93 Review of objectives ............................................................................................................................... 93 Summary of main findings ...................................................................................................................... 93 Contribution to the field of study ............................................................................................................ 95 Limitations of studies .............................................................................................................................. 96 Future directions ..................................................................................................................................... 97 References ................................................................................................................................................... 98 Appendix A: R code used in analysis ....................................................................................................... 107  vi  List of tables  Table 2.1  Pre-harvest site characteristics.  Adapted from Simard 1997. ..................................... 28 Table 2.2 Model results showing density and trenching effects on height and diameter of paper birch and Douglas-fir. ................................................................................................................... 29 Table 2.3. Coefficient of variation (CV) for height and diameter at breast height (dbh) by species (Spp) and trenching treatment.  Fd is Douglas-fir, Ep is paper birch.  “no” refers to untrenched treatment, “yes” to trenched. ......................................................................................................... 30 Table 2.4  Generalized additive mixed model (GAMM) results for the annual growth increment including both paper birch and Douglas-fir.  Terms in parentheses indicate estimate factor levels that results refer to.  Smooth terms show treatment combinations per species: “high” and "low" refer to planted densities, while “trench” and “un” refer to trenched and untrenched treatments.  Asterisks are for significance levels; *** refers to α<0.01. .......................................................... 31 Table 2.5  Generalized additive mixed model (GAMM) results for the annual growth increment of Douglas-fir.  Terms in parentheses indicate estimate factor levels that results refer to.  Smooth terms show treatment combinations per species: “high” and "low" refer to planted densities, while “trench” and “un” refer to trenched and untrenched treatments.  Asterisks are for significance levels; *** refers to α <0.01. .................................................................................... 32 Table 2.6  Generalized additive mixed model (GAMM) results for the annual growth increment of paper birch.  Terms in parentheses indicate estimate factor levels that results refer to.  Smooth terms show treatment combinations per species: “high” and "low" refer to planted densities, while “trench” and “un” refer to trenched and untrenched treatments.  Asterisks are for significance levels; *** refers to α <0.01. .................................................................................... 33 Table 2.7.  Model results for significant foliar nutrients and nutrient ratios in Douglas fir.  Asterisks refer to significance levels.  ** is for α < 0.05 test level and * for α < 0.10.   N:Mg is nitrogen to magnesium ratio. ........................................................................................................ 34 vii  Table 2.8.  Model results for significant foliar nutrients and nutrient rations in paper birch.  Asterisks refer to significance levels.  ** is for α < 0.05 test level and * for α < 0.10.   N:S is nitrogen to sulphur ratio. ............................................................................................................... 35 Table 3.1.  Model results for target tree volume index as a function of neighbourhood volume index of Douglas fir and paper birch. ........................................................................................... 73 Table 3.2. Understory vegetation MRT results across sites.   “Groups” are significantly different associations of understory species, as predicted by selected explanatory variables, in “Variables” column; “Levels” are thresholds or identities of those chosen variables making up the terminal nodes in MRT.   “Indval” is indicator species value. .................................................................... 74 Table 3.3.  MRT results within site.  “Groups” are significantly different associations of understory species, as predicted by selected explanatory variables, in “Variables” column; “Levels” are thresholds or identities of those chosen variables making up the terminal nodes in MRT.   “Indval” is indicator species value ................................................................................... 77  viii  List of figures Figure 2.1  Study site locations.  Insert shows approximate location in British Columbia. ......... 36 Figure 2.2.  Variation in the diameter of target trees according to planted density and presence or absence of trenching.  a) paper birch; b) Douglas-fir.  X-axis labels refer to low (800/400) and high (3200/1600) planted densities of paper birch/Douglas-fir. ................................................... 37 Figure 2.3.  Variation in the height of target trees according to planted density and presence or absence of trenching.  Top panel is for paper birch; bottom panel is for Douglas-fir.  X-axis labels refer to low (800/400) and high (3200/1600) planted density treatments. ......................... 38 Figure 2.4.  Average Diameter at breast height by species and treatment.  “Fir” is Douglas-fir, “birch” is paper birch.  High D and Low D are  high (3200/1600) and low (800/400) planted density treatments.  Bars are standard error.  Number of trees per species/treatment combination varied between 4 and 6 individuals. .............................................................................................. 39 Figure 2.5.  Average height by species and planted density.  “Fir” is Douglas-fir, “birch” is paper birch.  High D and Low D are high (3200/1600) and low (800/400) planted density treatments.  Bars are standard error.  Number of trees per species/treatment combination varied between 4 and 6 individuals. .......................................................................................................................... 40 Figure 2.6.   Environmental variables by trenching in Douglas-fir. ............................................. 41 Figure 2.7   Environmental variables by trenching in paper birch. ............................................... 42 Figure 2.8.  Variation in growth over time in each of the eight time series, corresponding to combination of species, planted density, and trenching. Top row shows the linear relationships for birch time series. The bottom row shows the smoothed relationships for Douglas fir, in the same order as for paper birch.  The Y axis shows growth increment centered around their means; positive values correspond to increases from the mean, while negative values correspond to decreases from the mean.  Broken lines are confidence bands. .................................................... 43 Figure 2.9.  Variation of significantly different foliar nutrient concentrations and ratios by planted density in Douglas-fir (nitrogen, and nitrogen to magnesium ratio).  Nitrogen is ix  statistically significant between low and high density at α=0.1 and nitrogen to magnesium ratio by trenching at α=0.05.  X-axis labels refer to low (800/400) and high (3200/1600) planted density treatments. ........................................................................................................................ 44 Figure 2.10.  Variation of significant foliar nutrient concentrations and ratios paper birch. Top row are aluminum and copper, middle row iron and nitrogen to sulphur ratio and bottom panel is sodium.  X-axis labels refer to low (800/400) and high (3200/1600) planted density treatments.45 Figure 2.11.  Douglas-fir (a) multivariate regression tree showing the relationships among foliar nutrients and (b) pie charts for nutrient concentrations at terminal leaves.  Legend at left corresponds to response variable matrix.  The threshold value of variable determining split is shown at the top center of chart.  Numbers below terminal leafs are relative error and sample number for associated leaf.  Bar charts below terminal leafs show average response variable levels at leafs.  These are represented in the pie charts for clarity.  Values below plots refer to relative error, cross validated error and standard error of the full tree. ........................................ 46 Figure 2.12.  PCA biplot showing the correlation among soil variables sampled around Douglas-fir.  Objects in blue are individual target trees, by site and treatment, where ML=Malakwa, AL=Adams Lake, HL=Hidden Lake, Low=low density, High=high density, TR=trenched, UN=untrenched.  Black labels refer to soil variables.  “s” refers to soil.  “sBraymgkg” refers to available soil P.  “sCEC refers to soil cation exchange capacity.  The other soil variables are the nutrient concentrations, prefaced with “s”.  Scaling was type two, meaning angles between vectors approximate their correlation. .......................................................................................... 47 Figure 2.13.  PCA biplot showing the correlation among soil variables sampled around paper birch.  Objects in blue are individual target trees, by site and treatment, where ML=Malakwa, AL=Adams Lake, HL=Hidden Lake, Low=low density, High=high density, TR=trenched, UN=untrenched.  Black labels refer to soil variables.  “s” refers to soil.  “sBraymgkg” refers to available soil phosphorus.  Scaling was type two; meaning angles between vectors approximate their correlations. .......................................................................................................................... 48 Figure 2.14.  Paper birch (a) multivariate regression tree showing the relationships among foliar nutrients and (b) pie charts for nutrient concentrations at terminal leaves. Legend at left x  corresponds to response variable matrix.  The threshold value of variable determining splits is shown at the top center of chart.  Numbers below terminal leafs are relative error and sample numbers.  Bar charts below terminal leafs show average response variable levels.  These are represented in the pie charts for clarity.  Values below plots refer to relative error, cross validated error and standard error of the full tree. ........................................................................................ 49 Figure 2.15.  Classification tree showing variables influencing the presence of Armillaria in Douglas-fir. “y” indicates Armillaria presence, while “n” indicates absence. “SM” is soil moisture, “pca1” refers to the first axis of the soil PCA for Douglas-fir.  The numbers below the decision “y/n” of the branch are the sample (number of individual target trees) and the infection ratios: i.e. 1:0 = 100% (of eight trees) not infected.  The Tree has a residual mean deviance of 0.765 and a misclassification error rate of 0.136. ......................................................................... 50 Figure 2.16.  Classification trees showing variables influencing the presence of Armillaria in paper birch.  “y” indicates Armillaria presence, while “n” indicates absence.  “c.b” is conifer to broadleaf ratio, “pca1” refers to the first axis of the soil pca for paper birch.  The tree has a residual mean deviance of 0.5975 and a misclassification error rate of 0.1579. .......................... 51 Figure 2.17.  Variation in annual growth increment according to species, planted density, and presence of trenching. The solid line corresponds to the summer heat to moisture index (SHM), averaged over the three sample sites. ............................................................................................ 52 Figure 3.1.  Location of study sites in the southern interior of British Columbia.  Inset map is distribution of ICH BEC zone (from Ecosystems of BC), with map area in yellow. ................... 79 Figure 3.2.  Study design.  Treatments were randomly assigned in field (not as shown).  White number is paper birch, black number is Douglas fir, in stems per hectare.  Each block is 40m x 40m. .............................................................................................................................................. 80 Figure 3.3.  Birch neighbourhood analysis results.  Y-axis is log volume index (VI) of target trees, X-axis is neighbour Douglas fir volume index (upper panel), and paper birch neighbour volume index (lower panel).  Mixed model statement was log VI birch = VI birch x VI fir.  Full model results are found in Table 3.1. ............................................................................................ 81 xi  Figure 3.4.  Douglas fir neighbourhood analysis results.  Y-axis is volume index (VI) of target trees, X-axis is neighbour Douglas fir volume index (upper panel), and paper birch neighbour volume index (lower panel).  Mixed model statement was log VI birch = VI birch x VI fir.  Full model results are found in Table 3.1. ............................................................................................ 82 Figure 3.5.  Paper birch foliar nutrient multivariate regression tree.  “AL” is Adams Lake, “HL”, Hidden Lake and “ML”, Malakwa.  “par” is photosynthetic active radiation, “sm” is soil moisture, and “p.arm” is percentage of Armillaria in neighbours.  Bar graphs at terminal nodes refer to cluster compositions of foliar nutrient concentrations, as shown in legend at left.  Numbers below bar charts are relative error at the terminal node and number of trees making up the cluster at the node, respectively. ............................................................................................. 83 Figure 3.6  Interior Douglas-fir foliar nutrient multivariate regression tree.   “b.vi” is paper birch neighbour volume index; “p.arm” is percentage armillaria in neighbours; “HL” is Hidden Lake and “ML”, Malakwa.  Bar graphs at terminal nodes refer to cluster compositions of foliar nutrient concentrations, as shown in legend at left.  Numbers below bar charts are relative error at the terminal node and number of trees making up the cluster at the node, respectively. ......... 84 Figure 3.7.  Terminal node foliar nutrient clusters for Douglas fir, corresponding to terminal node bar charts in Figure 3.6.  Leaves 2 through 7 correspond to terminal node cluster of foliar nutrient concentrations from left to right in Figure 3.6. ............................................................... 85 Figure 3.8.  Armillaria classification tree for paper birch.  Letters below terminal nodes represent a “yes” (armillaria present) or “no” (armillaria absent); numbers refer to number of trees in group; ratios are purity of node, first number = “no”, second, “yes”; if branch refers to treatment groupings, the treatments are placed beneath the identity (yes/no) of the node, in hundreds of stems per hectare.  “percentArm” is percentage of armillaria in neighbours, “vi” is target fir volume index, and B.vi is neighbour broadleaf volume index. .................................................... 86 Figure 3.9.  Classification tree for Armillaria in Douglas fir.  Letters below terminal nodes represent a “yes” (armillaria present) or “no” (armillaria absent); numbers refer to number of trees in group; ratios are purity of node, first number = “no”, second, “yes”; if branch refers to treatment groupings, the treatments are placed beneath the identity (yes/no) of the node, in xii  hundreds of stems per hectare.  C.p. is percent carbon in soil; percentArm is percentage of armillaria in neighbouring trees; C.N is number of conifers in the plot; Nmg.kg is milligrams of N per kilogram in soil; “Fd.vi” is volume index of Douglas fir neighbours; Ca is soil calcium concentration. ................................................................................................................................ 87 Figure 3.10.  Multivariate regression tree for understory vegetation at Adams Lake, Hidden Lake and Malakwa.  Bar graphs at terminal nodes refer to cluster compositions of foliar nutrient concentrations.  Numbers below bar charts are relative error at the terminal node and number of trees making up the cluster at the node, respectively.  Statistics at bottom of figure refer to relative error, cross-validated error and standard error (SE). ....................................................... 88 Figure 3.11.  Principal Component Analysis (PCA) biplots of indicator species per treatment, by site; a) Adams Lake, b) Hidden Lake, and c) Malakwa.  Blue Labels refer to treatment densities in stems per hectare; “T” is treatment; first number is paper birch, the second, Douglas fir.  Black labels refer to indicator species.  Axis scores for Adams Lake were 54% along primary axis and 25% along secondary axis; for Hidden Lake, 65% along primary axis and 17% along secondary axis, and for Malakwa, 64% along the primary and 15% along the secondary axis.  Full MRT results from which the biplots were constructed are found in Table 3.3. ..................................... 91 Figure 3.12.  Mean current vs. planted densities of birch and fir.  Birch values are first number, fir second along horizontal axis. ................................................................................................... 92 xiii  Acknowledgements I would like to thank my very special supervisor, Dr. Suzanne Simard, for her vision, enthusiasm, compassion and humour, in guiding me through the wilderness and always seeing the forest for the trees through the life of this project.  It goes without saying, but I could not have done it without her.  I would also like to thank my dear wife, Pascale, for her unflagging optimism and support in all parts of the journey.  My mother also inspired me greatly throughout the process, as she also had the courage and fortitude to return to graduate studies at an advanced age.  Furthermore, these three women are perhaps the people who have most firmly believed in me in my life.  I cannot thank them enough. My committee members, Dr. Gary Bradfield and Dr. Melanie Jones deserve credit for their empathy and wisdom, I could not have asked for more.  Dr. Lori Daniels was instrumental in allowing me the use and expertise of her lab.  Finally, I would like thank my lab members, past and present, who always challenged me and provided a safe environment to air matters of acedemic and personal importance.  Dr. Brian Pickles, our Post Doctoral Fellow, gave freely of his time and knowledge whenever asked; we wish him the best in his new post.  Funding for my Masters was provided through an NSERC CREATE grant, TerreWEB, which allowed me to grow as a communicator as well as a scientist.  I especially am endebted to Professor Emeritus, Les Lavkulich, in this regard, who took time from the busiest “retired” schedule possible to guide me surely through the perils of presenting one’s work to others.    1  Chapter 1 Introduction There are two main questions explored in this thesis: (1) what are the outcomes of competition in mixed Douglas-fir-paper birch plantations in southern interior British Columbia and (2) what role do belowground interactions play in mediating this competition. Mixedwoods Mixedwood forests include broadleaf and conifer tree species and occur naturally in many northern biomes, including the temperate forests of southern interior British Columbia.  Benefits of retaining the often-removed or reduced broadleaf component in managed forests include maintaining diversity of ectomycorrhizae (Jones et al. 1997) and understory plants (Baleshta et al. 2015; Chávez and Macdonald 2012 ), and increasing disease resistance, all of which contain reciprocal benefits for tree stands and the stability of the broader ecosystem.  The decision to remove or reduce broadleaf neighbours from managed stands often rests on the notion that broadleaves out-compete conifers at early stages of stand development, resulting in volume loss for valuable conifer or “crop” species (British Columbia Ministry of Forests 2000).  Contrary to this belief, evidence exists that in some stands, broadleaf inclusion actually increases conifer volume (Bauhus and Shmerbeck 2010).  Furthermore, while broadleaf growth rates normally exceed those of conifers in British Columbia interior forests during the stand initiation phase of development, this relationship is reversed after age forty (Simard and Sachs 2004), at which time a broadleaf competitor reduces the intensity of intraspecific competition between conifers.  This is due to both above-ground and below-ground interactions, where the roots of individuals of different species occupy distinct soil depths and contain distinct root architectures.  Broadleaf inclusion in conifer stands is also linked to reduced infection of conifers by root pathogens, such as Armillaria soldipes (Morrison et al. 1991; Simard et al. 2005; Cleary et al. 2008).  Finally, although few research studies have examined this topic, diverse canopy structures composed of mixed species and their associated light transmittance profiles, would be expected to create distinct understory compositions, which in turn would harbour diverse microfauna and mycorrhizal associations, all of which contribute to overall biodiversity, tree community health and ecosystem stability (Jactel et al. 2006; Haas et al. 2011; Knoke et al. 2  2007).  While recent attention has been paid to positive interactions between different tree species in mixed forests (Cavard et al. 2011; Drobyshev et al. 2013), much of this work has been done in observational studies or literature reviews.  Our study provides a unique opportunity to examine these relationships in a controlled and replicated long-term experiment.  Mycorrhizal networks Mycorrhizal networks (MNs) are recognized for their important role in plant interactions (van der Heijden and Horton 2009; Johnson and Gilbert 2014).  Mycorrhizae are symbioses between plant roots and mycorrhizal fungi, where plants provide the fungi with photosynthetic carbon and the fungi provide plants with water and essential nutrients acquired from the soil such as phosphorus and nitrogen (Smith and Read 2008).  When two or more plants are linked by the same mycorrhizal fungal individual, they form a MN, through which carbon, limiting nutrients and water can transfer between them (Selosse et al. 2006; Egerton-Warburton et al. 2007; Meding and Zasoski 2008). The majority of studies examining ectomycorrhizal (EM) networks show they have the effect of enhancing performance of seedlings when linked to nearby established trees (van der Heijden & Horton 2009; Dickie 2005; McGuire 2007; Teste et al. 2010; Bingham and Simard 2012).  In an examination of EM fungal communities in a 120 year-old mixed conifer-broadleaf chronosequence, the potential for MN formation between paper birch and interior Douglas-fir was established (Twieg et al. 2007).  The potential for formation of MNs was further shown to increase interior Douglas-fir establishment under the canopies of these mixed forests (Simard et al. 1997).  Less research, however, has examined the effects of ectomycorrhizal MNs on interspecific competition in plant mixtures, one exception being Perry et al. (1989), who found reduced competition between Douglas-fir and ponderosa pine with MN access in a pot experiment.  An even greater dearth of information exists on the long-term effects of MNs on mixed forest development across time.  MNs are known to transfer resources bi-directionally between trees along source-sink gradients, from nutrient-rich to nutrient-poor neighbors (Simard et al. 1997b, Song et al. 2015), and that the direction of net transfer varies with season (Philip and Simard, 2008).  As trees are long-lived organisms and their relative dominance changes as stands develop, patterns of nutrient exchange through, or benefit from, MNs ought to shift 3  concurrently.  There have been no field experiments to date examining the effects of MNs on mixed stand dynamics over extended time periods. Armillaria root disease Armillaria root disease is caused by a generalist pathogen, Armillaria solidipes, which attacks and kills woody shrubs and trees of all species and ages.  It may remain dormant in the soil as a saprotroph for many years until it encounters a living carbon source, when it can switch to its pathogenic lifestyle.  It spreads rapidly by root-to-root contact or through rhizomorphs.  It is responsible for a 2-3 million m3 loss in the Canada’s Pacific Northwest (Sturrock et al. 2007), and is expected to increase in severity with climate change (Sturrock et al. 2007).  Current forest practices use either destumping during site preparation or pushover logging during harvesting to reduce the inoculum potential of the pathogen.  A less ecologically invasive control technique is the inclusion of more disease-resistant, naturally-regenerated broadleaf species in mixture with planted conifers (Morrison et al. 1991; Simard et al. 2005; Cleary et al. 2008).  While observational studies report that mixedwoods have lower pathogen infection rates than pure conifer stands, there have been few controlled experiments comparing root disease incidence in mixed stands versus monocultures.  One exception is Morrison et al. (1988), who found that disease incidence in interior Douglas-fir and lodegepole pine was lower when they were mixed with paper birch or western red cedar.  Examining long-term experiments would provide further insight into the ability of mixtures to provide conifers protection from disease over the course of stand development, as well as identify optimal levels of mixing for both conifer growth and protection.      No studies have examined the effect of ectomycorrhizal MNs in conifer-broadleaf forests on Armillaria root disease spread.  Recent work in arbuscular mycorrhizal systems showed that tomato plants infected with a pathogen sent defense signals via MNs to uninfected neighbors, which then up-regulated their defense response (Song et al. 2010).  Protective strategies of EM fungi in forests are potentially many, including providing a protective mantle over the root, reducing root carbon, and associating with mycorrhizal helper bacteria (Marx 1972), which have been shown to be antagonistic to pathogens (Frey-Klett et al. 2007).   4  Understory composition  Forest understory plants carry out and maintain many vital ecosystem processes.  Understory plants enrich soils and cycle nutrients at levels disproportionate to their relatively small biomass (Gilliam 2007; Wedraogo et al. 1993). They provide habitat for insects and small mammals that are critical in nutrient cycling and the distribution and germination of tree seeds.  Herbaceous layers affect tree seedling regeneration, survival, growth and thus overstory composition (Muller 2003; Gilliam 2007). Additionally, understories contain much of the biodiversity in many forest ecosystems, and as such, contribute to their resilience to natural and anthropogenic disturbances (Yu and Sun 2013).  Previous work on the influence of canopy mixing on understory species diversity and composition remains divided, with some authors claiming greater diversity under monocultures (Barbier et al. 2008) and others enthusiastically proclaiming greater diversity beneath mixed forests (Yu and Sun 2013).  While these divided results may derive from vastly different study designs and objectives, it appears universally accepted that differences in light and soil resource uptake and availability in mixtures of tree functional types (deciduous and coniferous) create different understory niches and patchiness (Messier et al. 1998; Rodriguez-Calcerrada et al. 2011; Augusto et al. 2003).  Perhaps one of the most compelling arguments for managing mixed canopies to promote conservation of the native understory plant composition is to maintain the native soil bioregulation, defined as the ability of naturally occuring plants in soil to maintain the conditions necessary for their regeneration (Perry et al. 1989).  Natural, mixed species soils have been shown to contain greater diversity in terms of soil structure (pore and particle size), and microorganisms, which in turn maintain ecosystem processes such as water drainage, retention, soil aeration and nutrient cycling; whereas more homogeneous, clearcut soils have shown difficulty in supporting planted seedlings (Amaranthus and Perry 1989; Colinas et al. 1994) .   Overview of thesis The main objectives of this thesis, addressed in each of the research chapters (2-3), were: (1) to identify the role of belowground interactions in mediating competition between interior Douglas-fir and paper birch (chapter 2), and (2) to determine the outcomes of competition between interior Douglas-fir and paper birch 21 years after planting (chapter 3).  In Chapter 2, the minor 5  objective was to determine the effect of trenching on species differences in growth over time and Armillaria root disease infection rate.   The minor objectives in Chapter 3 were to determine the effects of neighbor density on (a) the volume of each focal tree species using a neighbourhood analysis; (b) foliar nutrient response of each focal species; and (c) Armillaria root disease infection rate and composition of the understory plant community.6  Chapter 2 Effects of root trenching on long-term stand dynamics in mixtures of Douglas-fir and paper birch Introduction Mixedwood forests of conifer and broadleaf trees are common, naturally-occurring, early successional ecotypes in the southern interior of British Columbia.  With few exceptions, the management paradigm in these forests has been to favour commercially-valuable conifer species at the expense of broadleaf neighbours, in spite of the long-term ecological and economic benefits of broadleaf inclusion in forest composition (Comeau et al. 1996; Bauhus and Schmerbeck 2010; Hawkins and Dhar 2011; Clair et al. 2013).  This paradigm rests on the belief that young broadleaves out-compete conifers and prevent planted species from reaching industry and government thresholds for sawlog production (British Columbia Ministry of Forests 2000).  This belief focuses solely on faster height growth of broadleaves than conifers in the early stages of stand development (Comeau et al. 2003) and does not take into account the ecological benefits that broadleaves provide over the rotation of the stand, or the fact that conifers naturally outgrow the broadleaves in mid-succession (Simard and Sachs 2004).  One important benefit ignored by the conifer management paradigm is the increased diversity associated with mixed versus monoculture forests.  Not only is tree species richness increased, but understory plant (Baleshta et al. 2015; Chávez and Macdonald 2012), unglulate and bird (Bunnell and Kremsater 1990; Aitken et al. 2002) diversity are enhanced in mixedwoods compared with pure conifer stands.  Belowground, we also find that ectomycorrhizal fungal communities tend to be more even in mixedwoods than monocultures (Jones et al. 1997; Kernaghan 2005).  Moreover, the mycorrhizal networks that link together multiple tree species in a mixed forest can provide direct pathways for resource sharing that benefit the nutrition of individual trees (Simard et al. 1997).  This diversity and the interactions it allows have the potential to increase the stability of the whole ecosystem (Simard et al. 2013; Walker et al. 2005).  The presence of broadleaf neighbours can also protect conifers from root pathogens in mixedwood forests through multiple pathways that involve the greater disease resistance of broadleaves than conifers, the reduced probability of infection of susceptible tree species, and the increased soil antibiosis associated with broadleaves (DeLong et al. 2002; Cleary et al. 2008; Chapman et al. 2011; Cruickshank et al. 2009).  Additionally, broadleaves enhance nutrient cycling in mixedwoods through addition of nutrient-7  rich leaf litter and faster initial decomposition rates (Prescott and Vesterdal 2013; Wang et al. 2000), contributing potential for greater stand productivity (Comeau et al. 1996; Simard et al. 1990).  Some studies have indeed found greater yields in mixed than pure stands (Man and Lieffers 1999a; Kelty 2006; Hawkins et al. 2012). In revisiting a 21 year-old experiment that separated above and belowground species interactions through root trenching in pure and mixed stands of paper birch (Betula papyrifera Marsh.) and interior Douglas-fir (Pseudotsuga menziesii var. glauca (Beissn.) Franco), we sought to examine the long-term outcomes of mixing broadleaf trees with conifers on stand development patterns. Mycorrhizal networks (MNs) are recognized for their important role in plant interactions (van der Heijden & Horton 2009; Johnson and Gilbert 2014), although little is known about their cumulative impacts on plant community dynamics over time.  A mycorrhiza is a symbiosis between a plant root and a mycorrhizal fungus, where the plant provides the fungus with photosynthetic carbon and the fungus provide the plant with water and essential nutrients such as phosphorus and nitrogen acquired from the soil (Smith and Read 2008).  When two or more plants are linked by the same mycorrhizal fungal individual, they form a MN, through which carbon, limiting nutrients and water can transfer between them (Selosse et al. 2006; Egerton-Warburton et al. 2007; Querejeta and Allen 2007; Meding and Zasoski 2008).  The elements are thought to transfer through MNs along a source-sink gradient, wherein a source plant produces or acquires more resources than it needs while a sink plant needs more than it has available (Kytöviita et al. 2003).   Most studies have found evidence that transfer in MNs follows source-sink patterns (Francis and Read 1983; Simard et al. 1997; Lerat et al., 2002; Teste et al. 2010; Bidartondo and Bruns, 2005; Selosse and Roy, 2009), although anomalies exist (Hirrel and Gerdemann, 1979; Waters and Borowicz, 1994).  The complex nature of forest stand dynamics could involve multiple competing sinks at any given time as well as species shifting from sinks to sources and the reverse as the stand matures and succeeds. The consequences of these potentially shifting patterns of network resource allocation between multiple tree species on forest development remain unexamined.    The source-sink mechanism of transfer raises the possibility that multiple tree species with different phenologies and growth patterns can mutually benefit over seasons or years from 8  joining an MN (Lerat et al. 2002).  In mixed forests of conifer and broadleaf species, carbon has been shown to transfer bidirectionally between paper birch and interior Douglas-fir in summer, with net gains to the shaded (Simard et al. 1997a) or smaller (Philip et al. 2010) species, in accordance with the source-sink hypothesis. Net transfer has also varied over seasons, with Douglas-fir supplementing paper birch in the spring and fall, when the broadleaf is budding or senescing, and birch supplementing Douglas-fir in the summer, when its photosynthetic rate outstrips that of the conifer (Philip 2006; Simard et al. 2012). Deslippe and Simard (2011) also found that carbon transfer between Betula nana individuals varied with season, with greater transfer to faster growing sinks in the spring.  Given that nitrogen has been shown to transfer concurrently with carbon (Teste et al. 2009), it has been suggested that these elements travel together in amino acids (Simard et al. 2012).  This previous work has focused on pairs of seedlings or pairs of established trees and seedlings during relatively short time periods in field or laboratory conditions (see reviews by van der Heijden & Horton 2009; Simard et al. 2012).  Given the seasonal pattern of nutrient exchange through conifer-broadleaf networks, as well as shifting resource demands among tree species as the forest ages, examining longer duration outcomes of conifer-broadleaf network dynamics could provide valuable insight into interspecific competition and facilitation.   The observed effects of MNs on interplant competition have been variable.  Some research has shown that MNs can reduce the negative effects of competition on tree seedling mortality and growth (Perry et al. 1989; Booth 2004; Nara 2006; Wallace et al. 2015, in review), while others show they can increase competitive disadvantages, whereby established plants appeared to increase in growth when connected to a network with seedlings (Kytöviita et al. 2003; Pietikäinen and Kytöviita 2007; Schroeder-Moreno and Janos 2008).  Studies finding that MNs increased competitive advantages for established or larger plants examined arbuscular mycorrhizal (AM) networks, and did not use tracer isotopes to determine if elemental transfer was a potential mechanism.  Furthermore, at least one case exists in which AM networks have caused an increase in interspecific advantage given an increase in intraspecific density, or competition (Schroeder-Moreno and Janos 2008).  The majority of studies examining ectomycorrhizal (EM) networks, by contrast, show they can reduce interplant competition by enhancing seedling performance near established trees with network access (van der Heijden and Horton; Dickie 2005; McGuire 2007; Teste et al. 2009; Bingham and Simard 2012).  Studies 9  examining the influence of ectomycorrhizal MNs on interplant competition have focused on relations between mature and establishing conspecifics (Teste et al. 2009; Bingham & Simard 2012) or between establishing seedlings grown in pairs or in pots over limited time periods (Asay 2013; Wallace et al. 2015, in review), but experimental work examining longer term cumulative effects is lacking.  The effects of MNs on interspecific competition in plant mixtures (Perry et al. 1989) have received less attention than their effects on intraspecific competition in pure stands, although at least one study has examined EM fungal communities and the potential for MN formation in a 120 year-old mixed conifer-broadleaf chronosequence (Twieg et al. 2007). Mycorrhizal fungi are known to enhance host plant defence against many soil-borne fungal pathogens (Smith & Read 2008), but the effects of MNs on tree root diseases are virtually unknown.  The single study examining MN interactions with fungal pathogens involved AM networks, and it showed that they transported defense signals from tomato plants (Lycopersicon esculentum Mill.) infected with the foliar necrotrophic pathogen, Alternaria solani, to uninfected tomato neighbours, which then up-regulated their own defense response (Song et al., 2010). The pathogen protection provided by AM fungi has been shown to depend on both plant and AM fungal identity (Sikes et al., 2009).   The differences in morphology and physiology between AM and EM fungi suggest that mechanisms by which ectomycorrhizae interact with root pathogens differs from how arbuscular mycorrhizae interact with foliar pathogens; however, this has received little attention.  Four decades ago, Marx (1972) suggested EM fungi deter soil-borne pathogens by: (1) creating a physical barrier in the protective mantle surrounding the root, (2) reducing the root’s carbon supply and making it less enticing to the pathogen, and (3) supporting helper bacteria that repulse pathogens.  Recently, Frey-Klett et al. (2007) concluded that mycorrhizal helper bacteria (MHB) can have anti-pathogenic qualities, although in limited cases they appear to assist pathogens.  No work has extended these theories to EM networks specifically.   There have been no studies exclusively investigating whether belowground interactions between paper birch and Douglas-fir play a role in reducing infection rates by the ubiquitous root pathogen, Armillaria solidipes (Peck) (formerly A. ostoyae).  Armillaria root disease is prevalent in the forests of southern interior British Columbia, responding to host resistance or vigour and 10  inoculum potential (Cleary et al. 2008).  For example, Douglas-fir has high susceptibility to the disease, whereas birch has low susceptibility (Cleary et al. 2008). Cutting of paper birch stems increases inoculum potential of sites because the remaining birch root systems becomes infected under the stress, and this has been shown to increase Armillaria infection rates of neighboring Douglas-fir in young mixed plantations by up to four times (Baleshta et al. 2005; Simard et al. 2005).  Healthy paper birch roots may, conversely, inhibit Armillaria ostoyae through their mycorrhizal helper bacteria.  For example, the population size of the mycorrhizosphere bacterium, Pseudomonas fluorescens, was four times greater in stands of pure paper birch or admixtures than Douglas-fir alone, and the bacteria isolates were antagonistic to Armillaria ostoyae in vitro (Delong et al. 2002).    Given the great lifespan of trees, long-term study plots are highly important for increasing our understanding of forest dynamics.  To examine interspecific interactions in mixed forests, replacement series, addition series and response surface designs have been commonly used (Shainsky and Radosevich 1991).  Additionally, a long-term experimental technique for separating the effects of above- from belowground processes on forest dynamics has involved root trenching.  Root trenching, or the practice of isolating a plant’s rooting area, has been used to examine the effects of root competition (Yamashita et al. 2004), mycorrhizal networks (Simard, 1997b) and soil drainage (Sajedi et al. 2012) on plant establishment.  Severing mycorrhizal networks with trenching in the field has been accomplished with single or repeated cuts in the soil (Simard et al. 1997b) or by inserting a physical barrier in the soil profile that excludes mycorrhizal hyphae (Booth 2004; Simard et al. 1997).  In addition to disabling the formation of mycorrhizal networks, reducing belowground competition and disrupting subsurface water flow, trenching can inhibit several other belowground interactions.  For example, trenching could exclude roots from accessing root exudates of neighbours, and thus reduce access to nutrients through soil, as well as fungal, pathways.  Trenching has also been demonstrated to lower decomposition rates in soil, which could reduce available nutrients to trees and other plants (Silver and Vogt 1993; Ferrier and Alexander 1985).  Previous greenhouse work has shown that MNs are more important pathways for nutrient transfers among plants than soil pathways (Philip et al. 2010), however, suggesting these additional trenching effects on non-mycorrhizal properties and processes may be small.  In 11  terms of species-specific interactions, trenching may affect the root architecture of different species distinctly, potentially favouring a species that exploit all strata of the soil profile extensively over those that prefer longer-range explorations of single horizons or strata in the soil matrix.   The objective of this study was to determine the role of belowground interactions in mediating the outcomes of interspecific competition over the long-term in temperate mixed conifer-broadleaf plantations comprised of Douglas-fir and paper birch.  We met this objective by comparing performance of individual Douglas-fir and paper birch trees between trenched (no MN or root interactions) versus untrenched (with MN and root interactions) treatments applied to mixed stands of low and high density. We examined several tree performance variables over time and when the stands were 21 years-old.  These variables were annual growth increment, total growth (height and diameter), foliar nutrient concentration (of current year’s growth) and Armillaria solidipes infection rate.  We tested five hypotheses as follows: 1) Our first hypothesis was that both Douglas-fir and paper birch individuals would grow larger where they had not been trenched than where they had been trenched.  The rationale behind this hypothesis was that, in untrenched plots, trees would have greater access to soil resources via both MNs and roots.   2) Our second hypothesis was that growth of Douglas-fir and paper birch individuals would be lower at high than low stand density.  This was expected because of greater competition for limited resources.  Related to this, we expected that the difference in performance between trenched and untrenched trees would increase with tree density, where access to MNs would be more important for resource acquisition and hence individual tree performance at higher than lower tree densities. 3) Our third hypothesis was that annual growth rates would be greater for untrenched than trenched trees during dry years. This was expected because of greater access to scarce soil resources via the MN and root expansion. 4) Our fourth hypothesis was that Douglas-fir foliage would be higher in nutrients in untrenched than trenched stands, but paper birch foliage would be lower in nutrients in untrenched than trenched stands.  The rationale for this hypothesis was the documented seasonal nature of MN-12  mediated C transfer between conifers and broadleaves, and the suggestion that nutrients are transferred along with carbon in amino acids.  As with growth, we expected the nutrient exchange to be more pronounced at higher than lower densities. 5) Finally, we hypothesized that both tree species would have lower Armillaria root disease incidence in untrenched than trenched stands.  This would occur if MNs or root proximity facilitated defense signaling between trees (Barto et al., 2011; Madison, unpublished data) or if root populations were more mixed in the untrenched treatment. Furthermore, we thought that infection rates would be greater at higher than lower density.  This result was expected because of decreased host vigour due to competition and hence decreased disease resistance (Cleary et al. 2008).  Methods Study sites This experiment was part of a larger study examining the effects of broadleaf and conifer competition on forest productivity.   The experiment was conducted in the Interior Cedar Hemlock (ICH) biogeoclimatic zone of southern interior British Columbia, locally referred to as the interior wet belt. The ICH zone is one of the wettest regions east of the Coast Mountains, and is characterized by a continental climate dominated by easterly moving air masses, cool wet winters, and warm, dry summers.  Mean annual precipitation ranges from 500-1200 mm, 25-50% of which falls as snow (Meidinger et al., 1991a).  The three replicate sites were situated in the moist, warm ICH subzone (ICHmw), which occupies the middle range of the precipitation gradient of the ICH zone (Figure 2.1).  Two sites, Adams Lake (51°97’, 119°28’N) and Malakwa (50°97’, 118°72’N) occur in the Thompson Moist Warm geographical variant (ICHmw3), while the third, Hidden Lake (50°56’, 119°28’), occurs in the Shuswap Moist Warm geographical variant (ICHmw2).  The sites were similar in pre-harvest elevation, aspect, soil characteristics and tree species (Table 2.1). All sites were clear-cut harvested in 1978 (Hidden Lake), 1987 (Adams Lake) and 1988 (Malakwa) and planted to interior spruce or interior Douglas-fir.  The original plantations failed 13  due to high infection rates of Armillaria solidipes at all sites as well as frost damage at Malakwa. In the fall of 1991, the sites were destumped and scarified with an excavator followed by replanting with experimental seedlings of paper birch (1+0 516 styroblock plugs) and Douglas-fir (1+0 312 styroblock plugs) in May-June of 1992.  A total of eighteen 40 m x 40 m plots were established at each site, and randomly assigned monoculture and admixture densities of paper birch and Douglas fir, including monoculture densities of 400, 800, 1600 and 3200 stems ha-1.  The densities were replicated at the site level, with one replicate each at Adams Lake, Malakwa and Hidden Lake.  We examined two of the admixture densities in this study. The high density was 3200/1600 stems ha-1 of paper birch/Douglas-fir. The low density was 800/400 stems ha-1 of paper birch/Douglas-fir.  Within each plot, a trenching treatment was randomly assigned to half of the area and no treatment was assigned to the other half.  Trenching consisted of digging a 1 m2 deep trench centered around the base of each seedling using a mini-excavator and shovels, creating ‘islands’ containing a single seedling.  The islands were wrapped with a double layer of polyethylene plastic, approximately 5 mm thick, and the trenches refilled with the original soil.  Seedlings were thus separated belowground from their neighbours by four layers of plastic to a depth of 1 m.  These layers were determined by visual inspection to be intact, without root invasion, at 21 years after they were installed. The experimental design was a split-plot, with one whole-plot factor (density) with two levels (low and high), and one within-plot factor (trenching), also with two levels (trenched and untrenched).  This design was replicated three times at the site level as described above.  Field data collection  Tree and soil properties were measured in 2013, 21 years after the plantations were established.  Measurements were taken in neighbourhood plots, where the target (focal) tree and all neighboring trees were measured within a 3.99 m radius (plot area=50 m2) centered on the target tree.  Target trees were either planted Douglas-fir or planted paper birch.  Since ingress of naturally regenerated trees had occurred since the establishment of the experiment, target trees were selected only if they were known to be of the planted cohort.  This was determined by the presence of permanent markers located at the base of the tree.  Two neighbourhood plots per target tree species were randomly located in each density X trenching treatment unit, for a total of 16 plots per site, or 48 plots in total over the three replicate sites.   14  Target tree and neighbour tree height (m) and diameter (cm) were measured with a vertex digital hypsometer and diameter tape, respectively. Photosynthetically active radiation (PAR, µmol m-2 s-1) incident on each target tree was measured with a 1-m long LICOR LI-250A Light Meter.  The PAR line intercept was measured in the four cardinal directions from the drip line of the foliage of each target tree and averaged.  Soil moisture content (%) was recorded with a HH2 moisture meter with an ML2x Theta probe (Delta-T Devices Ltd.) in a soil volume with 160 mm depth x 100 mm soil diameter. One reading was taken per target tree at a distance of 1 m from the tree bole.  Armillaria presence or absence was determined by exposing the root collar of each target and neighbourhood tree and examining the entire perimeter and cambium for visual characteristics of the disease.  Representative photos of the fungal pathogen in several developmental stages were shown to experts after sampling to confirm the identification of the disease.  Tree cores were collected 1.3 meters above the ground from two trees of each planted tree species per neighbourhood plot, including the target tree (total of 98 cores).  Neighbourhood trees were selected for coring within the 7.1 m radii using a stratified random method to avoid treatment edge effects.    Soil and foliar nutrients Samples for determining foliar and soil nutrients were collected in August 2013. In each neighborhood plot, a foliage sample was selected from the current year’s growth in the top third of the target tree.  In addition, a soil sample was collected from the top 40 cm mineral soil using an auger 1 m from the tree bole. Foliage and soil samples were analyzed at the British Columbia Ministry of Environment analytical lab in Victoria, BC.  Soil total N and total C was determined using combustion elemental analysis.  Cation exchange capacity (CEC) using soil exchangeable cations ([Ca], [Mg] and [K]) was determined by the neutral ammonium acetate method; available P was determined with the Bray P1 procedure and soil pH was determined in 0.01 mol CACl2 (Kalra and Maynard 1991).  Foliar macronutrients (C, N, K, Ca, Mg, P and S) and micronutrients (B, Cu, Fe, Mn, Mo, Na and Zn) were analyzed by ICP-AES (inductively coupled Plasma-Optical Emmission Spectrometer) after microwave digestion, with concentrated HNO3, 30% H2O2 and concentrated HCl.  Ratios of N:P, C:N, N:Mg and N:K were calculated using the examined concentrations. 15  Dendrochronology Tree cores were processed and measured in Lori Daniel’s Tree Ring Lab at UBC, Vancouver.  Tree cores were mounted on wooden supports and sanded using standard protocols (Stokes 1996).  Sanded cores were scanned using a high resolution (1,200 dots per inch) scanner.  Ring widths were measured using the program, CooRecorder (Larsson 2011a), and converted to numeric .pos files for analysis using the program CDendro (Larson 2011b).  Since the planting date of all trees was known, cross-dating was not necessary to verify the ring dates.  As tree cores were collected in late August (Adams Lake) and early October (Hidden Lake, Malakwa) of 2013 and therefore at the end of growing season, the outermost ring was determined to belong to 2013, and previous years’ rings were dated accordingly.  The ring width was converted to annual growth increment by calculating the area of each ring (πr2) before analysis. Statistical analysis All statistical analyses were performed in R, version 3.1.0 (R Core Team 2014).  Variations in all the tree-related and environmental measures were assessed with box-plots (Massart et al. 2005). The effects of the treatments on the diameter, height and foliar nutrient concentrations of the target trees were analysed using linear mixed models with the lme function (nlme library).  Multivariate regression trees (MRT) were used to analyse the relative importance of the density X trenching treatments on the same target tree variables, along with neighbourhood and environmental variables.  For these analyses, soil variables were consolidated using principal component analysis (PCA).  The first two axes of a PCA performed with the full soil variable matrix were extracted for use in MRTs and classification trees.  These analyses were performed using the mvpart package.  Armillaria root disease incidence was analysed using classification trees from the Tree package. Finally, annual growth increment was analyzed using a general additive mixed model (GAMM) with the gamm function from the mgcv package.  These techniques are described in more detail below. Linear mixed models are a class of regression analysis that allow for fixed and random model parameters, and look for differences in dependent variables in a similar fashion as two-way Analysis of Variance (ANOVA).  Random parameters are allowed to have separate variances per level and enable an examination of fixed parameters of interest beyond differences between 16  random parameters.  Site was used as the random parameter in the model examining variations in the response variables as a function of the whole-plot and split-plot treatments (planted density and trenching) and their interaction.  This means that each site is allowed a separate amount of variance around the intercept (Zuur et al. 2009).  The model was fit using restricted maximum likelihood (REML), which estimates slope and intercept while incorporating the random part of the equation (Zuur et al. 2009).  Multivariate Regression Trees are a mixture of regression and clustering techniques, and have been described as “constrained clustering” (Borcard et al. 2011) or “robust regression” (Logan 2011).  They can handle many response and explanatory variables, different underlying distributions, and situations with missing values.  MRT’s work through “binary recursive partitioning”, or finding threshold values of the explanatory variables that explain the greatest variation in the response variables (McCune et al. 2002).  This process works by ranking each value of the response variables, or combination of levels for categorical variables, and dichotomously splitting the response data at the level of the most important variable in minimizing the sum-of-squared-errors for the response matrix.  The splitting then continues independently along each branch of the tree until terminal leaves are created (McCune et al 2002; Borcard et al. 2011).  The number of terminal leaves in the MRT’s are determined by a process known as cross-validation (De’ath and Fabricius 2000). Multivariate regression trees of foliar nutrients were constructed separately for each tree species in relation to the density X trenching treatments, other environmental variables and two neighbourhood variables (number of neighbouring trees, and conifer to broadleaf ratio, which was calculated as total conifers/total number broadleaves among neighbour trees per plot).  The environmental variables were soil moisture content, PAR, and two soil variables extracted from the first two axes of a principal components analysis (PCA) conducted with all the soil variables (soil nutrient concentrations, total carbon and nitrogen, CEC. and soil pH) for each tree species.                   Classification trees were created with Armillaria presence or absence as a response to the same suite of explanatory variables as in the MRTs.  Classification trees are similar to regression trees but are used in cases of single categorical response variables.  The classification tree is constructed by seeking the threshold levels of explanatory variables that account for the greatest purity of response, or groups with highest percentage of the same value of the categorical 17  response variable (i.e., yes or no).   Impurity is expressed in terms of deviance, where a deviance of 0 represents perfect purity.  Splitting continues along successive branches until complete purity is obtained.  Trees are then pruned according to a similar method as cross validation, with an optimal tree being selected from several trees constructed from sub-sets of the data based on a cost-complexity measure (Ripley 2005).  Classification trees return a misclassification error rate statistic referring to the percentage of objects returned to incorrect leafs after pruning (Ripley 2005).   Annual growth increment was analyzed using the procedure GAMM in R, which is a type of regression analysis that allows the use of smoothers in place of linear estimators to accommodate the detection of non-linear trends in data (Zuur 2007).  GAMM also allows the use of correlation structures common to other mixed models that can deal with auto-correlated errors.  Fitting a GAMM with an appropriate error correlation structure to assess the variation in annual growth increments allowed for a similar model statement to that used to assess tree height, diameter, and foliar nutrients with unbiased estimates, in spite of the temporal auto-correlation present among the tree rings. Annual growth increment was averaged per site, species and treatment combination, and then modelled as a function of the density X trenching treatments, a climate variable, and time. The climate variable was the summer heat to moisture index, SHM (Wang et al. 2012), and was calculated from data taken at the nearest weather station to each site.  The SHM corresponds to the mean warmest monthly temperature / (summer precipitation/1000).  Summer months were May through September.   Optimal models were chosen using the Akaike Information Criterion (AIC) after testing models with different interaction terms and residual correlation structures, including one with no residual correlation structure.  None of the interactions were significant and all were removed from the final models. A model with a Gaussian distribution and an auto regressive moving average (ARMA) correlation structure was selected as most parsimonious when including both tree species (Douglas fir and paper birch).  A Douglas-fir-only model was selected containing the same parameters as the two species model, while a paper birch-only model found an auto regressive order one (AR1) correlation structure to be more appropriate, but was the same in other aspects.   18  Results Growth Neither planted density nor trenching, nor the interaction between the two factors, significantly influenced total height or diameter of paper birch or Douglas-fir according to the linear mixed models (Table 2.2, Figure 2.2, Figure 2.3, Figure 2.4, Figure 2.5). The coefficient of variation for height and diameter was consistently higher in the trenched than untrenched treatment for each species (Table 2.3). The distribution of the environmental variables by the trenching was examined visually using scatter charts to determine possible confounding effects of the treatment.  No clear patterns appeared in the charts (Figure 2.6, Figure 2.7).   Growth over time Average annual growth varied significantly over time, differed by density and species, and varied with SHM (Table 2.4).  Average annual growth was lower at the low than high planted density, for paper birch than Douglas-fir, and at higher SHM (i.e., lower growth rate in dry years).  By contrast, it was unaffected by the trenching treatment.  Average annual growth over time is represented by smooth terms in the model for the eight time series (2 density X 2 trenching X 2 species combinations).  These models show that average annual growth of paper birch did not vary significantly over time in the untrenched treatment at either low or high density (Figure 2.8).  However, paper birch growth declined approximately linearly over time in the trenched treatment at both low and high density.  The models also show that annual growth of Douglas fir varied significantly over time in all density X trenching treatment combinations.  At high density, Douglas-fir growth declined linearly with time in both the trenched and untrenched treatments.  The opposite trend occurred at low density. Here, growth increased in the same non-linear pattern in both the trenched and untrenched treatments (Figure 2.8).   Results were similar when models were built for each species separately (Table 2.5, Table 2.6). Average annual growth of Douglas fir was greater at low planting density and lower SHM (i.e. faster growth in wetter years). Again, there was no apparent effect of trenching on annual growth of Douglas fir.  At low density, Douglas-fir growth increased non-linearly with time in both trenched and untrenched treatments. At high density, Douglas-fir growth decreased linearly over 19  time (p<0.05 in trenched treatment; p<0.1 in untrenched treatment). For paper birch, average annual growth was significantly influenced by density but not trenching or SHM.  As in the two-species model, paper birch growth declined linearly with time in the trenched treatment but remained steady in the untrenched treatment at both densities. Foliar nutrients Several foliar nutrient concentrations and ratios varied significantly with density X trenching treatments for both species according to the linear mixed models (Table 2.7 for Douglas-fir and Table 2.8 for paper birch).  For Douglas-fir, N concentration was greater at low than high density (p<0.10, Figure 2.9), while N:Mg was increased in the trenched treatment at low density compared to all other treatments (p<0.05, Figure 2.9). No other Douglas-fir foliar element concentrations or ratios varied by treatment (p>0.1).  Significant trends in foliar elements among treatments were more common for paper birch (Table 2.8).  Al, Cu, Fe and Na concentrations of paper birch tended to be higher in the trenched than untrenched treatment, especially at low density, while N:S was greater in the untrenched treatment, particularly at high density (Figure 2.10). An MRT showed that foliar elements in Douglas-fir were best explained by PAR, where a single split solution was found at a (centered) threshold level of -0.7039 µmols m-2 s-1 (Figure 2.11).  Lower values of PAR were correlated with higher concentrations of Al, Ca, Mg, Mo and Zn, as well as higher N:K and N:S ratios (Figure 2.12).   By contrast, an MRT showed that paper birch foliar nutrient concentrations were best explained by the second soil PCA axis (Figure 2.14), with higher scores on the axis associated with higher concentrations of Al, Ca, Fe, Mg, Mo, Na, P and Zn (Figure 2.13).    Soil nutrients Principal components analyses (PCAs) were used to combine all the soil variables into two variables for the MRT and classification tree analyses. This was done separately for Douglas-fir and paper birch plots. There were no patterns in soil variables with density or trenching in either PCA (Figure 2.12, Figure 2.13). For Douglas-fir, Ca, K, Mg, N, Na and CEC dominated the variation in axis 1, while Al, Fe, Mo and pH (H2O) dominated variation in axis 2.  For paper 20  birch, CEC, N and C dominated the variation in axis 1, while Mg, pH (H2O), Na, Fe and Al drove axis 2.  Armillaria root disease incidence The classification tree examining factors affecting infection of Douglas-fir by Armillaria solidipes arrived at a two-split solution, with soil moisture creating the first split, and the first soil PCA axis creating the second (Figure 2.15). The threshold value for soil moisture content (%) was 0.0485, and trees growing in soils with values higher than this had lower disease incidence.  The trees growing in soils with lower soil moisture values were divided a second time according to a threshold value of soil variables from PCA axis 1.  This demonstrates that trees growing in soils with lower concentrations of Ca, K, Mg, N, Na and CEC were less likely to be infected (n=5; 80% not infected) than trees growing in soils with higher nutrient concentrations (n=9; 22% not infected).  These results show that lower disease incidence among Douglas-fir was associated with wetter yet more nutrient poor soils. The classification tree assessing factors explaining the presence of Armillaria in paper birch also derived a two split solution, with the conifer to broadleaf ratio creating the first split, and soil PCA axis 1 creating the second split (Figure 2.16).  The threshold value for the conifer to broadleaf ratio was 2.14, with a lower proportion of conifers to broadleaves leading to higher rates of infection in birch (n=7; 100% infection).  In other words, paper birch surrounded by more conifers suffered lower disease incidence than when surrounded by more paper birch. The threshold value for the second split based on soil PCA axis 1 was 1.48, with higher concentrations of C, N and CEC related to lower rates of infection of paper birch by Armillaria (n=5; 100% not infected). Discussion The trenching treatment was highly effective at eliminating interspecific root interactions and the potential for MN formation, thus allowing us to distinguish belowground from aboveground effects, based on our observation that the plastic barriers were still intact after 21 years.  In a complementary analysis by Lallemand (2015) of the ectomycorrhizal community of target trees, we found ten morphotypes common to Douglas-fir and paper birch that were colonizing 71% of root tips.  This result indicated high probability that mycorrhizal networks were linking the two 21  tree species belowground in the field. The dominant networking species was Cenococcum geophilum, colonizing 41% of the combined root tips, with the remaining 30% colonized by the nine other morphotypes (Lallemand, 2015). These results agree with previous experimental work showing strong potential for common mycelial networks to form between the two tree species in the field (Jones et al. 1997; Simard et al. 1997; Tweig et al. 2007; Philip et al. 2010).   Growth Our first hypothesis, that total height and diameter would be greater in networked trees, was not supported for either tree species. Neither height nor diameter of either tree species varied significantly with trenching (p > 0.05; Table 2.2). Both species had a lower coefficient of variation (Table 2.3) in the untrenched than trenched treatment, suggesting that belowground interactions play a role in reducing competitive inequalities.  This finding agrees with a recent controlled assessment of mycorrhizal network effects on structure of pure interior Douglas-fir stands of seedlings grown in pots (Wallace et al. 2015, in review).  Our second hypothesis, where we predicted facilitation through belowground interactions would be more important for individual tree performance at high than low tree density, was also not supported.  Height and diameter of Douglas-fir were unaffected by both trenching and density (Table 2.2, Figure 2.4, Figure 2.5).   The balance of these results indicates that density, through its effect on resource availability, played a larger role in determining tree growth than specific belowground effects.  Moreover, they show that the relatively weaker species, paper birch, benefited more from the belowground interactions than the stronger species, interior Douglas-fir, and that the overall effect of MNs appeared to decrease growth inequalities between the two ectomycorrhizal tree species grown in mixture.      Growth over time While our first hypothesis, that total growth would be greater for both species where root systems interacted, was not supported, our analysis of annual growth patterns provided insight into how stand dynamics were affected by interspecific competition and/or facilitation.  In support of our second hypothesis, paper birch responded to the trenching treatment, but rather 22  than annual growth increment increasing with unfettered contact of root systems and the possibility of MN formation, it declined in the absence of belowground interactions.   This could be explained by MN-mediated bidirectional transfer of nutrients along a source-sink gradient between the conifer and broadleaf trees as observed for carbon in previous work (Simard, 1997a; Philip et al., 2010), where in this case, over time, net transfer occurred from the relatively vigorous Douglas-fir to the struggling paper birch.  Alternatively, this result could be explained by access to larger soil volume in the untrenched treatment, which may have favoured the tree species with a more long-range exploration strategy, or by a greater nutrient subsidy to paper birch from richer Douglas-fir roots either through their exudates or decomposition.  There was no evidence of competitive interactions belowground between the two species.  Moreover,  competition as the belowground interaction mechanism could not account for the fact that only birch responded to trenching, unless Douglas-fir had not yet reached carrying capacity and thus was unaffected by competition.  This seems unlikely, however, since Douglas-fir had reduced annual growth rates in higher compared with lower density plots (Table 2.4).  If MNs or other types of belowground interactions facilitated birch growth over time because of the relatively poor condition of the trees, then the benefit would serve to diminish competitive effects, but not reverse them. That annual growth of Douglas-fir was sensitive to density, but not to the presence of belowground interactions (trenching), suggests that this relatively strong species did not suffer from facilitating the weaker species (possibly through transfer of excess nutrients), but did not stand to gain from it either.  This agrees with earlier theories that transfer through MNs follows source-sink gradients where donor trees can aid receivers while not suffering noticeable effects from their subsidies due to luxury consumption (Simard et al. 1997 and 2012; Perry et al. 1989).  This is also be consistent with tit-for-tat theory, whereby EM fungi provide more nutrients to host plants that provide them with more fixed carbon (Kiers et al. 2011). The annual growth patterns in Douglas-fir and paper birch did not support our prediction that the positive effects of networks would be more pronounced at higher densities. However, both species grew more slowly at high density, while annual growth of Douglas-fir was unaffected by trenching.  This outcome suggests that aboveground competition for resources played a more direct role in determining annual growth of healthy trees than access to networks or belowground 23  competition.  The fact that density did not affect birch growth patterns may indicate that, when trees are under stress, access to mycorrhiza networks and net flow of resources following source-sink patterns aid trees in coping with these stressful environmental conditions.   Our results did not fully support our third hypothesis that trees would grow faster where they had more belowground interactions than where they did not during dryer years.  This is indicated by the lack of significant interaction between SHM and trenching in all of the models tested; moreover, the box plots did not indicate any obvious directionality between the two independent variables (Table 2.4, Table 2.5, Table 2.6; Figure 2.17).   However, that annual growth of paper birch was unresponsive to SHM while that of Douglas fir decreased in dryer years maybe due to the fact that the birch in this study was so stressed that it could not react to climate while Douglas-fir reacted as expected for a healthy population.  Average birch heights on the study sites were between 4 and 8 m at age 21 years (Figure 2.5) compared with 10 m at age 16 on mesic (less productive) sites in the ICH (Simard and Vyse, 1992), showing they were underperforming compared with wild populations.  If we think of this outcome in light of the growth patterns over time, it suggests sink strength for possible resource subsidies was a more important determinant to birch growth than relative levels of environmental stress, since birch annual growth was not influenced by climate and decreased linearly in the absence of networks. This explanation is congruent with the stress gradient hypothesis, which posits that facilitation, in this case by access to mycorrhizal networks, is more important to tree growth where they are stressed.  Alternatively, an environmental covariate we have not considered may explain the variability in annual birch growth better than SHM.  Overall, these growth results support previous work suggesting that facilitation through belowground interactions reduces the negative effects of interspecific competition (Booth, 2004); however, we found little direct evidence that this facilitation increased with density or climate stress.  Instead, access to MNs and intermingling roots was important to maintaining growth of subordinate trees that were underperforming for other reasons. While we could not rule out the possibility that trenching acted instead to release birch from below-ground competition, this seems less likely than our network facilitation hypothesis due to the absence of reciprocal response by Douglas-fir neighbours.  Finally, using density as a proxy for competition, we found 24  that competition had a stronger immediate impact on annual growth of Douglas-fir than MNs, but MNs had the effect of ameliorating but not reversing negative effects of competition in birch.    Foliar nutrients We found partial evidence supporting our fourth hypothesis that foliar nutrient concentrations would be higher for Douglas-fir and lower for paper birch in the untrenched than trenched treatment due to potential interspecific nutrient transfer.  In each species, only a handful of nutrients were significant in the mixed models examining trenching and density effects.  However, the concentration of these nutrients in birch foliage was lower in untrenched than trenched plots, consistent with the hypothesis that there could be a mid-summer flow of excess carbon from paper birch to Douglas-fir through mycorrhizal networks (Simard et al. 2012).  For Douglas-fir, the nitrogen to magnesium ratio was lower in untrenched than trenched plots at lower density, suggesting any nitrogen subsidies from birch neighbors were not limited by magnesium.  Additionally, foliar nitrogen concentration in Douglas-fir decreased with planted density, suggesting the conifer was competing for nitrogen with greater numbers of neighbors and, conversely, acquiring greater nitrogen for increased growth rates at a lower density of neighbors.  The different species-specific foliar nitrogen responses can thus be explained by the relative vigour of the two species, where the slow-growing birch responded to the presence of networks (at low density) whereas the faster-growing Douglas-fir responded more to density, or competition.   Our hypothesis that differences in foliar nutrient levels between trenched and untrenched trees would increase with density as a result of network-facilitated transfer was not supported by the results. In contrast, nitrogen in Douglas-fir showed a marginal tendency to be more affected by density than trenching (p = 0.099; p = 0.102) and was greater at low density (Figure 2.9).  Paper birch may express greater differences between trenching treatments at low density because it was richer in nutrients at the time of sampling, and thus more capable of transferring excess nutrients to Douglas-fir.  That microelements Cu and Fe in paper birch were also lower in untrenched plots, suggestive of greater export to neighbours through networks, agrees with Asay (2013), who found that these micronutrients were elevated in receiver seedlings where they were linked with neighbours by MNs compared to where they were isolated.  While these results could stem 25  from reduced competition in trenched plots, the fact that the trend was not evident at high density, where competition was more intense, suggests this is an incongruent interpretation.   Overall, the foliar nutrient results provide some indirect evidence that there was potential for mid-summer transfer of excess nutrients from paper birch to Douglas fir through MNs.  A consistent pattern of reduced micronutrients in untrenched relative to trenched paper birch foliage suggests that excess nutrients may have transmitted through MNs to linked Douglas-fir during the peak of birch photosynthetic activity in summer.  However, the greater cumulative growth benefits paper birch received from the network than Douglas-fir suggests the balance of carbon transfer over all seasons, as shown by Philip (2006), was toward paper birch. In other words, within-season variation in transfer appears not to outweigh the accumulated transfer over the whole growing season.  This could only be verified by examining changes in foliar nutrients of paper birch and Douglas-fir over the entire growing season, rather than the one-time snapshot taken in mid-summer in this study.  The results also reiterate to some degree that paper birch was responding more intensely to MNs and Douglas fir more to density.   Armillaria root disease We did not find support for our fifth hypothesis that both tree species would have lower incidence of Armillaria root disease in untrenched than trenched stands.  However, paper birch appeared to benefit from interspecific facilitation as evidenced by lower incidence of Armillaria root disease in the untrenched than trenched treatment; by contrast, Douglas-fir infection responded more to resource availability.   The classification tree for paper birch revealed higher infection rates where birch trees were surrounded by fewer conifers and where soil nutrient levels were higher. Where conifer neighbor density was low, paper birch had more conspecific neighbors, and hence there was greater potential for the disease to spread from one infected individual to another via intraspecific root contact.  The risk of infection of the paper birch was high, regardless, because of its poor vigour (Ross-Davies et al. 2013). The greater incidence of infection in nutrient-rich soils may have resulted from faster root-root contact, but also suggests the birch was too weak to respond positively to the greater nutrient availability.  The classification tree for Douglas fir indicated that low soil moisture and higher soil nutrients were associated with greater incidence of 26  Armillaria root disease.  Dryer sites have been associated with higher instances of the disease in previous work (Cruikshank 2010; Kile et al. 1991).  Greater infection rates associated with high soil nutrient levels may reflect greater potential for root-root contact through faster root growth rates, and hence disease spread.   Conclusion The availability of essential plant resources and level of competition for these resources appears more important than belowground interactions such as access to MNs for long-term tree growth and foliar nutrient content.  However, the belowground interactions appeared to aid the struggling paper birch over the two-decade growth period. These findings serve to support a modified version of the source-sink hypothesis over longer time periods, showing cumulative benefits for sink species and an overall effect of balancing out competitive inequalities.   They also point towards the role of belowground intereactions in even- aged mixed conifer broadleaf forests in preserving species diversity and by extension ecosystem stability (sensu Walker, 1999).    These findings seem less related to autecology of the study species than the mechanism of sink strength itself, since early post-disturbance growth of shade-intolerant birch normally exceeds that of moderately shade-tolerant Douglas fir.  Testing this hypothesis would require long term labeling studies in which nutrient fluxes could be traced belowground.  Tracer experiments have been conducted between seedlings in the field (Teste et al., 2009) but not between larger trees or over long durations.  Long term labeling in controlled experiments could be attempted to unravel source-sink dynamics and which species or individuals receive net benefits over the long-term.  The foliar nutrient results in which birch appeared to suffer from network availability stood against the balance of evidence for total and annual growth showing birch benefitting from network availability.  This finding could represent a pattern of occasional benefits to multiple species with distinct growing seasons linked through networks, regardless of relative health or vigour, while over time the net effect favours the weaker species.  Possible reasons for this situation could be an increased investment in networks by relatively weak species, a higher seasonal “payback” to weaker species due to seasonal luxury consumption by stronger species, or that for healthier species, networks play a limited role in growth and resource acquisition.  27  Future research could undertake annual measurements across the growing season in long-term study plots to test our speculations in this regard. While we found evidence that the outcomes of competition were reduced for paper birch where it could interact belowground with neighbors, we found little evidence that this decrease was proportional to levels of competition (density) or that it changes with environmental stress.  The lack of paper birch response to increased competition may be related either to its subsistence vigor level, possibly higher early height growth in high density treatments, or insufficient stress imposed by competition or climate to affect tree growth and hence sink strength.  Alternatively, the mechanism of resource transfer could operate independently of biotic and abiotic stress, although how this would relate to a source-sink theory of resource transfer is difficult to say.  More experimental work with alternative methods of expressing competition, such as damaging selected individuals and repeated measures of multiple environmental variables could enhance our understanding of these phenomena.  Recommendations for forest practice While conducting experiments on long-lived organisms such as trees poses challenges in control and methodology, we feel that our efforts have unearthed some compelling hypotheses on an aspect of forest ecology that has received little attention.  Future work on the temporal dynamics of MNs in mixed-wood forests can gain from our experience.  Forest management also stands to benefit from our contributions.  If belowground interactions in temperate mixed forests tend to reduce species inequalities and increase co-existence and diversity, then maintaining broadleaves in mixture with planted conifers could increase conifer health over time.   Based on our results, however, a more compelling reason to maintain a broadleaf component in managed forests appears to be that of retaining a mechanism of long-term stability in our future forests.  Forests are complex ecosystems and the interactions of organisms and their environments they contain continue to surprise us with their ingenious strategies for survival and resilience.  One size-fits-all management solutions threaten to ignore the intricacies and perpetual adaptation of forests and thus risk making them more vulnerable to anthropogenic or stochastic disturbance, with the possible conclusion that it completely loses its capacity to recover (as per Scheffer et al. 2008).   28  Table 2.1  Pre-harvest site characteristics.  Adapted from Simard 1997.          Site Adams Lake Hidden Lake Malakwa  Characteristic        BEC variant ICHmw3 ICHmw2 ICHmw3  Site series 04,01 01 05,01  Elevation 700 m 650 m 750 m  Slope/Aspect 0-5%/east 0-10%/east 0%/flat  Soil class Humo-Ferric Podzol Dystric Brunisol Humo-Ferric Podzol  Soil texture (50 cm) Sandy Loam Loam Sandy Loam  Course Fragment content (50 cm) 10% 25% 10-30%  Parent Material Alluvial Blanket Morainal Blanket Alluvial Blanket  Dominant Tree Species Pseudotsuga menziesii Betula papyrifera Tsuga heterophylla Thuja plicata Pinus monticola Thuja plicata Tsuga heterophylla Betula papyrifera Pseudotsuga menziesii    Thuja plicata Tsuga heterophylla Betula papyrifera Pseudotsuga menziesii Pinus monticola    Stand Age (yr) 120 100 90  Dominant understory species Rubus Parviflorus Chimaphila umbellata Pachistima myrsinites Pachistima myrsinites Vaccinium L. Streptopus amplexifolius Tiarella unifoliata  29  Table 2.2 Model results showing density and trenching effects on height and diameter of paper birch and Douglas-fir.   Paper birch Diameter Fixed Terms coefficient stdE dof t p-valueintercept 2101.183 1517.475 11 1.385 0.194planted density -0.395 1.992 2 -0.198 0.861trenching 2.16 1.878 11 1.15 0.274Interaction 0.915 2.737 11 0.334 0.744Heightintercept 4.109 1.221 11 3.366 0.0063planted density 0.465 1.636 2 0.284 0.6201trenching 1.691 1.55 11 1.092 0.298Interaction 1.224 2.243 11 0.0546 0.596Douglas fir Heightintercept 7.243 1.107 14 6.54 0planted density 2.091 1.447 2 1.445 0.285trenching -0.259 1.269 14 -0.204 0.841Interaction 0.192 1.796 14 0.107 0.9162Diameterintercept 9.989 2.158 14 4.629 0.0004planted density 1.361 2.707 2 0.503 0.665trenching 0.128 2.695 14 0.048 0.963Interaction 0.886 3.189 14 0.232 0.819930  Table 2.3. Coefficient of variation (CV) for height and diameter at breast height (dbh) by species (Spp) and trenching treatment.  Fd is Douglas-fir, Ep is paper birch.  “no” refers to untrenched treatment, “yes” to trenched. Spp Variable Trench CV Fd height untrenched 0.26 Fd height trenched 0.33 Fd dbh untrenched 0.34 Fd dbh trenched 0.47 Ep height untrenched 0.42 Ep height trenched 0.5 Ep dbh untrenched 0.52 Ep dbh trenched 0.73             31  Table 2.4  Generalized additive mixed model (GAMM) results for the annual growth increment including both paper birch and Douglas-fir.  Terms in parentheses indicate estimate factor levels that results refer to.  Smooth terms show treatment combinations per species: “high” and "low" refer to planted densities, while “trench” and “un” refer to trenched and untrenched treatments.  Asterisks are for significance levels; *** refers to α<0.01.     Parametric terms Estimate Std Error t-value p-valueintercept 196.75 16.93 11.625 <2E-16 ***planted density(high) -46.94 10.909 -4.303 2.30E-05 ***Species (Psuemen) 173.426 10.925 15.875 <2E-16 ***Trench(yes) 13.585 10.892 1.247 0.213SHM -15.173 6.186 -2.453 0.0147 **Smooth TermsPaper birch dof F-value p-valuehigh/un 1 0.729 0.394low/un 1 0.137 0.711ig /trenc 1 9.009 0.003 ***l w/tr nch 1 4.87 0.028 **Douglas-firhigh/un 1 4.108 0.044 **low/un 3.981 4.421 0.002 ***high/trench 1 3.664 0.057 *low/trench 4.043 8.627 1.13E-06 ***32  Table 2.5  Generalized additive mixed model (GAMM) results for the annual growth increment of Douglas-fir.  Terms in parentheses indicate estimate factor levels that results refer to.  Smooth terms show treatment combinations per species: “high” and "low" refer to planted densities, while “trench” and “un” refer to trenched and untrenched treatments.  Asterisks are for significance levels; *** refers to α <0.01.     Parametric terms Estimate Std Error t-value p-valueintercept 377.07 19.25 19.59 <2E-16 ***planted density(high) -47.49 19.005 -2.5 0.013 **Trench y ) 2.09 15.34 0.136 0.89SHM -19.69 7.48 -2.63 0.0093 ***Smooth Terms dof F-value p-valuehigh/un 1 3.81 0.052low/un 4.367 4.366 0.00167 ***high/trench 1 2.986 0.0857 *low/trench 4.337 7.884 4.28E-06 ***33  Table 2.6  Generalized additive mixed model (GAMM) results for the annual growth increment of paper birch.  Terms in parentheses indicate estimate factor levels that results refer to.  Smooth terms show treatment combinations per species: “high” and "low" refer to planted densities, while “trench” and “un” refer to trenched and untrenched treatments.  Asterisks are for significance levels; *** refers to α <0.01.  Parametric terms Estimate Std Error t-value p-valueintercept 188.96 16.76 11.27 <2E-16 ***planted density(high) -42.69 14.68 -2.91 0.004 ***Trench y ) 21.92 14.64 1.5 0.136SHM -6.7 10.24 -0.65 0.514Smooth Terms dof F-value p-valuehigh/un 1 0.627 0.43low/un 1 0.22 0.64high/trench 1 9.78 0.0021 ***low/trench 1 5.56 0.02 **34  Table 2.7.  Model results for significant foliar nutrients and nutrient ratios in Douglas fir.  Asterisks refer to significance levels.  ** is for α < 0.05 test level and * for α < 0.10.   N:Mg is nitrogen to magnesium ratio.     Douglas fir Nutrient Fixed Terms coefficient stdE dof t p-valueNintercept 1.265 0.097 14 12.977 0planted density -0.315 0.107 2 -2.932 0.0993 *trenching -0.128 0.073 14 -1.752 0.1016Interaction 0.1745 0.1173 16 1.4881 0.1562N:Mgintercept 12.621 0.9453 14 13.3504 0planted density -4.021 1.229 2 -3.2722 0.0821 *trenching -3.84 1.2291 14 -3.124 0.0075 ***Interaction 4.202 1.7406 14 2.4142 0.03 **35  Table 2.8.  Model results for significant foliar nutrients and nutrient rations in paper birch.  Asterisks refer to significance levels.  ** is for α < 0.05 test level and * for α < 0.10.   N:S is nitrogen to sulphur ratio.    Paper birch Nutrient Fixed Terms coefficient stdE dof t p-valueAlintercept 178.321 35.5486 11 5.0163 0.0004planted density -45.01 49.2911 2 -0.9132 0.4576trenching -83.46 38.4137 11 -2.1727 0.0525 *Interaction 111.702 55.5744 11 2.01 0.0696 *Cuintercept 10.776 1.6304 11 6.6096 0planted density -1.8465 1.6784 2 -1.1001 0.386trenching -3.9796 1.5947 11 -2.4955 0.0297 **Interaction 2.3777 2.2975 11 1.0349 0.3229Feintercept 228.853 37.6596 11 6.0769 0.0001planted density -19.255 55.1568 2 -0.3491 0.7603trenching -93.604 40.3954 11 -2.3172 0.0408 **Interaction 107.443 58.5007 11 1.8366 0.0934 *N:Sintercept 12.9842 0.878 11 14.7886 0planted density 2.3489 1.268 2 1.8524 0.2052trenching 1.8973 0.7248 11 2.6176 0.0239 **Interaction -1.5739 1.0472 11 -1.5029 0.161Naintercept 35.8064 6.9824 11 5.128 0.0003planted density -9.9123 9.02246 2 -1.0986 0.3865trenching -17.422 8.5528 11 -2.037 0.0665 *Interaction 16.7365 12.3657 11 1.3535 0.203136   Figure 2.1  Study site locations.  Insert shows approximate location in British Columbia. 37    Figure 2.2.  Variation in the diameter of target trees according to planted density and presence or absence of trenching.  a) paper birch; b) Douglas-fir.  X-axis labels refer to low (800/400) and high (3200/1600) planted densities of paper birch/Douglas-fir. 38   Figure 2.3.  Variation in the height of target trees according to planted density and presence or absence of trenching.  Top panel is for paper birch; bottom panel is for Douglas-fir.  X-axis labels refer to low (800/400) and high (3200/1600) planted density treatments. 39   Figure 2.4.  Average Diameter at breast height by species and treatment.  “Fir” is Douglas-fir, “birch” is paper birch.  High D and Low D are  high (3200/1600) and low (800/400) planted density treatments.  Bars are standard error.  Number of trees per species/treatment combination varied between 4 and 6 individuals. 40    Figure 2.5.  Average height by species and planted density.  “Fir” is Douglas-fir, “birch” is paper birch.  High D and Low D are high (3200/1600) and low (800/400) planted density treatments.  Bars are standard error.  Number of trees per species/treatment combination varied between 4 and 6 individuals. 41   Figure 2.6.   Environmental variables by trenching in Douglas-fir. 42   Figure 2.7   Environmental variables by trenching in paper birch. 43    Figure 2.8.  Variation in growth over time in each of the eight time series, corresponding to combination of species, planted density, and trenching. Top row shows the linear relationships for birch time series. The bottom row shows the smoothed relationships for Douglas fir, in the same order as for paper birch.  The Y axis shows growth increment centered around their means; positive values correspond to increases from the mean, while negative values correspond to decreases from the mean.  Broken lines are confidence bands.44   Figure 2.9.  Variation of significantly different foliar nutrient concentrations and ratios by planted density in Douglas-fir (nitrogen, and nitrogen to magnesium ratio).  Nitrogen is statistically significant between low and high density at α=0.1 and nitrogen to magnesium ratio by trenching at α=0.05.  X-axis labels refer to low (800/400) and high (3200/1600) planted density treatments.    45   Figure 2.10.  Variation of significant foliar nutrient concentrations and ratios paper birch. Top row are aluminum and copper, middle row iron and nitrogen to sulphur ratio and bottom panel is sodium.  X-axis labels refer to low (800/400) and high (3200/1600) planted density treatments. 46    Figure 2.11.  Douglas-fir (a) multivariate regression tree showing the relationships among foliar nutrients and (b) pie charts for nutrient concentrations at terminal leaves.  Legend at left corresponds to response variable matrix.  The threshold value of variable determining split is shown at the top center of chart.  Numbers below terminal leafs are relative error and sample number for associated leaf.  Bar charts below terminal leafs show average response variable levels at leafs.  These are represented in the pie charts for clarity.  Values below plots refer to relative error, cross validated error and standard error of the full tree. Leaf #2 Leaf #3 47   Figure 2.12.  PCA biplot showing the correlation among soil variables sampled around Douglas-fir.  Objects in blue are individual target trees, by site and treatment, where ML=Malakwa, AL=Adams Lake, HL=Hidden Lake, Low=low density, High=high density, TR=trenched, UN=untrenched.  Black labels refer to soil variables.  “s” refers to soil.  “sBraymgkg” refers to available soil P.  “sCEC refers to soil cation exchange capacity.  The other soil variables are the nutrient concentrations, prefaced with “s”.  Scaling was type two, meaning angles between vectors approximate their correlation. -2024AL.High.UNHL.High.UNML.High.UnAL.High.TRHL.High.TRML.High.TRAL.Low .UNHL.Low .UNML.Low .UNAL.Low .TRHL.Low .TRML.Low .TRsAlsCasFesKsMgsMnsNasCECsH2OphsBraymgkgsNmgkgsN.sC.48   Figure 2.13.  PCA biplot showing the correlation among soil variables sampled around paper birch.  Objects in blue are individual target trees, by site and treatment, where ML=Malakwa, AL=Adams Lake, HL=Hidden Lake, Low=low density, High=high density, TR=trenched, UN=untrenched.  Black labels refer to soil variables.  “s” refers to soil.  “sBraymgkg” refers to available soil phosphorus.  Scaling was type two; meaning angles between vectors approximate their correlations.-2024AL.HighTRAL.High.UNAL.Low .TRAL.Low .UNHL.High.UNHL.High.TRHL.Low .TRHL.Low .UNML.High.TRML.High.UNML.Low .TRML.Low .UNsAlsCasFesKsMgsMnsNasCECsH2OphsBraymgkgsNmgkgsN.sC.49   Figure 2.14.  Paper birch (a) multivariate regression tree showing the relationships among foliar nutrients and (b) pie charts for nutrient concentrations at terminal leaves. Legend at left corresponds to response variable matrix.  The threshold value of variable determining splits is shown at the top center of chart.  Numbers below terminal leafs are relative error and sample numbers.  Bar charts below terminal leafs show average response variable levels.  These are represented in the pie charts for clarity.  Values below plots refer to relative error, cross validated error and standard error of the full tree.  Leaf #2 Leaf #3 a) b) 50   Figure 2.15.  Classification tree showing variables influencing the presence of Armillaria in Douglas-fir. “y” indicates Armillaria presence, while “n” indicates absence. “SM” is soil moisture, “pca1” refers to the first axis of the soil PCA for Douglas-fir.  The numbers below the decision “y/n” of the branch are the sample (number of individual target trees) and the infection ratios: i.e. 1:0 = 100% (of eight trees) not infected.  The Tree has a residual mean deviance of 0.765 and a misclassification error rate of 0.136.    51   Figure 2.16.  Classification trees showing variables influencing the presence of Armillaria in paper birch.  “y” indicates Armillaria presence, while “n” indicates absence.  “c.b” is conifer to broadleaf ratio, “pca1” refers to the first axis of the soil pca for paper birch.  The tree has a residual mean deviance of 0.5975 and a misclassification error rate of 0.1579.    70:170.43:0.5751:052   Figure 2.17.  Variation in annual growth increment according to species, planted density, and presence of trenching. The solid line corresponds to the summer heat to moisture index (SHM), averaged over the three sample sites.    53  Chapter 3 Long-term growth dynamics in experimental stands of planted interior Douglas-fir, paper birch and admixtures Introduction Silviculture practices in British Columbia favour reducing or eliminating broadleaves from managed forests with the goal of increasing early growth of commercially lucrative conifer species (British Columbia Ministry of Forests 2000).  The foundation for these practices lies in stocking standards that do not include broadleaf tree species as preferred or acceptable crop trees and free-to-grow standards that count them only as competing weeds (British Columbia Ministry of Forests 2000). The policies and ensuing practices hinge on the belief that broadleaves serve only to reduce growth of conifers, with no other measurable benefits to forest ecosystems.  A wide arsenal of brushing methods are thus brought to bear on broadleaf removal, including manual cutting with saws or clippers, girdling with chains, or cut-stump or broadcast herbicide application with glyphosate or triclopyr (Comeau et al. 2000).  In the productive mixed forests of interior British Columbia, consecutive manual treatments or doses of herbicides broadcast over the whole plant community are usually necessary to create the simplified conifer stands sought after (Comeau et al. 2000; Hawkins et al. 2012).  Glyphosate in particular eliminates all broadleaf species, greatly reducing biodiversity in managed stands, and sometimes inducing long term damage in conifers as well (Harrington et al. 1995).  These treatments incur great economic cost (Hawkins and Dhar 2011), can have unintended consequences for biodiversity and forest health (Simard et al. 2005), and usually achieve inconsistent or short-lived conifer growth improvements (Simard et al. 2001; Baleshta et al. 2015).  For example, manual brushing of broadleaves increases inoculum potential for root pathogens such as Armillaria solidipes (Peck) (formerly A. ostoyae) (Baleshta et al. 2004, Cleary et al. 2008), which can cause immense damage to commercially valuable conifers such as Douglas fir (Morrison et al. 1991). Where paper birch is maintained rather than removed from mixtures with interior Douglas-fir, the two species interact through multiple pathways involving competition and facilitation (Simard and Vyse 2006). Early in succession, paper birch usually overtops Douglas-fir and competes for light (Simard et al. 1991), and this changes as interior Douglas-fir naturally outgrows paper birch after crown closure. Later in succession, where overtopping broadleaves 54  are still occasionally present in Douglas-fir stands, light infiltration and light quality are enhanced compared with pure conifer canopies, thus increasing understory photosynthesis, photorespiration and thus nutrient acquisition rates (Heineman et al. 2006).  The two species also interact over soil resources in complex ways.  According to Simard and Sachs (2004), the intensity of competition for soil resources appears more related to density and stature than species identity. This may be related to niche partitioning, where interspecific competition for belowground resources in mixtures can be low because birch roots occupy different soil depths and have distinct root architectures from Douglas-fir (Bradley & Fyles 1998; Klinka et al. 2000).  Moreover, paper birch contributes nutrient-rich litterfall, which should increase nutrient availability to interior Douglas-fir in mixed stands (Sachs 1998; Legare et al. 2001).  Nutrients may also be directly transferred from paper birch to interior Douglas-fir in young stands in summer through mycorrhizal networks along source-sink gradients for carbon and nitrogen (Simard et al. 1997).  The direction of transfer can change with season, where nutrients transfer from Douglas-fir to paper birch in spring and fall (Philip 2006). These examples illustrate that interspecific interactions between paper birch and Douglas-fir are more complex than what is assumed in some silviculture policies and practices.  Armillaria root disease accounts for a great deal of damage and mortality in the mixed forests of southern interior British Columbia.  Tree volume lost to root disease in Canada’s Pacific and Yukon regions is estimated at 5,477,780 m3, with three quarters attributable to mortality, and most due to Armillaria root disease (Laflamme 2014).  Armillaria root disease appears most frequently and causes the most damage in the Interior Cedar Hemlock (ICH) biogeoclimatic zone (Morrison et al. 1991). Within the ICH zone, the disease is most prevalent in the moist, warm subzones, with 90% infection in the moist and dry extremes (Cleary et al. 2008). Armillaria root disease is more prevalent on droughty sites, and thus tree vulnerability is expected to increase with drought caused by climate change (Smith 2011).  Within the ICH zone, the disease affects all woody species, but is more prevalent on certain conifer species, including Douglas-fir (Cleary et al. 2008).  Paper birch has low vulnerability to the pathogen, especially before age 40 years (Cleary et al. 2008).  Mortality caused by Armillaria root disease peaks when stands reach 21 years-old and then declines with stand age (Cleary et al. 2008).   55  Armillaria root disease has been managed in British Columbia using three approaches: through removal of root systems from soil, biological control, or intermixing susceptible with less vulnerable tree species. Opinion is divided on which of these is the best practice to manage the disease.  The standard practice for the past three decades in British Columbia has been the use of destumping as a site preparation treatment or pushover logging as a harvesting treatment to remove tree roots and thus reduce inoculum potential (Morrison et al. 1991; Chapman 2011). Biological control using Hypholoma fasciculare (Huds. ex Fr.) Kummer has shown promise (Chapman and Xiao 200; Chapman et al. 2004; Laflamme 2014), but is currently not licensed for use in Canada. An alternative means of managing the disease is to favor intermixing broadleaves or other resistant species in conifer plantations (Morrison et al. 1991; Simard et al. 2005; Cleary et al. 2008).  This approach emulates natural succession processes.  Recent research shows that this passive approach can be accompanied with selective brushing for specific conifer individuals experiencing intense local competition from broadleaves, which serves to release the suppressed individuals while maintaining low levels of inoculum potential over the whole stand (Baleshta et al. 2015).  This treatment is in direct contradiction to silviculture policy (British Columbia Ministry of Forests 2000), however, and therefore has not been actively practiced in British Columbia. The study reported here is uniquely capable of assessing this passive management strategy for reducing volume loss to Armillaria root disease because (a) it includes well replicated mixtures of highly susceptible conifers and resistant broadleaves, (b) the experimental sites have high Armillaria inoculum loads, and (c) the stands having reached the age when the most damage by the pathogen has theoretically accumulated.   Forest understory plants carry out and maintain many vital ecosystem processes.  Understory plants enrich soils and cycle nutrients at levels disproportionate to their relatively small biomass (Gilliam 2007; Wedraogo 1993). They provide habitat for insects and small mammals that are critical in nutrient cycling and the distribution and germination of tree seeds.  Herbaceous layers affect tree seedling regeneration, survival, growth and thus overstory composition (Muller 2003; Gilliam 2007). Additionally, understories contain much of the biodiversity in many forest ecosystems, and as such, contribute to their resilience to natural and anthropogenic disturbances (Yu et al. 2013).  Recent broad-scale afforestation projects in China using monocultures and occasionally mixtures point to the efficacy of mixedwoods in promoting understory diversity and, in turn, tree seedling regeneration (Tsunekawa et al. 2014). 56  Previous work on the influence of canopy mixing on understory species diversity and composition remains divided, with some authors claiming greater diversity under monocultures (Barbier 2008) and others enthusiastically proclaiming greater diversity beneath mixed forests (Yu and Sun 2013).  Still others suggest that a positive relationship exists between canopy and understory diversity, but only a slight one, especially where environmental conditions are more influential (Halpern and Lutz 2013; Gracia et al. 2007).  The difference between these studies may stem from their observational nature, where starting conditions of tree communities is lacking, the duration of study is relatively short, the stage of stand development or season of measurement does not yield strong effects, or broader patterns preclude adequate comparisons (Trinder et al. 2013).  Nevertheless, it is reasonable to expect that differences in light and soil resource uptake and availability in mixtures of tree functional types (deciduous and coniferous) would create different understory niches and patchiness (Messier et al. 1998; Rodriguez-Calcerrada et al. 2011, Augusto et al. 2003).  This study evaluated tree responses in a 21 year-old planting experiment where paper birch (Betula papyrifera Marsh.) and interior Douglas-fir (Pseudotsuga menziesii var. glauca) were grown in pure stands and admixtures on clearcut sites in the ICH forests of southern interior British Columbia.  The objective of the original study was to determine the effects of paper birch and Douglas-fir density and proportion on individual and stand-level tree growth, with the intent of testing silviculture assumptions that broadleaves in managed stands reduce conifer volume and vigour. In the experiment, density and species proportion were varied systematically in an addition series design, also known as a response surface design.  The response surface design involves increasing density and proportion of each species separately and simultaneously along gradients, and is highly effective for evaluating interspecific interactions (Shainsky and Radosevich 1992).  The response surface design provided us an opportunity to test fundamental niche theory (Hutchinson 1957), where we expected intraspecific competition to have a more negative influence on individual tree growth than interspecific competition. It also allowed testing whether a competition threshold of paper birch density existed at which Douglas fir growth diminished (Simard et al. 2004).  In addition, treatment effects on foliar nutrition, incidence of Armillaria root disease in the two species, and diversity of the understory plant community were investigated to increase our understanding of underlying drivers of tree and stand-level responses. The results will allow us to evaluate whether standard forest practices that 57  reduce broadleaf neighbors achieve their goal of enhancing conifer performance, and whether there are unintended knock-on effects.  The study had two main objectives: 1) to observe growth dynamics and outcomes resulting from intra- and interspecific competition in pure and mixed stands of paper birch and interior Douglas-fir 21 years after planting; and 2) to examine other stand characteristics that may be influenced by the combinations of the two planted tree species.  For objective 1, we examined total volume, basal area increment, and foliar nutrient concentrations of each tree species. For objective 2, we examined Armillaria root disease incidence and understory plant species composition. We first hypothesized that intraspecific competition would negatively influence growth of both species more than interspecific competition, particularly for paper birch in the first decade after establishment, and then for Douglas-fir once it gains dominance. The difference in the two species was predicted because of the fast growth rate of young birch. We also expected to find a threshold paper birch density at which interior Douglas-fir growth would decline. Our second hypothesis was that foliar nutrient concentrations would be higher in both paper birch and interior Douglas-fir in admixtures than pure stands.  We expected the nutrient enrichment would be especially pronounced in interior Douglas-fir.  Our third hypothesis was that Armillaria root disease incidence would be lower in mixed than pure stands, and decrease with increasing evenness of the admixtures. This was partially based on the fact that different tree species have different levels of resistance, and the fungus must acclimate and thus spend more energy in adjusting to multiple resistance levels in mixed stands. We also expected that Douglas-fir health specifically would benefit from increased birch presence.  This expectation was based on the fact that young Douglas-fir is highly vulnerable to Armillaria solidipes infection, while young birch is one of the most resistant tree species (Cleary et al. 2008), possibly because it associates strongly with disease antagonistic fluorescent pseudomonad bacteria (Delong et al. 2004). Our fourth hypothesis was that distinctive plant communities would form under mixed canopies than monoculture canopies. 58  Methods Study sites This experiment was part of a larger study examining the effects of broadleaf and conifer intra- and interspecific competition on forest productivity.  The experiment was conducted in the ICH biogeoclimatic zone of southern interior British Columbia, locally referred to as the interior wet belt (Figure 3.1). The ICH zone is one of the wettest regions east of the Coast Mountains, and is characterized by a continental climate dominated by easterly moving air masses, cool wet winters, and warm, dry summers.  Mean annual precipitation ranges from 500-1200 mm, 25-50% of which falls as snow (Meidinger et al. 1991b).  The three replicate sites were situated in the moist, warm ICH subzone (ICHmw), which occupies the middle range of the precipitation gradient of the ICH zone.   Two sites, Adams Lake (51°97’, 119°28’N) and Malakwa (50°97’, 118°72’N) occur in the Thompson Moist Warm geographical variant (ICHmw3), while the third, Hidden Lake (50°56’, 119°28’), occurs in the Shuswap Moist Warm geographical variant (ICHmw2) (Figure 3.1).  The sites were similar in pre-harvest elevation, aspect, soil characteristics and tree species composition (Table 2.1). All sites were clear-cut in 1978 (Hidden Lake), 1987 (Adams Lake) and 1988 (Malakwa) then planted to interior spruce or interior Douglas-fir.  The original plantations failed due to high infection rates of Armillaria solidipes at all sites as well as frost damage at Malakwa. In the fall of 1991, the sites were destumped and scarified with an excavator followed by replanting with experimental paper birch (1+0 516 styroblock plugs) and Douglas-fir (1+0 312 styroblock plugs) seedlings in May-June of 1992.  A total of eighteen 40 m x 40 m plots were established at each site, and randomly assigned monoculture and admixture densities of paper birch and interior Douglas fir in an addition series using a randomized block design.  The treatments included monoculture densities of 400, 800, 1600 and 3200 stems ha-1 and admixtures of the majority of these, for a total of 17 treatments (Figure 3.2).  The densities were replicated three times at the site level, with one replicate each at Adams Lake, Malakwa and Hidden Lake. The addition series design allows for density dependent effects to be decoupled from species proportion effects.     59  Field data collection  Tree and soil properties were measured in 2013, 21 years after the plantation was established.  Measurements were taken in neighbourhood plots, where the target, or focal, tree and all neighboring trees were measured within a 7.1 m radius (plot area = ~90m2) centered on the target tree.  This distance was found in previous work on similar forest stands to demarcate the zone of maximum inter-tree competition (Simard and Sachs 2004).  Target trees were either planted interior Douglas-fir or planted paper birch.  Since ingress of naturally regenerated trees had occurred since the establishment of the experiment, target trees were selected only if they were known to be of the planted cohort.  This was determined by the presence of permanent markers located at the base of the tree.  Two neighbourhood plots per target tree species were randomly located in each of the 17 treatment units per site, for a total of 36 plots per site (note that some plots contained single species treatments), and 108 plots in total over the three replicate sites.  Target tree and neighbour tree height (m) and diameter (cm) were measured with a vertex digital hypsometer and diameter tape, respectively. The neighboring understory plant community was assessed by percent cover per species within the 7.1 m radius plots, using methods outlined in British Columbia Ministry of Forests & Range (2010).  Photosynthetically active radiation (PAR, µmol m-2 s-1) incident on each target tree was measured with a LICOR LI-250A Light Meter.  The PAR line intercept was measured in the four cardinal directions from the drip line of the foliage of each target tree and averaged.  Soil moisture content (%) was recorded with a HH2 moisture meter with an ML2x Theta probe (Delta-T Devices Ltd.) in a soil volume with 160mm depth x 100mm soil diameter. One reading was taken per target tree at a distance of 1 m from the tree bole.  Armillaria root disease presence or absence was determined by exposing the root collar of each target and neighbourhood tree and examining the entire perimeter and cambium for visual characteristics of the disease.  Representative photos of the fungal pathogen in several developmental stages were shown to experts to confirm the identification of the disease.   Samples for determining foliar and soil nutrients were collected in August 2013. In each neighborhood plot, a foliage sample was selected from the current year’s growth in the top third of the target tree.  In addition, a soil sample was collected from the top 40 cm mineral soil using an auger 1 m from the tree bole. Foliage and soil samples were analyzed at the British Columbia 60  Ministry of Environment Analytical Lab in Victoria, BC.  Soil total N and total C were determined using combustion elemental analysis and an elemental analyzer.  Cation exchange capacity (CEC) using soil exchangeable cations ([Ca], [Mg], [K]) was determined by the neutral ammonium acetate method; available phosphorus was determined with the Bray P1 procedure and soil pH was determined in 0.01 mol CaCl2 (Kalra and Maynard 1991).  Foliar macronutrients (C, N, K, Ca, Mg, P and S) and micronutrients (B, Cu, Fe, Mn, Mo, Na and Zn) were analyzed by ICP-OES (inductively coupled Plasma-Optical Emission Spectrometer) after microwave digestion, with concentrated HNO3, 30% H202 and concentrated HCl.  Ratios of N:P, N:C, N:Mg and N:K were calculated using the examined concentrations. Statistical analysis All statistical analyses were performed in R, version 3.1.0 (R Core Team 2014). A neighbourhood analysis was conducted on volume index (VI = height x diameter at 1.3 m) of the target trees using linear mixed models with the lme function (nlme library).  The general form of the model was: VI target species = VI paper birch x VI interior Douglas-fir     (1) Neighbourhood analysis is a commonly used technique in tree competition studies.  It allows for an analysis of multiple instances of competition by regressing performance measures for individual trees, such as height or volume, against the same or similar measures for a chosen area or suite of neighbours (Goldberg 1987), rather than using less nuanced measures such as mean density.  A major advantage of this technique is its ability to incorporate spatial variability in relatively simple analyses such as linear or mixed regression   Linear mixed models are a class of regression analysis that allow for fixed and random model parameters.  Random parameters are allowed to have separate variances per level and enable an examination of fixed parameters of interest beyond differences between random parameters.  Site was used as the random parameter in the model examining variations in target tree VI as a function of the interspecific and intraspecific neighbour tree VI and their interaction; treatment within site was additionally used as a random factor as the treatments were not replicated within the sites.  This means that each site is allowed a separate amount of variance around the intercept (Zuur et al. 2009).  The model was fit using restricted maximum likelihood (REML), which 61  estimates slope and intercept while incorporating the random part of the equation (Zuur et al. 2009). Multivariate regression trees (MRT) were used to analyse the relative importance of the density and proportion treatments on foliar nutrient concentrations versus the neighbourhood and environmental variables.  These analyses were performed using the mvpart package.  Armillaria root disease incidence was analysed using classification trees from the Tree package.  Understory vegetation was analyzed using a Kendal test as well as MRTs, as above, in combination with indicator species analysis (ISA).  The MRT/ISA results were further examined using principle component analysis (PCA), with a function from Pierre Legendre (http://adn.biol.umontreal.ca/~numericalecology/Rcode/).   Multivariate regression trees are a mixture of regression and clustering techniques, and have been described as “constrained clustering” (Borcard et al. 2011) or “robust regression” (Logan 2011).  They can handle many response and explanatory variables, different underlying distributions, and situations with missing values.  MRT’s work through “binary recursive partitioning”, or finding threshold values of the explanatory variables that explain the greatest variation in the response variables (McCune et al. 2002).  This process works by ranking each value of the response variables, or combination of levels for categorical variables, and dichotomously splitting the response data at the level of the most important variable in minimizing the sum-of-squared-errors for the response matrix.  The splitting then continues independently along each branch of the tree until terminal leaves are created (McCune et al 2002, Borcard et al. 2011). The number of terminal leaves in the MRT’s are determined by a process known as cross-validation (De’ath and Fabricius 2000), where the data are randomly divided into an equal number of groups (10% of objects, for example), and the remaining 90% are used to construct the tree.  The objects of the 10% groups are then assigned to the trees with leaves where they “fit” best, and the optimal number of branches is determined after several independent cross-validations by selecting the number of terminal branches most often accommodating all the objects in the test group (10% group).  The final tree contains an overall CVRE statistic calculated as the error of each test group run divided by the total error of all the Y data.  It can be interpreted as the ratio of variation unexplained by the tree to the total variation in Y.  62  Multivariate regression trees using a response matrix of foliar nutrient concentrations were constructed separately for each tree species in relation to other environmental variables and two neighbourhood variables, including number of neighbouring trees and conifer to broadleaf ratio, which included all trees over 2 m tall (calculated as total number conifers/total number of broadleaves among neighbour trees per plot).  The environmental variables were soil moisture content, PAR, soil nutrient concentrations, CEC, and soil pH.                   Classification trees were created with Armillaria root disease presence or absence as a response to the same suite of variables as in the MRTs.  Classification trees are similar to regression trees but are used in cases of single categorical response variables.  The classification tree is constructed by seeking the threshold levels of explanatory variables that account for the greatest purity of response, or groups with highest percentage of the same value of the categorical response variable (i.e., yes or no).   Impurity is expressed in terms of deviance, where a deviance of 0 represents perfect purity.  Splitting continues along successive branches until complete purity is obtained.  Trees are then pruned according to a similar method as cross validation, with an optimal tree being selected from several trees constructed from sub-sets of the data based on a cost-complexity measure (Ripley, 2005).  Classification trees return a misclassification error rate statistic referring to the percentage of objects returned to incorrect leafs after pruning (Ripley, 2005).  Using this method, classification trees were constructed for both target species to determine divisions in absence or presence of Armillaria root disease as predicted from site, treatment, tree size (VI), neighbourhood variables (including VI of broadleaves, conifers, paper birch and interior Douglas-fir) and environmental variables taken at the target tree level (including soil moisture, PAR, soil nutrient concentrations, soil pH and CEC).  Results Growth  In the paper birch neighborhood model, all parameters were significant (neighbour paper birch VI, p=0.0093; neighbour Douglas-fir VI, p=0.0242), including the interaction term (p=0.0282) (Table 3.1, Figure 3.3).  Here, the response variable, paper birch VI, was natural log transformed to meet the assumptions of linear regression. By contrast, no parameters were significant in the 63  interior Douglas-fir neighborhood model (Table 3.1, Figure 3.4) (neighbour interior Douglas-fir VI, p= 0.7993; neighbour paper birch VI, p=0.5288).  Foliar nutrients The paper birch MRT for foliar nutrient concentrations found site to be most important among the response variables, followed by PAR, soil moisture (chosen for two consecutive splits) and then incidence of Armillaria root disease in neighbour trees (Figure 3.5).  Response variables were centered to aid interpretation (Borcard et al. 2011).   The interior Douglas-fir MRT found birch neighbour VI to be most important in determining significant divisions in foliar nutrient concentrations, followed by the incidence of Armillaria in neighbouring trees, and then site (Figure 3.6).  The first split was determined by C, Al and Ca, with higher concentrations of these foliar nutrients in interior Douglas-fir where it was growing in association with greater volumes of birch neighbours (Figure 3.7). The second split showed that higher foliar concentrations of Fe, Mn and C were associated with greater incidence of Armillaria root disease (Figure 3.7).  Finally, foliar nutrient concentrations were significantly different in Douglas fir in Hidden Lake and Malakwa. Armillaria root disease The paper birch classification tree found percentage of Armillaria root disease in neighbouring trees to be the most important factor determining Armillaria root disease incidence in target trees, with lower percentages of neighbour infection associated strongly with absence of the disease in target trees (Figure 3.8).  The next important variable was tree volume index (VI), with larger trees less likely to have the disease.  The third split was by planting treatment, with target paper birch in treatments of 1600/0, 3200/400, 400/400, 800/0, 800/1600 and 800/800 paper birch/interior Douglas-fir stems per hectare more likely to be infected with Armillaria root disease.  The classification tree then found percentage of Armillaria root disease in neighbours to again determine a significant split in the data, with higher incidence of infected neighbours again favoring presence of the disease in target trees.  The two final splits found higher incidence of Armillaria root disease in paper birch associated with treatments 3200/400, 400/400, 800/0 and 800/800 stems per hectare paper birch/interior Douglas-fir, and in neighborhoods with higher volumes of paper birch.  64  The interior Douglas-fir classification tree was first split by soil C concentration, with lower incidence of Armillaria root disease associated with higher soil C concentration (Figure 3.9).  The tree then split by Armillaria root disease incidence in neighbours, where incidence of disease in Douglas-fir target trees was associated with higher incidence of Armillaria root disease in neighbours.  The third split was determined by treatment, with 3200/400, 400/800 and 800/800 stems per hectare of paper birch/interior Douglas-fir associated with absence of Armillaria disease and 0/1600, 0/3200, 0/800, 3200/800, 400/1600 stems per hectare correlated with presence of the disease.  The right branch of the tree then terminated with a final split by VI of Douglas-fir neighbours, with higher volumes associated with higher incidence of the disease.  The left branch continued by splitting by soil C:N, soil N concentration, and finally soil Ca concentration.  Higher C: N was associated with absence of the disease, low N concentration correlated with presence, and lower Ca concentration with absence of Armillaria root disease on Douglas-fir focal trees.   Understory plant community The MRT for the understory plant community found the first split occurred according to site, with Hidden Lake and Malakwa clustering together, apart from Adams Lake (Table 3.2, Figure 3.10).  Within the Hidden Lake and Malakwa branch, percentage of Armillaria in neighbours determined a second split.  MRTs then performed within sites showed that each site clustered into two groups of plant species determined by treatment (Table 3.3).  The Adams Lake MRT delineated plots into two groups, with group one composed of the pre-harvest species Paxistima myrsinites, Mahonia aquilinum, and Polytrichum juniperinum, and group two distinguished by Pteridium aquilinum (an allelopathic fern), Viccia spp. (a field-associated non-native plant) and Apocynum androsaemifolium.  In terms of the plot treatments, group 2 had lower planted tree densities, with some birch present in each treatment, and thus less canopy shading than group 1, which contained higher average tree densities and several birch-absent treatments (Table 3.3).  Similarly to Adams, the Malakwa MRT separated into two groups—with group 2 covarying according to native, pre-harvest species, Clintonia uniflora, Paxistima myrsinites, and Mahonia 65  aquilinum, while group 1 contained high abundances of the invasive weed, Hieraceum spp., and the lichen, Cladonia gracilis v. tur, and similar treatment separation to Adams Lake.   Although Hidden Lake separated into two MRT groups, its indicator species demonstrated a somewhat different pattern than the other sites.   The native species occurring in the more closed canopy grouping were Pteridum aquilinum and Hieraceum alba, both commonly occurring species in site series in the ICHmw, versus Hieraceum spp. and the common moss, Pleurozium schreberi in the more open canopy group.  While the first group contained generally higher levels of Douglas fir, the second group was not distinguishable by degree of mixing. PCA biplots were constructed using the indicator species for each MRT cluster by treatment within sites to examine patterns within the MRT group (Figure 3.11).   PCA biplots showed further site-specific variation.  In each site PCA, the primary axis separated indicator species according to the MRT groups, while the second axis showed variation that was somewhat different than that contained in the MRTs.  For Adams Lake, much of the second axis variation (25 percent) was divided between Apocynum androsaemifolium and Paxistima myrsinites.  For Malakwa, the variation along axis two (15%) was driven primarily by the presence or absence of Cornus canadensis.  Finally, for Hidden Lake, the second axis (17%) counterpoised Pleurozium schreberi and the native hawkweed, Hieraceum alba, against invasive hawkweeds, Hieraceum spp., and Pteridium aquilinum.   Discussion Growth dynamics in response to competition Our first hypothesis that intraspecific competition would negatively influence tree growth more intensely than interspecific competition was supported for paper birch, though not for interior Douglas-fir.  The intense intraspecific competition among paper birch likely resulted from its fast initial growth rates, which is typical of this species (Peterson et al. 1998), then accentuated as the species declined in vigour due to other confounding factors.  Paper birch normally still overtops interior Douglas-fir 21 years after establishment (Simard et al. 2004), but in this study it was overtaken by conifer neighbors earlier because of its poor vigour.  The poor vigour of paper 66  birch is illustrated in Figure 3.12, where paper birch populations had declined at higher planted densities, while interior Douglas-fir far exceeded planted densities in all treatments.  Paper birch also suffered growth losses due to interspecific interference from interior Douglas-fir, albeit less so than interference from conspecifics. Interior Douglas-fir volume, by contrast, was affected neither by intraspecific nor interspecific competition at this stage of stand development.  The most likely explanation is that the interior Douglas-fir population had not yet reached carrying capacity and resources were not yet limiting to this species on the sites. Why the weaker, smaller species (paper birch) appeared to have exhausted the site resources while the more vigorous species (Douglas-fir) had not by 21 years initially seems counterintuitive; however, considering paper birch likely had poor root growth due to disease or other damaging agents, its capacity to capture resources belowground may have been limited.   We had expected to identify a threshold density of paper birch at which Douglas-fir growth steeply declined, which could be useful in guiding management practices aiming to maintain a mixed stand without compromising interior Douglas-fir growth (Simard 1990). However, a threshold was not clear, possibly due to the low volumes of birch neighbors, reflecting their poor vigour (Figure 3.4).  Hence, Douglas-fir appeared to respond more to factors other than paper birch neighborhood density.  By contrast, the paper birch model contained a significant reaction and the response curves showed that density thresholds where target birch growth steeply declined existed (~0.5 VI), and were lower for conspecific (~0.5 m3) than Douglas fir (~5 m3) neighbour volumes (Figure 3.3).  In other words, paper birch was more sensitive to intraspecific than interspecific neighbour density, agreeing with fundamental niche theory (Hutchinson 1957).   Foliar nutrients Our second hypothesis, that foliar nutrition would be greater in admixtures than pure stands, was supported for Douglas-fir but not paper birch.  For birch, site was the most important determinant of foliar nutrients. Given the autecological differences between the two species, and the fact that paper birch foliage is nutrient-rich even on poor sites, we were not surprised that environmental factors were more important determinants of paper birch foliar nutrient concentrations than neighborhood composition.  This pattern also makes sense in light of the fact that paper birch competition was less important for Douglas-fir growth than for paper birch growth, as reflected in the model R2, or importance of competition,  for the two species (0.18 67  versus 0.68, respectively), and therefore would limit soil resource availability less to heterospecific than conspecific neighbours.  On the other hand, the high importance of paper birch neighbours to Douglas fir foliar nutrition supports our hypothesis that species mixing would lead to higher nutrient concentrations in the more nutrient-poor conifer species.  Interior Douglas-fir had greater concentrations of C, Al and Ca when associated with higher paper birch neighbour volumes (Figure 3.6).  The enrichment of these particular nutrients in Douglas-fir may have resulted from the addition and subsequent decomposition of the nutrient-rich litter of paper birch. It also provides indirect support for transfer of photosynthate-C from paper birch to interior Douglas-fir along a source-sink gradient through MNs in summer, when an excess of C may be present in birch (Simard et al. 1997).  This interpretation should be considered with caution, however, given that paper birch in this study was of very poor health and often barely capable of sustaining itself, never mind providing an excess of nutrients to neighbors.  Alternatively, the mycorrhizal fungi comprising the MN could have been playing a role in directing transfer from paper birch to interior Douglas-fir to meet its own needs for a healthy host (Song et al. 2015).   Armillaria root disease In the case of interior Douglas-fir, we found evidence to support our third hypotheses that the generalist pathogen would cause lower rates of infection in more evenly mixed stands.  The first two splits in the interior Douglas-fir classification tree were due to soil C concentration and incidence of Armillaria root disease in neighbours, with lower soil C associated with higher incidence of Armillaria root disease, and higher neighbour infection associated with greater focal tree infection, both results supporting previous work (Cruickshank et al. 2009; Chapman et al. 2011) and thus serving as a type of ecological model validation.  The association of disease incidence with lower soil C concentration speaks to the saprophytic lifestyle of the fungus, when it remains dormant in the soil and feeds on dead tissue until colonizing a live host and initiating its parasitic lifestyle (Chapman et al. 2011).  Lower soil C may reflect C consumption by the saprophytic fungus prior to switching to a live host.  The association between Armillaria root disease incidence in target Douglas-fir and density of infected neighbours likewise makes sense considering the disease spreads by root contact and rhizomorphs (Cleary et al. 2008).   68  Given the ecological significance of the first two MRT branches for Armillaria root disease in interior Douglas-fir, the third split, occurring at each branch with complete purity (all trees with the same response), finding presence or absence, respectively, based on density and proportion treatment, represents a robust result.  Taken together, the groupings at each terminal node support the hypothesis that Armillaria root disease incidence is lower in more mixed stands.  The treatments associated with Armillaria root disease absence were 3200/400, 400/800 and 800/800 stems per hectare of paper birch/interior Douglas fir, and those associated with Armillaria presence were 0/1600, 0/3200, 0/800, 3200/800 and 400/1600.  The treatment group associated with the absence of the disease is consistently mixed and always contains at least 50% birch, while the group associated with its presence includes three interior Douglas-fir monocultures, one stand with less than 25% birch in mixture, and one that was a high density paper birch mixture.  Absence of the disease among Douglas-fir grown in mixed stands may be linked to the presence of high populations of the Armillaria-antagonistic fluorescent pseudomonad bacteria associated with paper birch roots (Delong et al. 2004).  Inclusion of the latter two anomalous treatments where the disease was present may reflect the high spatial variability of Armillaria root disease rather than the species composition tested (Morrison et al. 1991, Cruickshank et al. 2009), even though the treatments were randomly assigned.  Due to the unbiased nature splitting algorithm, particularly strong results in one treatment could influence the entire model.  Alternatively, especially in the case of the 3200/800 treatment, the high root disease incidence of both interior Douglas-fir and paper birch, as well as the high paper birch mortality levels in the high paper birch density treatments (Figure 3.12), would have promoted spread of Armilliaria root disease.   Patterns of Armillaria root disease among paper birch provided less support of our third hypotheses that admixtures were more protective against the disease.  The treatments were again identified as important in explaining Armillaria presence in paper birch, but the only clear emergent pattern was the rarity of the disease in Douglas-fir-leading treatments.  This may be due to paper birch benefiting from associating with healthy Douglas-fir neighbors instead of weak and infected paper birch neighbours. A more likely explanation is that there was little variation in disease incidence among Douglas-fir-leading treatments.  Higher Armillaria infection of paper birch tended to occur in planted mixtures containing >50% birch as well.  This clear pattern of higher infection rates among target paper birch where there was greater infection 69  rates of neighbours makes sense for a pathogen that is transferred through root or rhizomorph contact.    Tree size was another variable identified as important to Armillaria infection of paper birch, but the results are inconsistent.  Greater infection occurred among smaller trees, which may reflect greater weakness of smaller trees and hence greater vulnerability to the disease; however, at a lower hierarchy level, we see that smaller trees have less disease.  This suggests there are two birch size threshold values for Armillaria infection; and may be interpreted to mean that smaller trees were less resistant to infection by Armillaria solidipes, but below a threshold size, there was too little tissue to be worthy of the pathogen’s investment.  This agrees with Cleary et al. (2008) who report that larger trees have greater chance of infection, mostly due to greater surface area of roots for spread of disease. Alternatively, the opposing result may mean the splitting algorithm did not yield meaningful thresholds; or perhaps that the highly variable and mostly unhealthy birch population did not contain clear patterns of infection.  Understory diversity Our fourth hypothesis that distinct plant communities would form under mixed versus monoculture canopies was supported.  However, this was secondary to the effect of geographical location of the sites. The global MRT separated sites into two groups, one containing Adams Lake and the other, Hidden Lake and Malakwa.  One possible reason for this distinction is that Hidden Lake and Malakwa are associated with agricultural lands: grazing by cattle was visible at both sites.  Adams Lake, on the other hand, was only in proximity of forestry activity.  Site location was similarly the primary influence on the ectomycorrhizal community (Lallemand 2015), possibly due to differences in native shrub community composition.  At Hidden Lake and especially Malakwa, incidence of Armillaria root disease was also an important influence on plant community composition. The differentiation of understory species by Armillaria presence could possibly be due to the fact that some understory species are more resistant to the disease, although levels of understory shrub resistance to the pathogen have yet to be studied (Cleary et al. 2008).  If understory shrubs have different levels of resistance, a more resistant community could aid canopy tree resistance, by creating a physical barrier to spread.  70  This second explanation seems tenable, given recollections and field notes citing signs of the disease in Vaccinium spp. and Epilobium angustifolia, both contained in group 1 (Table 3.2).   Within sites, MRTs consistently identified two plant community groups: one distinguished by open-canopy “grassland type” vegetation and another “normal forest” understory composition according to Lloyd et al. (1990).  The latter group included indicator species that were present in the pre-harvest understory at these sites, with the exception of Hidden Lake, where the allelopathic fern, Pteridium aquilinum, and the native hawkweed, Hieraceum alba, presented under more closed, Douglas fir-leading, canopies.  Light availability should be a major determinant of group identity; however, PAR did not appear in the regression tree.  Another possibility is that healthy stands of trees were associated with an ectomycorrhizal fungal community, whereas plots with high tree mortality may have been at risk of invasion by arbuscular mycorrhizal grasses and forbs.  The two functional types of mycorrhizal fungi can be antagonistic to one another, with potentially positive feedbacks reinforcing the plant community composition (Haskins and Gehring 2004; McHugh and Gehring 2006; Simard et al. 2012).    PCA biplots using the single-site MRT groups showed further within-group variation.  While the first PCA axis in each site delineated according to the MRT groups, the second axis contained additional information.  For Adams Lake, much of the second axis variation (25 percent) was divided between Apocynum androsaemifolium and Paxistima myrsinites, which may represent variation due to understory microclimate; Apocynum androsaemifolium associates with dry sites and does not perform well under the canopy, while Paxistima myrsinites flourishes under shaded canopies.  For Malakwa, the variation along axis two (15%) was driven primarily by the presence or absence of Cornus canadensis, a shade tolerant understory plant species (Parish et al. 2000) that would not grow in the open-canopy, dry treatments at the bottom of the axis (Figure 3.11).  At Hidden Lake, the second axis (17%) counterpoised the native hawkweed Hieraceum alba and common moss, Pleurozsium schreberi, against the allelopathic fern, bracken (Pteridium aquilinum), and the invasive hawkweeds.  This distinction may stem from more birch-dominated and open communities at the top end of the axis, which favour bracken and Hieraceum.      71  Conclusions Twenty-one years after establishment of the addition series experiment, the interior Douglas-fir populations were healthy and not suffering with any level of paper birch competition.  By contrast, the weaker paper birch populations were declining and responded negatively to both interspecific and especially intraspecific competition.  Foliar nutrition of interior Douglas-fir appeared to benefit from presence of paper birch, either due to decomposition of paper birch litter or nutrient transfer through ectomycorrhizal networks. Paper birch was not overtopping interior Douglas-fir, as is normally expected at this stand age, which may have increased the supply of multiples resources to Douglas-fir, thus enhancing foliar nutrient acquisition.  At any rate, these findings certainly cast doubt on the idea that leaving naturally occurring broadleaves in conifer plantations limits crop species’ productivity and health. The inclusion of paper birch in the Douglas-fir stands had additional benefits.  Incidence of Armillaria root disease was much less frequent among interior Douglas-fir where more paper birch neighbours were present.  This could be due to the greater resistance of paper birch to the disease, either due to autecological characteristics such as bark impermeability or the presence of associated antagonistic soil bacteria. Within sites, tree species mixtures appeared to favour understory plant communities with higher resemblance to the pre-harvest community.  In this sense, paper birch retention not only seems to affect Douglas-fir health, but health of the broader ecosystem; allowing it to maintain structure and continue its natural trajectory. Management Implications  The results of this study illustrate rather conclusively that allowing broadleaf species to grow in mixture with conifers in managed stands, thus emulating natural succession in the ICH zone, contributes to the health of conifers and the broader forest.  We strongly encourage allowing natural regeneration of broadleaves to occur in plantations at greater than current densities and favour planting strategies that utilize the natural regeneration where possible rather than applying intensive removal strategies. Furthermore, given the rather bleak forest prospects where intensive grazing and agriculture occurred near or within the plantations, we strongly recommend forest practices that prohibit 72  cattle grazing and takes edge effect of agricultural activities into account when planning.  In an age of uncertainty surrounding climate change, when regenerating viable forests is becoming progressively more difficult, these two recommendations could greatly contribute to the stability and longevity of our forested lands. 73  Table 3.1.  Model results for target tree volume index as a function of neighbourhood volume index of Douglas fir and paper birch.               Paper birch  Value Error DoF t-value p-value Conditional R2 Intercept -2.523 0.428 27 -5.899 0 0.612 Douglas-fir volume index 0.09 0.038 26 2.394 0.024**  Paper birch volume index 0.936 0.333 26 2.808 0.009***  interaction -0.142 0.061 26 -2.325 0.028**  Douglas-fir Intercept 1.16 0.229 30 5.076 0 0.184 Douglas-fir volume index 0.003 0.012 30 0.257 0.8  Paper birch volume index  0.076 30 0.637 0.529  74  Table 3.2. Understory vegetation MRT results across sites.   “Groups” are significantly different associations of understory species, as predicted by selected explanatory variables, in “Variables” column; “Levels” are thresholds or identities of those chosen variables making up the terminal nodes in MRT.   “Indval” is indicator species value. Group Variables Levels Indicator species indval pvalue 1 Site, incidence of Armillaria root disease Hidden Lake , Malakwa (mostly Malakwa), < 0.315 % incidence Spiraea .spp 0.67 0.001 Aralia nudicaulis 0.563 0.002 Epilobium angustifolium 0.534 0.003 Peltigera aphthosa 0.533 0.001 Hieracium  spp. 0.473 0.001 Anaphalis margaritacea 0.43 0.008 Vaccinium ovatum 0.412 0.002 Xerophyllum tenax 0.412 0.003 Picea engelmanii/glauca 0.304 0.028 Peltigera can. 0.26 0.042 Lycopodium ann. 0.235 0.036 75   Table 3.2 (Cont’d) Group Variables Levels Indicator species indval pvalue 2 Sites, per cent Armilaria HL, ML (mostly HL), > 0.315 Phalaris arundinacea 0.794 0.001 Rubus idaeus 0.678 0.001 Pteridium aquilinum 0.634 0.001 Cladinia gracilis 0.621 0.001 Populus tremuloides 0.515 0.002 Populus tremuloides 0.451 0.003 Thuja plicata 0.396 0.013 Aster ciliata 0.393 0.026 Rosa spp. 0.389 0.043 Streptopus lanceolatus 0.335 0.005 Trifolium aureum 0.299 0.038 Hieraceum alba 0.266 0.048 76  Table 3.2 (Cont’d)Group Variables Levels Indicator species indval pvalue 3 Sites All of Adams lake Symphyotrichum foliaceum 0.929 0.001 Calamagrostis rubescens 0.823 0.001 Leucanthemum vulgare 0.793 0.001 Arctostaphylos uva-ursi 0.793 0.001 Mahonia aquifolium 0.656 0.001 Pseudotsuga menziesii 0.624 0.001 Prunus virginiana 0.628 0.001 Polytrichum juniperinum 0.611 0.001 Cladinia gracilis 0.594 0.001 Danthonia spicata 0.563 0.001 Apocynum androsaemifolium 0.514 0.001 Arnica latifolia 0.5 0.001 Paxistima myrsinites 0.45 0.001 Fragaria virginiana 0.357 0.007 Festuca occidentalis 0.321 0.031 Stereocaulon paschale 0.286 0.015 Viccia spp. 0.286 0.019 77  Table 3.3.  MRT results within site.  “Groups” are significantly different associations of understory species, as predicted by selected explanatory variables, in “Variables” column; “Levels” are thresholds or identities of those chosen variables making up the terminal nodes in MRT.   “Indval” is indicator species value Site Group Variables Levels Indicator species indval pvalue Adams Lake 1 Treatment 0/1600, 0/3200, 0/400, 0/800, 1600/0, 3200/0, 3200/400, 3200/800, 800/800 Mahonia aquilinum 0.6 0.005 Paxistima myrsinites 0.592 0.013 Polytrichum juniperinum 0.623 0.027 2 Treatment 400/0, 400/1600, 400/400, 400/800, 800/1600 Pteridium aquilinum 1 0.002 Viccia spp. 0.8 0.008 Apocynum androsemifolia 0.891 0.001 Malakwa 1 Treatment 0/1600, 0/400, 3200/0, 3200/400, 400/0, 400/400, 800/0 Cladonia gracilus 0.544 0.04 Hieraceum spp. 0.579 0.001 Cornus canadensis 0.613 0.043 2 Treatment 0/3200, 0/800, 1600/0, 3200/800, 400/1600, 400/800, 800/1600, 800/800 Mahonia aquifolium 0.673 0.034 Clintonia uniflorum 0.945 0.001 Paxistima myrsinites 0.537 0.05 78  Table 3.3 (Cont’d)     Site Group Variables Levels Indicator species indval pvalue Hidden 1  Treatment  0/3200, 3200/800, 400/0, 400/1600  Pteridium aquilinum 0.766 0.02 Hieraceum alba 0.59 0.045 2 Treatment 0/1600, 0/400, 3200/400, 400/400, 800/0, 0/3200, 0/800, 1600/0, 3200/800, 400/1600, 400/800, 800/1600, 800/800 Hieraceum spp. 0.563 0.006 Pleurozium schreberi 0.636 0.035 79   Figure 3.1.  Location of study sites in the southern interior of British Columbia.  Inset map is distribution of ICH BEC zone (from Ecosystems of BC), with map area in yellow.  80    Figure 3.2.  Study design.  Treatments were randomly assigned in field (not as shown).  White number is paper birch, black number is Douglas fir, in stems per hectare.  Each block is 40m x 40m.81    Figure 3.3.  Birch neighbourhood analysis results.  Y-axis is log volume index (VI) of target trees, X-axis is neighbour Douglas fir volume index (upper panel), and paper birch neighbour volume index (lower panel).  Mixed model statement was log VI birch = VI birch x VI fir.  Full model results are found in Table 3.1.   -0.500.511.522.50 5 10 15 20 25log(vi) Target BirchNeighbors Vi Fir (m3)Adams LakeHidden LakeMalakwa -0.500.511.522.50 0.5 1 1.5 2 2.5 3 3.5 4log(vi) Target BirchNeighbors Vi Fir (m3)82    Figure 3.4.  Douglas fir neighbourhood analysis results.  Y-axis is volume index (VI) of target trees, X-axis is neighbour Douglas fir volume index (upper panel), and paper birch neighbour volume index (lower panel).  Mixed model statement was log VI birch = VI birch x VI fir.  Full model results are found in Table 3.1.   00.511.522.533.540 5 10 15 20 25 30 35 40 45 50vi Target FirNeighbors Vi Fir (m3)Adams LakeHidden LakeMalakwa00.511.522.533.540 0.5 1 1.5 2 2.5 3 3.5 4 4.5vi Target FirNeighbors Vi Birch (m3)83   Figure 3.5.  Paper birch foliar nutrient multivariate regression tree.  “AL” is Adams Lake, “HL”, Hidden Lake and “ML”, Malakwa.  “par” is photosynthetic active radiation, “sm” is soil moisture, and “p.arm” is percentage of Armillaria in neighbours.  Bar graphs at terminal nodes refer to cluster compositions of foliar nutrient concentrations, as shown in legend at left.  Numbers below bar charts are relative error at the terminal node and number of trees making up the cluster at the node, respectively.   84     Figure 3.6  Interior Douglas-fir foliar nutrient multivariate regression tree.   “b.vi” is paper birch neighbour volume index; “p.arm” is percentage armillaria in neighbours; “HL” is Hidden Lake and “ML”, Malakwa.  Bar graphs at terminal nodes refer to cluster compositions of foliar nutrient concentrations, as shown in legend at left.  Numbers below bar charts are relative error at the terminal node and number of trees making up the cluster at the node, respectively.    85   Figure 3.7.  Terminal node foliar nutrient clusters for Douglas fir, corresponding to terminal node bar charts in Figure 3.6.  Leaves 2 through 7 correspond to terminal node cluster of foliar nutrient concentrations from left to right in Figure 3.6.  86   Figure 3.8.  Armillaria classification tree for paper birch.  Letters below terminal nodes represent a “yes” (armillaria present) or “no” (armillaria absent); numbers refer to number of trees in group; ratios are purity of node, first number = “no”, second, “yes”; if branch refers to treatment groupings, the treatments are placed beneath the identity (yes/no) of the node, in hundreds of stems per hectare.  “percentArm” is percentage of armillaria in neighbours, “vi” is target fir volume index, and B.vi is neighbour broadleaf volume index. 87   Figure 3.9.  Classification tree for Armillaria in Douglas fir.  Letters below terminal nodes represent a “yes” (armillaria present) or “no” (armillaria absent); numbers refer to number of trees in group; ratios are purity of node, first number = “no”, second, “yes”; if branch refers to treatment groupings, the treatments are placed beneath the identity (yes/no) of the node, in hundreds of stems per hectare.  C.p. is percent carbon in soil; percentArm is percentage of armillaria in neighbouring trees; C.N is number of conifers in the plot; Nmg.kg is milligrams of N per kilogram in soil; “Fd.vi” is volume index of Douglas fir neighbours; Ca is soil calcium concentration.    88   Figure 3.10.  Multivariate regression tree for understory vegetation at Adams Lake, Hidden Lake and Malakwa.  Bar graphs at terminal nodes refer to cluster compositions of foliar nutrient concentrations.  Numbers below bar charts are relative error at the terminal node and number of trees making up the cluster at the node, respectively.  Statistics at bottom of figure refer to relative error, cross-validated error and standard error (SE). 89  a)      90  b)      91  c)  Figure 3.11.  Principal Component Analysis (PCA) biplots of indicator species per treatment, by site; a) Adams Lake, b) Hidden Lake, and c) Malakwa.  Blue Labels refer to treatment densities in stems per hectare; “T” is treatment; first number is paper birch, the second, Douglas fir.  Black labels refer to indicator species.  Axis scores for Adams Lake were 54% along primary axis and 25% along secondary axis; for Hidden Lake, 65% along primary axis and 17% along secondary axis, and for Malakwa, 64% along the primary and 15% along the secondary axis.  Full MRT results from which the biplots were constructed are found in Table 3.3.  92   Figure 3.12.  Mean current vs. planted densities of birch and fir.  Birch values are first number, fir second along horizontal axis.      93  Chapter 4 Summary and conclusions The results of this study illustrate that allowing broadleaf species to grow in mixture with conifers in managed stands, thus emulating natural succession in the ICH zone, contributes to the health of conifers and the broader forest.  Within the moist, warm ICH subzone, MNs appeared to aid a struggling paper birch population over the two decade growth period. My findings provide support that source-sink dynamics occur over longer time periods in developing stands, where rich neighbors facilitate poor neighbours through MNs, resulting in cumulative benefits for sink species and balancing out competitive inequalities over the long term.  They also point toward the important role of belowground interactions and potentially MNs in even-aged mixed conifer-broadleaf forests for conserving species diversity and, by extension, ecosystem stability.    Review of objectives There was one main objective addressed in each of the two research chapters.  The first was to determine to identify the role of belowground interactions and ectomycorrhizal networks in mediating this competition between interior Douglas-fir and paper birch (Chapter 2) and the second was to determine the outcome of competition between interior Douglas fir and paper birch (Chapter 3). The minor objective in Chapter 2 was to examine the effects of belowground interactions on foliar nutrition and rates of Armillaria root disease.  The minor objective in Chapter 3 was to determine the effect of species admixtures on foliar nutrition, rates of Armillaria root disease, understory vegetation composition.   Summary of main findings Major Objectives Objective 1 (Chapter 2) —Belowground mediation of competition The availability of essential plant resources and level of competition for these resources appeared more important than belowground interactions and potential access to MNs for long-term tree 94  growth and foliar nutrient content.  However, access to intermingling roots and MNs appeared to aid struggling paper birch over the two decade growth period. Objective 2 (Chapter 3) —Outcomes of competition Twenty-one years after establishment of the addition series experiment, the interior Douglas-fir populations were healthy and not suffering with any level of paper birch competition.  By contrast, the weaker paper birch populations were declining and responded negatively to both interspecific and especially intraspecific competition.   Minor Objectives Objective 1—Belowground effects on foliar nutrition While belowground interactions and potential access to mycorrhizal networks facilitated paper birch growth with no negative consequence for Douglas-fir, foliar nutrients of paper birch appeared to suffer.  This finding could represent a pattern of occasional benefits to multiple species with distinct growing seasons linked through networks, regardless of relative health or vigour, with the net effect of favoring the weaker species over time. Objective 2—Belowground effects on Armillaria root disease incidence Paper birch had lower incidence of Armillaria root disease in the untrenched than trenched treatment; by contrast, Douglas-fir infection responded more to resource availability. Objective 3—Admixture effects on foliar nutrition Foliar nutrition of interior Douglas-fir appeared to benefit from presence of paper birch, which may either be due to decomposition of paper birch litter or nutrient transfer through ectomycorrhizal networks. Paper birch was not overtopping interior Douglas-fir, as is normally expected at this stand age, which may have increased the supply of multiples resources to Douglas-fir, thus enhancing foliar nutrient acquisition. Objective 4—Admixture effects on Armillaria root disease incidence Incidence of Armillaria root disease was much lower among interior Douglas-fir where more paper birch neighbours were present.  This could be due to the greater resistance of paper birch 95  to the disease, either due to autecological characteristics such as bark impermeability or the presence of associated soil bacteria. Objective 5—Admixture effects on understory composition While understory composition across sites appeared to vary more with geographical location and to a lesser degree, Armillaria root disease incidence, mixing tree species generally appeared to favour a more natural understory community, with higher resemblance to the pre-harvest assemblage.  In this sense, paper birch retention not only seems to benefit Douglas-fir health, but health of the broader ecosystem; thereby allowing the forest to maintain structure and continue its natural successional trajectory. Contribution to the field of study To my knowledge, this is the first study to examine the effects of belowground interactions and putative EM networks on forest stand dynamics in the field over the long term, and the first to investigate these phenomena within the context of interspecific relationships between conifers and broadleaves.  In a climate and landscape experiencing large scale anthropogenic disturbance and the uncertainties of climate change, knowledge of the longer term consequences of belowground interactions and EM networks on mixed species stand dynamics could be important for sustainable forest management.  We found evidence for the stabilizing role of belowground networks in ICH forests, both by reducing interspecific competitive intensity and facilitating persistence of struggling populations, resulting in more diverse forest stands.  This finding supports the hypothesis that MNs transfer resources across gradients from source to sink trees, with potential cumulative benefits on broader ecosystem structure and function.   Furthermore, while ecologists have long considered that mixed forests, and by extension, more diverse plantations, have benefits for individual tree species and ecosystem integrity, this is one of few studies to provide experimental support for these ideas.   Using an extensive response surface design replicated across three sites, and with exhaustive spatial sampling using a neighbourhood analysis, we found evidence that broadleaves provide benefits for conifers in mixture; these benefits included decreased disease incidence and increased foliar nutrition, and were accompanied by no signs of growth limitations caused by interspecific competition with birch neighbours for resources.  Related to this, there was evidence that intraspecific competition 96  was more intense than interspecific competition. I also found more natural understory communities under mixed versus monoculture stands, contributing to a more natural successional trajectory.  Limitations of studies While our study benefitted from well-established experimental designs and allowed us greater confidence than observational approaches to tree species interactions and their associated MNs, some of our conclusions were more observational in nature.  Armillaria root disease, for example, was never introduced as an experimental variable, and thus initial conditions of the disease and its progress were not controlled for.  While these facts limit the amount of inference we can draw from our findings, the scenario we investigated is one occurring across the landscape, and accurately captures natural circumstances after harvesting and replanting clear-cuts.   Our study also was hampered by occasional confounding of sampling and set-up designs.  While the mixtures experiment was designed to be measured and analysed using neighbourhood methods, as was done, the trenching experiment was not.  The trenching experiment was a split-plot design, and although a suitable mixed-model was used, the data was collected using the neighbourhood method, which was not optimal for revealing trends.  A more suitable approach would have been to increase the sample size of trees randomly measured in each treatment, thus maximizing sampling effort.  I suspect that with increased sample size, the results of our total height and diameter analyses would have demonstrated significant differences between trenched and untrenched trees. Neighbourhood plots were taken in the trenching experiment in the interest of comparing results across the two experiments, but this objective was not possible since plot size in the trenching experiment was reduced to 3.99 m2 from the mixtures plot size of 7.1m2 in order to increase sample size in the limited area of the treatment blocks.    Finally, environmental variables were collected during a single season, and may not be representative of conditions across the years, which could account for some of the changes attributed to the explanatory variables. 97  Future directions The results of each of the research chapters contain findings that can be explored further in future work.  More exclusive experimental designs could be established over long time periods using mesh bags of different pore sizes and continuous measures of isotope labelling; this would support or build upon our findings regarding the influence of EM networks on tree growth in mixed forests.  This would be expensive and the results would take years to gather, but annual findings on many aspects of EM and tree stand functioning could be published in order to maintain interest in the project.  Eventually, expanding these experiments along climate gradients could be highly valuable in gaining insight into both the ecology of EM symbiosis, which will become increasingly important as species migrate and contract with climate change (Pickles et al. 2015). As for the mixtures experiment, using tree core analysis in combination with neighbourhood plots could be extended to the many long term study plots established by the BC Ministry of Forests over the past three decades.  Remaining mindful of the lessons learned in this study, our method could allow for reasonably easy examination of the spectrum of mixed-wood and climatic types present in British Columbia, their adaptation to changing climate, and their interactions with broadleaf neighbours.  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Mixed Effects Models and Extensions in Ecology with R (Springer Science & Business Media).   107  Appendix A: R code used in analysis ### Chapter 1  ## lme models b<-read.csv("birch.csv", header=TRUE) b$Treatment=as.factor(b$Treatment) library(nlme) b1<-lme(Height ~ Trenched * Treatment.names, random = ~1|Site/Treatment, b) summary(b1) anova(b1,type="marginal")  str(b) trb<-factor(b$Trenched, levels=c("y","n")) dpb<-factor(b$Treatment.names, levels=c("800/400","3200/1600")) dp<-factor(b$Treatment, levels = c("1","2"))###to get factor levels in right order###  b1<-lme(Height ~ trb * dpb, random = ~1|Site/dp, b)  b2<-lme(VI ~ trb * dpb, random = ~1|Site/dp, b) summary(b2) anova(b2,type="marginal")  b2<-lme(DBH ~ dpb * trb, random = ~1|Site/dp, b) red1<-resid(b2) fed1<-fitted(b2) par(mfrow=c(3,3)) hist(red1) plot(x=fed1,y=red1) boxplot(red1~b$Treatment) boxplot(red1~b$Trenched) plot(density(red1)) summary(b2)  f<-read.csv("fir.csv", header=TRUE) str(f) f$Treatment=as.factor(f$Treatment) trf<-factor(f$Trenched, levels=c("y","n")) dpf<-factor(f$Treatment.names, levels=c("800/400","3200/1600")) dpfi<-factor(f$Treatment, levels = c("1","2"))###to get factor levels in right order###  f1<-lme(Height ~ trf * dpf, random = ~1|Site/dpfi, f) red1<-resid(f1) fed1<-fitted(f1) par(mfrow=c(3,3)) hist(red1) plot(x=fed1,y=red1) 108  boxplot(red1~f$Treatment) boxplot(red1~f$Trenched) plot(density(red1)) summary(f1)  f2<-lme(DBH ~ trf * dpf, random = ~1|Site/dpfi, f) red1<-resid(f2) fed1<-fitted(f2) par(mfrow=c(3,3)) hist(red1) plot(x=fed1,y=red1) boxplot(red1~f$Treatment) boxplot(red1~f$Trenched) plot(density(red1)) summary(f2)  FoliarNutrients####  ##fir### ##K## fk<-lme(K ~ trf * dpf, random = ~1|Site/dpfi, f) rffk<-resid(ffk) fffk<-fitted(ffk) par(mfrow=c(3,3)) hist(rffk) plot(x=fffk,y=rffk)##bad## boxplot(rffk~fd$Treatment) boxplot(rffk~fd$Trenched) plot(density(rffk)) summary(ffk)  ##Ca## fca<-lme(Ca ~ trf * dpf, random = ~1|Site/dpfi, f) rfca<-resid(fca) ffca<-fitted(fca) par(mfrow=c(3,3)) hist(rfca) plot(x=ffca,y=rfca) boxplot(rfca~f$Treatment) boxplot(rfca~f$Trenched) plot(density(rfca)) summary(fca) ###bit of fan in residuals##  fca2<-lme(log(Ca) ~ trf * dpf, random = ~1|Site/dpfi, f) rfca<-resid(fca2) ffca<-fitted(fca2) par(mfrow=c(3,3)) 109  hist(rfca) plot(x=ffca,y=rfca) boxplot(rfca~f$Treatment) boxplot(rfca~f$Trenched) plot(density(rfca)) summary(fca2) ###better####  ###N:P## fnp<-lme(N.P ~ trf * dpf, random = ~1|Site/dpfi, f) rfnp<-resid(fnp) ffnp<-fitted(fnp) par(mfrow=c(3,3)) hist(rfnp) plot(x=ffnp,y=rfnp) boxplot(rfnp~f$Treatment) boxplot(rfnp~f$Trenched) plot(density(rfnp)) summary(fnp)  ##N## fn<-lme(N ~ trf * dpf, random = ~1|Site/dpfi, f) rfn<-resid(fn) ffn<-fitted(fn) par(mfrow=c(3,3)) hist(rfn) plot(x=ffn,y=rfn)##bit of fan## boxplot(rfn~f$Treatment) boxplot(rfn~f$Trenched) plot(density(rfn)) summary(fn)  ##N.Mg## fnmg<-lme(N.Mg ~ trf * dpf, random = ~1|Site/dpfi, f) rfnmg<-resid(fnmg) ffnmg<-fitted(fnmg) par(mfrow=c(3,3)) hist(rfnmg) plot(x=ffnmg,y=rfnmg) boxplot(rfnmg~f$Treatment) boxplot(rfnmg~f$Trenched) plot(density(rfnmg)) summary(fnmg)  ##N.S1## fns1<-lme(N.S1 ~ trf * dpf, random = ~1|Site/dpfi, f) rfns1<-resid(fns1) ffns1<-fitted(fns1) 110  par(mfrow=c(3,3)) hist(rfns1) plot(x=ffns1,y=rfns1) boxplot(rfns1~f$Treatment) boxplot(rfns1~f$Trenched) plot(density(rfns1)) summary(fns1)  ##N.S2## fns2<-lme(N.S2 ~ trf * dpf, random = ~1|Site/dpfi, f) rfns2<-resid(fns2) ffns2<-fitted(fns2) par(mfrow=c(3,3)) hist(rfns2) plot(x=ffns2,y=rfns2) boxplot(rfns2~f$Treatment) boxplot(rfns2~f$Trenched) plot(density(rfns2)) summary(fns2)  ###Birch### ##Al##  bal2<-lme(Al ~ dpb * trb, random = ~1|Site/dp, b) rbal2<-resid(bal2) fbal2<-fitted(bal2) par(mfrow=c(3,3)) hist(rbal2) plot(x=fbal2,y=rbal2)##much better## boxplot(rbal2~b$Treatment) boxplot(rbal2~b$Trenched) plot(density(rbal2)) summary(bal2)  ##Cu### bcu<-lme(Cu ~ dpb * trb, random = ~1|Site/dp, b) rbcu<-resid(bcu) fbcu<-fitted(bcu) par(mfrow=c(3,3)) hist(rbcu) plot(x=fbcu,y=rbcu) boxplot(rbcu~b$Treatment) boxplot(rbcu~b$Trenched) plot(density(rbcu)) summary(bcu)  ##Fe## bfe<-lme(Fe ~ dpb * trb, random = ~1|Site/dp, b) 111  rbfe<-resid(bfe) fbfe<-fitted(bfe) par(mfrow=c(3,3)) hist(rbfe) plot(x=fbfe,y=rbfe) boxplot(rbfe~b$Treatment) boxplot(rbfe~b$Trenched) plot(density(rbfe)) summary(bfe)   ##N.S1## bns1<-lme(N.S1 ~ dpb * trb, random = ~1|Site/dp, b) rbns1<-resid(bns1) fbns1<-fitted(bns1) par(mfrow=c(3,3)) hist(rbns1) plot(x=fbns1,y=rbns1) boxplot(rbns1~b$Treatment) boxplot(rbns1~b$Trenched) plot(density(rbns1)) summary(bns1)   ##Na## bna<-lme(Na ~ dpb * trb, random = ~1|Site/dp, b) rbna<-resid(bna) fbna<-fitted(bna) par(mfrow=c(3,3)) hist(rbna) plot(x=fbna,y=rbna) boxplot(rbna~b$Treatment) boxplot(rbna~b$Trenched) plot(density(rbna)) summary(bna)   ##S.ICAAP## bs1<-lme(S..ICAP. ~ dpb * trb, random = ~1|Site/dp, b) rbs1<-resid(bs1) fbs1<-fitted(bs1) par(mfrow=c(3,3)) hist(rbs1) plot(x=fbs1,y=rbs1) boxplot(rbs1~b$Treatment) boxplot(rbs1~b$Trenched) plot(density(rbs1)) summary(bs1) 112  ####a bit of a fan in resids##  bs2<-lme(log(S..ICAP.) ~ dpb * trb, random = ~1|Site/dp, b) rbs2<-resid(bs2) fbs2<-fitted(bs2) par(mfrow=c(3,3)) hist(rbs2) plot(x=fbs2,y=rbs2) boxplot(rbs2~b$Treatment) boxplot(rbs2~b$Trenched) plot(density(rbs2)) summary(bs2) ##not much better##  bs3<-lme(sqrt(S..ICAP.) ~ dpb * trb, random = ~1|Site/dp, b) fbs3<-fitted(bs3) rbs3<-resid(bs3) par(mfrow=c(3,3)) hist(rbs3) plot(x=fbs3,y=rbs3) boxplot(rbs3~b$Treatment) boxplot(rbs3~b$Trenched) plot(density(rbs3)) summary(bs3) ##not much better## AIC(bs1,bs2,bs3) ###bs3 is lowest##    df       AIC bs1  7 -33.81650 bs2  7  18.53555 bs3  7 -28.75467 ###and nothing is significant now###  bs3<-lme(sqrt(S..ICAP.) ~ dpb * trb, random = ~1|Site/dp, b) fbs3<-fitted(bs3) rbs3<-resid(bs3) par(mfrow=c(3,3)) hist(rbs3) plot(x=fbs3,y=rbs3) boxplot(rbs3~b$Treatment) boxplot(rbs3~b$Trenched) plot(density(rbs3)) summary(bs3)  table1=cbind(b$pca1,b$pca2,b$PAR,b$SM) colnames(table1)=c("pca1", "pca2", "PAR", "SM")  ## need to copy what is below to have panel.cor working 113  panel.cor <- function(x, y, digits = 2, prefix = "", cex.cor, ...) {     usr <- par("usr"); on.exit(par(usr))     par(usr = c(0, 1, 0, 1))     r <- abs(cor(x, y))     txt <- format(c(r, 0.123456789), digits = digits)[1]     txt <- paste0(prefix, txt)     if(missing(cex.cor)) cex.cor <- 0.8/strwidth(txt)     text(0.5, 0.5, txt, cex = cex.cor * r) }  pairs(table1, lower.panel = panel.smooth, upper.panel = panel.cor)  ##Height### b2<-lme(Height ~ dpf * tr, random = ~1|Site, fd)  rb1<-resid(b1) fb1<-fitted(b1) par(mfrow=c(3,3)) hist(rb1) plot(x=fb1,y=rb1) boxplot(rb1~b$Treatment) boxplot(rb1~b$Trenched) plot(density(rb1)) summary(f2)  tre<-factor(eb$Trenched, levels=c("y","n")) dpe<-factor(eb$Treatment, levels=c("800/400","3200/1600"))  e2<-lme(Height ~ dpe * tre, random = ~1|Site, eb) re2<-resid(e2) fe2<-fitted(e2) par(mfrow=c(3,3)) hist(re2)###a little to left plot(x=fe2,y=re2) boxplot(re2~eb$Treatment) boxplot(re2~eb$Trenched) plot(density(re2)) summary(e2)  ###Diameter### ##fir## fd1<-lme(DBH ~ dpf * tr, random = ~1|Site, fd) rfd1<-resid(fd1) ffd1<-fitted(fd1) par(mfrow=c(3,3)) hist(rfd1) plot(x=ffd1,y=rfd1) 114  boxplot(rfd1~fd$Treatment) boxplot(rfd1~fd$Trenched) plot(density(rfd1))###validation graphs look okay### summary(fd1)  ##birch## ##VI## ##fir## fv1<-lme(VI ~ dpf * tr, random = ~1|Site, fd) rfv1<-resid(fv1) ffv1<-fitted(fv1) par(mfrow=c(3,3)) hist(rfv1) plot(x=ffv1,y=rfv1) boxplot(rfv1~fd$Treatment) boxplot(rfv1~fd$Trenched) plot(density(rfv1))###two humps### summary(fv1)  fv2<-lme(log(VI) ~ dpf * tr, random = ~1|Site, fd) rfv2<-resid(fv1) ffv2<-fitted(fv1) par(mfrow=c(3,3)) hist(rfv2) plot(x=ffv2,y=rfv2) boxplot(rfv2~fd$Treatment) boxplot(rfv2~fd$Trenched) plot(density(rfv2))##log does not change normality--normal enough decided## summary(fv2)  ##ev1<-lme(VI ~ dpe * tre, random = ~1|Site, eb) rev1<-resid(ev1) fev1<-fitted(ev1) par(mfrow=c(3,3)) hist(rev1) plot(x=fev1,y=rev1)##a little fan## boxplot(rev1~eb$Treatment) boxplot(rev1~eb$Trenched) plot(density(rev1))##squewed## summary(ev1)   ev2<-lme(sqrt(VI) ~ dpe * tre, random = ~1|Site, eb) rev2<-resid(ev2) fev2<-fitted(ev2) par(mfrow=c(3,3)) hist(rev2) plot(x=fev2,y=rev2)## better## 115  boxplot(rev2~eb$Treatment) boxplot(rev2~eb$Trenched) plot(density(rev2))##not better## summary(ev2)  ev3<-lme(log(VI) ~ dpe * tre, random = ~1|Site, eb) rev3<-resid(ev3) fev3<-fitted(ev3) par(mfrow=c(3,3)) hist(rev3) plot(x=fev3,y=rev3)##better## boxplot(rev3~eb$Treatment) boxplot(rev2~eb$Trenched) plot(density(rev3))##much better## summary(ev3)  AIC(ev1,ev2,ev3)    df       AIC ev1  6 322.69692 ev2  6 169.12854 ev3  6  67.68153##best model##  ##Foliar Nutrients## ##fir## ##Al## fal<-lme(Al ~ dpf * tr, random = ~1|Site, fd) rfal<-resid(fal) ffal<-fitted(fal) par(mfrow=c(3,3)) hist(rfal) plot(x=ffal,y=rfal) boxplot(rfal~fd$Treatment) boxplot(rfal~fd$Trenched) plot(density(rfal)) summary(fv2)  fal<-lme(Al ~ dpf * tr, random = ~1|Site, fd) rfal<-resid(fal) ffal<-fitted(fal) par(mfrow=c(3,3)) hist(rfal) plot(x=ffal,y=rfal) boxplot(rfal~fd$Treatment) boxplot(rfal~fd$Trenched) plot(density(rfal)) summary(fal)  fal2<-lme(log(Al) ~ dpf * tr, random = ~1|Site, fd) 116  rfal2<-resid(fal2) ffal2<-fitted(fal2) par(mfrow=c(3,3)) hist(rfal2) plot(x=ffal2,y=rfal2) boxplot(rfal2~fd$Treatment) boxplot(rfal2~fd$Trenched) plot(density(rfal2)) summary(fal2)  fal3<-lme(sqrt(Al) ~ dpf * tr, random = ~1|Site, fd) rfal3<-resid(fal3) ffal3<-fitted(fal3) par(mfrow=c(3,3)) hist(rfal3) plot(x=ffal3,y=rfal3) boxplot(rfal3~fd$Treatment) boxplot(rfal3~fd$Trenched) plot(density(rfal3)) summary(fal3)  neither transformation fixes variance or normality issues##AIC best for log (fal2)##go with fal2##      df       AIC fal   6 228.76909 fal2  6  34.19278 fal3  6 105.92443   ##P## fp<-lme(P ~ dpf * tr, random = ~1|Site, fd) rfp<-resid(fp) ffp<-fitted(fp) par(mfrow=c(3,3)) hist(rfp) plot(x=ffp,y=rfp)##increasing--not hetero## boxplot(rfp~fd$Treatment) boxplot(rfp~fd$Trenched) plot(density(rfp)) summary(fp)  fp2<-lme(log(P) ~ dpf * tr, random = ~1|Site, fd) rfp2<-resid(fp2) ffp2<-fitted(fp2) par(mfrow=c(3,3)) hist(rfp2) plot(x=ffp2,y=rfp2)##increasing--not hetero## boxplot(rfp2~fd$Treatment) 117  boxplot(rfp2~fd$Trenched) plot(density(rfp2)) summary(fp2)  fp5<-lme((P)^3 ~ dpf * tr, random = ~1|Site, fd) rfp5<-resid(fp5) ffp5<-fitted(fp5) par(mfrow=c(3,3)) hist(rfp5) plot(x=ffp5,y=rfp5)##increasing--not hetero## boxplot(rfp5~fd$Treatment) boxplot(rfp5~fd$Trenched) plot(density(rfp5)) summary(fp3)  fp4<-lme((P)^2 ~ dpf * tr, random = ~1|Site, fd) rfp4<-resid(fp4) ffp4<-fitted(fp4) par(mfrow=c(3,3)) hist(rfp4) plot(x=ffp4,y=rfp4)##increasing--not hetero## boxplot(rfp4~fd$Treatment) boxplot(rfp4~fd$Trenched) plot(density(rfp4))  transformations don't work,heterosced continues; go with fp### ##B## fb<-lme(B ~ dpf * tr, random = ~1|Site, fd) rfb<-resid(fb) ffb<-fitted(fb) par(mfrow=c(3,3)) hist(rfb) plot(x=ffb,y=rfb)##some increase## boxplot(rfb~fd$Treatment) boxplot(rfb~fd$Trenched) plot(density(rfb)) summary(fb)  ##C## fc<-lme(C ~ dpf * tr, random = ~1|Site, fd) rfc<-resid(fc) ffc<-fitted(fc) par(mfrow=c(3,3)) hist(rfc) plot(x=ffc,y=rfc) boxplot(rfc~fd$Treatment) boxplot(rfc~fd$Trenched) plot(density(rfc)) 118  summary(fc)  ##Ca## fca<-lme(Ca ~ dpf * tr, random = ~1|Site, fd)* rfca<-resid(fca) ffca<-fitted(fca) par(mfrow=c(3,3)) hist(rfca) plot(x=ffca,y=rfca) boxplot(rfca~fd$Treatment) boxplot(rfca~fd$Trenched) plot(density(rfca)) summary(fca)  ##Cu## fcu<-lme(Cu ~ dpf * tr, random = ~1|Site, fd) rfcu<-resid(fcu) ffcu<-fitted(fcu) par(mfrow=c(3,3)) hist(rfcu) plot(x=ffcu,y=rfcu)##bad## boxplot(rfcu~fd$Treatment) boxplot(rfcu~fd$Trenched) plot(density(rfcu)) summary(fcu)  fdcu<-fd[-6,] dpfcu<-dpf[-6] trfcu<-tr[-6] ##to take out outlier##  fcu2<-lme(Cu ~ dpfcu * trfcu, random = ~1|Site, fdcu) rfcu2<-resid(fcu2) ffcu2<-fitted(fcu2) par(mfrow=c(3,3)) hist(rfcu2) plot(x=ffcu,y=rfcu)##still bad## boxplot(rfcu2~fdcu$Treatment) boxplot(rfcu2~fdcu$Trenched) plot(density(rfcu2)) summary(fcu2)  fcu3<-lme((Cu)^3 ~ dpf * tr, random = ~1|Site, fd) rfcu3<-resid(fcu3) ffcu3<-fitted(fcu3) par(mfrow=c(3,3)) hist(rfcu3) plot(x=ffcu3,y=rfcu3)##still bad## 119  boxplot(rfcu3~fd$Treatment) boxplot(rfcu3~fd$Trenched) plot(density(rfcu3))  fcu4<-lme(Cu ~ dpf * tr, random = ~1|Site, fd,weights=varIdent(form=~1|tr)) rfcu4<-resid(fcu4) ffcu4<-fitted(fcu4) par(mfrow=c(3,3)) hist(rfcu4) plot(x=ffcu4,y=rfcu4) boxplot(rfcu4~fd$Treatment) boxplot(rfcu4~fd$Trenched) plot(density(rfcu4))  fcu5<-lme(Cu ~ dpf * tr, random = ~1|Site, fd,weights=varIdent(form=~1|dpf)) rfcu5<-resid(fcu5) ffcu5<-fitted(fcu5) par(mfrow=c(3,3)) hist(rfcu5) plot(x=ffcu5,y=rfcu5) boxplot(rfcu5~fd$Treatment) boxplot(rfcu5~fd$Trenched) plot(density(rfcu5)) ##transformations don't work; report on fcu and note problems with hetero of resids###  ##Fe## ffe<-lme(Fe ~ dpf * tr, random = ~1|Site, fd) rffe<-resid(ffe) fffe<-fitted(ffe) par(mfrow=c(3,3)) hist(rffe) plot(x=fffe,y=rffe)##bad## boxplot(rffe~fd$Treatment) boxplot(rffe~fd$Trenched) plot(density(rffe)) summary(ffe)  ##K## ffk<-lme(K ~ dpf * tr, random = ~1|Site, fd)** rffk<-resid(ffk) fffk<-fitted(ffk) par(mfrow=c(3,3)) hist(rffk) plot(x=fffk,y=rffk)##bad## boxplot(rffk~fd$Treatment) boxplot(rffk~fd$Trenched) plot(density(rffk)) 120  summary(ffk)  ##Mg## fmg<-lme(Mg ~ trf * dpf, random = ~1|Site/dpfi, f) rfmg<-resid(fmg) ffmg<-fitted(fmg) par(mfrow=c(3,3)) hist(rfmg) plot(x=ffmg,y=rfmg) boxplot(rfmg~f$Treatment) boxplot(rfmg~f$Trenched) plot(density(rfmg)) summary(fmg)  ##Mn## fmn<-lme(Mn ~ dpf * tr, random = ~1|Site, fd) rfmn<-resid(fmn) ffmn<-fitted(fmn) par(mfrow=c(3,3)) hist(rfmn) plot(x=ffmn,y=rfmn) boxplot(rfmn~fd$Treatment) boxplot(rfmn~fd$Trenched) plot(density(rfmn)) summary(fmn)  ###N:P## fnp<-lme(N.P ~ dpf * tr, random = ~1|Site, fd)** rfnp<-resid(fnp) ffnp<-fitted(fnp) par(mfrow=c(3,3)) hist(rfnp) plot(x=ffnp,y=rfnp) boxplot(rfnp~fd$Treatment) boxplot(rfnp~fd$Trenched) plot(density(rfnp)) summary(fnp)  ##N## fn<-lme(N ~ dpf * tr, random = ~1|Site, fd)** rfn<-resid(fn) ffn<-fitted(fn) par(mfrow=c(3,3)) hist(rfn) plot(x=ffn,y=rfn)##bit of fan## boxplot(rfn~fd$Treatment) boxplot(rfn~fd$Trenched) plot(density(rfn)) 121  summary(fn)  fn2<-lme(log(N) ~ dpf * tr , random = ~1|Site, fd) rfn2<-resid(fn2) ffn2<-fitted(fn2) par(mfrow=c(3,3)) hist(rfn2) plot(x=ffn2,y=rfn2)##still a bit of fan## boxplot(rfn2~fd$Treatment) boxplot(rfn2~fd$Trenched) plot(density(rfn2)) summary(fn2)  fn3<-lme(N ~ dpf * tr, random = ~1|Site, fd, weights=varIdent(form=~1|dpf)) rfn3<-resid(fn3) ffn3<-fitted(fn3) par(mfrow=c(3,3)) hist(rfn3) plot(x=ffn3,y=rfn3) boxplot(rfn3~fd$Treatment) boxplot(rfn3~fd$Trenched) plot(density(rfn3))  fn4<-lme(N ~ dpf * tr, random = ~1|Site, fd, weights=varIdent(form=~1|tr)) rfn4<-resid(fn4) ffn4<-fitted(fn4) par(mfrow=c(3,3)) hist(rfn4) plot(x=ffn4,y=rfn4) boxplot(rfn4~fd$Treatment) boxplot(rfn4~fd$Trenched) plot(density(rfn4)) ##none of these fixes the variance problem## check AIC## AIC(fn,fn2,fn3,fn4)##none have more difference than two numbers; go with fn##  ###N.K### fnk<-lme(N.K ~ dpf * tr, random = ~1|Site, fd) rfnk<-resid(fnk) ffnk<-fitted(fnk) par(mfrow=c(3,3)) hist(rfnk) plot(x=ffnk,y=rfnk) boxplot(rfnk~fd$Treatment) boxplot(rfnk~fd$Trenched) plot(density(rfnk)) summary(fnk)  ##N.Mg## 122  fnmg<-lme(N.Mg ~ dpf * tr, random = ~1|Site, f) rfnmg<-resid(fnmg) ffnmg<-fitted(fnmg) par(mfrow=c(3,3)) hist(rfnmg) plot(x=ffnmg,y=rfnmg) boxplot(rfnmg~f$Treatment) boxplot(rfnmg~f$Trenched) plot(density(rfnmg)) summary(fnmg)  ##N.S1## fns1<-lme(N.S1 ~ dpf * tr, random = ~1|Site, fd)** rfns1<-resid(fns1) ffns1<-fitted(fns1) par(mfrow=c(3,3)) hist(rfns1) plot(x=ffns1,y=rfns1) boxplot(rfns1~fd$Treatment) boxplot(rfns1~fd$Trenched) plot(density(rfns1)) summary(fns1)  ##N.S2## fns2<-lme(N.S2 ~ dpf * tr, random = ~1|Site, fd)* rfns2<-resid(fns2) ffns2<-fitted(fns2) par(mfrow=c(3,3)) hist(rfns2) plot(x=ffns2,y=rfns2) boxplot(rfns2~fd$Treatment) boxplot(rfns2~fd$Trenched) plot(density(rfns2)) summary(fns2)  ##Na## fna<-lme(Na ~ dpf * tr, random = ~1|Site, fd) rfna<-resid(fna) ffna<-fitted(fna) par(mfrow=c(3,3)) hist(rfna) plot(x=ffna,y=rfna)##bad## boxplot(rfna~fd$Treatment) boxplot(rfna~fd$Trenched) plot(density(rfna)) summary(fna)  fdna<-fd[-16,] 123  dpfna<-dpf[-16] trna<-tr[-16]###to get rid of outlier## fna2<-lme(Na ~ dpfna * trna, random = ~1|Site, fdna) rfna2<-resid(fna2) ffna2<-fitted(fna2) par(mfrow=c(3,3)) hist(rfna2) plot(x=ffna2,y=rfna2)##better## boxplot(rfna2~fdna$Treatment) boxplot(rfna2~fdna$Trenched) plot(density(rfna2)) summary(fna2) ##fit vs resids better without outlier--went with fna2##  ##S.ICAP## fs1<-lme(S..ICAP. ~ dpf * tr, random = ~1|Site, fd) rfs1<-resid(fs1) ffs1<-fitted(fs1) par(mfrow=c(3,3)) hist(rfs1) plot(x=ffs1,y=rfs1) boxplot(rfs1~fd$Treatment) boxplot(rfs1~fd$Trenched) plot(density(rfs1)) summary(fs1)  ##S.Comb## fsc<-lme(S.Comb. ~ dpf * tr, random = ~1|Site, fd) rfsc<-resid(fsc) ffsc<-fitted(fsc) par(mfrow=c(3,3)) hist(rfsc) plot(x=ffsc,y=rfsc) boxplot(rfsc~fd$Treatment) boxplot(rfsc~fd$Trenched) plot(density(rfsc)) summary(fsc)  ##Zn## fzn<-lme(Zn ~ dpf * tr, random = ~1|Site, fd) rfzn<-resid(fzn) ffzn<-fitted(fzn) par(mfrow=c(3,3)) hist(rfzn) plot(x=ffzn,y=rfzn)##bit of fan boxplot(rfzn~fd$Treatment) boxplot(rfzn~fd$Trenched) plot(density(rfzn)) 124  summary(fzn)  fzn2<-lme(Zn ~ dpf * tr, random = ~1|Site, fd, weights=varIdent(form=~1|dpf)) rfzn2<-resid(fzn2) ffzn2<-fitted(fzn2) par(mfrow=c(3,3)) hist(rfzn2) plot(x=ffzn2,y=rfzn2)##still there## boxplot(rfzn2~fd$Treatment) boxplot(rfzn2~fd$Trenched) plot(density(rfzn2)) summary(fzn2)  fzn3<-lme(log(Zn) ~ dpf * tr, random = ~1|Site, fd) rfzn3<-resid(fzn3) ffzn3<-fitted(fzn3) par(mfrow=c(3,3)) hist(rfzn3) plot(x=ffzn3,y=rfzn3)##better## boxplot(rfzn3~fd$Treatment) boxplot(rfzn3~fd$Trenched) plot(density(rfzn3)) summary(fzn3) ##went with fzn3; fan pattern better in resids##  #############Birch######### ##Al##  bal<-lme(Al ~ dpe * tre, random = ~1|Site, eb) rbal<-resid(bal) fbal<-fitted(bal) par(mfrow=c(3,3)) hist(rbal) plot(x=fbal,y=rbal)##bit of fan boxplot(rbal~eb$Treatment) boxplot(rbal~eb$Trenched) plot(density(rbal)) summary(bal)  ebal<-eb[-8,] dpeal<-dpe[-8] treal<-tre[-8]###to get rid of outlier (6919.2 vs.65-203)## bal2<-lme(Al ~ dpeal * treal, random = ~1|Site, ebal)* rbal2<-resid(bal2) fbal2<-fitted(bal2) par(mfrow=c(3,3)) hist(rbal2) plot(x=fbal2,y=rbal2)##much better## 125  boxplot(rbal2~ebal$Treatment) boxplot(rbal2~ebal$Trenched) plot(density(rbal2)) summary(bal2) ##all val graphs much better without outlier--went with bal2##  ##B## bb<-lme(B ~ dpe * tre, random = ~1|Site, eb) rbb<-resid(bb) fbb<-fitted(bb) par(mfrow=c(3,3)) hist(rbb) plot(x=fbb,y=rbb)##bit of fan boxplot(rbb~eb$Treatment) boxplot(rbb~eb$Trenched) plot(density(rbb)) summary(bb) #####redoing these three with outlier removed### bb2<-lme(B ~ dpe2 * tre2, random = ~1|Site, eb2) rbb2<-resid(bb2) fbb2<-fitted(bb2) par(mfrow=c(3,3)) hist(rbb2) plot(x=fbb2,y=rbb2) boxplot(rbb2~eb2$Treatment) boxplot(rbb2~eb2$Trenched) plot(density(rbb2)) summary(bb2)  ##C## bc<-lme(C ~ dpe * tre, random = ~1|Site, eb) rbc<-resid(bc) fbc<-fitted(bc) par(mfrow=c(3,3)) hist(rbc) plot(x=fbc,y=rbc)##bit of fan boxplot(rbc~eb$Treatment) boxplot(rbc~eb$Trenched) plot(density(rbc)) summary(bc)  ##redoing with outlier removed## bc2<-lme(C ~ dpe2 * tre2, random = ~1|Site, eb2) rbc2<-resid(bc2) fbc2<-fitted(bc2) par(mfrow=c(3,3)) hist(rbc2) plot(x=fbc2,y=rbc2)##bit of fan 126  boxplot(rbc2~eb2$Treatment) boxplot(rbc2~eb2$Trenched) plot(density(rbc2)) summary(bc2)  ##Ca## bca<-lme(Ca ~ dpe * tre, random = ~1|Site, eb) rbca<-resid(bca) fbca<-fitted(bca) par(mfrow=c(3,3)) hist(rbca) plot(x=fbca,y=rbca)##bit of fan boxplot(rbca~eb$Treatment) boxplot(rbca~eb$Trenched) plot(density(rbca)) summary(bca)  bca2<-lme(Ca ~ dpe2 * tre2, random = ~1|Site, eb2)##redoing with outlier removed## rbca2<-resid(bca2) fbca2<-fitted(bca2) par(mfrow=c(3,3)) hist(rbca2) plot(x=fbca2,y=rbca2) boxplot(rbca2~eb2$Treatment) boxplot(rbca2~eb2$Trenched) plot(density(rbca2)) summary(bca2)   ##Cu### bcu<-lme(Cu ~ dpe * tre, random = ~1|Site, eb) rbcu<-resid(bcu) fbcu<-fitted(bcu) par(mfrow=c(3,3)) hist(rbcu) plot(x=fbcu,y=rbcu) boxplot(rbcu~eb$Treatment) boxplot(rbcu~eb$Trenched) plot(density(rbcu)) summary(bcu)  ebcu<-eb[-8,] dpecu<-dpe[-8] trecu<-tre[-8]##outlier out## bcu2<-lme(Cu ~ dpecu * trecu, random = ~1|Site, ebcu)** rbcu2<-resid(bcu2) fbcu2<-fitted(bcu2) par(mfrow=c(3,3)) 127  hist(rbcu2) plot(x=fbcu2,y=rbcu2) boxplot(rbcu2~ebcu$Treatment) boxplot(rbcu2~ebcu$Trenched) plot(density(rbcu2)) summary(bcu2)  ##Fe## bfe<-lme(Fe ~ dpe * tre, random = ~1|Site, eb) rbfe<-resid(bfe) fbfe<-fitted(bfe) par(mfrow=c(3,3)) hist(rbfe) plot(x=fbfe,y=rbfe) boxplot(rbfe~eb$Treatment) boxplot(rbfe~eb$Trenched) plot(density(rbfe)) summary(bfe)  eb2<-eb[-8,] dpe2<-dpe[-8] tre2<-tre[-8]# bfe2<-lme(Fe ~ dpe2 * tre2, random = ~1|Site, eb2)* rbfe2<-resid(bfe2) fbfe2<-fitted(bfe2) par(mfrow=c(3,3)) hist(rbfe2) plot(x=fbfe2,y=rbfe2) boxplot(rbfe2~eb2$Treatment) boxplot(rbfe2~eb2$Trenched) plot(density(rbfe2)) summary(bfe2)  ##K## bk<-lme(K ~ dpe2 * tre2, random = ~1|Site, eb2) rbk<-resid(bk) fbk<-fitted(bk) par(mfrow=c(3,3)) hist(rbk) plot(x=fbk,y=rbk) boxplot(rbk~eb2$Treatment) boxplot(rbk~eb2$Trenched) plot(density(rbk)) summary(bk)  ##Mg## bmg<-lme(Mg ~ dpe2 * tre2, random = ~1|Site, eb2) rbmg<-resid(bmg) 128  fbmg<-fitted(bmg) par(mfrow=c(3,3)) hist(rbmg) plot(x=fbmg,y=rbmg) boxplot(rbmg~eb2$Treatment) boxplot(rbmg~eb2$Trenched) plot(density(rbmg)) summary(bmg)  ##Mn## bmn<-lme(Mn ~ dpe2 * tre2, random = ~1|Site, eb2) rbmn<-resid(bmn) fbmn<-fitted(bmn) par(mfrow=c(3,3)) hist(rbmn) plot(x=fbmn,y=rbmn) boxplot(rbmn~eb2$Treatment) boxplot(rbmn~eb2$Trenched) plot(density(rbmn)) summary(bmn)  ##N## bn<-lme(N ~ dpe2 * tre2, random = ~1|Site, eb2) rbn<-resid(bn) fbn<-fitted(bn) par(mfrow=c(3,3)) hist(rbn) plot(x=fbn,y=rbn) boxplot(rbn~eb2$Treatment) boxplot(rbn~eb2$Trenched) plot(density(rbn)) summary(bn)  ##N.K## bnk<-lme(N.K ~ dpe2 * tre2, random = ~1|Site, eb2) rbnk<-resid(bnk) fbnk<-fitted(bnk) par(mfrow=c(3,3)) hist(rbnk) plot(x=fbnk,y=rbnk) boxplot(rbnk~eb2$Treatment) boxplot(rbnk~eb2$Trenched) plot(density(rbnk)) summary(bnk)  ##N.Mg## bnmg<-lme(N.Mg ~ dpe2 * tre2, random = ~1|Site, eb2) rbnmg<-resid(bnmg) 129  fbnmg<-fitted(bnmg) par(mfrow=c(3,3)) hist(rbnmg) plot(x=fbnmg,y=rbnmg) boxplot(rbnmg~eb2$Treatment) boxplot(rbnmg~eb2$Trenched) plot(density(rbnmg)) summary(bnmg)  ##N.P## bnp<-lme(N.P ~ dpe2 * tre2, random = ~1|Site, eb2) rbnp<-resid(bnp) fbnp<-fitted(bnp) par(mfrow=c(3,3)) hist(rbnp) plot(x=fbnp,y=rbnp) boxplot(rbnp~eb2$Treatment) boxplot(rbnp~eb2$Trenched) plot(density(rbnp)) summary(bnp)  ##N.S1## bns1<-lme(N.S1 ~ dpe2 * tre2, random = ~1|Site, eb2) rbns1<-resid(bns1) fbns1<-fitted(bns1) par(mfrow=c(3,3)) hist(rbns1) plot(x=fbns1,y=rbns1) boxplot(rbns1~eb2$Treatment) boxplot(rbns1~eb2$Trenched) plot(density(rbns1)) summary(bns1)  ##N.S2## bns2<-lme(N.S2 ~ dpe2 * tre2, random = ~1|Site, eb2) rbns2<-resid(bns2) fbns2<-fitted(bns2) par(mfrow=c(3,3)) hist(rbns2) plot(x=fbns2,y=rbns2) boxplot(rbns2~eb2$Treatment) boxplot(rbns2~eb2$Trenched) plot(density(rbns2)) summary(bns2)  ##Na## bna<-lme(Na ~ dpe2 * tre2, random = ~1|Site, eb2) rbna<-resid(bna) 130  fbna<-fitted(bna) par(mfrow=c(3,3)) hist(rbna) plot(x=fbna,y=rbna) boxplot(rbna~eb2$Treatment) boxplot(rbna~eb2$Trenched) plot(density(rbna)) summary(bna)  ##P## bp<-lme(P ~ dpe2 * tre2, random = ~1|Site, eb2) rbp<-resid(bp) fbp<-fitted(bp) par(mfrow=c(3,3)) hist(rbp) plot(x=fbp,y=rbp) boxplot(rbp~eb2$Treatment) boxplot(rbp~eb2$Trenched) plot(density(rbp)) summary(bp)  ##S.ICAAP## bs1<-lme(S..ICAP. ~ dpe2 * tre2, random = ~1|Site, eb2) rbs1<-resid(bs1) fbs1<-fitted(bs1) par(mfrow=c(3,3)) hist(rbs1) plot(x=fbs1,y=rbs1) boxplot(rbs1~eb2$Treatment) boxplot(rbs1~eb2$Trenched) plot(density(rbs1)) summary(bs1)  ##S.comb## bs2<-lme(S.Comb. ~ dpe2 * tre2, random = ~1|Site, eb2) rbs2<-resid(bs2) fbs2<-fitted(bs2) par(mfrow=c(3,3)) hist(rbs2) plot(x=fbs2,y=rbs2) boxplot(rbs2~eb2$Treatment) boxplot(rbs2~eb2$Trenched) plot(density(rbs2)) summary(bs2)  ##Zn## bzn<-lme(Zn ~ dpe2 * tre2, random = ~1|Site, eb2) rbzn<-resid(bzn) 131  fbzn<-fitted(bzn) par(mfrow=c(3,3)) hist(rbzn) plot(x=fbzn,y=rbzn) boxplot(rbzn~eb2$Treatment) boxplot(rbzn~eb2$Trenched) plot(density(rbzn)) summary(bzn)   #########foliar nutrients birch##################### bp_fn<-read.csv("fn4.csv", header=TRUE) bp.b<-bp_fn[bp_fn$Spp=="Eb",] names<-c("800/400","3200/1600")  par(mar=c(1,3,1,1),mfrow=c(3,2)) boxplot(Al ~ Treatment, data = bp.b,xaxt="n",         boxwex = 0.22, at = 1:2 - 0.22,   varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "light grey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,0.0405), yaxs = "i")  boxplot(Al ~ Treatment, data = bp.b, add = TRUE,xaxt="n",         boxwex = 0.22, at = 1:2,   varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "grey22") mtext("Al(%)", side=2, line=2, at=0.02, cex=0.8) axis(side=1,at=c(1:length(names)),las=1,labels=paste(names,sep=""),cex.axis=0.8) legend(2.0, 400, c("Trenched", "Untrenched"),        fill = c("light grey", "grey22"), cex=0.7)   boxplot(Cu ~ Treatment, data = bp.b,         boxwex = 0.2, at = 1:2 - 0.22, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "light grey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,0.0016), yaxs = "i") ## outlier removed boxplot(Cu ~ Treatment, data = bp.b, add = TRUE,         boxwex = 0.2, at = 1:2, xaxt="n",  varwidth = FALSE, 132   range = 1.5,         subset = Trenched == "n", col = "grey22")   mtext("Cu(%)", side=2, line=2, at=0.0008, cex=0.8) axis(side=1,at=c(1:length(names)),las=1,labels=paste(names,sep=""),cex.axis=0.8)  boxplot(Fe ~ Treatment, data = bp.b,         boxwex = 0.2, at = 1:2 - 0.22, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "light grey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,0.0400), yaxs = "i")  boxplot(Fe ~ Treatment, data = bp.b, add = TRUE,         boxwex = 0.2, at = 1:2, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "grey22")     mtext("Fe(%)", side=2, line=2, at=0.02, cex=0.8) axis(side=1,at=c(1:length(names)),las=1,labels=paste(names,sep=""),cex.axis=0.8)   boxplot(N.S1 ~ Treatment, data = bp.b,         boxwex = 0.2, at = 1:2 - 0.22, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "light grey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,18), yaxs = "i")  boxplot(N.S1 ~ Treatment, data = bp.b, add = TRUE,         boxwex = 0.2, at = 1:2, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "grey22")   mtext("N/S", side=2, line=2, at=9, cex=0.8) axis(side=1,at=c(1:length(names)),las=1,labels=paste(names,sep=""),cex.axis=0.8)  par(mar=c(3,3,1,1)) boxplot(Na ~ Treatment, data = bp.b,         boxwex = 0.2, at = 1:2 - 0.22, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "light grey",         main = "",         xlab = "", 133          ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,0.0072), yaxs = "i")  boxplot(Na ~ Treatment, data = bp.b, add = TRUE,         boxwex = 0.2, at = 1:2, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "grey22")  mtext("Density", side=1, line=1.8, at=1.5, cex=0.8)       mtext("Na(%)", side=2, line=2, at=0.0036, cex=0.8) axis(side=1,at=c(1:length(names)),las=1,labels=paste(names,sep=""),cex.axis=0.8)   #################bp fir############################# bp.f<-read.csv("fir.bp.csv", header=TRUE)##changed spreadsheet to have "names" ##column### names<-c("800/400","3200/1600")  par(mar=c(3,3,1,1),mfrow=c(1,2)) boxplot(N ~ Treatment, data = bp.f,         boxwex = 0.2, at = 1:2 - 0.22, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "light grey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,2), yaxs = "i")  boxplot(N ~ Treatment, data = bp.f, add = TRUE,         boxwex = 0.2, at = 1:2, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "grey22") mtext("N(%)", side=2, line=2, at=1, cex=0.8) mtext("Density", side=1, line=1.8, at=1.5, cex=0.8)   axis(side=1,at=c(1:length(names)),las=1,labels=paste(names,sep=""),cex.axis=0.8)   par(mar=c(3,3,1,1)) boxplot(N.Mg ~ Treatment, data = bp.f,         boxwex = 0.2, at = 1:2 - 0.22, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "light grey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,16.5), yaxs = "i")  boxplot(N.Mg ~ Treatment, data = bp.f, add = TRUE, 134          boxwex = 0.2, at = 1:2, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "grey22")  mtext("Density", side=1, line=1.8, at=1.5, cex=0.8)       mtext("N/Mg", side=2, line=2, at=8.25, cex=0.8) axis(side=1,at=c(1:length(names)),las=1,labels=paste(names,sep=""),cex.axis=0.8) legend(1.7, 16, c("Trenched", "Untrenched"),        fill = c("light grey", "grey22"), cex=0.7)     ####################################################################### #### Generalized Additive Mixed Models (GAMMs) results  #### plotting raw time series per site allok.3=read.csv("all.ok3.csv", header=TRUE) library(lattice) plot(allok.3$AGI ~ allok.3$Year, col=allok.3$Site)  par(mfrow=c(2,4)) eb84y<-allok.3[allok.3$Spp=="Eb"& allok.3$DP=="84" &allok.3$Trench=="yes",] interaction.plot(eb84y$Year,eb84y$Site,eb84y$AGI)###works  eb84n<-allok.3[allok.3$Spp=="Eb"& allok.3$DP=="84" & allok.3$Trench=="no",] interaction.plot(eb84n$Year,eb84n$Site,eb84n$AGI)  fd84y<-allok.3[allok.3$Spp=="Fd"& allok.3$DP=="84" & allok.3$Trench=="yes",] interaction.plot(fd84y$Year,fd84y$Site,fd84y$AGI)  fd84n<-allok.3[allok.3$Spp=="Fd"& allok.3$DP=="84" & allok.3$Trench=="no",] interaction.plot(fd84n$Year,fd84n$Site,fd84n$AGI)  eb3216y<-allok.3[allok.3$Spp=="Eb"& allok.3$DP=="3216" & allok.3$Trench=="yes",] interaction.plot(eb3216y$Year,eb3216y$Site,eb3216y$AGI)  eb3216n<-allok.3[allok.3$Spp=="Eb"& allok.3$DP=="3216" & allok.3$Trench=="no",] interaction.plot(eb3216n$Year,eb3216n$Site,eb3216n$AGI)  fd3216y<-allok.3[allok.3$Spp=="Fd"& allok.3$DP=="3216" & allok.3$Trench=="yes",] interaction.plot(fd3216y$Year,fd3216y$Site,fd3216y$AGI)  fd3216n<-allok.3[allok.3$Spp=="Fd"& allok.3$DP=="3216" & allok.3$Trench=="no",] interaction.plot(fd3216n$Year,fd3216n$Site,fd3216n$AGI)  ## to look at three sites similarity for SH:M, they looked pretty similar curve, but Malakwa was always dryer### 135   shm=read.csv("shm.csv", header=TRUE) library(lattice) interaction.plot(shm$Year,shm$Site,shm$SHM)  interaction.plot(ef1$Treatment,ef1$Trenched,ef1$N) library(plyr) ave.shm<-ddply(shm,"Year",summarize,aveshm=mean(SHM))  write.csv(ave.shm,file="ave.shm.csv")    #### Doing the correlation table (Table. 16.2 in Zuur yellow) all.ok=read.csv("all.ok.csv", header=TRUE)  aveagi<-ddply(all.ok,c("Year","Spp","Trench","DP"),summarize,aveagi=mean(AGI))   ep84n<-aveagi[aveagi$Trench=="no" & aveagi$Spp=="Eb" & aveagi$DP=="84",] y1=ep84n[,c(1,5)] ep84n=rename(y1,c("aveagi"="ep84n")) write.csv(ep84n,file="ep84n.csv")  ep84y<-aveagi[aveagi$Trench=="yes" & aveagi$Spp=="Eb" & aveagi$DP=="84",] y2=ep84y[,c(1,5)] ep84y=rename(y2,c("aveagi"="ep84y")) write.csv(ep84y,file="ep84y.csv")   ep3216n<-aveagi[aveagi$Trench=="no" & aveagi$Spp=="Eb" & aveagi$DP=="3216",] y3=ep3216n[,c(1,5)] ep3216n=rename(y3,c("aveagi"="ep3216n")) write.csv(ep3216n,file="ep3216n.csv")  ep3216y<-aveagi[aveagi$Trench=="yes" & aveagi$Spp=="Eb" & aveagi$DP=="3216",] y4=ep3216y[,c(1,5)] ep3216y=rename(y4,c("aveagi"="ep3216y")) write.csv(ep3216y,file="ep3216y.csv")  fd84n<-aveagi[aveagi$Trench=="no" & aveagi$Spp=="Fd" & aveagi$DP=="84",] y5=fd84n[,c(1,5)] fd84n=rename(y5,c("aveagi"="fd84n")) write.csv(fd84n,file="fd84n.csv")  fd84y<-aveagi[aveagi$Trench=="yes" & aveagi$Spp=="Fd" & aveagi$DP=="84",] y6=fd84y[,c(1,5)] fd84y=rename(y6,c("aveagi"="fd84y")) 136  write.csv(fd84y,file="fd84y.csv")  fd3216n<-aveagi[aveagi$Trench=="no" & aveagi$Spp=="Fd" & aveagi$DP=="3216",] y7=fd3216n[,c(1,5)] fd3216n=rename(y7,c("aveagi"="fd3216n")) write.csv(fd3216n,file="fd3216n.csv")  fd3216y<-aveagi[aveagi$Trench=="yes" & aveagi$Spp=="Fd" & aveagi$DP=="3216",] y8=fd3216y[,c(1,5)] fd3216y=rename(y8,c("aveagi"="fd3216y")) write.csv(fd3216y,file="fd3216y.csv")  allagi<-merge(ep84n,ep84y,ep3216n,ep3216y,fd84n,fd84y,fd3216n,fd3216y,by "Year",  incomparables = NA)  all.ok=read.csv("all.ok.csv", header=TRUE)  x8<-read.csv("a8.csv", header=TRUE)   cor(x8$aveshm,x8$ep84n) library(car) library(lattice)  scatterplotMatrix(~x8$aveshm+x8$ep84n+x8$ep84y+x8$ep3216n+x8$ep3216y+x8$fd84n, x8$fd84y+x8$fd3216n+ x8$fd3216y,data=x8,upper.panel=panel.smooth, lower.panel=panel.cor)  library(car) scatterplotMatrix(~lceo + ec1o + ec2o + SM , data = ef1, lower.panel=panel.smooth, upper.panel=panel.cor)    ###trying to get correlation table for series(avg)### x8<-read.csv("a8.csv", header=TRUE) library(MASS) library(stats)  table_16_2 <- matrix(nrow = 9, ncol = 9) # to collect correlations table_16_3 <- matrix(nrow = 9, ncol = 9) # to collect max cross-corr for (i in 1:8) {      for (j in (i+1):9) {          temp_cor <- cor.test(x8[, i+1], x8[, j+1],                                use = "complete.obs")          table_16_2[i, j] <- as.numeric(temp_cor$estimate)          if (as.numeric(temp_cor$p.value)<0.05) {          table_16_2[j, i] <- T 137           } else {          table_16_2[j, i] <- F          }                    temp_cor <- ccf(x8[, i+1], x8[, j+1],                            num_of_lags = 8, plotf = F)          temp_max <- which.max(abs(temp_cor$cross_cor))          table_16_3[i, j] <- temp_cor$cross_cor[temp_max]          table_16_3[j, i] <- temp_cor$lag_k[temp_max]                    } }  table.cor<-round(table_16_2, 2) round(table_16_3, 3)  cor.test(x8$aveshm,x8$ep84n) cor.test(x8$aveshm,x8$ep84y)  table_16_2 <- matrix(nrow = 9, ncol = 9) # to collect correlations for (i in 1:8) {      for (j in (i+1):9) {          temp_cor <- cor.test(x8[, i+1], x8[, j+1],                                use = "complete.obs")          table_16_2[i, j] <- as.numeric(temp_cor$estimate)          if (as.numeric(temp_cor$p.value)<0.05) {          table_16_2[j, i] <- T          } else {          table_16_2[j, i] <- F          } } } table_16_2  write.csv(table.cor,file="tsxcor.csv") write.csv(ave.shm,file="ave.shm.csv")   ## Iterations of GAMM models with the different correlation and error structures m1=gamm(aveagi~dp + Spp + Trench + aveshm + s(Year, by=id3), random=list(Site=~1), data=gam3,        correlation=corAR1(form=~Year|id3)) ##smooth: can't find by variable##--had to get Spp in model and then get id as a factor## gam.check(m1$gam) r1<-resid(m1$lme) acf(r1)###still the autocorrelation at time lag 1## par(mfrow=c(2,4)) plot(m1$gam, scale=FALSE)  138  m1=gamm(aveagi~dp + Spp + Trench + shm + s(Year, by=id3), random=list(Site=~1), data=gam3,        correlation=corAR1(form=~Year|id3))   m2=gamm(aveagi~dp + Spp + Trench + shm + s(Year, by=id3), random=list(Site=~1), data=gam3,        correlation=corARMA(form=~Year|id, p=1,q=2))  r2<-resid(m2$lme) acf(r2) gam.check(m1$gam) gam.check(m2$gam) AIC(m1$lme, m2$lme)   par(mfrow=c(2,4)) plot(m2$gam) ###so m2 drops down the AIC like this### ###m2 above worked###   m3=gamm(log(aveagi)~dp + Spp + Trench + shm + s(Year, by=id3), random=list(Site=~1), data=gam3,        correlation=corARMA(form=~Year|id, p=1,q=2))  m4=gamm(log(aveagi)~dp + Spp + Trench + shm + s(Year, by=id3), random=list(Site=~1), data=gam3,        correlation=corAR1(form=~Year|id3))  AIC(m1$lme, m2$lme,m4$lme) gam.check(m4$gam) gam.check(m5$gam)  summary(m4$gam)  m6=gamm(aveagi~dp * Spp * Trench * shm + s(Year, by=id3), random=list(Site=~1), data=gam3,        correlation=corARMA(form=~Year|id, p=1,q=2)) gam.check(m6$gam) summary(m6$gam) r2<-resid(m2$lme) acf(r2)  gameb<-gam3[gam3$Spp=="Eb",]###try gam by species### dpe=as.factor(gameb$DP) shme<-rescale(gameb$aveshm) gameb$ide=paste(gameb$Trench,gameb$DP,sep="_") gameb$ide<-as.factor(gameb$ide)  m3=gamm(aveagi~dpe + Trench + shme + s(Year, by=ide), random=list(Site=~1), data=gameb,        correlation=corARMA(form=~Year|ide, p=1,q=2)) gam.check(m3$gam) 139  ##little wonky fit vs resids  m7=gamm(log(aveagi)~dpe + Trench + shme + s(Year, by=ide), random=list(Site=~1), data=gameb,        correlation=corARMA(form=~Year|ide, p=1,q=2)) gam.check(m7$gam)  m8=gamm(aveagi~dpe + Trench + shme + s(Year, by=ide), random=list(Site=~1), data=gameb,        correlation=corAR1(form=~Year|ide)) ####more normal with corAR1### gam.check(m8$gam) summary(m8$gam) par(mfrow=c(2,2)) plot(m8$gam)  gamfd<-gam3[gam3$Spp=="Fd",]###try gam by species### dpf=as.factor(gamfd$DP) shmf<-rescale(gamfd$aveshm) gamfd$idf=paste(gamfd$Trench,gamfd$DP,sep="_") gamfd$idf<-as.factor(gamfd$idf)  m9=gamm(aveagi~dpf + Trench + shmf+ s(Year, by=idf), random=list(Site=~1), data=gamfd,        correlation=corAR1(form=~Year|idf))  gam.check(m9$gam)  m10=gamm(aveagi~dpf + Trench + shmf+ s(Year, by=idf), random=list(Site=~1), data=gamfd,        correlation=corARMA(form=~Year|idf, p=1,q=2)) gam.check(m10$gam) summary(m10$gam)  AIC(m9$lme,m10$lme)###aic's not sig. different, validation graphs pretty much the same, too. par(mfrow=c(1,2)) r9<-(residuals(m9$lme)) acf(r9) r10<-(residuals(m10$lme)) acf(r10) ###acfs exactly the same, too## summary(m9$gam) par(mfrow=c(2,2)) plot(m9$gam)  m11=gamm(aveagi~dpf + Trench + shmf+ s(Year, by=idf), random=list(Site=~1), data=gamfd,        correlation=corARMA(form=~Year|idf, p=3,q=3)) gam.check(m10$gam) r11<-(residuals(m11$lme)) acf(r11)  m12=gamm(aveagi~dpf + Trench + shmf+ s(Year, by=idf), random=list(Site=~1), data=gamfd, 140         correlation=corARMA(form=~Year|idf, p=4,q=3)) gam.check(m12$gam) r12<-(residuals(m12$lme)) acf(r12) AIC(m10$lme,m11$lme,m12$lme)  m13=gamm(aveagi~dpf + Trench + shmf+ s(Year, by=idf), random=list(Site=~1), data=gamfd) ###does not converge###without correlation structure  m14=gamm(aveagi~dpf * Trench * shmf + s(Year, by=idf), random=list(Site=~1), data=gamfd,        correlation=corARMA(form=~Year|idf, p=4,q=3)) gam.check(m14$gam) summary(m14$gam)##no significant interactions##     ## Trying model for birch only gameb<-gam1[gam1$Spp=="Eb",]###try gam by species###   m8=gamm(aveagi~DP + Trench + shm + s(Year, by=id), random=list(Site=~1, DP=~1), data=gameb,        correlation=corAR1(form=~Year|id)) summary(m8$gam)  par(mfrow=c(1,4)) plot(m8$gam, scale=FALSE) plot.gam(m3$gam, residuals=FALSE, rug=TRUE, shade=TRUE)  ## residuals and normality panels gam.check(m8$gam)  ## residuals of the 8 time series e1<-resid(m8$lme,type="normalized") xyplot(e1~Year|id,col=1, ylab="Residuals", data=gameb)  # figure with the 8 splines par(mfrow=c(2,4)) plot(m8$gam, scale=FALSE)    ## Trying model for fir only gamfd<-gam1[gam1$Spp=="Fd",]###try gam by species###   m9=gamm(aveagi~DP + Trench + shm + s(Year, by=id), random=list(Site=~1, DP=~1), data=gamfd,        correlation=corAR1(form=~Year|id)) 141  summary(m9$gam)  par(mfrow=c(1,4)) plot(m9$gam, scale=FALSE) plot.gam(m9$gam, residuals=FALSE, rug=TRUE, shade=TRUE)  ## residuals and normality panels gam.check(m9$gam)  ## residuals of the 8 time series e1<-resid(m9$lme,type="normalized") xyplot(e1~Year|id,col=1, ylab="Residuals", data=gamfd)  # figure with the 8 splines par(mfrow=c(2,4)) plot(m9$gam, scale=FALSE)  ############# #### Foliar nutrients  ## Multivarite regression trees   ###### Birch  # doing PCA on soil variables averaged per treatment-site (both plots averaged) PCA.soil=read.csv("PCA.soil.csv", header=TRUE, row.names=1) PCA.soilCR=apply(PCA.soil,2,scale,center=TRUE,scale=TRUE) ## standardized the variables  ##running the PCA pca2=PCA(PCA.soilCR, stand=FALSE, scaling=2, color.obj="blue", color.var="black") ## axis 1=42%, axis 2=32% object2=pca2$F[,1:2] variables2=pca2$U[,1:2]  col=c(4,1) labels=read.csv("labels.csv", header=TRUE) labelsok=labels[,5] labelsok2=labels[,6]  par(mar=c(1,1,1,1)) biplot(object2,variables2,var.axes=TRUE,col,cex=0.7, xlabs=labelsok2, xlim=c(-3.5,4), xlab="", ylab="")   write.csv(object2, file="data.csv")  ##variables2: scores on the two axis                 [,1]         [,2] 142  sAl       -0.2134332  0.410885294 sCa       -0.2863867 -0.313418273 sFe       -0.1877432  0.412929509 sK        -0.2834573 -0.235821212 sMg       -0.2605240 -0.286473735 sMn       -0.2116653  0.051294707 sNa       -0.2309458  0.364323259 sCEC      -0.3221521 -0.273014396 sH2Oph     0.2774621 -0.324201182 sBraymgkg -0.1051587 -0.288924939 sNmgkg    -0.2548447 -0.141790184 sN.       -0.4061756  0.008468946 sC.       -0.4111841  0.078057583  ###object2: those are the sites scores (see excel file for what numbers correspond to; e.g. 1=AL.High.TR)    [,1]        [,2]  [1,]  3.5146232  0.43013440  [2,]  0.6983034  0.25682743  [3,]  2.5123998 -0.32117856  [4,]  2.4979255 -0.42172701  [5,]  1.3486781  0.98130347  [6,] -2.7908451 -3.13525792  [7,] -0.8388840 -1.75503209  [8,]  0.6161702  0.05507922  [9,] -2.5864342 -1.11356416 [10,]  0.8480645  0.60832956 [11,] -2.5955442 -0.90669101 [12,] -3.2244570  5.32177666   ###### running MVT  foliar=read.csv("foliar.b.TR.csv", header=TRUE, row.names=1) foliarCR=apply(foliar,2,scale,center=TRUE,scale=TRUE)  indep.b=read.csv("indep.TR.csv", header=TRUE, row.names=1) indepCR.b=apply(indep.b[,6:9],2,scale,center=TRUE,scale=TRUE) indepok=cbind(indep.b[,1:5], indepCR.b)  birch=mvpart(data.matrix(foliarCR) ~., indepok, margin=0.08, cp=0, xv="pick", xval=10, xvmult=500, which=4)  res=residuals(birch) residuals.eb=melt(res)  ## residuals tree par(mfrow=c(1,2)) hist(residuals(birch), col="grey") 143  plot(residuals.eb$value, main="Residuals") abline(h=0, lty=3, col="grey")  #group identity (groups.mrt=levels(as.factor(birch$where)))  ## composition of foliar nutrients at first leaf foliarCR[which(birch$where==groups.mrt[1]),]  # environmental variables at first leaf write.csv(indepok[which(birch$where==groups.mrt[1]),], file="data.csv")  write.csv(indepok[which(birch$where==groups.mrt[2]),], file="data.csv")  ## gives piechart with the importance of each foliar at each nodes leaf.sum=matrix(0,length(groups.mrt), ncol(foliar)) colnames(leaf.sum)=colnames(foliar) for(i in 1:length(groups.mrt)) { leaf.sum[i,] = apply(foliarCR[which(birch$where==groups.mrt[i]),],2,sum) } leaf.sum  par(mfrow=c(1,2), mar=c(1,1,2,1)) for(i in 1:length(groups.mrt)) { pie(which(leaf.sum[i,]>0), radius=1, main=c("leaf#", groups.mrt[i])) }    ######## Fir # doing PCA on soil variables averaged per treatment-site (both plots averaged) PCA.soil=read.csv("PCA.soilF.csv", header=TRUE, row.names=1) PCA.soilCR=apply(PCA.soil,2,scale,center=TRUE,scale=TRUE) ## standardized the variables  ##running the PCA pca=PCA(PCA.soilCR, stand=FALSE, scaling=2, color.obj="blue", color.var="black") ## axis 1=48%, axis 2=31% object=pca$F[,1:2] variables=pca$U[,1:2]  col=c(4,1)  labels=read.csv("labels.csv", header=TRUE) labelsok=labels[,5]  par(mar=c(1,1,1,1)) biplot(object,variables,var.axes=TRUE,col,cex=0.7, xlim=c(-4.5, 3.4),xlabs=labelsok, xlab="", ylab="") 144   write.csv(object, file="data.csv")  ## variables scores                  [,1]        [,2] sAl       -0.13126881  0.42954281 sCa       -0.34360526 -0.23475032 sFe       -0.12791454  0.30259061 sK        -0.30908485 -0.24226581 sMg       -0.35066117 -0.21328251 sMn       -0.04916674  0.42456949 sNa       -0.33401177  0.05298855 sCEC      -0.36667792 -0.17939058 sH2Oph    -0.02227031 -0.46734440 sBraymgkg -0.17623298 -0.09628206 sNmgkg    -0.37265279  0.11361361 sN.       -0.32879022  0.17705455 sC.       -0.32075539  0.27831031   ## sites scores -- again, numbers are detailed in the excel spreadsheet; note that the labels are not in the same order for fir and birch     [,1]        [,2]  [1,]  1.8491418  0.06509590  [2,] -4.4013935 -2.67282402  [3,] -1.8747442  4.72704662  [4,]  2.6901168 -1.02674912  [5,] -3.8482042 -1.73446127  [6,]  0.1655678  0.75884050  [7,]  1.9289948 -1.67154499  [8,] -2.2739272  1.52725142  [9,]  0.4206432  1.47254356 [10,]  1.6961563  0.16777223 [11,]  0.7409588 -1.57962307 [12,]  2.9066896 -0.03334775    ###### running MVT  foliar=read.csv("foliar2.csv", header=TRUE, row.names=1) foliarCR=apply(foliar,2,scale,center=TRUE,scale=TRUE)  indep.b=read.csv("indep.TR.csv", header=TRUE, row.names=1) indepCR.b=apply(indep.b[,6:9],2,scale,center=TRUE,scale=TRUE) indepok=cbind(indep.b[,1:5], indepCR.b)  145  fir.MVT=mvpart(data.matrix(foliarCR) ~., indepok, margin=0.08, cp=0, xv="pick", xval=10, xvmult=500, which=4)   ## preparing residuals for plotting ## would have been easier to use function"melt" as for birch, see above pred=predict(fir.MVT) write.csv(pred, file="data.csv") res=residuals(fir.MVT) write.csv(res, file="data.csv")  resid=read.csv("residuals.csv", header=TRUE)  ## residuals tree par(mfrow=c(1,2)) hist(residuals(fir.MVT), col="grey") plot(resid[,3], main="Residuals")   abline(h=0, lty=3, col="grey")  #group identity (groups.mrt=levels(as.factor(fir.MVT$where)))  ## composition of foliar nutrients at first leaf foliarCR[which(fir.MVT$where==groups.mrt[1]),]  # environmental variables at first leaf write.csv(indepok[which(fir.MVT$where==groups.mrt[1]),], file="data.csv")  write.csv(indepok[which(fir.MVT$where==groups.mrt[2]),], file="data.csv")  ## gives piechart with the importance of each foliar at each nodes leaf.sum=matrix(0,length(groups.mrt), ncol(foliar)) colnames(leaf.sum)=colnames(foliar) for(i in 1:length(groups.mrt)) { leaf.sum[i,] = apply(foliarCR[which(fir.MVT$where==groups.mrt[i]),],2,sum) } leaf.sum  par(mfrow=c(1,2), mar=c(1,1,2,1)) for(i in 1:length(groups.mrt)) { pie(which(leaf.sum[i,]>0), radius=1, main=c("leaf#", groups.mrt[i])) }   ######################### PCA Soil Fir # PCA on soil variables averaged per treatment-site (both plots averaged) PCA.soil=read.csv("PCA.soilF.csv", header=TRUE, row.names=1) 146  PCA.soilCR=apply(PCA.soil,2,scale,center=TRUE,scale=TRUE) ## standardized the variables  ##running the PCA pca=PCA(PCA.soilCR, stand=FALSE, scaling=2, color.obj="blue", color.var="black") ## axis 1=48%, axis 2=31% object=pca$F[,1:2] variables=pca$U[,1:2]  col=c(4,1)  labels=read.csv("labels.csv", header=TRUE) labelsok=labels[,5]  par(mar=c(2,2,2,2)) biplot(object,variables,var.axes=TRUE,col,cex=0.7, xlabs=labelsok, xlab="", ylab="")  ##############################PCA soil Birch ####legendre pca function copied in########## `PCA` <-     function(Y, stand=FALSE, scaling=1, color.obj="black", color.var="red") #  # Principal component analysis (PCA) with options for scalings and output # # stand = FALSE : center by columns only, do not divide by s.d. # stand = TRUE  : center and standardize (divide by s.d.) by columns # scaling = 1 : preserves Euclidean distances among the objects # scaling = 2 : preserves correlations among the variables # #          Pierre Legendre, May 2006 {    Y = as.matrix(Y)    if(length(which(scaling == c(1,2))) == 0) stop("Scaling must be 1 or 2")    obj.names = rownames(Y)    var.names = colnames(Y)    size = dim(Y)    Y.cent = apply(Y, 2, scale, center=TRUE, scale=stand)    Y.cov = cov(Y.cent)    Y.eig = eigen(Y.cov)    k = length(which(Y.eig$values > 1e-10))    U  = Y.eig$vectors[,1:k]    F  = Y.cent %*% U    U2 = U %*% diag(Y.eig$value[1:k]^(0.5))    G  = F %*% diag(Y.eig$value[1:k]^(-0.5))    rownames(F)  = obj.names    rownames(U)  = var.names    rownames(G)  = obj.names    rownames(U2) = var.names # 147  # Fractions of variance    varY = sum(diag(Y.cov))    eigval = Y.eig$values[1:k]    relative = eigval/varY    rel.cum = vector(length=k)    rel.cum[1] = relative[1]    for(kk in 2:k) { rel.cum[kk] = rel.cum[kk-1] + relative[kk] } # out <- list(total.var=varY, eigenvalues=eigval, rel.eigen=relative,         rel.cum.eigen=rel.cum, U=U, F=F, U2=U2, G=G, stand=stand,         scaling=scaling, obj.names=obj.names, var.names=var.names,        color.obj=color.obj, color.var=color.var, call=match.call() ) class(out) <- "PCA" out }  `print.PCA` <-     function(x, ...) {     cat("\nPrincipal Component Analysis\n")     cat("\nCall:\n")     cat(deparse(x$call),'\n')     if(x$stand) cat("\nThe data have been centred and standardized by column",'\n')     cat("\nTotal variance in matrix Y: ",x$total.var,'\n')     cat("\nEigenvalues",'\n')     cat(x$eigenvalues,'\n')     cat("\nRelative eigenvalues",'\n')     cat(x$rel.eigen,'\n')     cat("\nCumulative relative eigenvalues",'\n')     cat(x$rel.cum.eigen,'\n')     invisible(x)  }  `biplot.PCA` <-     function(x, ...) { if(length(x$eigenvalues) < 2) stop("There is a single eigenvalue. No plot can be produced.")  par(mai = c(1.0, 0.75, 1.0, 0.5))  if(x$scaling == 1) {     # Distance biplot, scaling type = 1: plot F for objects, U for variables    # This projection preserves the Euclidean distances among the objects        biplot(x$F,x$U,col=c(x$color.obj,x$color.var),xlab="PCA axis 1",ylab="PCA axis 2")    title(main = c("PCA biplot","scaling type 1"), family="serif", line=4)  148     } else {     # Correlation biplot, scaling type = 2: plot G for objects, U2 for variables    # This projection preserves the correlation among the variables        biplot(x$G,x$U2,col=c(x$color.obj,x$color.var),xlab="PCA axis 1",ylab="PCA axis 2")    title(main = c("PCA biplot","scaling type 2"), family="serif", line=4)     } invisible() } #####################end function  # PCA on soil variables averaged per treatment-site (both plots averaged) PCA.soil=read.csv("PCA.soil.csv", header=TRUE, row.names=1) PCA.soilCR=apply(PCA.soil,2,scale,center=TRUE,scale=TRUE) ## standardized the variables  ##running the PCA pca2=PCA(PCA.soilCR, stand=FALSE, scaling=2, color.obj="blue", color.var="black") ## axis 1=42%, axis 2=32% object2=pca2$F[,1:2] variables2=pca2$U[,1:2]  col=c(4,1) labels=read.csv("labels.csv", header=TRUE) labelsok=labels[,5] labelsok2=labels[,6]  par(mar=c(2,2,2,2)) biplot(object2,variables2,var.axes=TRUE,col,cex=0.7, xlabs=labelsok2, xlab="", ylab="")  #################### Box plots with environmental variables ### bplot.fir=read.csv("bplot.fir.csv", header=TRUE)  ## soil moisture   par(bty="l",mar=c(3,3,2,2)) boxplot(SM ~ Density, data = bplot.fir,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,0.1), yaxs = "i") boxplot(SM ~ Density, data = bplot.fir, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE, 149   range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2, 0.1, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil Moisture (%)", side=2, line=2.2, at=0.05, cex=0.8)  # PAR par(bty="l",mar=c(3,3,2,2)) boxplot(PAR ~ Density, data = bplot.fir,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,1450), yaxs = "i") boxplot(PAR ~ Density, data = bplot.fir, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2, 1400, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("PAR (umol m-2 s-1)", side=2, line=2.2, at=725, cex=0.8)    # soil PCA 1 par(bty="l",mar=c(3,3,2,2)) boxplot(pca1 ~ Density, data = bplot.fir,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(-6.9,3.1), yaxs = "i") boxplot(pca1 ~ Density, data = bplot.fir, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2.1, 3.1, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) 150  mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil PCA 1", side=2, line=2.2, at=-2, cex=0.8)    # soil PCA 2 par(bty="l",mar=c(3,3,2,2)) boxplot(pca2 ~ Density, data = bplot.fir,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(-1.8,6.9), yaxs = "i") boxplot(pca2 ~ Density, data = bplot.fir, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2.1, 6, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil PCA 2", side=2, line=2.2, at=2.5, cex=0.8)     ## The four together  layout(matrix(1:4, 2,2, byrow=TRUE))   par(bty="l",mar=c(2,3.1,1,1)) boxplot(SM ~ Density, data = bplot.fir,xaxt="n",         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,0.1), yaxs = "i") boxplot(SM ~ Density, data = bplot.fir, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") mtext("Soil Moisture (%)", side=2, line=2.2, at=0.05, cex=0.8) 151   par(bty="l",mar=c(2,2.5,1,1)) boxplot(PAR ~ Density, data = bplot.fir,xaxt="n",         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,1450), yaxs = "i") boxplot(PAR ~ Density, data = bplot.fir, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(0.6, 1400, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("PAR (umol m-2 s-1)", side=2, line=2.2, at=725, cex=0.8)    par(bty="l",mar=c(3,3.1,1,1)) boxplot(pca1 ~ Density, data = bplot.fir,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(-6.9,3.1), yaxs = "i") boxplot(pca1 ~ Density, data = bplot.fir, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil PCA 1", side=2, line=2.2, at=-2, cex=0.8)    par(bty="l",mar=c(3,2.5,1,1)) boxplot(pca2 ~ Density, data = bplot.fir,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey", 152          main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(-1.8,6.9), yaxs = "i") boxplot(pca2 ~ Density, data = bplot.fir, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil PCA 2", side=2, line=2.2, at=2.5, cex=0.8)    ### Birch bplot.birch=read.csv("bplot.birch.csv", header=TRUE)  ## soil moisture   par(bty="l",mar=c(3,3,2,2)) boxplot(SM ~ Density, data = bplot.birch,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,0.1), yaxs = "i") boxplot(SM ~ Density, data = bplot.birch, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2, 0.1, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil Moisture (%)", side=2, line=2.2, at=0.05, cex=0.8)  # PAR par(bty="l",mar=c(3,3,2,2)) boxplot(PAR ~ Density, data = bplot.birch,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "", 153          xlim = c(0.5, 2.5), ylim= c(0,1100), yaxs = "i") boxplot(PAR ~ Density, data = bplot.birch, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2, 1100, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("PAR (umol m-2 s-1)", side=2, line=2.2, at=550, cex=0.8)    # soil PCA 1 par(bty="l",mar=c(3,3,2,2)) boxplot(pca1 ~ Density, data = bplot.birch,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(-5.5,3.5), yaxs = "i") boxplot(pca1 ~ Density, data = bplot.birch, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2.1, 3.1, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil PCA 1", side=2, line=2.2, at=-1.5, cex=0.8)    # soil PCA 2 par(bty="l",mar=c(3,3,2,2)) boxplot(pca2 ~ Density, data = bplot.birch,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(-3.7,6), yaxs = "i") boxplot(pca2 ~ Density, data = bplot.birch, add = TRUE, 154          boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil PCA 2", side=2, line=2.2, at=1, cex=0.8)    ## All together   par(bty="l",mar=c(3,3,2,2)) boxplot(SM ~ Density, data = bplot.birch,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,0.1), yaxs = "i") boxplot(SM ~ Density, data = bplot.birch, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2, 0.1, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil Moisture (%)", side=2, line=2.2, at=0.05, cex=0.8)   par(bty="l",mar=c(3,3,2,2)) boxplot(PAR ~ Density, data = bplot.birch,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(0,1100), yaxs = "i") boxplot(PAR ~ Density, data = bplot.birch, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2, 1100, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) 155  mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("PAR (umol m-2 s-1)", side=2, line=2.2, at=550, cex=0.8)   par(bty="l",mar=c(3,3,2,2)) boxplot(pca1 ~ Density, data = bplot.birch,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(-5.5,3.5), yaxs = "i") boxplot(pca1 ~ Density, data = bplot.birch, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") legend(2.1, 3.1, c("Trenched", "Untrenched"),        fill = c("lightgrey", "gray17"), cex=0.8) mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil PCA 1", side=2, line=2.2, at=-1.5, cex=0.8)   par(bty="l",mar=c(3,3,2,2)) boxplot(pca2 ~ Density, data = bplot.birch,         boxwex = 0.2, at = 1:2 - 0.1,  varwidth = FALSE,  range = 1.5,         subset = Trenched == "y", col = "lightgrey",         main = "",         xlab = "",         ylab = "",         xlim = c(0.5, 2.5), ylim= c(-3.7,6), yaxs = "i") boxplot(pca2 ~ Density, data = bplot.birch, add = TRUE,         boxwex = 0.2, at = 1:2+0.1, xaxt="n",  varwidth = FALSE,  range = 1.5,         subset = Trenched == "n", col = "gray17") mtext("Density", side=1, line=1.5, at=1.5, cex=0.8) mtext("Soil PCA 2", side=2, line=2.2, at=1, cex=0.8)      ### Classification tree with armallaria 156   ## birch a.b.tree<-tree(Arm ~ Treatment + SM + Trenched + PAR + pca1 + pca2 + X.n + c.b,data=b2) a.b.tree plot(a.b.tree); text(a.b.tree) summary(a.b.tree) plot(prune.tree(a.b.tree)) summary(a.b.tree) node), split, n, deviance, yval, (yprob)       * denotes terminal node  1) root 19 25.860 y ( 0.4211 0.5789 )     2) c.b < 2.14286 7  0.000 y ( 0.0000 1.0000 ) *   3) c.b > 2.14286 12 15.280 n ( 0.6667 0.3333 )       6) pca1 < 1.48453 7  9.561 y ( 0.4286 0.5714 ) *     7) pca1 > 1.48453 5  0.000 n ( 1.0000 0.0000 ) *  Classification tree: tree(formula = Arm ~ Treatment + SM + Trenched + PAR + pca1 +      pca2 + X.n + c.b, data = b2) Variables actually used in tree construction: [1] "c.b"  "pca1" Number of terminal nodes:  3  Residual mean deviance:  0.5975 = 9.561 / 16  Misclassification error rate: 0.1579 = 3 / 19   ## tree a.f.tree<-tree(Arm ~ Treatment + SM + Trenched + PAR + pca1 + pca2 + X.n + c.b,data=f) a.f.tree plot(a.f.tree); text(a.f.tree) summary(a.f.tree) plot(cv.tree(a.f.tree)) plot(prune.tree(a.f.tree))   a.f.tree node), split, n, deviance, yval, (yprob)       * denotes terminal node  1) root 22 28.840 n ( 0.6364 0.3636 )     2) SM < 0.0485 14 19.120 y ( 0.4286 0.5714 )       4) pca1 < 0.300401 5  5.004 n ( 0.8000 0.2000 ) *     5) pca1 > 0.300401 9  9.535 y ( 0.2222 0.7778 ) *   3) SM > 0.0485 8  0.000 n ( 1.0000 0.0000 ) * > summary(a.f.tree)  Classification tree: tree(formula = Arm ~ Treatment + SM + Trenched + PAR + pca1 +      pca2 + X.n + c.b, data = f) 157  Variables actually used in tree construction: [1] "SM"   "pca1" Number of terminal nodes:  3  Residual mean deviance:  0.7652 = 14.54 / 19  Misclassification error rate: 0.1364 = 3 / 22      ####################################################################################### ################# Chapitre 2 d5<-read.csv("n5.csv", header=TRUE) str(d5) library(plyr)  check<-read.csv("neigbors.csv",header=TRUE) unique(check[,2]) unique(check[,6])  d.c<-ddply(d5,c("Site","Treatment","Plot"),summarize,vi=sum(viN.m2.))  d.arm<-ddply(d5,c("Site","Treatment","Plot"),summarise,arm=sum(Armillaria))   d.arm<-ddply(d5,c("Site","Treatment","Plot"),summarise,arm=sum(Armillaria)) d.arm.y<-ddply(d5,c("Site","Treatment","Plot"),summarise,arm.y=length(Armillaria)) d.xf<-ddply(d5.fd,c("Site","Treatment","Plot"),summarise,xfd=length(Spp)) d.x<-ddply(d5,c("Site","Treatment","Plot", "Spp"),summarise,x=length(Spp)) fd.vi<-ddply(d5.fd,c("Site","Treatment","Plot"),summarize,vi=sum(viN.m2.)) d.xep<-ddply(d5.ep,c("Site","Treatment","Plot"),summarise,xep=length(Spp)) ep.vi<-ddply(d5.ep,c("Site","Treatment","Plot"),summarize,vi=sum(viN.m2.))  Arm.ok=join(d.arm, d.arm.y, by=c("Site", "Treatment", "Plot")) Arm=ddply(Arm.ok, c("Site","Treatment","Plot"),summarize,percentArm=arm/arm.y)   write.csv(Arm, file = "armpc.csv") write.csv(d.arm.y,file="armN.csv") write.csv(d.c,file="dvi.csv") write.csv(d.xn,file="xn.csv") write.csv(d.xf,file="xf.csv") write.csv(fd.vi,file="fd.vi.csv") write.csv(d.xep,file="xep.csv") write.csv(ep.vi,file="ep.vi.csv")   d5.fd<-subset(d5,c(Spp=="Fd")) d5.ep<-subset(d5,c(Spp=="Ep")) 158  unique(d5$Spp)  d5.ep   ######## Redoing it more directly with plyr and cast d.x<-ddply(d5,c("Site","Treatment","Plot", "Spp"),summarise,x=length(Spp)) vi<-ddply(d5,c("Site","Treatment","Plot", "Spp"),summarize,vi=sum(viN.m2.)) d.group<-ddply(d5,c("Site","Treatment","Plot", "Group"),summarise,x.gr=length(Group)) vi.gr<-ddply(d5,c("Site","Treatment","Plot", "Group"),summarise,vi.gr=sum(viN.m2.))  count.spp=cast(d.x, Site+Treatment+Plot ~Spp) vi.spp=cast(vi, Site+Treatment+Plot ~Spp) count.group=cast(d.group, Site+Treatment+Plot ~Group) vi.group=cast(vi.gr, Site+Treatment+Plot ~Group)  All.ok=join(count.spp, vi.spp, by=c("Site", "Treatment", "Plot")) All=join(All.ok, count.group, by=c("Site", "Treatment", "Plot")) All.final=join(All, vi.group,by=c("Site", "Treatment", "Plot")) Allok=join(All.final, Arm, by=c("Site", "Treatment", "Plot"))  write.csv(Allok, file = "All.Neighbors.csv")  #####getting counts per treatment for graphs####  nb<-read.csv("nb.csv",header=TRUE) str(nb) nb$Csph=as.integer(nb$Csph) nb.tr<-ddply(nb,c("Treatment"),summarize,fd.trt=mean(Fd.sph), Ep.trt=mean(Ep.sph), C.trt=mean(Csph),B.trt=mean(Bsph))  write.csv(n6, file = "data.csv")  ####starting neighborhood analysis##### n6<-read.csv("n6.csv",header=TRUE) library(nlme)  fd<-n6[n6$Spp=="Fd",] ep<-n6[n6$Spp=="Ep",]  fd1<-lme(vi ~ Fd.vi * Ep.vi, random = ~1|Site/Treatment, fd) red1<-resid(fd1) fed1<-fitted(fd1) par(mfrow=c(2,2)) hist(red1) plot(x=fed1,y=red1) plot(density(red1)) summary(fd1) 159  ###nothing significant, so take out interaction###  fd2<-lme(vi ~ Fd.vi + Ep.vi, random = ~1|Site/Treatment, fd) red1<-resid(fd1) fed1<-fitted(fd1) par(mfrow=c(2,2)) hist(red1) plot(x=fed1,y=red1) plot(density(red1)) summary(fd2)  Fixed effects: vi ~ Fd.vi + Ep.vi                  Value  Std.Error DF  t-value p-value (Intercept) 1.1604528 0.22863476 30 5.075574  0.0000 Fd.vi       0.0031851 0.01241737 30 0.256503  0.7993 Ep.vi       0.0757992 0.11893987 30 0.637290  0.5288  Correlation:        (Intr) Fd.vi  Fd.vi -0.568        Ep.vi -0.276  0.015 ##nothing significant###  ep1<-lme(log(vi) ~ Fd.vi * Ep.vi, random = ~1|Site/Treatment, ep)** red1<-resid(ep1) fed1<-fitted(ep1) par(mfrow=c(2,2)) hist(red1) plot(x=fed1,y=red1) plot(density(red1)) summary(ep1)  ###log takes care of cone in residuals###  Fixed effects: log(vi) ~ Fd.vi * Ep.vi                   Value Std.Error DF   t-value p-value (Intercept) -2.5230640 0.4277202 27 -5.898866  0.0000 Fd.vi        0.0899981 0.0376041 26  2.393306  0.0242** Ep.vi        0.9356337 0.3332214 26  2.807844  0.0093*** Fd.vi:Ep.vi -0.1418787 0.0610315 26 -2.324681  0.0282**  Correlation:              (Intr) Fd.vi  Ep.vi  Fd.vi       -0.690               Ep.vi       -0.475  0.440        Fd.vi:Ep.vi  0.152 -0.360 -0.687  #################################now sph density#########  fd1<-lme(Fd.sph ~ Fd.ps * Ep.ps, random = ~1|Site/Treatment, fd) 160  red1<-resid(fd1) fed1<-fitted(fd1) par(mfrow=c(2,2)) hist(red1) plot(x=fed1,y=red1) plot(density(red1)) summary(fd1) ########fan in residuals#####  fd2<-lme(log(Fd.sph) ~ Fd.ps * Ep.ps, random = ~1|Site/Treatment, fd) red1<-resid(fd2) fed1<-fitted(fd2) par(mfrow=c(2,2)) hist(red1) plot(x=fed1,y=red1) plot(density(red1)) summary(fd2) ###interaction not sig######take out interaction###  fd3<-lme(log(Fd.sph) ~ Fd.ps + Ep.ps, random = ~1|Site/Treatment, fd) red1<-resid(fd3) fed1<-fitted(fd3) par(mfrow=c(2,2)) hist(red1) plot(x=fed1,y=red1) plot(density(red1)) summary(fd3)  ###zero p-value??### Fixed effects: log(Fd.sph) ~ Fd.ps + Ep.ps                 Value Std.Error DF   t-value p-value (Intercept) 6.636909 0.3416283 32 19.427280  0.0000 Fd.ps       0.000577 0.0000887 28  6.501306  0.0000**?? Ep.ps       0.000026 0.0000618 28  0.415146  0.6812  Correlation:        (Intr) Fd.ps  Fd.ps -0.343        Ep.ps -0.242  0.317  ep2<-lme((Ep.sph) ~ Ep.ps + Fd.ps, random = ~1|Site/Treatment, ep) red1<-resid(ep2) fed1<-fitted(ep2) par(mfrow=c(2,2)) hist(red1) plot(x=fed1,y=red1) plot(density(red1))  summary(ep2) 161  ###can't get pattern out of residuals###  library(lmmfit)  #x2##########  library(rsm)  ep1<-lme(log(vi) ~ Fd.vi * Ep.vi, random = ~1|Site/Treatment, ep)  par(mfrow=c(1,3)) image(ep1, vi ~ Fd.vi) contour(ep1, vi ~ Fd.vi) persp(ep1, vi ~ Fd.vi, zlab = "Ep.vi")  ep1$fitted ep1$coefficients ep1$VarFix   library(lattice) wireframe(vi~ Fd.vi*Ep.vi,data=ep, drape=TRUE, colorkey=TRUE)  ??wireframe  g <- expand.grid(x = 1:10, y = 5:15, gr = 1:2) g$z <- log((g$x^g$gr + g$y^2) * g$gr) wireframe(z ~ x * y, data = g, groups = gr,           scales = list(arrows = FALSE),           drape = TRUE, colorkey = TRUE,           screen = list(z = 30, x = -60))  ep<-data.matrix(ep)  wireframe(Fd.sph~Ep.ps*Fd.ps, fd,            scales = list(arrows = FALSE),           drape = TRUE, colorkey = TRUE,           screen = list(z = -30, x = -60))  plot((vi)*100) ~ Fd.vi * Ep.vi,  ep))   str(ep)  x <- seq(1, 3, by=0.25) y <- seq(-4, 4, by=0.25) mydata <- expand.grid(x=x,y=y) p <- 1/(1+exp(-0.12*mydata$x + 0.35*mydata$y)) mydata <- data.frame(x=mydata$x,y=mydata$y,p) 162  require(lattice) wireframe(p~x*y, data=mydata)   library(rgl) require(rgl)  plot3d(ep$vi,ep$Fd.vi,ep$Ep.vi,type="h")   r.squared.lme(ep1)   Class   Family     Link  Marginal Conditional      AIC 1   lme gaussian identity 0.1280217   0.6119155 211.6518  r.squared.lme(fd2)   Class   Family     Link    Marginal Conditional     AIC 1   lme gaussian identity 0.006997884   0.1845012 152.884  #########foliar nutrients######## fn<-read.csv("soil_fol_working.csv",header=TRUE) library(plyr)  fn2<-ddply(fn,c("Site","Treatment","Spp"),summarize,al=mean(Al), b=mean(B), c=mean(C),ca=mean(Ca),cu=mean(Cu),fe=mean(Fe),k=mean(K),mg=mean(Mg),mn=mean(Mn),n=mean(N), na=mean(Na),p=mean(P), s=mean(S..ICAP.),zn=mean(Zn))  xv<-read.csv("x.vars.csv",header=TRUE)  unique(xv$PARup..mol.M2.s.)  str(xv)  xv.2=ddply(xv,c("Site","Treatment","Spp"),summarize,T.vi=mean(vi),b.vi=mean(B.vi),c.vi=mean(C.vi),  ep.vi=mean(Ep.vi),fd.vi=mean(Fd.vi),p.arm=mean(percentArm),sm=mean(SMR.M3.M.3.),par=mean(PARup..mol.M2.s.),  nEp=mean(Ep.N), nFd=mean(Fd.N),nB=mean(B.N),nC=mean(C.N),nOC=mean(OC),nOB=mean(OB))  fn.x=join(fn2, xv.2, by=c("Site", "Treatment","Spp"))  write.csv #################covariance########### pairs(fn2[,4:14]) b<-read.csv("birch.pairs.csv", header=TRUE)  table1=cbind(b$Soil.PCA1,b$Soil.PCA2,b$PAR,b$SM,b$"X.n",b$"c.b") colnames(table1)=c("Soil.PCA1", "Soil.PCA2", "PAR", "SM","X.n","c.b")  163  ## need to copy what is below to have panel.cor working panel.cor <- function(x, y, digits = 2, prefix = "", cex.cor, ...) {     usr <- par("usr"); on.exit(par(usr))     par(usr = c(0, 1, 0, 1))     r <- abs(cor(x, y))     txt <- format(c(r, 0.123456789), digits = digits)[1]     txt <- paste0(prefix, txt)     if(missing(cex.cor)) cex.cor <- 0.8/strwidth(txt)     text(0.5, 0.5, txt, cex = cex.cor * r) }  pairs(table1, lower.panel = panel.smooth, upper.panel = panel.cor)  f<-read.csv("fir.pairs.csv", header=TRUE)  table2=cbind(f$PCA.soilF1,f$PCA.soilF2,f$PAR,f$SM,f$"X.n",f$"c.b") colnames(table2)=c("Soil.PCA1", "Soil.PCA2", "PAR", "SM","X.n","c.b")  ## need to copy what is below to have panel.cor working panel.cor <- function(x, y, digits = 2, prefix = "", cex.cor, ...) {     usr <- par("usr"); on.exit(par(usr))     par(usr = c(0, 1, 0, 1))     r <- abs(cor(x, y))     txt <- format(c(r, 0.123456789), digits = digits)[1]     txt <- paste0(prefix, txt)     if(missing(cex.cor)) cex.cor <- 0.8/strwidth(txt)     text(0.5, 0.5, txt, cex = cex.cor * r) }  pairs(fn2[,4:14], lower.panel = panel.smooth, upper.panel = panel.cor)  str(xv) s<-read.csv("soil_working.csv", header=TRUE) str(fn)  library(plyr)  s2<-ddply(s,c("Site","Treatment","Spp"),summarize,s.al=mean(Al), s.c=mean(C.p),s.ca=mean(Ca),s.fe=mean(Fe), s.k=mean(K),s.mg=mean(Mg),s.mn=mean(Mn),s.n=mean(N.p),s.na=mean(Na),s.nmg.kg=mean(Nmg.kg, s.p=mean(Bray), s.CEC=mean(CEC),s.H20=mean(H20)))   fn.x.s=join(fn.x, s2, by=c("Site", "Treatment","Spp"))  164  write.csv(fn.x.s,file="fol.all.csv")  ###############foliar nutrient tree fna<-read.csv("fn.csv",header=TRUE) fn.fd<-subset(fna,c(Spp=="Fd")) ep.fd<-subset(fna,c(Spp=="Ep"))  #########fir################### library(mvpart)  foln.f<-fn.fd[,4:17] fol.fc=apply(foln.f,2,scale,center=TRUE,scale=TRUE) ind.f<-fn.fd[,18:41] site=fn.fd$Site indfok=cbind(site,ind.f) str(indfok)     fir=mvpart(data.matrix(fol.fc) ~., indfok, margin=0.08, cp=0, xv="pick", xval=10, xvmult=500, which=4)   library(reshape)  res=residuals(fir) residuals.fd=melt(res)  ## residuals tree par(mfrow=c(1,2)) hist(residuals(fir), col="grey") plot(residuals.fd$value, main="Residuals") abline(h=0, lty=3, col="grey")  #group identity (groups.mrt=levels(as.factor(fir$where)))    ## gives piechart with the importance of each foliar at each nodes leaf.sum=matrix(0,length(groups.mrt), ncol(foln.f)) colnames(leaf.sum)=colnames(foln.f) for(i in 1:length(groups.mrt)) { leaf.sum[i,] = apply(fol.fc[which(fir$where==groups.mrt[i]),],2,sum) } leaf.sum  165  par(mfrow=c(2,2), mar=c(1,1,2,1)) for(i in 1:length(groups.mrt)) { pie(which(leaf.sum[i,]>0), radius=1, main=c("leaf#", groups.mrt[i])) }    ######## birch##################  foln.e<-ep.fd[,4:17] fol.ec=apply(foln.e,2,scale,center=TRUE,scale=TRUE) ind.e<-ep.fd[,18:41]  site=ep.fd$Site indepok=cbind(site,ind.e) str(indepok)    birch2=mvpart(data.matrix(fol.ec) ~., indepok, margin=0.08, cp=0, xv="pick", xval=10, xvmult=500, which=4)  library(reshape)  res=residuals(birch) residuals.ep=melt(res)  ## residuals tree par(mfrow=c(1,2)) hist(residuals(birch), col="grey") plot(residuals.ep$value, main="Residuals") abline(h=0, lty=3, col="grey")  #group identity groups.mrt2=c("3", "4", "6", "8", "10", "11")  ## gives piechart with the importance of each foliar at each nodes leaf.sum=matrix(0,length(groups.mrt2), ncol(foln.e)) colnames(leaf.sum)=colnames(foln.e) for(i in 1:length(groups.mrt2)) { leaf.sum[i,] = apply(fol.ec[which(birch2$where==groups.mrt2[i]),],2,sum) } leaf.sum  par(mfrow=c(3,2), mar=c(1,1,2,1)) for(i in 1:length(groups.mrt2)) { pie(which(leaf.sum[i,]>0), radius=1, main=c("leaf#", groups.mrt[i])) 166  }    leaf.sum=matrix(0,length(groups.mrt), ncol(foln.e)) colnames(leaf.sum)=colnames(foln.e) for(i in 1:length(groups.mrt)) { leaf.sum[i,] = apply(fol.ec[which(birch$where==groups.mrt[i]),],2,sum) } leaf.sum  par(mfrow=c(2,2), mar=c(1,1,2,1)) for(i in 1:length(groups.mrt)) { pie(which(leaf.sum[i,]>0), radius=1, main=c("leaf#", groups.mrt[i])) }   ############# arm=join(xv,s, by=c("Site", "Treatment","Plot")) ar<-read.csv("a.csv",header=TRUE) ar.b<-subset(ar,Spp=="Ep") ar.f<-subset(ar,Spp=="Fd")  library(tree)  a.f.tree<-tree(Armillaria.on.tree ~ Site + Treatment + vi + B.vi + C.vi + Ep.vi + Fd.vi +  percentArm+SMR.M3.M.3.+PARup..mol.M2.s.+Ep.N+Fd.N+B.N+C.N+OC+OB+Al+Ca+Fe+K+Mg+Mn+Mn+Na+CEC+H2O+Bray+ Nmg.kg+N.p+C.p,data=ar.f)  a.f.tree plot(a.f.tree); text(a.f.tree) summary(a.f.tree) plot(prune.tree(a.f.tree)) plot(residuals(a.f.tree)~ predict(a.f.tree))###???? residuals(a.f.tree)  node), split, n, deviance, yval, (yprob)       * denotes terminal node   1) root 63 85.410 n ( 0.5873 0.4127 )      2) C.p < 4.12 53 73.450 n ( 0.5094 0.4906 )        4) percentArm < 0.578397 34 42.810 n ( 0.6765 0.3235 )          8) Treatment: 3200/400,400/800,800/800 8  0.000 n ( 1.0000 0.0000 ) *        9) Treatment: 0/1600,0/3200,0/400,0/800,3200/800,400/1600,400/400,800/1600 26 35.430 n ( 0.5769 0.4231 )           18) C.N < 19.5 17 23.030 y ( 0.4118 0.5882 )   167            36) Nmg.kg < 16.005 6  0.000 y ( 0.0000 1.0000 ) *           37) Nmg.kg > 16.005 11 14.420 n ( 0.6364 0.3636 )               74) Ca < 4.625 6  0.000 n ( 1.0000 0.0000 ) *             75) Ca > 4.625 5  5.004 y ( 0.2000 0.8000 ) *         19) C.N > 19.5 9  6.279 n ( 0.8889 0.1111 ) *      5) percentArm > 0.578397 19 19.560 y ( 0.2105 0.7895 )         10) Treatment: 3200/400,400/400,400/800,800/800 10 13.460 y ( 0.4000 0.6000 )           20) Fd.vi < 8.06705 5  6.730 n ( 0.6000 0.4000 ) *         21) Fd.vi > 8.06705 5  5.004 y ( 0.2000 0.8000 ) *       11) Treatment: 0/1600,0/3200,0/800,3200/800,400/1600 9  0.000 y ( 0.0000 1.0000 ) *    3) C.p > 4.12 10  0.000 n ( 1.0000 0.0000 ) *   ##########armillaria###############  a.b.tree<-tree(Armillaria.on.tree ~ Site + Treatment + vi + B.vi + C.vi + Ep.vi + Fd.vi +  percentArm+SMR.M3.M.3.+PARup..mol.M2.s.+Ep.N+Fd.N+B.N+C.N+OC+OB+Al+Ca+Fe+K+Mg+Mn+Mn+Na+CEC+H2O+Bray+ Nmg.kg+N.p+C.p,data=ar.b)  plot(a.b.tree); text(a.b.tree) a.b.tree summary(a.b.tree) plot(cv.tree(a.b.tree)) plot(prune.tree(a.b.tree))  Classification tree: tree(formula = Armillaria.on.tree ~ Site + Treatment + vi + B.vi +      C.vi + Ep.vi + Fd.vi + percentArm + SMR.M3.M.3. + PARup..mol.M2.s. +      Ep.N + Fd.N + B.N + C.N + OC + OB + Al + Ca + Fe + K + Mg +      Mn + Mn + Na + CEC + H2O + Bray + Nmg.kg + N.p + C.p, data = ar.b) Variables actually used in tree construction: [1] "percentArm" "vi"         "Treatment"  "B.vi"       Number of terminal nodes:  7  Residual mean deviance:  0.3898 = 19.49 / 50  Misclassification error rate: 0.08772 = 5 / 57   node), split, n, deviance, yval, (yprob)       * denotes terminal node   1) root 57 78.860 n ( 0.5263 0.4737 )      2) percentArm < 0.13961 14  0.000 n ( 1.0000 0.0000 ) *    3) percentArm > 0.13961 43 56.770 y ( 0.3721 0.6279 )        6) vi < 0.68465 35 39.900 y ( 0.2571 0.7429 )         12) Treatment: 1600/0,3200/400,400/400,800/0,800/1600,800/800 20 27.530 y ( 0.4500 0.5500 )           24) percentArm < 0.576037 10 12.220 n ( 0.7000 0.3000 )             48) Treatment: 3200/400,400/400,800/0,800/800 5  0.000 n ( 1.0000 0.0000 ) *           49) Treatment: 1600/0,800/1600 5  6.730 y ( 0.4000 0.6000 ) * 168          25) percentArm > 0.576037 10 10.010 y ( 0.2000 0.8000 )             50) B.vi < 0.4142 5  6.730 y ( 0.4000 0.6000 ) *           51) B.vi > 0.4142 5  0.000 y ( 0.0000 1.0000 ) *       13) Treatment: 3200/0,3200/800,400/0,400/1600,400/800 15  0.000 y ( 0.0000 1.0000 ) *      7) vi > 0.68465 8  6.028 n ( 0.8750 0.1250 ) *    ###### PCA per site with treatments and indicator species PCA_Adams=read.csv("PCA_Adams.csv", header=TRUE) Adams.Hel=decostand(PCA_Adams[,4:9], "hel")  pca.AD=PCA(Adams.Hel, stand=TRUE, scaling=1, color.obj="blue", color.var="black") object=pca.AD$F[,1:2] variables=pca.AD$U[,1:2] col=c(4,1) names=PCA_Adams[,3]   biplot(object,variables) par(mar=c(0.5, 0.5, 0.5, 0.5)) biplot(object,variables,var.axes=TRUE,col,cex=0.8,xaxt="n", yaxt="n", xlab="", ylab="",  xlabs=names, xlim=c(-5,2.5),ylim=c(-3,2.5))  ##Hidden PCA_Hd=read.csv("PCA_Hidden.csv", header=TRUE) Hd.Hel=decostand(PCA_Hd[,4:7], "hel")  pca.Hd=PCA(Hd.Hel, stand=TRUE, scaling=1, color.obj="blue", color.var="black") object.Hd=pca.Hd$F[,1:2] variables.Hd=pca.Hd$U[,1:2] col=c(4,1) names.Hd=PCA_Hd[,3]   biplot(object.Hd,variables.Hd) par(mar=c(0.5, 0.5, 0.5, 0.5)) biplot(object.Hd,variables.Hd,var.axes=TRUE,col,cex=0.8,xaxt="n", yaxt="n", xlab="", ylab="",  xlabs=names.Hd, xlim=c(-4,2.5),ylim=c(-1.5,1.8))   ##Malakwa PCA_Ml=read.csv("PCA_Malakwa.csv", header=TRUE) Ml.Hel=decostand(PCA_Ml[,4:9], "hel")  pca.Ml=PCA(Ml.Hel, stand=TRUE, scaling=1, color.obj="blue", color.var="black") object.Ml=pca.Ml$F[,1:2] variables.Ml=pca.Ml$U[,1:2] col=c(4,1) names.Ml=PCA_Ml[,3]  169   biplot(object.Ml,variables.Ml) par(mar=c(0.5, 0.5, 0.5, 0.5)) biplot(object.Ml,variables.Ml,var.axes=TRUE, expand=1, col,cex=0.8,xaxt="n", yaxt="n", xlab="", ylab="",  xlabs=names.Ml, xlim=c(-4.4,4),ylim=c(-2,1.5)) 

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