Study area description
Study sites were located near Smithers (54°35′N, 126°55′W), north-western British Columbia, in the sub-boreal spruce (Moist Cold subzone Babine Variant) part of the Canadian Boreal Forest Region (Banner et al. 1993). The continental climate of this area has cold, snowy winters with temperatures below 0 °C for 4–5 months and short, warm summers; 25–50% of the 440–900 mm mean annual precipitation falls as snow (Meidinger, Pojar & Harper 1991). Subalpine fir (Abies lasiocarpa [Hook.] Nutt.), interior spruce (Picea glauca × engelmanii [Moench] Voss) and lodgepole pine (Pinus contorta Dougl. ex Loud. var. latifolia) are the dominant coniferous tree species and often occur in mixed stands with the dominant broadleaved species, trembling aspen (Populus tremuloides Michx.).
Topographical and geomorphic variation over the mountainous landscape has led to a wide range of soil fertility conditions in our study area that have been described by Banner et al. (1993). Glacial and alluvial deposits and processes have created this diverse mixture of site types, sometimes in very close association and not necessarily predicable because of slope position. Briefly, the driest, poorest sites are typically found on shallow, rocky or coarse-textured soil with acidic Ae horizons and a thin forest floor dominated by fungi. The medium sites best reflect the climactic inputs of the region with medium-textured, well-drained soil, little soil acidification (no Ae horizon) and a thicker forest floor with fungal and soil fauna influences. The richest sites have finer-textured soils with organic matter incorporated into the mineral soil (Ah horizon) by active soil fauna and quickly decomposing herbaceous flora.
Tree sampling and mensuration
Our goal was to sample trees distributed evenly across a soil fertility gradient, across a range of stand age, density and composition and across tree size. We selected trees for sampling from 126 stem-mapped sites located in over 50 geographically separate locations to represent the full range of soil fertility and stand type present in the landscape (Table 1), including stands initiated from fire in 1784, 1854, 1863, 1907 and 1936, stands with partial cutting and under planting throughout the 1950's and stands clear-cut between 1964 and 1983. Stem maps included subalpine fir, interior spruce, lodgepole pine and/or trembling aspen target trees (cored trees with DBH > 5 cm and no disease, pests or physical deformities such as forks or large scars) and the neighbour trees (live trees with DBH > 5 cm) within 8 m around them. Target trees were selected to cover the full range of canopy positions, including overtopped trees, emergent trees and canopy trees in tree neighbourhoods with different species combinations. Our data set contains 651 fir, 825 spruce, 484 pine and 267 aspen target sample trees. We had good sample size for all species across all site types except for aspen target trees on the poorest sites (Table 1). This low sample size could cause parameter estimation difficulties (c.f. Astrup, Coates & Hall 2008)
Table 1. Species composition of stands sampled (e.g. PlBl), number of stem maps, sample trees and cored trees by site type
|No. Cored trees|
|No. Stem maps||2||2||1||4||1||2||5||9||13||1||3||43|
|No. Cored trees|
|No. Stem maps||5||0||2||0||3||1||2||5||4||3||9||34|
|No. Cored trees|
|Very rich sites|
|No. Stem maps||5||0||1||0||2||0||2||2||1||2||8||23|
|No. Cored trees|
Target and neighbourhood trees (14 357 trees total) in stem maps were identified to species, and all DBHs and tree stem coordinates were measured and recorded. Tree cores were taken at a height of 1.3 m from target trees and were mounted, dried and sanded with progressively finer grades of sandpaper as necessary until tree rings were clearly visible. A Velmex microscope-sliding stage system (Velmex Inc., Bloomfield, NY, USA) was used to measure ring widths for the last five full growing seasons on each core. The annual radial growth of each target tree was determined by taking the mean of the five ring width measurements. The diameter of each target tree prior to the measured five growing seasons was calculated by subtracting twice the radial growth over five years from the outside bark diameter.
As a measure of soil fertility, both soil moisture and nutrient availability indices were assessed from soil pits within each stem map. Small stem maps with consistent slopes and understorey plant communities contained at least one soil pit. Larger stem maps and any stem maps with changes in slope or plant community contained more than one soil pit as needed to accurately classify the soil fertility for each target tree. Soil moisture index was assessed on a scale from 0 to 1 (0 = xeric and 1 = hygric) based on landform, aspect, slope position, depth to bedrock, water-table fluctuations and depth, soil texture and coarse fragment content according to the B.C. Biogeoclimatic Classification System soil moisture regime key (Banner et al. 1993). Soil nutrient index was assessed on a scale from 0 to 1 (0 = very poor and 1 = very rich) based on slope position, depth to bedrock, soil texture, coarse fragment content and type, pH, presence and depth of eluviation in the A horizon, soil colour and humus form according to the B.C. Biogeoclimatic Classification System soil nutrient regime table (Banner et al. 1993). This classification has been shown to define strong correlated soil moisture and nutrient availability gradients. From poor sites to very rich sites, there is a linear increase of more than 200% in gravimetric soil moisture, available N and exchangeable cations and a 170% increase in asymptotic stand height (Kranabetter, Dawson & Dunn 2007; Kranabetter & Simard 2008).
We began our analysis on competitive effects across soil fertility gradients by building on our previous work and that of our colleagues in tree neighbourhood dynamics in mesic forests (e.g. Uriarte et al. 2004; Canham et al. 2006; Coates, Canham & LePage 2009). Model 1 (full function in Table 2) contained the principal components found to be most important for predicting tree growth in previous work and for sub-boreal spruce forests (see Table S1 in Appendix S1 of Supporting Information):
- (eqn 1)
Table 2. Tested model functional forms, parameters, and corresponding hypotheses using variables target tree diameter (dbh), soil fertility (SF; tested with soil nutrients and soil moisture separately) and neighbour tree diameters (DBH), species and distances to predict annual radial growth at breast height (1.3 m)
|Model No.||Functional form||Parameters||Hypothesis tested|
|1|| || |
MaxGrowth: maximum potential radial growth (mm)
Xb: width of growth peak and slope of the tail
A: shape of the response to light competition
C: shape of the response to overall crowding
Xo: dbh at which peak growth occurs
NCI: Σ Σ λi × (DBHi α/DISTANCEi β)
α: shape of the neighbour size effect
β: shape of the neighbour distance effect
λi: magnitude of the competitive effect of each species (i)
|Tree growth rates do not change in response to soil fertility either directly or through effects on competitive relationships|
|2|| ||N: shape of the change in MaxGrowth with SF||Growth rates respond directly to soil fertility, but do not respond to soil fertility effects on competitive relationships.|
|3|| ||m: modifier of the SF effect on A (shape of the response to light competition)||Growth rates respond directly to soil fertility. Growth responses to light competition also change with soil fertility|
|4|| ||o: modifier of the SF effect on C (shape of the response to overall crowding)||Growth rates respond directly to soil fertility. Growth responses to overall crowding also change with soil fertility|
|5|| || ||Growth rates respond directly to soil fertility. Growth responses to light and to overall crowding also change with soil fertility|
|6|| || |
μ: modifier of the SF effect on aspen competition
ω: modifier of the SF effect on spruce competition
θ: modifier of the SF effect on pine competition
υ: modifier of the SF effect on fir competition
|Growth rates respond directly to soil fertility. Species-specific neighbour effects on growth rates also change with soil fertility|
|7|| || ||Growth rates respond directly to soil fertility. Species-specific neighbour effects on growth rates also change with soil fertility, as do growth responses to overall crowding|
|8|| || |
x: modifier of the SF effect on α (shape of the neighbour size effect)
v: modifier of the SF effect on β (shape of the neighbour distance effect)
|Growth rates respond directly to soil fertility. The crowding effects of neighbouring tree size and distance on growth rates also change with soil fertility|
|9|| || ||Growth rates respond directly to soil fertility. The crowding effects of neighbouring tree size and distance on growth rates also change with soil fertility, as do growth responses to overall crowding|
MaxGrowth was the maximum potential growth rate experienced by a hypothetical ‘free-growing’ tree, which was multiplied by growth modifier functions representing the growth–tree size relationship, the effect of light competition and the effect of crowding (all remaining effects of neighbouring trees after accounting for shading; Coates, Canham & LePage 2009).
A lognormal function represented the change in growth rate with tree size in model 1. In this function, X0 determined the DBH (of the target tree) at which peak growth occurred, and Xb determined peak width and tail slope:
- (eqn 2)
To simplify the interpretation of soil fertility effects on competition, X0 and Xb values were set a priori from parameter estimates of trees on mesic and rich sites using the full model (without γ) from Coates, Canham & LePage (2009). Parameter estimates were 20, 13, 10 and 5.8 (for X0) and 1.5, 1.1, 0.9 and 1.5 (for Xb) for subalpine fir, interior spruce, lodgepole pine and aspen, respectively (data not shown)
The light competition effect in model 1 was a power function forced to go through the origin and (1, 1) that had the flexibility to represent an asymptotic curve if the estimated parameter A < 1, an exponential curve if A > 1 or a linear relationship if A = 1 (Sit & Poulin-Costello 1994):
- (eqn 3)
where Light was the proportion of above canopy light reaching the target tree as determined by a canopy tree shading model (described by Canham, LePage & Coates 2004). Briefly, the canopy tree shading model represents neighbouring tree crowns as opaque two-dimensional billboards that block light (incident, seasonal total photosynthetic photon flux density) from reaching the target tree. Tested in interior cedar hemlock forests also containing all of our study species, this model predicted understorey light levels with an R2 of 80% (Canham, LePage & Coates 2004).
The effect of crowding on tree growth incorporated all direct and indirect interactions among trees other than shading. These interactions may include negative effects on growth like water and nutrient pre-emption and positive or negative effects on growth that are less well understood like shared mycorrhizal networks, nutrient enhancement by litterfall or disease transmission. The crowding effect function had the same form as in Coates, Canham & LePage (2009) where the net degree of crowding overall was represented by a Neighbourhood Competition Index (NCI). In the crowding effect function, the response of a target tree to a given NCI was adjusted by the estimated parameter C in a negative exponential function:
- (eqn 4)
In the NCI, the crowding effects of neighbours were a net measurement of positive and negative interactions that had the possibility of changing according to neighbour number, size, species and distance:
- (eqn 5)
Neighbour effects were assumed to decrease with increasing distance between trees and increase with increasing diameter of the neighbour tree. The estimated parameter α determined the shape of the size effect, and the parameter β determined the shape of the distance effect. A species-specific competition index parameter (λi) ranging between 0 and 1 adjusted the crowding effect of each neighbour tree depending on its species. The total crowding effect was the summed effect of all neighbours (j = 1, …, n) of all species (i = 1, …, s) within an 8 m radius of the target tree. Four species-specific competition indexes were included in our models: λfir for subalpine fir neighbours, λspruce for interior spruce neighbours, λpine for lodgepole pine neighbours and λaspen for trembling aspen neighbours. Neighbour trees of other species were few and were included in the above competition indexes: western hemlock (Tsuga heterophylla [Raf.] Sarg.) were grouped with subalpine fir, black spruce (Picea mariana [Mill.] Britton, Sterns & Poggenburg) were grouped with interior spruce and paper birch (Betula papyrifera Marsh.), and black cottonwood (Populus balsamifera subsp. trichocarpa [Torr. & A. Gray] Brayshaw) were grouped with aspen.
To determine how soil fertility interacts with competition to affect tree growth rates, we then developed a series of nested models that corresponded with our alternative hypotheses (Table 2). In the simplest alternative model (model 2), soil fertility directly affected tree radial growth rates, but did not affect any neighbourhood competitive dynamics. In model 2, the soil fertility effect was multiplied by MaxGrowth and the growth modifier functions in (eqn 1) to account for the well-understood decline in growth rates with decreasing soil fertility (Table 2):
- (eqn 6)
We also took advantage of the flexibility of a power function for the soil fertility effect to allow asymptotic, exponential or linear relationships between soil fertility (SF) and growth rates:
- (eqn 7)
The alternative models 3–9 were built from model 2. They allowed soil fertility to affect growth directly as in model 2 and also indirectly by modifying tree competition via shading, crowding, intra- and interspecific effects and neighbour distance and size effects. To accomplish this analysis, the parameter estimates for A, C, α, β, λfir, λspruce, λpine and λaspen were allowed to vary with soil fertility using the soil fertility effect function ((eqn 7)) as a multiplier (Table 2). In models 3 and 4, parameters A (shape of the response to light competition) and C (shape of the response to overall crowding), respectively, varied with soil fertility, and in model 5, both A and C did. In model 6, λfir, λspruce, λpine and λaspen (species-specific competitive effects) varied with soil fertility, and in model 7, C was allowed to vary with the λs. In Model 8, α (shape of the neighbour size effect) and β (shape of the neighbour distance effect) varied with soil fertility, and in model 9, C was allowed to vary with α and β (Table 2). We tested separate soil nutrient and soil moisture availability indices as the soil fertility measurement in our models.