Forest Ecology and Management 202 (2004) 301–312 www.elsevier.com/locate/foreco
Selecting a small tree height growth model for mixed-species stands in the southern interior of British Columbia, Canada Ce´line Boisvenuea,*, Hailemariam Temesgenb,1, Peter Marshallc,2 a
College of Forestry and Conservation, University of Montana, Missoula, MT 59812, USA b Oregon State University, 280 Peavy Hall, Corvallis, OR 97331-5703, USA c Department of Forest Resources Mgmt., University of British Columbia, 2424 Main Mall, Vancouver, BC, Canada V6T 1Z4 Received 5 December 2003; received in revised form 23 July 2004; accepted 23 July 2004
Abstract Several small tree height growth models were compared for their fit to data from major tree species in the southern interior of British Columbia (BC), Canada. Using data collected in the interior cedar hemlock (ICH) and interior Douglas-fir (IDF) zones of the BC Biogeoclimatic Ecosystem Classification (BEC) system, small tree height growth was estimated as a function of tree size, competition measure, and site variables using various model forms and independent variable combinations. A non-linear model using transformations and combinations of slope, aspect, current height, and basal area of larger trees was determined to best predict small tree height growth of both coniferous and hardwoods. This model will be subsequently incorporated into the ongoing modelling effort to adapt a version of the US-based Forest Vegetation Simulator (FVS) for BC (PrognosisBC). # 2004 Elsevier B.V. All rights reserved. Keywords: Growth and yield; Model selection; Height prediction; Regression
1. Introduction Accurate growth and yield predictions of trees and forests are important metrics for facilitating sustainable management of forest resources. Height growth of trees is an essential feature of most growth and yield models, which are a principal tool of forest manage* Corresponding author. Tel.: +1 406 243 4325; fax: +1 406 243 6656. E-mail address:
[email protected] (C. Boisvenue),
[email protected] (H. Temesgen),
[email protected] (P. Marshall). 1 Tel.: +1 541 737 8549; fax: +1 541 737 3049. 2 Tel.: +1 604 822 4918; fax: +1 604 822 8645.
ment planning. The wide use of height growth as a driving variable in growth and yield predictions can be ascribed to the relative independence of height growth from competition, the relative ease of height measurement, and the close relationship between tree height and volume (Lanner, 1985). The time required for a tree to reach a given height varies with its current height, species, site quality, geographic location, site attributes (Carmean, 1975; Oliver and Larson, 1996), competition (Cobb et al., 1993), stand structure, and establishment factors (Oliver and Larson, 1996). The impact of these factors has been examined by a number of authors. For example, Peterson and Peterson (1994) found that
0378-1127/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2004.07.037
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most of the variation in height growth in harsh environments was due to species differentiation, with site and aspect as contributing factors. Kneeshaw and Bergeron (1996) found that some species have positive impacts on each other’s growth. Individual tree height growth partly changes the stand structure and in turn the stand structure is a determinant of individual tree height growth. Hence, attributing species height differences or height growth patterns to site quality, competition, genetics, age, stand dynamics, or other factors is a difficult process. Models of small tree height growth, often required following various forms of partial cutting, generally attempt to capture a portion of this complexity. Many of the height growth models commonly used in North America (e.g., Curtis, 1967; Monserud and Ek, 1977; Dolph, 1988; Lappi and Bailey, 1988; Huang and Titus, 1992, Huang and Titus, 1994; Nigh and Sit, 1996) were built from stem analysis databases and fitted using least squares (LS) regression techniques. These models offer reasonable predictions and are widely accepted. Generally, the variability in height (or height growth) increases with increasing tree size. Unless weighted LS regression methods are used, large size tree observations will dominate the overall fit, as the range of variation for large sized trees will be greater than the range for smaller sized trees. Hence, height growth curves that do not account for differences in variances are not precise for small tree predictions. Moreover, most of these models were developed using even-aged single species data, and provide poor fits for young tree height growth patterns in mixed-species or multi-cohort stands. The greater impact of large trees in fitting height growth models has been mainly addressed by fitting equations for large and small trees separately (e.g., Nigh, 1999). In the United States, the growth and yield models ORGANON (Hann et al., 1993) and CACTOS (Wensel et al., 1986), linked with SYSTUM-1 (Ritchie and Powers, 1993), use a separate linear regression model for small tree height growth. The Forest Vegetation Simulator (FVS) model, formerly referred to as Prognosis (Stage, 1973), also simulates small and large tree growth using separate equations. The objective of this paper is to find a regression model that adequately predicts tree height of small trees in complex stands in the southeastern interior of British Colombia (BC), Canada. A number of models
for predicting small tree height growth are evaluated. The selected model will be used as part of a comprehensive project to calibrate FVS for zonelevel growth and yield predictions in complex stands in southern BC (PrognosisBC).
2. Data Data were collected in the Interior Cedar Hemlock (ICH) and Interior Douglas-Fir (IDF) Biogeoclimatic Ecosystem Classification (BEC) zones of BC (Braumandal and Curran, 1992). The ICH and IDF zones are the dominant and most productive zones in the managed forests of southeastern BC. Specific subzone variants sampled were: (1) the ICH moist warm subzone, variant 2 (ICHmw2) (Boisvenue, 2000); (2) the ICH moist cool subzone, variant 1 (ICHmk1) (DeLong, 2001); (3) the IDF dry cool subzone, variants 1, 2, and 3 (IDFdk1, IDFdk2, IDFdk3); and (4) the IDF dry moist subzone, variant 2 (IDFdm2). Accessible stands were stratified by BEC site series, site preparation method, regeneration method, over-story retention, aspect, and elevation. Most stands were partially cut between 2 and 20 years prior to sampling to a range of residual basal areas, although, some of the stands were undisturbed and others were clearcut. Stands were randomly selected within each stratum and plots were systematically located with a random start within each selected stand. The number of plots per stand depended on the size and variability of the stand. Each stand had a minimum of two plots. Additional plots were established if the stand was variable in terms of structure and stratification criteria, and if its size and shape permitted the establishment of more plots. No more than seven plots were located in any stand. Small trees (defined as trees less than 7.5 cm diameter at breast height (dbh) with a measurable dbh at re-measurement) in the ICH subzone variants were sampled using a fixed area plot of 3.99 m radius (0.005 ha), in which species, dbhs, and heights of all small trees were recorded. Small trees in the IDF subzone variants were sampled using a fixed area plot of 11.28 m radius (0.04 ha). Two trees per species in all plots were sub-sampled for age and height increment. Each tree selected in the sub-sample was felled for measurement of total age, and the last complete 5-year
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height growth increment was recorded. For determinant species, such as Interior Douglas-fir (Pseudotsuga menziesii var. glauca (Beissn.) Franco) and lodgepole pine (Pinus contorta Dougl.), whorls were counted to ascertain 5-year height growth. For non-determinant species, such as western redcedar (Thuya plicata Donn) and western hemlock (Tsuga heterophylla (Raf.) Sarg.), trees were sectioned until the 5-year height increment period could be established and measured. Site and stand information were collected at each plot location. This included: BEC system site series, slope (%), aspect (degrees), elevation (m), postharvest retention level (basal area in m2/ha and species), stand condition observations, and any other relevant site attribute. Large trees were sampled with a fixed area plot of 11.28 m in radius (0.04 ha). Information collected for larger trees was only used in this project for identifying residual basal area per hectare (ba/ha) and crown competition factor (CCF). The data set was comprised of 2895 small trees, representing 14 species. 3. Analytical methods Three linear and two non-linear model forms for small tree height growth predictions were selected for comparison. Dependent variables in these models included competition measures, tree size (e.g., dbh, height, age), site (e.g., elevation, slope, aspect), and stand density variables such as crown competition factor, residual basal area and their transformations. The selected models were: LNðHTGÞ ¼ b0 þ b1 SL COSðASPÞ b2 SL SINðASPÞ b3 SL þ b4 LNðHTÞ þ b5 CCF BAL þ b6 þ e1 100
(1)
HTG ¼ b0 þ b1 SL COSðASPÞ b2 SL SINðASPÞ b3 SL þ b4 LNðHTÞ þ b5 CCF þ b6 BAL þ e2 100
(2)
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HTG ¼ b0 þ b1 SL COSðASPÞ b2 SL SINðASPÞ b3 SL þ b4 HT þ b5 HT2 þ b6 LNðCCFÞ þ b7 LNðBALÞ þ e3 HTG ¼ EXP b0 þ b1 SL COSðASPÞ þ b2 SL SINðASPÞ þ b3 SL þ b4 HT þ b5 LNðHTÞ þ b6 CCF BAL þ b7 þ e4 100
(3)
(4)
HTG ¼ EXP½b0 þ b1 SL COSðASPÞ b2 SL SINðASPÞ b3 SL þ b4 HT þ b5 HT2 þ b6 CCF þ b7 LNðBALÞ þ e5
(5)
where HTG is the 5-year tree height increment (in m), SL is stand slope ratio (%/100), COS(ASP) is the cosine of stand aspect (in degrees), SIN(ASP) is the sine of stand aspect (in degrees), HT is tree height (in m), CCF is crown competition factor, BAL is the basal area in larger trees (in m2/h), LN is the natural logarithm, b0–b7 are regression parameters that vary by tree species and zone, EXP is the exponential function where the Naperian constant (i.e., ffi 2.718) is elevated to the power in the following brackets, and e1–e5 represent the error terms for each model. The variables in all five equations are intended to represent the basic biological processes of tree height growth. The slope and aspect variables and their combinations, in the mountainous terrain for southeastern BC, are surrogates for the amount of incident solar energy in the system. Solar energy may have both a positive and/or a negative effect on height growth depending on other limiting factors, and on the time of year. For example, south aspects may benefit from increased sunlight during the early part of the growing season when water is abundant, but it may cause stomatal closure later in the growing season when water is limiting. The tree’s current height represents the photosynthetic material and vertical structure of the tree, and is anticipated to have a positive effect as photosynthetic material and vertical
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structure, or in this case current height, represent the tree’s growth engine. The BEC zones specify site conditions (moisture and site nutrients) and species brings genetics into the equation; either of these factors may have positive or negative effects on height growth. Finally, CCF and BAL are indices of competition and light interception and are expected to have negative effects on height growth. The selection of these specific model forms is based on two main sources. In a study evaluating the small tree height growth sub-model of the northern Idaho FVS variant for its applicability to the ICHmw2 subzone, Boisvenue (2000) found superior fits with different sets of predictor variables than those used in the FVS northern Idaho sub-model. Hence, despite the adoption of the FVS framework, the northern Idaho FVS variant small tree height growth sub-model was not included in this study. Eq. (2) differs from Eq. (1) only in that height growth was used as dependent variable instead of the natural logarithm of height growth. Comparing diagnostic statistics (R2a or I 2a and standard errors of estimates (S.E.E.)), Boisvenue (2000) found that Eq. (2) better fit the ICHmw2 subzone data for tolerant and intolerant species than both Eq. (1), and the FVS northern Idaho variant model form for small tree height growth. Eq. (1) provided a better fit for intermediate shade tolerant species than either Eq. (2) or the FVS model. After comparing nine small tree height growth equations for the IDF BEC zone, Lencar (2002) found that Eqs. (3) and (4) provided better fit statistics (R2a or I2 and S.E.E.) than the other equations tested. To incorporate optimal or maximum initial height and CCF effects on small tree height growth, the quadratic height and CCF terms were included in Eq. (5), as a variant of Eq. (3). Parameters in Eqs. (1)–(3) were estimated using ordinary least squares regression (OLS). Eqs. (4) and (5) were fitted using non-linear least squares and the Marquardt iterative method for parameter convergence (Statistical Analysis System (SAS) v.6.0, SAS Institute Inc., PROC NLIN procedure). The starting value of each parameter was varied to produce several model runs from which a global minimum residual mean square could be determined. Initial approximations for each parameter were obtained from linear transformation of the models where possible. Eqs. (1)– (5) were fit separately for each BEC zone (ICH and
IDF) and each species, as well as for species groupings within each zone. Specifies groupings stem from the theory that certain species are thought to have similar developmental patterns. Ashton (1992) used a similar approach where height growth patterns, together with information from shade-tolerance tables (Baker, 1953), were used to place species into groupings with similar developmental characteristics. Favrichon (1998) chose to separate trees into groups based on growth behavior, with reference to shade tolerance and maximum potential size, to model early height growth in mixed-tropical forests. Based on field observations, we speculate that height growth patterns differ among with shade-tolerance levels in the ICH and IDF zones (Cameron, 1996a,b; Boisvenue, 2000). Coniferous tree species were therefore placed into three shadetolerance groupings (shade tolerant, intermediate, and intolerant) where: (1) subalpine fir (Bl – Abies lasiocarpa), western red cedar (Cw – Thuja plicata), western hemlock (Hw – Tsuga heterophylla), and interior spruce (Sx – Picea glauca X engelmannii) formed the tolerant group; (2) interior Douglas fir (Fd – Pseudotsuga menziesii) and western white pine (Pw – Pinus monticola) formed the intermediate group; and (3) western larch (Lw – Larix occidentallis), lodgepole pine (Pl – Pinus contorta), and ponderosa pine (Py – Pinus ponderosa) formed the intolerant group. Other species in these stands are mostly intolerant disturbance species with growth patterns differing from the intolerant conifer species grouping (Braumandal and Curran, 1992). Hence, trembling aspen (At – Populus tremuloides), black cottonwood (Ac – Populus trichocarpa), white birch (Ep – Betula papyrifera), Douglas maple (Mp – Acer gladrum var. douglasii), and Rocky mountain juniper (Rj – Juniperus scopulorum) were combined under the designation ‘‘hardwoods’’, although Rocky mountain juniper is a conifer. Three of the 22 species/BEC zone combinations were sparsely represented in the small tree data set: Ac/ICH, Bl/IDF, and Cw/IDF with 12, 13, and 5 trees, respectively. To obtain stable parameter estimates, equations were only fit for species with more than 20 sample trees in a given zone. The predictive abilities of the models were evaluated by comparing residuals against the predicted 5year height growth, and calculating standard errors of
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estimates, adjusted coefficients of determination (R2a or I 2a ), and asymptotic 95% confidence intervals. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SSRES S:E:E: ¼ n ðn 1Þ SSRES R2a or I 2a ¼ 1 ðn k 1Þ SSTOT where R2a is adjusted coefficient of determination, n is number of trees, k is number of independent variables in the model, SSRES is the sum of squares of the residuals, SSTOT is the sum of squares total, and I 2a is used to denote back-transformed values from transformed variables for equal comparisons to R2a . The assumptions of normality and independence were checked using residual plots and the Shapiro– Wilks (Shapiro and Wilks, 1965) normality test. After
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considering how well the models fit by examining R2a , S.E.E., and residual plots, one model form was selected for tree height growth predictions in the complex stands of the southern interior of BC. All statistical calculations were performed with the statistical package SAS (SAS version 6.0, SAS Institute Inc.) and in Microsoft Excel (1997 version, Microsoft Corporation). Significance levels were set at 0.05 unless otherwise indicated.
4. Results The measured 5-year height increments ranged from 0.02 to 3.91 m, with standard deviations ranging from 0.18 to 0.75 m; measured small tree heights ranged from 0.32 to 13.20 m with standard deviations ranging from 0.52 to 1.91 m (Table 1).
Table 1 Number of trees and minimum (Min.), mean, maximum (Max.), and standard deviation (S.D.) of small tree height (m) and 5-year height growth by species and zone Zone
Species*
Min.
Mean
Max.
S.D.
Min.
Mean
Max.
S.D.
ICH
Ac At Ep Md Fd Pw Lw Pl Bl Cw Hw Sx
12 33 51 43 93 31 37 105 40 141 82 79
3.04 2.14 2.38 0.32 1.93 1.60 2.48 1.38 0.46 0.34 2.05 0.34
4.23 4.85 4.65 4.55 3.56 3.32 4.07 2.92 2.58 3.31 3.95 2.95
5.81 8.69 9.60 7.47 10.42 6.40 7.06 6.10 5.03 6.80 6.80 5.28
0.92 1.50 1.37 1.41 1.55 1.17 1.10 0.84 1.09 1.10 1.10 0.84
0.83 0.39 0.12 0.15 0.06 0.28 0.32 0.56 0.04 0.03 0.06 0.18
1.38 2.01 2.05 1.10 1.42 1.25 1.69 1.75 1.04 0.52 0.77 1.20
1.84 3.45 3.58 2.06 2.94 2.92 3.07 3.91 1.99 2.48 2.60 2.14
0.32 0.71 0.68 0.43 0.71 0.75 0.59 0.59 0.41 0.45 0.57 0.45
IDF
At Ep Rj Fd Lw Py Pl Bl Cw Sx
57 32 23 1285 44 29 407 13 5 253
2.27 2.52 2.16 1.61 2.21 1.49 1.57 2.00 3.25 1.52
3.96 4.22 3.08 4.20 4.00 2.78 3.63 3.32 4.17 3.70
8.60 8.60 4.08 11.50 7.87 3.94 13.20 6.00 5.38 10.70
1.36 1.69 0.52 1.66 1.41 0.70 1.91 1.31 0.92 1.46
0.69 0.43 0.14 0.05 0.40 0.27 0.02 0.13 0.30 0.07
1.46 1.46 0.45 0.69 1.87 0.97 1.34 0.58 0.62 1.00
2.63 2.57 0.86 2.77 3.11 1.96 3.17 2.14 0.83 2.77
0.40 0.52 0.18 0.54 0.74 0.45 0.56 0.65 0.20 0.57
*
Number of trees
Small tree height (m)
5-Year height growth (m)
The codes correspond to the following species: Ac (Populus trichocarpa – black cottonwood); At (Populus tremuloides – trembling aspen); Bl (Abies lasiocarpa – subalpine fir); Cw (Thuja plicata – western redcedar); Ep (Betula papyrifera – white birch); Fd (Pseudotsuga menziesii var. glauca – interior Douglas-fir); Hw (Tsuga heterophylla – western hemlock); Lw (Larix occidentalis – western larch); Md (Acer gladrum var. douglasii – Douglas maple); Pl (Pinus contorta – lodgepole pine); Pw (Pinus monticola – western white pine); Py (Pinus ponderosa – ponderosa pine); Rj (Juniperus scopulorum – Rocky mountain juniper); and Sx (Picea engelmannii – interior spruce).
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Table 2 Coefficient of determination (R2a or I 2a ) values, with the highest values bolded and standard error of estimates (S.E.E.), with the lowest values bolded, by species, species group, and BEC zone Zone
Species* or species group
ICH
At Ep Md Hardwood (At+Ac+Ep+Md) Fd Pw Intermediate (Fd+Pw) Lw Pl Intolerant (Lw+Pl) Bl Cw Hw Sx Tolerant (Bl+Cw+Hw+Sx)
IDF
At Ep Rj Hardwood (At+Ep+Rj) Fd Intermediate (Fd) Lw Py Pl Intolerant (Lw+Pl+Py) Sx Tolerant (Bl+Cw+Sx)
N
Adjusted R2 values model
Standard error estimate (m) model 1
2
3
4
5
1
2
3
4
5
33 51 43 139 93 31 124 37 105 142 40 141 82 79 342
0.32 0.21 0.34 0.48 0.22 0.34 0.31 0.42 0.25 0.36 0.24 0.26 0.29 0.31 0.31
0.42 0.28 0.37 0.57 0.31 0.48 0.39 0.46 0.32 0.44 0.31 0.44 0.52 0.33 0.43
0.43 0.81 0.35 0.56 0.35 0.44 0.42 0.45 0.31 0.44 0.28 0.41 0.56 0.33 0.42
0.28 0.66 0.32 0.46 0.20 0.28 0.28 0.41 0.24 0.36 0.21 0.23 0.28 0.30 0.30
0.30 0.67 0.32 0.45 0.19 0.30 0.26 0.41 0.24 0.36 0.21 0.23 0.29 0.30 0.30
0.80 0.82 0.36 0.57 0.90 0.79 0.82 0.49 0.83 0.62 0.66 0.68 0.74 0.53 0.68
0.65 0.81 0.26 0.39 0.82 0.59 0.70 0.39 0.71 0.46 0.44 0.06 0.17 0.45 0.39
0.62
0.82
0.30 0.41 0.75 0.65 0.67 0.40 0.72 0.44 0.53 0.16 0.01 0.47 0.41
0.84 0.82 0.42 0.61 0.92 0.85 0.85 0.51 0.84 0.63 0.73 0.74 0.76 0.56 0.69
0.41 0.61 0.93 0.83 0.87 0.51 0.83 0.63 0.73 0.74 0.74 0.55 0.70
57 32 23 112 1285 1285 44 29 407 480 253 271
0.38 0.41 0.06 0.43 0.49 0.49 0.39 0.34 0.52 0.53 0.52 0.52
0.37 0.41 0.09 0.51 0.49 0.49 0.48 0.35 0.55 0.56 0.51 0.50
0.39 0.41 0.10 0.52 0.48 0.48 0.40 0.33 0.54 0.56 0.50 0.50
0.37 0.38 0.04 0.38 0.45 0.45 0.33 0.32 0.47 0.48 0.47 0.47
0.38 0.37 0.04 0.37 0.45 0.45 0.33 0.30 0.47 0.48 0.48 0.48
0.08 0.38 0.90 0.44 0.18 0.18 0.73 0.41 0.14 0.22 0.16 0.19
0.12 0.39 0.76 0.21 0.20 0.20 0.59 0.38 0.03 0.11 0.21 0.24
0.04 0.34 0.70 0.16 0.21 0.21 0.70 0.42 0.06 0.12 0.22 0.25
0.10 0.45 0.95 0.56 0.31 0.31 0.79 0.48 0.30 0.36 0.30 0.32
0.06 0.48 0.94 0.57 0.30 0.30 0.79 0.54 0.30 0.35 0.27 0.29
* The codes correspond to the following species: Ac (Populus trichocarpa – black cottonwood); At (Populus tremuloides – trembling aspen); Bl (Abies lasiocarpa – subalpine fir); Cw (Thuja plicata – western redcedar); Ep (Betula papyrifera – white birch); Fd (Pseudotsuga menziesii var. glauca – interior Douglas-fir); Hw (Tsuga heterophylla – western hemlock); Lw (Larix occidentalis – western larch); Md (Acer gladrum var. douglasii – Douglas maple); Pl (Pinus contorta – lodgepole pine); Pw (Pinus monticola – western white pine); Py (Pinus ponderosa – ponderosa pine); Rj (Juniperus scopulorum – Rocky mountain juniper); and Sx (Picea glauca X engelmannii – interior spruce).
Eq. (2) had the highest S.E.E. and Eq. (3) had the lowest R2a values of the height growth models examined, while Eq. (4) had the lowest S.E.E. and highest R2a values (Table 2). In general, Eqs. (1)–(3) had higher S.E.E. and lower R2a or I 2a than Eqs. (4) and (5). Eqs. (4) and (5) behaved similarly; R2a or I 2a values for Eq. (4) ranged from 0.10 to 0.95 and the S.E.E. ranged from 0.039 to 0.480 m, while R2a or I 2a values for Eq. (5) varied between 0.308 and 0.958, and S.E.E. values varied between 0.043 and 0.484 m. The predictive abilities of models 2 and 3 were poor for lodgepole pine and trembling aspen in the IDF BEC zone, with low R2a values. Similar poor results were
also observed for western red cedar and western hemlock in the ICH BEC zone. Based on plotted residuals and fit statistics, Eq. (4) was selected for use in the southern interior of BC. The confidence intervals for some parameters of Eq. (4) included zero for some species; the equation was therefore refitted for each species and zone using only significant variables. For At, Bl, Cw, EP, and Hw in the ICH and Rj in the IDF BEC zones, most of the individual tree variables were not significant at alpha = 0.05. In order to vary height growth by initial tree height for operational use of the model, either height or LN(height) was included in the model when they
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were significant at alpha level of 0.1. The species/zone combinations where alpha = 0.1 was used are given in bold in Table 3. The parameter estimates for the refitted Eq. (4) varied widely by species and zone (Table 3). The S.E.E. was generally small, and variances were approximately homogenous over the full range of predicted values, as shown for interior Douglas-fir in the IDF in Fig. 1(a). For most tree species, the residual plots also indicated that 5-year height growth was predicted well across the range of small tree heights, as shown for western hemlock in Fig. 1(b). However, the performance of the model was poor for white birch alone (Fig. 2). To compare the performance of species groupings to the individual species they contain, adjusted R2 values were calculated, since the number of observations in the data groupings differed. Generally, the species groupings had lower adjusted R2 values than the individual species they contain; hence, they did not explain more of the variation present in the data than the individual species models. R2a values for Eq. (4) were much lower for species groupings when compared to individual species except for Cw, Hw, and Mp. We speculate that these lower values maybe expressing the tendencies for Hw and Cw to be present in the understory pre-disturbance (advance regeneration). This point as well as the relevance of the species groupings is further discussed in the following section. Douglas maple is a marginal species in these BEC zones and exhibits a wide range of height growth; hence, no equation is likely to yield high R2a values. The higher R2a value of the hardwood grouping is due to the higher R2a of Ep and Ac, when the species are grouped. Coefficient signs seem to generally correspond to the biological reasoning depicted earlier. Incident energy, represented by variable combinations of slope and aspect, had both a positive and negative impact on small tree height growth, depending on aspect and site moisture levels. The initial height had mostly positive coefficients corresponding to the positive contribution to height growth of the initial height, and hence the photosynthetic capability of an individual tree. Finally, competition, represented by CCF and BAL, had negative coefficients with the exception of those for lodgepole pines in the ICH zone (Table 3).
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5. Discussion The main hurdle for developing a good early height growth model is that it requires an excellent and extensive data set, which involves sampling the full range of important factors (Monserud, 1987). In irregular stands (and most ecosystems), this is difficult to achieve. Species in these stands often respond differently to a given set of environmental factors. Eq. (4), a non-linear model using transformations and combinations of slope, aspect, current height, and basal area of large trees was determined to predict small tree height growth of both coniferous and hardwood tree species reasonably well (low S.E.E. and high R2a ) for most species. However, individual tree growth varies with the species mixture and is influenced by the structure of the residual stand. Partial cutting on a large scale in the southern interior of BC is a relatively recent phenomenon and many of the sample trees did not adequately reflect the full range of small tree sizes (32 cm in height to 7.5 cm in dbh); there were many more trees towards the smaller end of this range. In addition, partial cutting systems are harder to implement on steep slopes; consequently, most of the sampled plots were on mid-slope (usually mesic) sites. The species that would have captured growing space on wetter or drier sites were, more than likely, not well represented in the data set. Hence, the available data did not represent the full range of small tree growing conditions. Another possible confounding factor is that a substantial proportion of the height growth observations in the data were likely obtained from advance regeneration (regeneration established prior to the most recent partial cut). It may be beneficial to estimate the height growth of small trees associated with advance regeneration separately from that of trees that regenerated post-disturbance (subsequent regeneration). In certain species, advance regeneration can have different growth patterns from subsequent regeneration, exhibiting periodically higher and lower rates of height growth, as they are released by temporary overstory gaps and later are suppressed with gap closure. The data used in this study did not allow for separating trees that regenerated subsequent to disturbance and advance regeneration. Early height growth obviously represents only a portion of the overall height growth patterns of trees.
308
Table 3 Parameter estimates obtained for the re-fit model 4 by species, species group, and BEC zone Zone
ICH
At Ep Md Hardwood (At+Ac+Ep+Md) Fd Pw Intermediate (Fd+Pw) Lw Pl Intolerant (Lw+Pl) Bl Cw Hw Sx Tolerant (Bl+Hw+Sx) At Ep Rj Hardwood (At + Ac + Ep + Md + Rj) Fd Intermediate (Fd) Lw Py Pl Intolerant (Lw + Pl + Py) Sx Tolerant (Bl + Cw + Sx)
No. of trees
Parameter estimates Intercept
SL*COS(ASP)
33 51 43 139
0.352240 0.782481 0.293391 0.23844
93 31 124
0.803509 0.024924 0.6368518
37 105 142
0.002845 0.283474 0.3236232
40 141 82 79 342
0.217737 0.314948 0.216672 0.364175 0.0878875
57 32 23 112
0.158014 0.592163 0.878816 0.2041308
1285 1285 44 29 407 480
0.573832 0.5738321 0.022159 0.223303 0.038830 0.0998574
0.004423 0.004423421
253 271
1.061167 0.9885648
0.010205 0.011543749
S.E.E. SL*SIN(ASP)
0.008889
SL 0.259531 0.516756
HT
LN(HT)
0.407467 1.011608
0.512144 0.5121443
0.003946
1.103796 1.182421
0.00243
0.564863 0.163740 0.386893543
2.247773778
0.0076175 0.004741
0.40686086
0.579568 0.751002 1.89791257
2.901805
0.009147
0.520901
0.416015 0.416014668 0.392524
0.313824 2.523730 0.302126544 0.266120 2.532172 0.374470 0.520337043
0.284172 0.277808048
1.873005 1.873005401 1.932391 0.635346 1.177024 1.380037667
0.602296 0.562750419
2.920551 2.757015881
4.935718 1.0014793
1.553055 0.00182229 2.729545
0.392953 0.076995 0.670848
2.606677
0.41 0.66 0.42 0.71
0.513303
0.616953
0.011413
BAL/100
0.021220 0.136764 0.26785
0.0191203
CCF
0.011216 0.004841 6.088652 0.0081857 1.295102
0.0181535
0.005883 0.0058833
2.035739 7.53696
0.48 0.52 0.51 0.54 0.44 0.51 0.31 0.42 0.50 0.31 0.43 0.37 0.45 0.16 0.48
1.194987 1.1949869 5.571479 4.483499 1.863450
0.47 0.47 0.36 0.34 0.53 0.52
2.630196 2.7702553
0.49 0.49
0.0049829
Values in bold indicate that estimated parameter was significantly different at alpha = 0.1 probability level. * The codes correspond to the following species: Ac (Populus trichocarpa –black cottonwood); At (Populus tremuloides – rembling aspen); Bl (Abies lasiocarpa – ubalpine fir); Cw (Thuja plicata – estern redcedar); Ep (Betula papyrifera – hite birch); Fd (Pseudotsuga menziesii var. glauca – nterior Douglas-fir); Hw (Tsuga heterophylla – estern hemlock); Lw (Larix occidentalis – estern larch); Md (Acer gladrum var. douglasii – Duglas maple); Pl (Pinus contorta – lodgepole pine); Pw (Pinus monticola – western white pine); Py (Pinus ponderosa – ponderosa pine); Rj (Juniperus scopulorum – Rocky mountain juniper); and Sx (Picea glauca X engelmannii – interior spruce).
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IDF
Species* or species group
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Fig. 1. Residuals (actual – predicted) vs. predicted 5-year height growth for Douglas-fir, using Eq. (4) in the IDF BEC zone (a) and residuals (actual – predicted) vs. total height (b) for Hw, using Eq. (4) in the ICH BEC zone.
Site conditions and physiological traits still drive height growth, and most early height growth has been assumed to follow a fast or slow linear model (e.g., SYSTUM-1, Ritchie and Powers, 1993). Contrary to this assumption, which may hold for even-aged managed stands, the best performing model in this study was a non-linear model using variables representing light, drainage, photosynthetic capacity, and competition, per species (representing genetics) and zone (representing moisture and nutrients). This suggests that non-linear relationships may better represent small tree height growth in mixed-species variable structure stands. The northern Idaho variant of FVS uses a log-linear equation to model small tree height growth and is also used for mixed-species (conifers only) variable structure stands; however, that model did not perform well for the ICHmw2 portion of
this data set (Boisvenue, 2000). The inclusion of hardwoods may have contributed to the difference in the choice of a non-linear fit for the best performing model versus a log-linear fit. All five equations had the same representation of light and drainage (SL COS(ASP), SL SIN(ASP), and SL), but slight differences in the representation of photosynthetic capacity (combinations of HT, HT2, and LN(HT)) and competition (combinations of CCF, LN(CCF), BAL/100, and LN(BAL)). The best performing equation used both HT and LN(HT) for representing photosynthetic capability, and CCF and BAL/100 for competition representation. These variables reflect the relationship of height growth to photosynthetic capability and to competition in the multi-species variable-structure stands examined. Further research into the best representation of these
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Fig. 2. Residuals (actual – predicted) vs. predicted 5-year height growth (a) and total height (b) for paper birch, using Eq. (4) in the ICH BEC zone.
driving factors in small tree height growth would be necessary to confirm the validity of these relationships for more general applications to other multi-species variable-structure stands. One apparent problem with the choice of Eq. (4) for predicting 5-year height growth was the poor performance of the model for white birch (Table 2 and Fig. 2). However, white birch is not a dominant species in the conifer dominated ICH and IDF zones. It often occupies marginal or low productivity sites, and is often out-competed by intolerant conifer species. Hence, the poor performance of the model can be partly ascribed to the erratic growth pattern of white birch. The true factors determining site productivity are poorly understood and very difficult to measure (Curtis, 1971). Eq. (4) uses the BEC system as a surrogate to site productivity. The use of a classification system is just one method of estimating site
quality. Like all other methods, it has advantages and disadvantages (Carmean, 1975; Klinka and Carter, 1990). To date, no method seems to come close to providing perfect estimates of site productivity. Hence, all approaches may perpetuate their errors in the growth models that use them. The parameter estimates for Eq. (4) varied widely across species and BEC zones leading to the conclusion that species and site productivity variations are taken into account by Eq. (4), although sometimes confounded with other factors. The use of coniferous species groupings did not improve the fit of the equations. The appropriateness of these groupings in representing species of similar height growth patterns is therefore in question. Boisvenue (2000) used these groupings as a way to combine observations thought to have similar height growth patterns, but also because her database had
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relatively low numbers of observations per species. The extensive database used in this study did not show any improvement in combining the observations, with the exception of the hardwoods grouping. Thus, the data and analysis did not support the species groupings considered. Like most models, the height growth equations resulting from this study should be used with caution. The context in which the model is calibrated and the logical basis of the model need to be well understood by users. The data used for calibration also indicate the limitations of the model. The equations in this paper were not tested using independent data. Nevertheless, the equation selected represents an improvement over the existing equation forms and coefficients and can serve to supplement and guide silvicultural decisions in irregular stands in the ICH and IDF ecosystems of the BEC system of the province of BC.
6. Conclusion The objective of this paper was to select an early height growth equation for mixed-species multicohort stands for use in southern BC. Of the five model forms included in the analysis, a non-linear model out-performed the linear and linearized model forms that we examined. Pooling of coniferous species into groups based on shade tolerance did not improve the performance of the selected model. Increasing the amount of data involved in fitting this model should remedy many of the errors and biases discussed. The selected equation was incorporated into PrognosisBC as a generic (zone-level) small tree height growth model for the ICH and IDF zones. The new set of coefficients ensures reasonable small tree height growth estimates in these zones and improves the predictive ability of the large tree height growth model in PrognosisBC. The improvement is ascribed to the different weights given for height growth estimates obtained from the small and large tree height growth models, as the height growth estimates gradually shift from the small tree to the large tree equations when the dbh falls between 5 and 25 cm. In reality, each tree has its own growth curve depending on species, site, stand structure, and where the tree sits in terms of that stand’s particular structure. It comes down to finding a suitable balance for each
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stand, within each landscape, for each region, based on each tree as an individual production unit. Thus, early height growth modelling is difficult to do well in practice despite its apparent simplicity in concept, and this study provided another step towards acceptable modelling tools for small tree height growth.
Acknowledgements This research was funded by the Resource Inventory Branch, Research Branch and Forest Practices Branch of the BC Ministry of Forests via Forest Renewal BC. Special thanks to Barry Snowdon and Dr. Abdel-Azim Zumrawi of the Ministry of Forest for their technical and administrative contributions. The paper benefited greatly from reviews by Drs. Abdel Azim Zumrawi and Valerie LeMay of the University of British Columbia and Drs. Hans Zuuring and Kelsey S. Milner of the University of Montana in its draft stages. Cornel Lencar, Badre Hassani, and Deb MacKillop, former students of the University of British Columbia, contributed to the data collection efforts of this research.
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