Predicting average growth and size distributions of Douglas-fir ...

New Forests 5 : 109-130, 1991 . © 1991 KluwerAcademic Publishers . Printed in the Netherlands .

Predicting average growth and size distributions of Douglas-fir saplings competing with sprout clumps of tanoak or Pacific madrone TIMOTHY B . HARRINGTON, JOHN C . TAPPEINER II and THOMAS F . HUGHES Department of Forest Science, College of Forestry, Oregon State University, Corvallis, OR 97331, USA

Received 22 October 1990 ; accepted 30 May 1991

Key words : growth model, crown cover, hardwood competition, plantation, Weibull function Application . Effects of hardwood competition on average annual growth and size distributions of Douglas-fir saplings can be described with a series of biologically derived equations, which may also be applicable to other species of conifers and hardwoods growing in mixture. At equal levels of cover, tanoak was a more severe competitor with Douglas-fir than was madrone. Suppression of understory shrubs and herbs did not increase Douglas-fir growth unless hardwood competition was absent . Hardwood competition limited the proportion of Douglas-fir saplings that became dominant members of the stand . These growth and size distribution equations have been implemented in a microcomputer model called PSME that provides forest managers with predictions of early stand development for southwestern Oregon . Abstract . The average growth and size distributions of Douglas-fir (Pseudotsuga menziesii) saplings in three plantations were studied for 7 years (1983-1989) after thinning of associated sprout clumps of tanoak (Lithocarpus densiflorus) or Pacific madrone (Arbutus menziesii) ; in some cases understory vegetation (shrubs and herbs) was experimentally suppressed . Biologically based nonlinear equations explained 66, 90, and 53% of the variation in the average annual increment of Douglas-fir height, diameter-squared, and cover, respectively . Equations for annual increment of cover of hardwood and understory vegetation explained only 10 to 12% of the variation, because these parameters exhibited a high degree of variability. Model simulations demonstrated that, for the same initial levels of cover, tanoak had faster rates of cover growth than madrone and also caused greater limitations in growth of Douglas-fir . Suppression of understory vegetation increased growth of Douglas-fir only when hardwood cover was absent . Weibull functions adequately described size distributions for Douglas-fir in 92% of the individual-tree data sets . Regression functions of hardwood cover and average Douglas-fir size explained 51, 93, and 24% of the variation in the Weibull A, B, and C parameters, respectively . Model simulations with predicted Weibull parameters demonstrated that hardwood competition caused a positive skewing in size distributions for height and stem diameter of Douglas-fir .

11 0 Introduction Evergreen hardwood trees, principally tanoak (Lithocarpus densiflorus [Hook . & Arn .] Rehd .) and Pacific madrone (Arbutus menziesii Pursh), are common associates of Douglas-fir (Pseudotsuga menziesii [Mirb .] Franco var . menziesii) in southwestern Oregon and northwestern California . After cutting or burning, these hardwoods sprout vigorously (Tappeiner et al . 1984), ensuring their presence in newly developing conifer stands . Competition from tanoak or madrone sprout clumps can impede growth of Douglas-fir saplings (Radosevich et al . 1976 ; Roy 1981 ; Tappeiner et al . 1987 ; Jaramillo 1988 ; Hughes et al. 1990 ; Harrington and Tappeiner 1991) . Vegetation management treatments such as manual cutting or the application of herbicides are typically used to reduce competition from these species to a level that ensures survival and promotes growth of associated Douglas-fir saplings . Interspecific competition can affect not only the average growth of young conifers, but also the symmetry of their size distributions . Petersen (1988) found that for stem volume distributions of young ponderosa pine (Pinus ponderosa Dougl .), positive skewness developed earlier in the presence of pinegrass (Calamagrostis rubescens Buckl .) competition than in its absence, because competition caused increased variation in relative growth rates of pine. Current nursery and silvicultural practices in southwestern Oregon usually achieve acceptable levels of survival for planted Douglas-fir (Rost 1988) . However, little information exists to help managers anticipate early stand growth and development of Douglas-fir and associated hardwoods, shrubs, and herbs . Such information would facilitate decision-making and treatment-scheduling in vegetation management by providing managers with indices of plantation development. Because vegetation management treatments typically are applied to broad areas of land rather than to individual trees, forest managers need stand-level information, such as mean tree size and crown cover, to evaluate growth and site occupancy during the early stages of plantation development . Information on the size distribution of a conifer stand is also needed to predict the number of "crop" trees that can be managed through rotation age . Growth predictions for young conifers often are relevant only to a given site or vegetation type when they are derived from empirical functions of competition indices . To be generalizable to a range of initial stand conditions (e .g ., Douglas-fir size and competitor abundance) and site qual-

111 ities, conifer growth predictions should be based on relationships that provide a biologically meaningful description of tree response to competition . The scenario of Douglas-fir regeneration and young-stand management in southwestern Oregon is typical of silvicultural practices throughout the world in that following the successful establishment of crop species, decisions for treatment of competing vegetation are based largely on intuition rather than on quantitative information . Predicting stand development for a diversity of sites and silvicultural objectives requires flexible and biologically based growth models . In this study, our objective was to provide a theoretical framework for characterizing the effects of competition from different plant species over time on growth of young conifer stands . This required the development of a series of biologically based equations for predicting : a) competitor development (hardwood and understory vegetation) ; and b) the competitive effects of this vegetation on the average growth and size distributions of associated conifers . To demonstrate their applicability, we fit the equations to re-measured growth data from three young stands of Douglas-fir .

Methods Site descriptions and treatments

Douglas-fir/hardwood stand development was studied at three sites in southwestern Oregon that are typical of those being managed for conifer wood production and other resources (Table 1) . Tanoak was the principal hardwood competitor at the Squaw and Fir Point sites, while Pacific madrone was dominant at Shoestring . Each site contained an existing Douglas-fir plantation that was established by the operational planting of 2-year-old bare-root seedlings at a density of approximately 1,076/ha . To describe stand development for a range of competition levels, we required repeat measurements of Douglas-fir growth in association with various levels of hardwood, shrub, and herbaceous competition. First, we established 20 X 20 m plots in areas at each site having a relatively homogeneous cover (25-35 %) of hardwood sprout clumps . Then we thinned hardwood sprout clumps to establish a range of initial cover levels . The study was replicated three times at each site in a randomized complete-block design that included four levels of hardwood cover : high (H) = untreated ; medium (M) = 50 % of untreated ; low (L) = 25 % of untreated; and zero (Z).



112 Table 1 . Characteristics of the Douglas-fir plantations. Sites Site characteristics

Squaw

Fir Point

Shoestring

Hardwood species Location

tanoak T39S R6W S21 Cave Jct, OR old-growth Douglas-fir 1980 spring 1981 spring 1981 spring 1983 900 E/SE 30-65 127 14 Pollard/ Beekman gravelly loam'

tanoak T32S R6W S17 Glendale, OR old-growth Douglas-fir 1980 spring 1981 spring 1982 spring 1983 800 W/SW 30-65 127 14 Josephine/ Speaker clay loamd 37

madrone T31S R6W S1 Riddle, OR 28-year-old madrone 1979 spring 1979 winter 1979 fall 1982 700 SW 20-60 108 13 Vermissa/ Beekman gravelly loame 25-30

Previous stand Harvest Broadcast burn Planting Treatment Elevation (m) Aspect Slope (%) Annual ppt . (cm)a May-Sept . ppt. (cm)b Soil series

D. fir Site Index, 00 (m)f

35

a Froehlich et al . (1982) . n McNabb et al . (1982) . • Meyer and Amaranthus (1979). • Hubbard (1980) . • Hughes et al. (1990). r McArdle et al . (1961) .

At Squaw and Shoestring, understory vegetation (shrubs and herbs) was suppressed in an additional replicated set of the four hardwood levels, giving a total of 24 plots per site . At Fir Point, suppression of understory vegetation was applied only to an additional replication of cover level Z, giving a total of 15 plots at this site . For tanoak, sprout clumps in each plot were counted by 25-cm crownwidth classes in March, 1983 . Multiplying crown-width class frequencies by respective class midpoints for crown area and summing these values gave an estimate of initial crown area per plot . Prior to hardwood thinning the size distribution of crown widths for tanoak was positively skewed . To maintain this distribution in plots receiving treatments M and L, we calculated the number of sprout clumps to be removed for a given crown-

1 13 width class according to that class' proportion of the total crown area per plot. The estimated number of sprout clumps per plot remaining after treatment was used to calculate an approximate tanoak spacing . For madrone, which had a normal size distribution of crown widths, sprout clumps were removed in treatments M and L to create approximate spacings of 5 .5 X 5 .5 m and 7 .9 X 7.9 m, respectively, which corresponded to the desired cover levels . At Squaw and Fir Point, we removed individual tanoak sprout clumps in treatments M, L, and Z using a directed spray of triclopyr ester herbicide (2% in water with surfactant) in April, 1983 . At Shoestring, a 3% solution of 2,4-D ester in diesel was applied as a basal spray in September, 1982, to remove individual sprout clumps of madrone . The Douglas-fir were covered to protect them during herbicide application . In the years following the one-time herbicide application, recovering hardwood sprouts in treatment Z were manually removed . Understory vegetation was suppressed on plots receiving this additional treatment by broadcast application of glyphosate herbicide (2% in water) in April, 1983, at Squaw and Fir Point and in September, 1982, at Shoestring. Thereafter the effects from understory competition were minimized by manual removal (March, 1984) and installation of a 2 X 2 m square of porous polyester fabric' around individual Douglas-fir (March, 1985) . Douglas-fir measurements

On each plot, 15 Douglas-fir were systematically located ; each tree was at least 2 m from the boundary of an adjacent plot . The following variables were measured annually on these trees during October of 1983-89 : stem diameter (mm) at a fixed height of 15 cm above ground (permanently marked with tree paint), total height (cm), height increment (cm), and average crown width (cm) at the base of the tree . Crown width was not measured at Shoestring in 1983 . In 1988-89, dbh (mm at 1 .37 m) was measured at Squaw and Fir Point . Increment in diameter-squared (SQDG), which is directly proportional to basal area growth, was selected as a response variable for Douglas-fir stem growth because it was found to be more responsive to the effects of competition than diameter increment . SQDG can also be directly converted to quadratic mean diameter, a meaningful index of growth response for young stands . Individual crown area values for Douglas-fir were converted to the percent cover they would represent at a density of 1,076 saplings/ha.

1 14 For each of the 1983-89 growing seasons, we calculated annual increments in diameter-squared and in percent cover for individual Douglas-fir . Values for these variables and for height increment were averaged by year for each plot, and the data from the three sites were combined into a single set . Hardwood and understory measurements Total crown area of tanoak was measured annually in September-October of 1983-87 by the methods described above . For madrone, we randomly. selected either five (treatment H) or eight sprout clumps (treatments M and L) per plot and measured their crown width annually in September-October of 1983-88 . Total crown area of madrone was calculated by multiplying the average crown area per clump by the number of sprout clumps per plot . Dividing the plot values for hardwood crown area by the plot area X 100% gave hardwood percent cover . Annual increments in hardwood cover were calculated by plot for each year, and the data from the three sites were combined into a single set . At Squaw and Fir Point only, five Douglas-fir seedlings per plot were systematically selected and used as reference points for estimating percent cover of understory vegetation . In June of 1985-87, crown cover (%) of each understory species was estimated visually with a 1-m 2 square frame at a fixed location 1 m uphill from each reference Douglas-fir . In 1985, understory cover was estimated only for plots in which this vegetation had not been suppressed . Total understory cover was summed for each reference tree, and these values were averaged to give plot means . Annual increments in understory cover were calculated by plot for each year, and the data from the two sites were combined into a single set . Derivation of growth equations The effects of interspecific competition on growth of young trees have been quantified by correlations of single-year measurements of tree size or growth with the current or past abundance of associated vegetation (Brand 1986 ; Byrne and Wentworth 1988 ; Wagner and Radosevich 1991a, b) . However, our objective was to provide a biologically plausible description of competition effects over time . Therefore, we chose general model (1) because it provides a simple framework in which to make dynamic predictions of growth for trees of various ages (Shifley and Fairweather 1983 ; Waldrop et al . 1986; Wensel et al. 1987 ; Powers et al. 1989 ; Opalach et al . 1990) :



1 15 G = PG *COMP

(1)

where G = annual growth or increment in tree size, PG = annual potential growth, and COMP = competition modifier . We define potential growth (PG) of Douglas-fir as that expected for trees growing free of competition and other deterrents of growth (e .g ., animal damage and disease) ; thus PG is strictly a function of current tree size and morphology . In competition-free conditions, the annual size increase of saplings of Douglas-fir (Wagner 1991a ; Hughes et al . 1990 ; Harrington and Tappeiner 1991) and probably many other tree species can approach exponential rates . Thus, their PG can be described as a fixed or gradually declining proportion of tree size, as quantified by an equation such as (2) or (3) : PG, = bo + b * (SIZE, _ 1)

(2)

PG, = bo * ( SIZE, _

(3)

1) b

where PG, = potential growth in year t, SIZE, _ 1 = Douglas-fir size in year t - 1, and bo, b = regression coefficients . PG is limited by the quality of growing conditions on a given site . To account for variation in tree growth due to site quality, the bo parameter (above) can be described as a function of the average annual rate of PG for a given site : bo

= a * PG avg, i

(4)

where PGa,g, i = average annual rate of potential growth for site i, and a = regression coefficient . Competition limits the amount of potential growth that is expressed in a given growing season by reducing the daily relative rates and/or seasonal duration of growth (Harrington and Tappeiner 1991) . Reductions in Douglas-fir growth have been functionally related to interspecific competition level, expressed as percent crown cover (Harrington 1989 ; Wagner 1991a, b) . Thus, an equation such as (5) can be used to describe the proportion of potential growth expressed in a given year as a result of competition : COMP, = exp(c * COVER,)

(5)

where COMP, = value for competition modifier in year t, COVER, =



1 16 percent crown cover in competing vegetation in year t, and c = regression coefficient . When COVER, equals zero in Eq . (5), COMP, equals one, indicating a full expression of potential growth in the absence of competition . Because COMP, is defined as a negative exponential function with domain (0, 1), the "competition coefficient," c, is a unitless parameter and its values can be compared among models for Douglas-fir height, diameter, and cover . Equations (6) and (7) represent fully specified models that describe current-year tree growth as a function of site quality, previous-year tree size, and previous-year competition level : G, = (a * PG avg , ; + b * (SIZE, _ 1)) * exp(c * COVER1, t

(6)

G, = (a * PGavg,, * ( SIZE,-,)b) * exp(c * COVER1,,-,)

(7)

where G t = tree growth in year t, and COVER, , _ , = percent crown cover for vegetation j (tanoak, madrone, or understory vegetation) in year t 1. We used a monomolecular growth function (Draper and Smith 1981) to describe increment in hardwood or understory cover : COVGI,, = k * (100 - COVER,,,_,)

(8)

where COVGJ,, = increment in cover for vegetation j in year t and k = regression coefficient (rate constant of the growth pattern; Draper and Smith 1981) . This growth function was selected because it describes the asymptotic approach of hardwood or understory cover toward a maximum value of 100% . Site quality (T . B . Harrington and J. C . Tappeiner II, unpub . data) and level of understory vegetation (Harrington 1989 ; Hughes et al . 1990) had little or no effect on cover development of tanoak and madrone during the first 10 years after sprouting of hardwoods . In addition, preliminary analyses indicated that the monomolecular function fit the data with lower values for the mean-squared error than linear, logistic, or Richard's functions . Because of its flexibility, the Weibull function has been used to describe many of the possible size distributions that are exhibited by mature western conifers (Schreuder and Swank 1974 ; Little 1983 ; Opalach 1989) . We used the Weibull function to characterize the influence of competition on size distributions of Douglas-fir saplings, because its predictions can provide an estimate of stand structure, as well as of the proportion of trees emerging as dominants . In addition, we developed regression equations for predicting height and dbh of individual Douglas-fir for the full range of stem diameters (at



1 17 15 cm height) encountered in the study . When combined with a Weibull diameter distribution, these predictions can be used to generate a list of individual tree sizes for input into computer models of stand growth and yield . Parameter estimation for the growth equations In repeated-measures data such as those in this study, parameter estimates obtained from regression analyses are unbiased and consistent (Kmenta 1971) . However, in such regressions the estimates of the variance are biased as a result of serial correlation, making hypothesis-testing inappropriate. To incorporate the influences of site quality and species of hardwood competitor, we combined data from the three sites to develop the growth equations . Model parameterizations were selected on the basis of the size of the mean-squared error and the normality of the residuals when plotted against predicted values for a given dependent variable . For each model, a Student's t-test (a = 0 .05) provided an index with which to select among potential parameters (Ratkowsky 1983) . We estimated the parameters for Eqs (6) and (7) using least-squares nonlinear regression (Wilkinson 1988a) . We used the weighted regression approach of Paine and Hann (1982) to correct for non-homogeneity in the residual variance for the equations predicting increment in diameter-squared and cover of Douglasfir. First we calculated a series of weights proportional to the reciprocal of the residual variance : Weight = (SIZE, _ ,) - w

(9)

where W = 0 .5, 1, 1 .5, or 2 . Then we used Furnivals's (1961) goodnessof-fit index to determine the most appropriate value for W . For the hardwood cover model, we specified an indicator variable (SPP = 1 for madrone, SPP = 0 for tanoak) to estimate separate k parameters for each species . The shape of the residual distribution suggested that the rate constant, k, was related linearly to the square of previous-year cover : k=bob + b, * (COVER1,,_,) 2

(10)

where bob = regression intercept for vegetation j (tanoak or madrone), b, = regression slope, and (COVERj,, _,) 2 = covert in year t - 1 for vegetation j (tanoak or madrone) . The fully specified model for increment in hardwood cover is given by substituting Eq. (10) for k in Eq. (8) : COVGJ,, = ( bob + b, * (COVER1 , _ i ) 2 ) * (100 - COVER1, , _,)

(11)



118 Competition from tanoak or madrone limited the development of understory vegetation (Harrington 1989 ; Hughes et al . 1990) . This competitive effect was included in the understory cover model by specifying k as a function of predicted tanoak cover (understory cover data were not collected in the madrone study) :

k = bo + b, * PCOVER ta , _ 1

(12)

where : bo , b, = regression coefficients, and PCOVERtan,,_ I = predicted tanoak cover in year t - 1 (from Eq . (11)) . The variable "previous-year understory cover" was not included in Eq . (12), because it did not explain additional variation in understory cover increment . As described above for the hardwood cover model, the fully specified model for increment in understory cover is given by substituting Eq . (12) for k in Eq. (8) : COVGI,, = (bo + b, * PCOVERtan ,, _ i ) * ( 100 - COVER,,(13) where : COVERj, - , = understory cover in year t - 1 . Average rates of potential growth (PGavg) were calculated by site for Douglas-fir height, diameter-squared, and cover . These variables were incorporated into Eqs (6) and (7) to account for variation in site quality and to improve the estimation of separate competitive effects for tanoak and madrone . We compared Eqs (6) and (7) for their ability to predict average increment in Douglas-fir height, diameter-squared, and cover from previous-year values of hardwood cover by plot, predicted from Eq . (11) . Increment in Douglas-fir height was described best by Eq. (6), while Eq. (7) provided the best descriptor for increment in diameter-squared and cover. To determine whether Douglas-fir growth limitations imposed by hardwood competition differed between tanoak and madrone, we estimated separate competition parameters (c in Eqs (6) or (7)) . for each species by including an indicator variable (SPP) in each model . Preliminary regression analyses indicated that suppression of understory vegetation increased Douglas-fir growth, but only in the absence of hardwood cover . The following indicator variable was specified to quantify this Douglas-fir growth response : UND = 1 for understory not suppressed and hardwood cover equal to 0%, UND = 0 otherwise . We performed simulations for each of the hardwood, understory, and Douglas-fir models to provide a visual comparison of the development of stand parameters with time . For hardwood cover, we varied initial cover values 1 year after treatment from 0 to 50% and predicted total hardwood cover through the seventh year after treatment . We held the initial value for understory cover constant at 15% and predicted the effect of various

119 levels of initial hardwood cover (0 to 50%) on total understory cover through the seventh year after treatment. For the Douglas-fir models, we held initial tree size constant at mean values for the first year after treatment (height = 50 cm, diameter = 9 mm, cover = 0 .5%) and used the models to predict the effect of hardwood competition on each Douglas-fir parameter through the seventh year after treatment . We used a distance-weighted least-squares method to smooth and plot the three-dimensional relationships of the predicted hardwood, understory, or Douglas-fir parameters versus time and initial hardwood cover (Wilkinson 1988b) . Parameter estimation for the Weibull equations To provide reasonable parameter estimates for the Weibull function, an adequate sample size (n > 30) of individual tree measurements was needed . For each year, individual measurements of Douglas-fir height or diameter were combined for the three plots (replications) of each level of hardwood and understory vegetation present on a given site - a total of 45 trees . For each data set of Douglas-fir height or diameter (n = 45), we estimated the A, B, and C parameters of the cumulative Weibull function using maximum likelihood estimation . We used WBFIT (Opalach 1989) to estimate parameters and to calculate chi-squared goodness-of-fit tests (a = 0.05) (Snedecor and Cochran 1980) for each of the 147 data sets of Douglas-fir height or diameter (21 populations X 7 annual measurements) . The estimated Weibull parameters for Douglas-fir height and diameter were combined into a single data set (n = 294) . We averaged the three plot values (replications) for first-year hardwood cover corresponding to each population of Douglas-fir. The average cover value for year 1 was input into Eq . (11) to predict previous-year hardwood cover for years 2 through 7 for each Douglas-fir population . We used stepwise linear regression (Wilkinson 1988a) to develop equations for predicting each of the Weibull parameters from the following population characteristics : PCOVER1 _ ,, years since treatment, SIZE„ SPP, UND, and an indicator variable denoting the Douglas-fir parameter (height or diameter) . All two-way interactions of the above variables were also included in the regression analyses . Variable entry and removal was controlled at an experimentwise error level of a = 0 .05 . Residuals for regressions of the Weibull A and B parameters had non-homogeneous variation when plotted against predicted values for the dependent vari-

1 20 ables . For these models, we utilized weighted regression to correct for non-homogeneity in the residual variance (Paine and Hann 1982) . An independent data set of individual tree sizes was constructed for developing regression equations of Douglas-fir height or dbh versus diameter (at 15 cm height) . For each sample Douglas-fir, a single annual measurement of dbh (Squaw and Fir Point only), diameter, and height was randomly selected . We used the size of the mean-squared error to choose among linear, power, and exponential functions for predicting either height or dbh from diameter, PCOVER 1 _ 1 , SPP, and UND . Independent variables and their two-way interactions were included in the models if they increased the adjusted R2 by at least 0 .01 . Weighted regression was used to correct for non-homogeneity in the residual variance of each equation (Paine and Hann 1982).

Results and discussion Hardwood and understory cover

Model simulations demonstrated that for a range of initial levels of hardwood cover (0 to 50%), predicted cover of tanoak exceeded that of madrone in each of the 7 years after treatment (Fig. 1a) . These species' differences in rates of cover development were greatest at low levels of initial hardwood cover (< 30%) . For example, when initial cover was 10%, seventh-year cover was 56% for tanoak and 33% for madrone . In the hardwood cover model (Eq. (11)), tanoak's value (0 .0663) for the regression intercept that predicts the rate of cover growth, k, was over twice that of madrone (0 .0288) (Table 2) . Tanoak cover strongly limited understory cover (Fig . 1b) . When initial tanoak cover exceeded 20%, predicted increment in understory cover was negative by the seventh year after treatment . At initial cover values for tanoak and understory vegetation of 0 and 15%, respectively, unimpeded development of understory vegetation resulted in a predicted cover of 68% by the seventh year . Only 10 to 12% of the variation in the increment of hardwood and understory cover was explained by the regression models, because these parameters exhibited a high degree of variability (Table 2). However, because the integrated forms of these models (absolute cover as a function of time) explained 94 and 68% of the variation in hardwood and understory cover, respectively, we feel that the monomolecular model is an adequate descriptor of cover development . Expressing k as a function of previous-year hardwood cover increased the predictive capability of the

121

Fig. 1. Simulated cover development of (A) tanoak or madrone and (B) understory vegetation 7 years after establishment of a range of initial hardwood cover levels .

hardwood model . A weakness of the linear relationships describing k (Eqs (10) and (12)) is that if previous-year cover becomes equal to . 0%, predicted cover increment must be constrained to equal 0% . Douglas-fir growth

Height of Douglas-fir was more strongly limited by tanoak than by madrone (Fig . 2a) . For a given value of initial hardwood cover, simulated seventh-year height of Douglas-fir was 20 to 46 cm less for trees in competition with tanoak than for those competing with madrone . Using analysis of variance, Hughes et al . (1990) detected no reduction in the height growth trajectory of Douglas-fir attributable to madrone competition at Shoestring . However, with regression analysis we estimated the competition coefficient (c in Eq . (6)) for madrone's effect on Douglas-fir

122

Fig . 2 . Simulated development of Douglas-fir (A) height, (B) stem diameter, and (C) cover

7 years after establishment of a range of initial levels of tanoak or madrone cover .

height increment (-0 .00354) to be about half of that estimated for tanoak (-0 .00665) (Table 3) . Suppression of understory vegetation increased Douglas-fir height only in the absence of hardwood cover (Fig . 2a) . Seven years after treatment, predicted height of Douglas-fir growing free of competition from hardwood and understory vegetation was 66 cm greater than that of trees growing where only hardwoods were removed . Given the rapid development of understory vegetation following hardwood removal (Fig . lb), it is not surprising that understory vegetation more strongly limited height increment of Douglas-fir than did < 10% cover of tanoak or < 35% of madrone. For each initial value of hardwood cover, tanoak had a slightly greater competitive effect than madrone on the predicted growth trajectory for

123 Table 2 . Regression coefficients (standard errors below in parentheses) for models that predict increment in cover of tanoak, Pacific madrone, and understory vegetation.

Type of vegetation Regression coefficientsa bo

0 .663E-1 (0 .631 E-2) 0 .509 E-4 (0 .535 E-5)

b,

Adjusted sy . x n

tanoakb

R2

0 .122 4 .08 182

Pacific madroneb

understory vegetation

0 .288E-1 (0 .906 E-2) 0 .509 E-4 (0 .535 E-5)

0 .150 (0 .340 E-1) -0 .269 E-2 (0 .100 E-2)

0 .122 4 .08 182

0 .102 10 .7 62

a See Eq. (11) for hardwoods or Eq . (13) for understory vegetation . b The models for tanoak and madrone were developed from a single pooled data set .

Table 3. Regression coefficients (standard errors below in parentheses) for models that predict average increment in height, diameter-squared, and cover of Douglas-fir in competition with tanoak, madrone, or understory vegetation .

Douglas-fir parameter

Regression coefficients,

height (cm) 0 .457 (0 .230 0 .196 (0 .845 -0 .665 (0 .522 -0 .354 (0 .527 -0 .167 (0 .321

Adjusted sy . x n

R2

0 .658 8 .21 378

E-1) E-2) E-2 E-3) E-2 E-3) E-1)

diametersquared (mm-') 0 .552 (0 .458 1 .502 (0 .239 -0 .920 (0 .792 -0 .524 (0 .832 -0 .795 (0 .362 0.900 124 378

E-2 E-3) E-1) E-2 E-3) E-2 E-3) E-1 E-1)

cover (%)

0 .307 (0 .183 0 .581 (0 .287 (-0 .348 (0 .145 -0 .207 (0 .144 -0 .515 (0 .830 0 .528 1 .26 354

a See Eq . (6) for Douglas-fir height or Eq . (7) for Douglas-fir diameter-squared or cover . b Regression coefficient for indicator variable UND . See text for details .

E-1) E-1) E-2 E-2) E-2 E-2) E-1 E-1)

1 24 diameter of Douglas-fir (Fig . 2b) . At high levels of initial hardwood cover (> 30%), predicted diameter of Douglas-fir 7 years after treatment was about 7 mm less for trees in competition with tanoak than for those competing with madrone . The model explained considerably more variation for increment in diameter-squared (R2= 0.90) than for increment in height (R 2 = 0.66) (Table 3) . For the same range in initial hardwood cover (0 to 50%), Douglas-fir size 7 years after treatment varied by factors of 1 .78 and 1 .41 for diameter and height, respectively . Suppression of understory vegetation increased Douglas-fir diameter increment, like height increment, only when hardwood cover was zero . Predicted Douglas-fir cover 7 years after treatment varied from 23 to 16% for initial hardwood cover levels of 0 to 50% (Fig . 2c) - a factor of 1.42, which is similar to that found for Douglas-fir height . Tanoak limited the steepness of the growth trajectory for Douglas-fir cover more than madrone, but these species' differences in competitive effects were much less than observed in the models for increment in height and diametersquared . The competition coefficients (c in Eq . (7)) in the cover increment model (c = -0 .00348 for tanoak ; c = -0 .00207 for madrone) were considerably less than those estimated in models for increment in height and diameter-squared (Table 3) . As was the case for Douglas-fir height and diameter, suppression of understory vegetation increased Douglas-fir cover only when hardwood cover was zero (Fig . 2c) . Two types of evidence may explain why tanoak is a more vigorous competitor than madrone . First, the average leaf area index of a tanoak sprout clump (7 .0 m2 leaf area/m 2 ground area) is almost twice that of madrone (4 .1 m 2/m2) ( Harrington et al . 1984) . Thus, light is probably much less available to Douglas-fir saplings that are overtopped by tanoak than to those overtopped by madrone. Second, cover development, which is closely correlated with leaf area development (Harrington et al . 1984), occurred at a faster rate for tanoak than for madrone (Fig . la) . This latter result suggests that for the same initial levels of cover, tanoak is expanding its site occupancy, and presumably its consumption of light and soil water, at a faster rate than madrone . Predicting Douglas fir size distributions The chi-squared goodness-of-fit test provided a test for the following null hypothesis: The size distribution for a given Douglas fir population can be described by a Weibull function .

125 This null hypothesis was rejected in 23 of the 294 data sets of individual tree measurements for Douglas-fir . Of these 23 data sets, all were for diameter distributions, and 19 resulted from the first two annual measurements of the Douglas-fir (1983 and 1984) . Scatterplots of frequency versus size revealed that stem diameter for these populations did not vary greatly enough to be described by the Weibull function . Each of the A, B, and C parameters for the Weibull function was significantly related to current-year values for average tree size (Table 4) . The A and B parameters were also significantly related to the interaction variable, previous-year hardwood cover times average tree size . The regression relationships for predicting the Weibull parameters suggest that, for a given Douglas-fir population, hardwood competition

Table 4 . Regression coefficients (standard errors below in parentheses) for models that predict Weibull function parameters for size distributions of Douglas-fir height and stem diameter .

Weibull function parameters Regression coefficients,

Douglas-fir parameter

Hardwood species

bo

diameter

tanoak madrone

height

tanoak madrone

b,

diameter

tanoak madrone

b2

Adjusted R2 sy . x n

diameter or height

B

6 .318 (0 .562) 6 .318 (0 .562) 6 .318 (0 .562) 6 .318 (0 .562)

-0 .603 E-1 (0 .205 E-1) 0 .270 (0 .218 E-1) 0 .210 (0 .205 E-1) 0 .359E-3 (0 .390 E-3)

-1 .949 (0 .658) -1 .949 (0 .658) -14 .760 (3 .359) -14 .760 (3 .359) 0 .797 (0 .407 E-1) 0 .921 (0 .241 E-1) 0 .797 (0 .407 E-1) 0 .921 (0 .241 E-1) 0 .151 E-2 (0 .503 E-3)

0 .506 16 .4 252

0 .929 21 .1 252

tanoak madrone

height

A

tanoak or madrone

C 1 .662 (0 .979 E-1) 1 .963 (0 .808 E-1) 1 .662 (0 .979 E-1) 1 .963 (0 .808 E-1) 0 .224 E-1 (0 .306 E-2) 0 .224 E-1 (0 .306 E-2) 0 .457E-2 (0 .276 E-2) 0 .457 E-2 (0 .276 E-2) -

0 .235 0 .672 294

aWeibull function parameters are predicted from the following equation : A, B, or C = b0 + b, * SIZE, + b2 * (SIZE, variables .

X

PCOVER,See text for definitions of



1 26 directly limits both the minimum (A parameter) and average (B parameter) tree sizes (Little 1983) . Because the C parameter was found to be proportional to average Douglas-fir size, restrictions in tree size from competition cause predicted C to be maintained at values less than 3 .6 the value that approximates a normal distribution (Schreuder and Swank 1974) - resulting in a positively skewed distribution (Fig . 3) . Thus hardwood competition limited the proportion of Douglas-fir saplings that became dominant members of the stand . Size distributions for Douglas-fir influenced by madrone had a similar shape at much higher levels of initial hardwood cover (> 80%) . Of the . models tested for predicting individual tree height or dbh from diameter and other variables, linear regressions had the lowest values for the mean-squared error . The variables SPP and UND were not included in the following equations because they did not explain at least 1% of additional variation in either height or dbh :

40

30

20

z 0

10

:) CL

0

2 U.0

100 150 200 250 300 350 400 450 500 550 600 650

700

DOUGLAS-FIR HEIGHT CLASS (cm) 40

W

v

a

30

20

10

0 10 20

30 40 50

60

70

80 90

100 110 120

DOUGLAS-FIR DIAMETER CLASS (mm)

Fig. 3. Simulated Weibull size distributions for (A) height and (B) stem diameter of

Douglas-fir in the seventh year after establishment of initial tanoak cover levels of 0 and 35%.



1 27 height (cm) = 12 .909 + 4 .961 * diameter (mm) + 0 .678 * PCOVER, _ ,

(14)

adjusted R 2 = 0.86 1, Sy ., = 33 .728, n = 937 dbh (mm) = -13 .772 + 0 .710 * diameter (mm) + 0 .0898 * PCOVER, _,

(15)

adjusted R 2 = 0 .834, Sy . X = 5 .290, n = 578

Conclusions Through this research we have derived a set of simple yet biologically meaningful equations for characterizing the competitive effects of different hardwood species on growth of Douglas-fir saplings . Because the equations provide a general description of early trends in stand growth, we feel this modeling approach can be applied to other species of conifers and sprouting hardwoods growing in mixture . Tanoak had a greater competitive effect than madrone on the average annual growth of Douglas-fir . In the absence of hardwood competition, understory vegetation imposed a limitation upon growth of Douglas-fir similar to that caused by low levels of hardwood cover . When these reductions in annual growth of Douglas-fir were integrated through time, we found that competition limited the average stem diameter of a Douglas-fir stand more than it limited its average height or cover . Competition limited the proportion of individual Douglas-fir that became dominant members of the stand . Douglas-fir that remain subordinate in height to associated tanoak or madrone through the tenth year of a plantation may not survive . Thus, such a conifer stand may not reach crown closure because it would be composed of a few widely spaced "crop" trees . Such heterogeneity in stand structure is not correctable by thinning or hardwood removal, thus emphasizing the need for early vegetation management treatments in tanoak or madrone vegetation types . The predictive equations presented in this paper can be used to compare relative differences in development of young stands for various initial levels of hardwood cover in southwestern Oregon . To facilitate use of this information, we have incorporated the growth equations into PSME (Plantation Simulator-Mixed Evergreen), a software program for microcomputers . PSME and a program user manual (Harrington et al . 1991) can be obtained by writing to the following address and requesting Forest Research Laboratory Special Publication 21 : Forestry Publications Office Oregon State University Forest Research Laboratory 225 Corvallis, Oregon 97331-5708

128 Acknowledgments Financial support for this research was provided by the USDI Bureau of Land Management and USDA Forest Service under the auspices of the Southwest Oregon Forestry Intensified Research (FIR) program (grant no . PNW-85-422) . The author appreciates the field assistance of Mr . R. J. Pabst and the editorial advice of Ms . J . Thomas . This is Paper 2523 of the Forest Research Laboratory, Oregon State University, Corvallis 97331 . Notes 1.

Terra-Mat E, Terra Enterprises, Inc ., Moscow, ID 83843 . The mention of tradenames or commercial products does not constitute endorsement or recommendation for use by the authors or their institution .

This publication reports research involving pesticides . It does not contain recommendations for their use, nor does it imply that uses discussed have been registered . All uses of pesticides must be registered by appropriate state and federal agencies before they can be recommended .

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