stand structure and dynamics of young red alder as affected by...

Forest Ecologyand

ManagementELSEVIER Forest Ecology and Management 82 (1996) 69-85

Stand structure and dynamics of young red alder as affected byplanting density

Steven A. Knowe *, David E. HibbsDepartment of Forest Science, Oregon State University, Corvallis, OR 97331, USA

Accepted 6 November 1995

Abstract

The response of stand structure and dynamics of young red alder (Alnus rubra Bong.) was examined over a gradient inplanting density. Data from three Nelder plots, representing ages 1-7 years and planting densities from 238 to 101 218 treesha -1 , were used to develop biomathematical models for dominant height, diameter, and survival. The models accounted for88-99% of the observed variation in projected height, diameter, and survival, with planting density accounting for 0.6-2.6%of the variation in diameter and height and 7.1% of the variation in survival. Height growth rate exhibited a quadraticrelationship with planting density up to 24 670 trees ha-1 and a linear relationship at greater planting densities. The naturallogarithm of planting density exhibited a linear relationship with change in relative diameter and quadratic mean diametergrowth rates. These functional relationships between growth rates and planting density were consistent with the concepts ofcompetition thresholds: height and diameter growth rates were more affected by planting density at lower than at higherplanting density while mortality rate increased linearly with increasing density. At high planting density, annual height andquadratic mean diameter growth were less and reached a maximum at younger ages than at low planting density. Thedominant height projection function depicts a temporal ripple in maximum height growth that progresses outward over timefrom the high planting densities in the center of Nelder plots to the lower densities near the edge of the plots.

Keywords: Nelder plots; Height growth; Diameter growth; Mortality

1. Introduction

Red alder (Alnus rubra Bong.) is a widely distributed hardwood species in the Pacific Northwest that hasproliferated as a result of harvesting in the Douglas-fir ( Pseudotsuga menziesii (Mirb.) Franco) region (Hibbs etal., 1994). In 1975, it was the predominant species on 12% of the forested land base (Bassett and Oswald,1981a, Bassett and Oswald, 1981b, Bassett and Oswald, 1982; Gedney et al., 1986a, Gedney et al., 1986b,Gedney et al., 1987). Interest in red alder management as a timber resource has increased in recent years (Hibbset al., 1989). According to Ahrens et al. (1992), red alder is also an alternative to conifer planting, especially on

Corresponding author. Tel. 503-737-6084; fax. 503-737-5814; e-mail:[email protected] 3059, Forest Research Laboratory, Oregon State University, Corvallis, OR, USA.

Elsevier Science B.V.SSDI 0378-1127(95)03690-3

70 S.A. Knowe, D.E. Hibbs/Forest Ecology and Management 82 (1996) 69-85

sites infected with laminated root rot (Phellinus weirii). The potential for nitrogen fixation in mixed stands withDouglas-fir is an incentive for many landowners to manage red alder (Tarrant et al., 1983).

Much of the growth and yield research in red alder has been conducted in natural stands and focused onsize-density relationships (Hibbs, 1987; Hibbs and Carlton, 1989; Puettmann et al., 1992), thinning effects(Hibbs et al., 1989, Hibbs et al., 1995), and height-age curves (Harrington and Curtis, 1986). Despite the need,very little is known about growth and development of red alder plantations. One of the most critical needs isinformation regarding the consequences of different planting densities. Ahrens et al. (1992) reported that redalder stands at spacings closer than 3 m will dominate a site within 2-3 years, but seedlings planted at widerspacings may be more vulnerable to interspecific competition. More detailed quantitative information is neededto evaluate the long-term consequences of silvicultural practices required for various planting densities.

Among forest tree species, height and height growth are thought to be relatively unaffected by stand densitywithin a wide range of intraspecific competition (Smith and DeBell, 1974; Lanner, 1985) and interspecificcompetition (Wagner and Radosevich, 1991; Knowe, 1994a). Individual-tree height growth models forDouglas-fir (Ritchie and Hann, 1986; Hann and Ritchie, 1988) indicate that stand density has little effect onheight growth of trees that are in an advantageous position with respect to their competitors. In contrast, for agiven diameter and age, height of individual Douglas-fir trees has been shown to increase temporarily inresponse to intraspecific competition (Cole and Newton, 1987) and interspecific competition (Knowe, 1994a).For red alder, maximum height is often attained at intermediate stand densities (Bormann and Gordon, 1984;Giordano and Hibbs, 1993), and height growth may decrease after thinning (Hibbs et al., 1989).

Unlike tree height and height growth, diameter and diameter growth are dependent on current resources,particularly water, and have a lower priority for photosynthate allocation than does height growth (Waring,1987). As a consequence, trees under competition for water will typically exhibit reductions in diameter growthbefore height growth. Harrington and Tappeiner (1991) demonstrated that interspecific competition in Douglas-firlimited both the rate and the duration of basal area growth, but only the rate of height growth was reduced.

The purpose here is to develop models that may be used to examine the effects of planting density on thestand structure and dynamics of young red alder. This examination was accomplished by using seven annualremeasurements of red alder in a Nelder density series to develop models for height and diameter growth andsurvival. The relationships between growth rate parameters in the models and planting density were investi-gated. Thus, the models may be considered biomathematical because the parameters can be interpreted withrespect to biological phenomenon. Components of stand structure considered in this study were dominantheight, diameter growth obtained by using a stand table projection method that combines predictions from bothstand- and tree-level diameter growth models, and survival.

2. Methods

2.1. Data

Details of the study were presented by Giordano and Hibbs (1993). The study area is at 330 m elevation inthe Casacade Head Experimental Forest, Oregon, in a transition between the Sitka spruce (Picea sitchensis(Bong.) Carr.) and the western hemlock (Tsuga heterophylla (Raf.) Sarg.) zones (Franklin and Dyrness, 1973).The site receives 250 cm of precipitation per year, and the average growing season is 180 days. The175-year-old spruce-hemlock stand was clearcut and burned in 1984. Three Nelder (type la) density plots(Nelder, 1962) of 24 spokes (15° angle) and 15 arcs, were planted in 1985. Each of these plots was split and 125kg ha' triple superphosphate was applied to half of the Nelder circle. No attempt was made to incorporatefertilizer effects in the present analyses. Measurements were obtained for 16 spokes (8 per half plot) and theinterior 13 arcs representing planting densities of 238, 345, 584, 984, 1660, 2804, 4759, 8048, 13 623, 23 016,37 864, 64 672, and 101 218 trees ha*

S.A. Knowe, D.E. Hibbs/Forest Ecology and Management 82 (1996) 69-85 71

Total height (m) of all surviving trees was measured annually between plantation ages 1 and 7 years.Diameter at 1.37 m (dbh) was measured annually between ages 2 and 7 years. The surviving trees in each arcwere used to compute plot-level means. Therefore, a plot consisted of all trees at a given planting density withina Nelder circle. Plot and individual-tree data were arranged in nonoverlapping annual-growth intervals. Realgrowth series from remeasured plots or trees potentially have less problems with serial correlation when the dataare arranged in nonoverlapping growth intervals rather than all possible intervals (Borders et al., 1988). Theresulting datasets consisted of 234 observations of height growth and survival (3 replications, 13 densities, and 6growth intervals), 195 observations of mean diameter growth (5 growth intervals), and 2711 observations ofdiameter growth for individual trees (5 growth intervals for 16 trees per arc, less mortality).

2.2. General modeling approach

The approach was to develop functions to describe stand dynamics of red alder plantations and to examinethe relationships of these functions to planting density. Functions were developed to project dominant height,individual-tree diameters, and survival, all of which are important components of stand structure. In contrast toprediction models, which directly predict size at specified ages, projection models provide estimates of futuresize from growth over short intervals added to known current size. Using the derivative-integral relationshipbetween growth and yield, a yield model is differentiated with respect to age. Integration of the resulting growthequation and expression as an algebraic difference (Borders et al., 1984; Knowe, 1994a; Knowe, 1994b)produces a projection equation because integration is the continuous-variable equivalent of summation fordiscrete variables. Differences in the growth rate parameter for each function were examined in relation toplanting density by using an indicator variable approach. This approach has been used to compare height growthpatterns among planting densities (Pienaar and Shiver, 1984), loblolly pine (Pinus taeda L.) families (Knoweand Foster, 1989), and vegetation management treatments (Knowe, 1994a). First, a projection function wasobtained for all planting densities combined. The hypotheses of differences in the rate parameters associatedwith initial planting density were tested by obtaining separate parameter estimates for each of 13 discreteplanting density classes with an indicator-variable approach:

12

P = Po + E1

where Z = 1 for the j th planting density, 0 otherwise, p o represents the rate parameter for the highest plantingdensity, and f3 represents the effect of the j th planting density expressed as a deviation from [3 0 . Residual sumsof squares for full and reduced regression models were compared in an F test (Neter et al., 1985). The reducedmodel for testing planting density effects was the model without indicator variables, which expresses theaverage effect of planting density, and the full model was the model with /3 which incorporates the indicatorvariables for planting density. These tests are not exact because of nonindependence of observations in theNelder plots and serial correlation.

The rate parameters estimated for each of 13 planting density classes were graphed to examine trendsassociated with planting density. A function was selected to describe the relationship between the estimated rateparameters for density classes and planting density; it was then incorporated into the appropriate equation. Theconstant percentage of increase in space between successive densities in the Nelder plots suggests that a naturallogarithmic transformation of planting density would be appropriate (Cole and Newton, 1987). Giordano andHibbs (1993) reported a strong linear relationship between relative growth rate for biomass and the naturallogarithm of planting density in these Nelder plots at age 4. Residual sums of squares for full and reducedregression models were compared in an F test by using the model without indicator variables for plantingdensities as the reduced model and the model with the rate parameter expressed as a function of planting densityas the full model. The effects of planting density on dominant height, individual-tree diameters, and survival

72 S.A. Knowe, D.E. Hibbs/Forest Ecology and Management 82 ( 1996) 69-85

were examined by comparing graphs of predicted values for planting densities of 345, 984, 2804, 8048, 23 016,and 64 72 trees ha-I.

2.3. Dominant height projection function

Curtis et al. (1974) recommends that height-age curves be developed by using either a fixed number of treesper acre or a fixed percentage of surviving trees to calculate average dominant height. In similar studiesinvolving remeasured plots, dominant height has been based on the tallest two-thirds (Nance and Wells, 1981)and the taller one-half (Golden et al., 1981; Boyer, 1983; Knowe, 1994a) of surviving trees at each age; Bufordand Burkhart (1987) used the tallest 100 trees per acre (250 trees ha') for measuring dominant height. For thepresent study, dominant height was defined as the average height of the tallest one-quarter of surviving trees ateach age.

A sigmoid growth model (Richards, 1959), which has been used to describe height-age relationships fornatural stands of red alder (Harrington and Curtis, 1986) and Douglas-fir (Means and Sabin, 1989), was selectedfor describing height-age relationships. An algebraic difference formulation (Borders et al., 1984; Knowe andFoster, 1989) was used to project and compare height growth patterns for young red alder plantations:

( 1 — expt( — 13/0) )0H2 = H, (1)

1 — exp{ — ( 0A1)))+ e

where H, is the height (m) at the start of the growth interval, H2 is the height (m) at the end of the growthinterval, A, is the age (years) at the start of the growth interval, A 2 is the age (years) at the end of the growthinterval, [3 is the rate parameter, 0 is the shape parameter, and E is the random error component.

The rate parameter ( f3) determines how rapidly the asymptotic height is approached, with larger valuesindicating rapid attainment of maximum height. The shape parameter (0) determines the degree of inflection ingrowth, with values close to 1.0 indicating no inflection and larger values indicating an inflection and producinga sigmoid curve. Desirable features of this equation are that each curve has an implied asymptote and that thefunctions are implied growth models that are both age- and path-invariant. The age-invariance property allowsany base age to be selected and used to produce a family of anamorphic height-age curves by substituting siteindex (S) for H2 and base age ( A b ) for A 2 . The path-invariance property allows the same height to be obtainedeven if projections are made to intermediate ages. In addition, the site index specified is obtained at index age(H2 = H, when A 2 =Ai).

2.4. Stand-table projection system

The advantages of stand-table projection methods for predicting future diameters include the following: thefunctional form of the diameter distribution (e.g. Weibull) does not have to be assumed, multimodaldistributions can be reproduced, and information on initial stand structure is used (Borders and Patterson, 1990).Pienaar and Harrison (1988) developed a two-part system to project stand tables by using tree- and stand-levelfunctions. The tree-level function is based on relative tree size, defined as the ratio of individual-tree basal areato average basal area per tree in the stand and changes in relative size over time. The second part of thestand-table projection system is projected mean size obtained from stand-level basal area and survival functions.Thus, the future diameter of individual trees can be estimated from the product of projected relative size andprojected mean size obtained from stand-level basal area and survival functions. The relative size projectionfunction for individual trees can be constrained to ensure consistency of the future stand table with stand-levelbasal area and survival functions.

S.A. Knowe, D.E. Hibbs /Forest Ecology and Management 82 (1996) 69-85 73

For the analyses of young trees in a Nelder series, relative size was defined as the ratio of individual-treediameter to quadratic mean diameter (Knowe, 1994b):

Dq2 (

Dq

) (A2/4,)-

+ E (2)

where d,, is the dbh (cm) for the P h tree at the start of the growth interval, d 2i is the dbh (cm) for the tree atthe end of the growth interval, Do is the quadratic mean diameter (cm) at the start of the growth interval, D q2 isthe quadratic mean diameter (cm) at the end of the growth interval, w is the rate parameter, and other terms areas previously defined. The parameter co is estimated by nonlinear regression, with the sign of co indicating thefuture contribution of individual trees in the projected stand. If positive, the relative contribution to Dq in thefuture stand will increase for trees larger than average relative size and decrease for trees smaller than averagerelative size. Conversely, if negative, then the relative contribution will decrease for larger trees and increase forsmaller trees, as had been reported for young Douglas-fir (Knowe, 1994b).

The second part of the stand-table projection system for young red alder is a function for projected mean treesize. This arrangement permits individual-tree diameters to be estimated as the product of projected relative sizeand projected mean size. Several nonlinear and linear models were considered, and, on the basis of explainedvariation and association between parameters and planting density, the following was determined to be mostsuitable for projecting quadratic mean dbh of red alder:

Dq2 = Do + At H 2 H + E (3)

with terms as previously defined. Preliminary regressions indicated that a nonlinear quadratic mean diameterprojection model,

Dq2 = Do( H2 /H, ) A e

resulted in slightly smaller residual sum of squares than Eq. (3), but the relationship between the rate parametersand planting density was not as consistent and produced a poorer fit.

2.5. Survival projection function

A general survival function based on the assumption that survival is proportional to age (Pienaar and Shiver,1981) was selected:

N2 = N ,expf a i ( —AN} (4)

where N, is the number of trees ha- ' surviving at the start of the growth interval, N2 is the number of trees ha-1surviving at the end of the growth interval, a, is the instantaneous mortality rate, a 2 is the age-proportionalityparameter, and other terms are as previously defined.

One advantage of this function is that survival can be expressed as either number of trees ha' or as apercentage. Stand mortality can be allocated to individual trees in the projected stand table by using theprocedures developed by Pienaar and Harrison (1988). Their approach is based on the assumption that mortalityis inversely proportional to relative size (e.g. Dq/cl i ). Thus, larger trees in the stand will have a smaller chanceof dying while smaller trees will have a larger chance of dying.

2.6. Evaluation of diameter projections

The two-sample Kolmogorov-Smirnoff test (Sokal and Rohlf, 1981) was used to determine whether theobserved and projected diameter distributions are samples from the same population. This test is not exact anddoes not validate the projection system, but verifies that the observed and projected stand tables are similar foryoung red alder plantations.

74 S.A. Knowe, D.E. Hibbs / Forest Ecology and Management 82 (1996) 69-85

Beginning with a plantation of age 3, planting density and observed values at the start of each 1-year growthinterval were used to predict surviving number of trees, dominant height, quadratic mean dbh, and individual-treedbh at the end of the interval. Stand mortality was allocated proportional to the inverse of relative diameter (e.g.Dq/d i ), and was then used to compute the cumulative diameter distribution at the end of each growth interval.In addition, observed and predicted dbh for individual trees was compared graphically for 1- and 4-year (ages 3to 7) growth intervals.

3. Results and discussion

3.1. Dominant height projection

The reduced model for projecting dominant height with no planting density effects accounted for 92.8% ofthe variation in projected height (Table 1). Including indicators for planting density classes accounted for anadditional 2.8% of the variation and was significant at the 0.0001 level. Inspection of the estimated rateparameters (Fig. 1) indicated that the relationship between height growth rate and planting density (/3 *) wasquadratic at densities less than 25 000 trees har l and linear at greater densities. Thus, a quadratic and a linearfunction were splined such that the resulting function was smooth and continuous at the join point (Borders etal., 1984):

0* = 0 0 + 0 1TpH +13 2 ( 13 3 - Tpl-) 2 * L

where TpH is the planting density (trees ha -1 ), [3 3 is the join point, and 1= 1 if 03 > TpH and 0 otherwise.This function implies that maximum height growth occurs at earlier ages in stands with high planting densitythan in stands with low density. Expressing the rate parameter in Eq. (1) as a splined function in plantingdensity accounted for 2.8% of the variation and reduced the mean squared error (MSE) by 38% as compared toEq. (1). Thus, replacing the 12 indicator variables with a splined function in planting density resulted in lessthan 0.1% reduction in explained variation. Comparison of the estimates obtained for density classes with thosefor the function revealed that the splined function provided an accurate representation of the rate parameterthroughout the range of planting densities (Fig. 1).

Table 1Proportion of explained variation (R 2 and partial R 2 ) and partial analysis of variance for addition of indicator variables for discrete plantingdensity classes and of functions for planting density in young red alder

Function Model and R2 Partial R 2 df Error Sum F Prob > Fequation of Squares

Dominant height Reduced (1) 0.9284 232 84.76(means at ages 1-7 years) Indicators 0.9566 0.0282 220 51.39 11.904 0.0001

Function (5) 0.9563 0.0279 229 51.77 48.636 0.0001Relative diameter Reduced (2) 0.8764 2711 34.38(individual trees at ages 2-7 years) Indicators 0.8855 0.0091 2699 31.86 17.797 0.0001

Function (6) 0.8839 0.0075 2710 32.31 173.950 0.0001Quadratic mean diameter Reduced (3) 0.9898 194 72.29(means at ages 2-7 years) Indicators 0.9957 0.0059 182 30.26 21.061 0.0001

Function (7) 0.9956 0.0058 193 31.10 255.680 0.0001Survival (ages 1-7 years) Reduced (4) 0.8562 232 263.06

Indicators 0.9284 0.0722 220 130.98 18.486 0.0001Function (8) 0.9272 0.0710 231 133.22 225.143 0.0001

Equation numbers correspond to those used in the text.a R 2 = [corrected total Sum of Squares(SS) - residual SSI/corrected total SS.b F = {[Error Sum of Squares (SSE)reclucd SSfull1)/(df reduced dffun )/(SSE ruii/dfruil ) •

S.A. Knowe, D.E. Hibbs / Forest Ecology and Management 82 (1996) 69-85 75

1.0:

0.97

0.8:

• Density Classes

Function of Density

0.4

0.3

0.2 0 10 20 30 40 50 60 70 80 90 100 110

Planting Density (Trees/Ha x 1000)

Fig. 1. Relationship between the rate parameter in the dominant height projection function for red alder and planting density for 13 discretedensity classes and the function of density, 00 + 13 1 Tp H+ /32( /3 3 - T,H)2 1 where TpH equals trees per hectare.

The final dominant height projection function for red alder includes a splined quadratic-linear function ofplanting density for the rate parameter:

2.2048791 - exp{ - (0.524971 + 4.34 X 10 -6 TpH - 3.83 X 10 -10 (24669.684002 - TpH) 2 I) A2}

H2= H1 1 - exp{ - (0.524971 + 4.34 X 10 -6 TpH - 3.83 X 10- I °(24669.684002 - TpH) 2 A,}

(5)

with L = 1 if TpH < 24 669.68 and 0 otherwise, and other terms as previously defined. The function was basedon 234 observations and accounted for 95.6% of the variation in dominant height growth. The respectiveasymptotic standard errors are 0.090339, 2.00 X 10 -6 , 1.00 X 10 -9 , and 11 854.401224 for the rate parametersand 0.085717 for the shape parameter. As indicated by the quadratic-linear function for the height growth rateparameter, asymptotic height is lower and occurs at younger ages for higher planting density than at lowerplanting density. Therefore, annual height growth peaked at earlier ages and at lower levels for red alder at highplanting density. This result is demonstrated for red alder trees with observed mean height of 2.45 m at age 2years, which is when the absolute differences among densities are smallest (Fig. 2A). At 64 672 trees ha',maximum annual height growth was 1.5 m year' and occurred at age 1. At 345 trees ha', maximum annualheight growth was 2.1 m year - ' and occurred at age 3. Thus, the dominant height growth function exhibits atemporal ripple in maximum height growth that begins at very young ages in high planting densities at thecenter of the Nelder plots and quickly progresses outward to the lower planting densities, a phenomenon alsoreported by Giordano and Hibbs (1993) for these same Nelder plots. The cumulative height-age trajectoriesindicate a height difference of 6.7 m at age 7 between planting densities of 345 and 64 627 trees ha -I , eventhough height at age 2 was equal (Fig. 2B).

We could find few references of similar height responses in other species. Cameron et al. (1989, Cameron etal., 1991) described a temporal ripple in a young Eucalyptus grandis spacing study in Australia. In their study,maximum biomass production shifted to increasingly lower densities between ages 16 and 42 months. Cole and

0 1 2 3 4 5 7

2.5

PlantingDensity

(Trees/Ha)

345984

2804

8048

230160.0

6

cT) 5

4

0

76 S.A. Knowe, D.E. Hibbs / Forest Ecology and Management 82 ( 1996) 69-85

12

11

10 984

9 2804

8

7 8048

0 1 2 3 4Age (years)

Fig. 2. Effects of planting density on dominant height of red alder as depicted by Eq. 5 with H 1 = 2.45m and A i = 2 years: (A) annualheight growth; (B) cumulative height—age curves.

Newton (1987) found similar results for height growth in young Douglas-fir, as did Pienaar and Shiver (1993)for loblolly pine and Krinard (1985) for eastern cottonwood ( Populus deltoides). Scott et al. (1993) presented anexample of both height and diameter increases with increasing density in 7- to 9-year-old Douglas-firplantations. While the prevailing rule of thumb in silviculture is that density has minimal effect on height(Lanner, 1985), how young trees respond to density is unclear, especially for the height component of growth.More systematic study of young stand dynamics and mechanisms of response will be needed to clarify theresults of this and other studies and to determine the management implications.

3.2. Relative diameter projection

The reduced model for change in relative diameter with no planting density effects accounted for 87.6% ofthe variation in projected relative diameter (Table 1). Inclusion of indicator variables for planting density classes

PlantingDensity

(Trees/Ha)

345

23016

64672


0.2

0.0

•-0.2

-0.4

Density classes

— Function of density

0 10 20 30 40 50 60 70 80 90 100 110

Planting Density (Trees/Ha X 1000)

Fig. 3. Relationship between the rate parameter in the relative diameter projection function for red alder and planting density for 13 discretedensity classes and the function of density, co, + w1ln(TpH).

accounted for an additional 0.9% of the variation and was significant at the 0.0001 level. Inspection of theestimated rate parameters (Fig. 3) indicated that a linear-log function would describe the relationship betweenrate of change in relative diameter and planting density (co* ):

w* = (.0 0 + co ,ln(TpH)

with variables as previously defined. This function implies that the rate of change over time in relative diameteris more pronounced in stands with low planting density than in stands with high density. Expressing theparameter in Eq. (2) as a linear-log function in planting density accounted for 0.7% of the variation and reducedthe MSE by 7% as compared to Eq. (2). Thus, replacing the 12 indicator variables with a function for plantingdensity resulted in only 0.2% loss in explained variation. Comparison of the estimates obtained for densityclasses with those for the function revealed a tendency of the function to underpredict the rate of change inrelative diameter between planting densities of 10 000 and 40 000 trees ha' (Fig. 3).

The final projection function for relative diameter of red alder is, , A2,, 1 ,_ I .963486+0.180171 In(TpH)

dzr a Dy e Dqi

with variables as previously defined. The function was based on 2712 observations and accounted for 88.4% ofthe variation in change in relative diameter. The respective asymptotic standard errors are 0.119074 and0.013431. The function implies no change in relative diameter for red alder in stands with a planting density of54 057 trees ha - ' because the parameter is zero. For planting densities of less than 54 057 trees ha -I , red aldertrees with smaller-than-average diameters increase over time in relative diameter while trees with larger-than-average diameters decrease in relative diameter. The converse is true for stands with planting densities greaterthan 54 057 trees ha-I . Therefore, diameter distributions in red alder stands with planting densities less than54 057 trees ha' become less skewed and less variable over time than stands with a higher planting density. At64 672 trees ha -I , projected relative diameter between ages 2 and 7 years exhibited very little change throughout

aa

a

(6)

PlantingDensity

(Trees/Ha)

64 672

23 016

8048

2804984

345

78

3.0-

2.5-

ci) 2.0-

"E 1.5-E

a

1.0-12—'CC

0.5-

0.0

S.A. Knowe, D.E. Hibbs / Forest Ecology and Management 82 (1996) 69-85

00

0.5

1 . 0

1.5

2.0

2.5

Relative Diameter at Age 2

Fig. 4. Effects of planting density on projected relative diameter of red alder between ages 2 and 7 years as depicted by Eq. 6.

the range in initial relative diameter (Fig. 4). At 345 trees ha -1 , projected relative diameter between ages 2 and 7years increased for trees with initial relative diameters less than 1 and decreased for trees with initial relativediameters greater than I.

3.3. Quadratic mean diameter projection

The reduced model for quadratic mean diameter with no planting density effects accounted for 99.0% of thevariation in projected Dq (Table 1). Inclusion of indicator variables for planting density classes accounted for anadditional 0.6% of the variation and was significant at the 0.0001 level. Inspection of the estimated parameters(Fig. 5) indicated that a linear-log function would describe the relationship between D q growth rate and plantingdensity (A * ):

A* = A 0 + A,In(TpH)

with variables as previously defined.Expressing the parameter in Eq. (3) as a linear-log function in planting density accounted for 0.6% of the

variation and reduced the MSE by 57% as compared to Eq. (3). Thus, replacing the 12 indicator variables with afunction of planting density resulted in less than 0.1% loss in explained variation. Comparison of the estimatesobtained for density classes with those for the function revealed adequate description of Dq growth ratethroughout the range in observed planting densities (Fig. 5).

The final quadratic mean diameter projection function for red alder is

Dq2 = Dq , + [2.763147 — 0.213443 In(TpH)] ( H2 — H1)

(7)with variables as previously defined. The function was based on 194 observations and accounted for 99.6% ofthe variation in change in projected Dq . The respective asymptotic standard errors are 0.108756 for the interceptand 0.013351 for the slope. This function implies that the rate of D q growth is greater in stands with low

• Density Classes

— Function of Density


1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.000 10 20 30 40 50 60 70

80

90

100 110


Fig. 5. Relationship between the rate parameter in the quadratic mean diameter projection function for red alder and planting density for 13discrete density classes and the function of density, Ao + A t In (TpH).

planting density, particularly those with less than 20 000 trees ha-I , than in stands with high density. Atcomparable planting densities, Smith and DeBell (1974) and Bormann and Gordon (1984) observed proportion-ally greater reductions in mean dbh at low planting densities than at higher densities - a relationship similar tothe logarithmic one between mean diameter growth rate and planting density in the current study.

As with dominant height growth, the maximum Dq growth for high planting densities occurred at youngerages and at lower levels as compared to low planting densities. Cumulative Dq trajectory over time revealed aslight increase through age 4 for 64 672 trees ha -I and a nearly linear increase in Dq between ages 2 and 7 yearsfor 345 trees ha-I.

3.4. Survival

The reduced model for survival with no planting density effects accounted for 85.6% of the variation inprojected density (Table 1). Inclusion of indicator variables for planting density classes accounted for anadditional 7.2% of the variation and was significant at the 0.0001 level. Inspection of the estimated parameters(Fig. 6) indicated that a quadratic function without an intercept would describe the relationship betweenmortality rate and planting density (a i*):

a,* = a , oTpH + a „TpH 2

with variables as previously defined.Expressing the parameter in Eq. (4) as a quadratic function in planting density accounted for 7.1 % of the

variation and reduced the MSE by 49% as compared to Eq. (4). Thus, replacing the 12 indicator variables with afunction of planting density resulted in only 0.1% loss in explained variation. Comparison of the estimatesobtained for density classes with those for the function revealed adequate description of mortality ratethroughout the range in observed planting densities (Fig. 6).

2 0.7

0.0

0.9

0.8

1.0

0.6

0.5

PlantingDensity

(Trees/Ha)

345

9842804

8048

23 016

64 672

80 S.A. Knowe, D.E. Hibbs/Forest Ecology and Management 82 ( 1996) 69-85

0.000

-0.001

-0.002

-0.003

0 -0.004

0E -0.005

-0.0060cc -0.007

-0.008

-0.009

-0.010

-0.0110 10 20 30 40 50 60 70 80 90 100 110


Fig. 6. Relationship between the mortality rate parameter in the survival function for red alder and planting density for 13 discrete densityclasses and the function of density, a 10 TpH + a „TpH2.

The final survival function for red alder is

N 2 = N i expa —5.54 X 10 -8 TpH — 3.96 X 10- 13 Tpli 2 ( A 22 .607735 Ai .607735 )1 (8)

• Density classes

— Function of density

0.40 1 2 3 4

5

Age (years)

Fig. 7. Effects of planting density on survival of red alder through age 7 as depicted by Eq. (8).

6

7

10 15 200 5B. 984 trees/ha

150 5 Observed dbh (cm) 1 0

A. 345 trees/haProjection

Interval3-44-55-6

cl 6-73-7

20 ProjectionInterval

3-44-55-66-73-7

0 0

•5 10 15 20

C. 2804 trees/haProjection

Interval3-44-55-66-73-7

15

10-

5-

0


Fig. 8. Observed and predicted dbh at ages 4 to 7 obtained by using models (5), (6), and (7) with 1- and 4-year projection intervals. (A) 345trees ha -1 ; (B) 984 trees ha -1 ; (C) 2804 trees ha -1 ; (D) 8048 trees ha - I ; (E) 23 016 trees ha - ; and (F) 64672 trees ha -

with variables as previously defined. The function was based on 234 observations and accounted for 92.7% ofthe variation in survival. The respective asymptotic standard errors are 2.99 X 10 -8 , 1.00 X 10 -15 , and 0.221835.This function implies that the rate of mortality is lower in stands with low planting density and increases slightlywith increasing density throughout the entire range of planting densities included in the Nelder plots.

Stands planted with less than 1000 trees ha-1 had at least 98% survival at age 7 (Fig. 7). Stands planted withup to 10 000 trees per acre had 90% survival or greater at age 7. In comparison, survival for the 64 672 trees ha-1planting density was 90% until age 3, after which mortality rate increased rapidly so that only 44% of the treesplanted were alive at age 7. In comparison, mortality observed by Bormann and Gordon (1984) was about threetimes greater at age 5 than in this study.

D. 8048 trees/ha11 10 -9 -8 -7 -6 -543 -2 -1 -0 I I I

0 1 2 3 4E. 23016 trees/ha

8 7 -6 -5 -4 --a

75 3---c5

2•-

00

ProjectionInterval

ProjectionInterval

3-44-5

3-4cl 4-5

5-66-73-7

6-73-7

1 2 3

5

4

6

5

7 8

6

9

7

10 1 1

8


2 3 4 5 6 7Observed dbh (cm)

Fig. 8 (continued).

3.5. Evaluation of diameter projections

The stand table projection models were evaluated by comparing observed and projected diameter distribu-tions. This was accomplished by using the two-sample Kolmogorov-Smirnoff test (Sokal and Rohlf, 1981)conducted at the 95% confidence level. None of the 156 projected diameter distributions differed significantlyfrom the observed distributions.

The stand table projection models were further evaluated by graphical comparisons of observed and projecteddbh for selected planting densities (Fig. 8). These comparisons revealed a tendency of the models tounderpredict dbh at the lower and the higher planting densities, particularly 345 and 64 672 trees ha -I , at older

F. 64672 trees/ha7

6 -

5 -

4 -

3 -

2 -

1 -

0 0

Knowe, D.E. Hibbs/Forest Ecology and Management 82 (1996) 69-85 83

ages (projections from age 6 to age 7 years), and in the 4-year growth interval. Borders et al. (1988) and Knowe(1994b) also reported a decrease in precision of projection equations as the length of the growth intervalincreased.

4. Conclusions

Biomathematical models for dominant height, diameter, and survival were effective in synthesizing theeffects of a gradient in planting density on structure and dynamics in young red alder plantations. The finalmodels accounted for 88-99% of the observed variation in projected future size. Planting density was astatistically significant effect in the projection models, suggesting that intraspecific competition in young plantedred alder is intense, but accounted for 0.6-2.6% of the variation, indicating that competition is relativelyunimportant (Weldon and Slausen, 1986). The relationship between the height growth rate parameter andplanting density was quadratic at densities less than 24 669 trees ha 1 and linear at greater densities. Therelationship between the parameter associated with growth rate and the natural logarithm of planting density(Cole and Newton, 1987; Giordano and Hibbs, 1993) was linear in the case of relative change in diameter andquadratic mean diameter growth. Replacing indicator variables for discrete planting density classes with afunction of planting density resulted in only 0.1-0.2% loss in explained variation. The relationship between themortality rate parameter and planting density was quadratic. Planting density accounted for 7% of the observedvariation in survival, indicating slightly greater importance of intraspecific competition than for height ordiameter growth.

The response to planting density of the rate parameter in the dominant height projection function was greaterat lower planting densities than at higher densities. As a result, annual height growth of red alder at highplanting density was less and peaked at younger ages than at lower densities. The dominant height projectionfunction depicts a temporal ripple in maximum height growth that progresses from the high to the low plantingdensities over time. This is consistent with results by Bormann and Gordon (1984), Cole and Newton (1987),and Hibbs et al. (1989) in that optimum height growth is observed at an intermediate density that decreases withincreasing stand age. Several micro-environmental factors such as temperature, humidity, and wind (Giordanoand Hibbs, 1993) may be responsible for these differences in height growth patterns. Taller trees at high levelsof inter- or intraspecific competition may indicate reallocation of photosynthate to shoot growth at the expenseof cambial growth because of competition (Waring, 1987). Another possibility is an escape mechanism fromcompetition (Ballare et al., 1990, Ballare et al., 1991). A photomorphic response may occur in trees as a resultof changes in light quality (ratio of red to far-red light) and quantity (reduction of photons in the red and thefar-red wavelengths). Greater weed competition or animal browsing at wide spacings may also contribute todifferent growth patterns.

The relative diameter of individual trees with respect to others at the same planting density was also affectedmore by lower than by higher planting density. At low density, trees that were smaller than average diameterincreased relative to others, while trees that were larger than average decreased relatively. At planting densitiesgreater than 54 000 trees ha -i , trees exhibited very little change in relative diameter. Quadratic mean diametergrowth included both direct effects of planting density, which indicated proportionally greater increases ingrowth rate with decreasing planting density, and indirect effects through increases in dominant height growth atlower densities. As a result, maximum diameter growth was less and occurred at earlier ages for red alder athigh planting densities than at lower densities.

Mortality was less at lower than at higher planting densities. Mortality through age 7 was less than 5% fordensities below about 7500 trees ha-/ and 5-20% for planting densities between 7500 and 22 000 trees ha* Athigher planting densities, mortality rate increased slightly with increasing density.

In general, diameter is considered to be more sensitive to competition than is either height or mortality. Aninspection of the parameter functions for height, diameter, and mortality confirms this pattern for red alder. The


rate parameters for height and diameter were more sensitive to small increments in planting density at the lowerend of the tested range, which corresponds to operational planting densities. In addition, the rate parameter forthe height projection function does not have an asymptote and increases throughout the range of plantingdensities tested. These relationships are consistent with the different types of competition thresholds for tree sizeand survival (Wagner et al., 1989). In general, reductions in height and diameter growth occurred at low levelsof intraspecific competition while survival reductions occurred at much higher levels of competition.

References

Ahrens, G.R., Dobkowski, A. and Hibbs, D.E., 1992. Red alder: guidelines for successful regeneration. Oreg. State Univ. For. Res. Lab.Spec. Publ. 24, Corvallis, OR, 11 pp.

Ballare, C.L., Scopel, A.L. and Sanchez, R.A., 1990. Far-red radiation reflected from adjacent leaves: an early signal of competition in plantcanopies. Science, 247: 329-332.

Ballare, C.L., Scopel, A.L. and Sanchez, R.A., 1991. Photocontrol of stem elongation in plant neighbourhoods: effects of photon fluencerate under natural conditions of radiation. Plant Cell Environ., 14: 57-65.

Bassett, P.M. and Oswald, D.D., 1981a. Timber resource statistics for southwest Washington. USDA For. Serv. Resour. Bull. PNW-91, Pac.Northwest For. Range Exp. S M., Portland, OR, 24 pp.

Bassett, P.M. and Oswald, D.D., 1981b. Timber resource statistics for the Olympic Peninsula, Washin gton. USDA For. Serv. Resour. Bull.PNW-93, Pac. Northwest For. Range Exp. Stn., Portland, OR, 31 pp.

Bassett, P.M. and Oswald, D.D., 1982. Timber resource statistics for the Puget Sound Area, Washington. USDA For. Serv. Resour. Bull.PNW-96, Pac. Northwest For. Range Exp. Stn., Portland, OR, 31 pp.

Borders, B.E. and Patterson, W.D., 1990. Projecting stand tables: a comparison of the Weibull diameter distribution method, apercentile-based projection method, and a basal area growth projection method. For. Sci., 36: 413-424.

Borders, B.E., Bailey, R.L. and Clutter, M.L., 1988. Forest growth models: parameter estimation using real growth series. In: A.R. Ek, S.R.Shiflaj and T.E. Burk (Editors), Proc. IUFRO Forest Growth Modeling and Prediction Conf., 24-28 August 1987, Minneapolis, MN.USDA For. Serv. Gen. Tech. Rep. NC-120, North Central For. Exp. Sm., St. Paul, MN, pp. 660-667.

Borders, B.E., Bailey, R.L. and Ware, K.D., 1984. Slash pine site index from a polymorphic model by joining (splining) nonpolynomialsegments with an algebraic difference method. For. Sci., 30: 411-423.

Bormann, B.T. and Gordon, J.C., 1984. Stand density effects in young red alder plantations: productivity, photosynthate partitioning, andnitrogen fixation. Ecology, 62: 394-402.

Boyer, W.D., 1983. Variations in height-over-age curves for young loblolly pine plantations. For. Sci., 29: 15-27.Buford, M.A. and Burkhart, H.E., 1987. Genetic improvement effects on growth and yield of loblolly pine plantations. For. Sci., 33:

707-724.Cameron, D.M., Rance, S.J., Jones, R.M. and Charles-Edwards, D.A., 1991. Trees and pasture: a study on the effects of spacing. Agrofor.

Today, 3: 8-9.Cameron, D.M., Rance, S.J., Jones, R.M., Charles-Edwards, D.A. and Barnes, A., 1989. Project STAG: an experimental study in

agroforestry. Aust. J. Agric. Res., 40: 699-714.Cole, E.C. and Newton, M., 1987. Fifth-year responses of Douglas-fir to crowding and nonconiferous competition. Can. J. For. Res., 17:

181-186.Curtis, R.O., DeMars, D.J. and Herman, F.R., 1974. Which dependent variable in site-index-height-age regressions? For. Sci., 20: 74-87.Franklin, J.F. and Dymess, C.T., 1973. Natural vegetation of Oregon and Washington. USDA For. Serv. Gen. Tech. Rep. PNW-8, Pac.

Northwest For. Range Exp. Stn., Portland, OR, 417 pp.Gedney, D.R., Bassett, P.M. and Mei, M.A., 1986a. Timber resource statistics for non-federal forest land in northwest Oregon. USDA For.

Serv. Resour. Bull. PNW-RB-140, Pac. Northwest Res. Sm., Portland, OR, 26 pp.Gedney, D.R., Bassett, P.M. and Mei, M.A., 1986b. Timber resource statistics for non-federal forest land in southwest Oregon. USDA For.

Serv. Resour. Bull. PNW-RB-138, Pac. Northwest Res. Sm., Portland, OR, 26 pp.Gedney, D.R., Bassett, P.M. and Mei, M.A., 1987. Timber resource statistics for non-federal forest land in west-central Oregon. USDA For.

Serv. Resour. Bull. PNW-RB-143, Pac. Northwest Res. Stn., Portland, OR, 26 pp.Giordano, P.A. and Hibbs, D.E., 1993. Morphological response to competition in red alder: the role of water. Funct. Ecol., 7: 462-468.Golden, M.S., Meldahl, R., Knowe, S.A. and Boyer, W.D., 1981. Predicting site index for old field loblolly pine plantations. South. J. Appl.

For., 5: 109-114.Hann, D.W. and Ritchie, M.W., 1988. Height growth rate of Douglas-fir: a comparison of model forms. For. Sci., 34: 165-175.Harrington, C.A. and Curtis, R.O., 1986. Height growth and site index curves for red alder. USDA For. Serv. Res. Pap. PNW-358, Pac.

Northwest Res. Stn., Portland, OR, 14 pp.


Harrington, T.B., and Tappeiner, J.C., II., 1991. Competition affects shoot morphology, growth duration, and relative growth rates ofDouglas-fir saplings. Can J. For. Res., 21: 474-481.

Hibbs, D.E., 1987. The self-thinning rule and red alder management. For. Ecol. Manage., 18: 273-281.Hibbs, D.E. and Carlton, G.C., 1989. A comparison of diameter- and volume-based stocking guides for red alder. West. J. Appl. For., 4:

113-115.Hibbs, D.E., DeBell, D.S. and Tarrant, R.F. (Editors), 1994. Biology and Management of Red Alder. OSU Press, Corvallis, OR, 256 pp.Hibbs, D.E., Emmingham, W.H. and Bondi, M.C., 1989. Thinning red alder: effects of method and spacing. For. Sci., 35: 16-29.Hibbs, D.E., Emmingham, W.H. and Bondi, M.C., 1995. Responses of red alder to thinning. West. J. Appl. For., 10: 17-23.Knowe, S.A., 1994a. Effect of competition control treatments on height-age and height-diameter relationships in young Douglas-fir

plantations. For. Ecol. Manage., 67: 101-111.Knowe, S.A., 1994b. Incorporating the effects of interspecific competition and vegetation management treatments into stand table projection

models for Douglas-fir saplings. For. Ecol. Manage., 67: 87-99.Knowe, S.A. and Foster, G.S., 1989. Application of growth models for simulating genetic gain of loblolly pine. For. Sci., 35: 211-228.Krinard, R.M., 1985. Cottonwood development through 19 years in a Nelder design. USDA For. Serv. Res. Note SO-322, South. For. Exp.

Sta., New Orleans, LA, 4 pp.Lanner, R.M., 1985. On the insensitivity of height growth to spacing. For. Ecol. Manage., 13: 143-148.Means, J.E. and Sabin, T.E., 1989. Height growth and site index curves for Douglas-fir in the Siuslaw National Forest, Oregon. West. J.

Appl. For., 4: 136-142.Nance, W.L. and Wells, 0.0., 1981. Site index models for height growth of planted loblolly pine (Pinus taeda L.) seed sources. In: Proc.

16th South. For. Tree Improve. Conf., 27-28 May 1981, VPI and SU, Blacksburg, VA., pp. 86-96.Nelder, J.A., 1962. New kinds of systematic designs for spacing experiments. Biometrics, 18: 283-307.Neter, J., Wasserman, W. and Kutner, M.H., 1985. Applied Linear Statistical Models, 2nd edn. Richard D. Irwin, Inc., Homewood, IL, 1127

pp.Pienaar, L.V. and Harrison, W.M., 1988. A stand table projection approach to yield prediction in unthinned even-aged stands. For. Sci., 34:

804-808.Pienaar, L.V. and Shiver, B.D., 1981. Survival functions for site-prepared slash pine plantations in the flatwoods of Georgia and northem

Florida. South. J. Appl. For., 5: 59-62.Pienaar, L.V. and Shiver, B.D., 1984. The effect of planting density on dominant height in unthinned slash pine plantations. For. Sci., 30:

1059-1066.Pienaar, L.V. and Shiver, B.D., 1993. Early results from an old-field loblolly pine spacing study in the Georgia Piedmont with competition

control. South. J. Appl. For., 17: 193-196.Puettmann, K.J., Hibbs, D.E. and Hann, D.W., 1992. The dynamics of mixed stands of Alnus rubra and Pseudotsuga menziesii: extension

of size-density analysis to species mixture. J. Ecol., 80: 449-458.Richards, F.J., 1959. A flexible growth function for empirical use. J. Exp. Bot., 10: 290-300.Ritchie, M.W. and Hann, D.W., 1986. Development of a tree height growth model for Douglas-fir. For. Ecol. Manage., 15: 135-145.Scott, W., Meade, R., Leon, R. and Hyink, D., 1993. Observations from 7- to 9-year-old Douglas-fir variable density plantation test beds.

Timberlands Forest Resources R&D, For. Res. Field Notes 93-1, Weyerhaeuser Co., Centralia, WA, 2 pp.Smith, J.H.G. and DeBell, D.S., 1974. Some effects of stand density on biomass of red alder. Can. J. For. Res., 4: 335-340.Sokal, R.R. and Rohlf, F.J., 1981. Biometry: The Principles and Practice of Statistics in Biological Research, 2nd edn. W.H. Freeman and

Co., San Francisco, CA, 859 pp.Tarrant, R.F., Bormann, B.T., DeBell, D.S. and Atkinson, W.A., 1983. Managing red alder in the Douglas-fir region: some possibilities. J.

For., 81: 787-792.Wagner, R.G. and Radosevich, S.R., 1991. Neighborhood predictors of interspecific competition in young Douglas-fir plantations. Can. J.

For. Res., 21: 821-828.Wagner, R.G., Petersen, T.D., Ross, D.W. and Radosevich, S.R., 1989. Competition thresholds for the survival and growth of ponderosa

pine seedlings associated with woody and herbaceous vegetation. New For., 3: 151-170.Waring, R.H., 1987. Characteristics of trees predisposed to die. BioScience, 37: 569-574.Weldon, C.W. and Slausen, W.L., 1986. The intensity of competition versus its importance. An overlooked distinction and some

implications. Q. Rev. Biol., 61: 23-44.

stand structure and dynamics of young red alder as affected by...

Documents