Comparative tree growth efficiency in Sierra Nevada mixed-conifer forests

Forest Ecology and Management 219 (2005) 95–108 www.elsevier.com/locate/foreco

Comparative tree growth efficiency in Sierra Nevada mixed-conifer forests Rolf F. Gersonde a,*, Kevin L. O’Hara b,1 a

Watershed Management Division, Seattle Public Utilities, 19901 Cedar Falls Road SE, North Bend, WA 98045, USA b Department of Environmental Science, Policy & Management, 137 Mulford Hall, University of California, Berkeley, CA 94720-3114, USA Received 26 March 2005; received in revised form 31 August 2005; accepted 1 September 2005

Abstract Tree growth efficiency, or volume growth increment per unit leaf area, was calculated in multiaged mixed-conifer stands in the Sierra Nevada, California. Five conifer species with a range of tolerance to shade were sampled over a wide range of canopy positions and ages to detect species-specific patterns of growth efficiency (GE). All species showed non-linear, sigmoidal trends of volume increment with increasing leaf area. This pattern indicates slow increase in GE in shaded understory conditions and a peak in GE at intermediate tree size in mid-canopy positions. Larger trees showed lower GE than intermediate size trees. Species with lower shade tolerance had greater GE than species with greater tolerance. To test the effect of local light environment on tree volume growth, we used a light model to calculate the growing season average of absorbed light for individual trees. Models of volume increment as a function of weighted leaf area showed increased GE for small trees, indicating that the slow increase in volume increment in smaller understory trees was an effect of limited light conditions. Patterns of growth efficiency in multiaged mixed-species stands can be used to predict growth patterns of sub-canopy trees and judge relative shade tolerance. # 2005 Elsevier B.V. All rights reserved. Keywords: Leaf area; Light model; Multiaged; Shade tolerance; Leaf area index; Mixed-species

1. Introduction Tree growth efficiency (GE) is the relationship between growth and occupied resource space. It has * Corresponding author. Tel.: +1 206 233 1513; fax: +1 206 233 1527. E-mail addresses: [email protected] (R.F. Gersonde), [email protected] (K.L. O’Hara). 1 Tel.: +1 510 642 2127; fax: +1 510 643 5438.

been used to explain growth performance of trees in different canopy positions and competitive status of stand components, such as cohorts or species. A common way to define GE is to express stem volume increment per unit leaf area for individual trees (Assmann, 1970; Waring, 1983; O’Hara, 1988), assuming both variables to be a function of resource availability and biomass partitioning. Results from several studies suggest that a clear pattern for the development of GE with relative

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Table 1 Location and stand characteristics of sample sites in Sierra Nevada mixed-conifer forests Ownership stand

Latitude (8N)

Volume (m3 ha
1)

Longitude (8W)

Elevation (m)

Canopy structure

Age-structure

LAI

Sierra Pacific Industries M1 38.47 M2 38.47 M3 38.43 M4 38.44 M5 38.44


120.51
120.51
120.45
120.45
120.45

1075 1075 1146 1160 1160

Gap (0.06 ha) Irregular Continuous Continuous Irregular

2-Cohort 3-Cohort 2-Cohort 3-Cohort 3-Cohort

4 3.7 3.9 4.7 6.3

431.3 383.4 448.9 519.2 654.0

Eldorado National Forest E1 38.60 E2 38.68 E3 38.99


120.49
120.43
120.41

1340 1400 1720

Continuous Gap (0.03 ha) Irregular

2-Cohort 2-Cohort 4-Cohort

9.5 7.7 5.3

1405.2 990.5 742.5

Blodgett Forest Research Station B80 38.92 B210 38.90


120.65
120.67

1250 1320

Continuous Continuous

2-Cohort 1-Cohort

3.7 8.4

284.8 557.2

Collins Pine Company CA1 40.26


121.26

1430

Gap (0.13 ha)

3-Cohort

2.7

394.3

LAI: leaf area index; volume: stand stem volume.

canopy position does not exist and that patterns are specific to species or possibly stand structure (Seymour and Kenefic, 2002, Table 1). For several species, GE is reported to peak in intermediate size trees of mid-canopy position. Other studies have found suppressed or dominant canopy positions to have the highest GE within the canopy (O’Hara, 1996; Reid et al., 2004). While some of the observed differences might be explained by species-specific allocation patterns, others point to the effect of stand structure on GE patterns due to variations in resource environment (Roberts et al., 1993; Binkley et al., 2002). In evenaged, single-species stands, trees are at similar developmental stages and while they differentiate into crown classes, they often share the same resource environment in a single canopy layer. Multiaged stands, on the other hand, often contain a wide range of tree ages and developmental stages and trees in lower and upper canopy layers experience greater differences in resource conditions. Thus, observations made in even-aged stands can provide insight into the relationship between crown differentiation and GE, while multiaged stands add the effect of age and canopy layering, offering insights of a species’ GE relationships under a range of resource conditions. A number of models have been suggested for development of GE with increasing leaf area (Seymour and Kenefic, 2002) as well as functional

relationships that underlie the observed patterns. Increasing GE with relative tree size is thought to result from improved resource availability with relative canopy position (Roberts et al., 1993; Gilmore and Seymour, 1996; Brunner and Nigh, 2000; Claveau et al., 2002). The decrease in growth of larger trees, and the decline in GE, has been attributed to such factors as the relative increase of non-photosynthetic tissue with increasing leaf area (Ma¨kela¨, 1986; Givnish, 1988), increasing restrictions in water relations with tree size (Ryan and Yoder, 1997) and age (Seymour and Kenefic, 2002). Together, these factors result in the non-linear relationships observed in many tree species and suggest that patterns of GE might indicate species-specific ecological life history traits. Although single-species stands often form characteristic stand structures, mixed-species stands provide an opportunity to compare species-specific patterns of GE in vertically complex canopies. Few studies have investigated patterns of GE in mixedspecies stands with trees growing in a wide range of canopy positions. Such stands often form vertically structured canopies with complex growth dynamics and GE of individual stand components has strong implications for mixed-species management. While shade-tolerant species generally produce less volume increment per unit of leaf area, they can achieve similar productivity to intolerant species by main-

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taining higher leaf area (O’Hara et al., 1999). The ability of shade-tolerant species to maintain higher leaf area density under shaded conditions (Gersonde et al., 2004) may provide them with an advantage in the competition for light resources. Knowledge of changes in GE with increasing tree size and for trees of a range of shade tolerance could aid understanding of the growth dynamics in mixed-species forests. The importance of light capture to competitive interactions of trees is based on the linear relationship between intercepted photosynthetically active radiation (PAR) and plant productivity (Cannell, 1989), which depends on the amount of incident light and the leaf area available to intercept light. While the production of non-photosynthetic tissue (stem volume) can place foliage in better light environments, the amount of leaf area available for light absorption determines productivity. This amount of leaf area in turn is effected by environmental site conditions (Della-Tea and Jokela, 1991) and species-specific allometric relationships (Whitehead et al., 1984), whereas incident light is largely determined by the competitive status and relative canopy position. The relationship of absorbed PAR and plant productivity is the light use efficiency of a tree. Brunner and Nigh (2000) used this concept to develop a resourcedependent competition index, weighted leaf area (WLA), to quantify the competitive status of individual trees depending on the amount of absorbed light during the growing season. WLA showed a strong correlation with volume increment and could be used to show changes in growth efficiency with competitive status or relative canopy position. If such patterns could be quantified for individual species in mixed-species stands, they could be used to predict the productivity and dynamics of multiaged mixedspecies stands. Our objectives for this study were to determine: (a) if individual species showed differences in the development of volume growth with increasing tree leaf area and (b) what the effect of local light conditions were on the pattern of GE. We chose the Sierra Nevada mixed-conifer forests as an example as they are composed of conifer species with a wide range in shade tolerance. Mixed-species stands are often composed of species that display great differences in ecological traits, such as foliage morphology, shade tolerance, crown geometry and

97

growth patterns. The combination of these traits determines the species’ competitive interactions, and subsequently, shape the stand development patterns in mixed forests. We hypothesized that shade-tolerant and shade-intolerant species would differ in patterns of GE. Furthermore, if the effect of local light environment on GE could be quantified through WLA, such relationship would be useful for forest growth models and stocking guidelines for multiaged, mixedspecies stands.

2. Methods 2.1. Study area Study sites were located in the central Sierra Nevada mixed-conifer forests at elevations between 1000 and 2000 m. The climate in this region of California is characterized by pronounced summer drought and cold, wet winters. Growing season for mixed-conifers spans from May to August and varies with elevation and exposure (Royce and Barbour, 2001). Eleven sample stands were selected to represent managed stands of mixed-conifers ranging in structure from uniform even-aged stands to irregular multiaged stands, including stands with distinct canopy gaps and shelterwood structures. Sample plots in these stands were sized to incorporate the structural variability and ranged in size from 0.16 to 1.16 ha. Stand location and stand structure are given in Table 1 and are further described in Gersonde et al. (2004). The stands were selected to include multiaged mixed-conifers, including white fir (Abies concolor (Gord. and Hildebr.), incense-cedar (Calocedrus decurrens (Torr.) Florin), Douglas-fir (Pseudotsuga menzieii var. menziesii (Mirb.) Franco), sugar pine (Pinus lambertiana Dougl.) and ponderosa pine (Pinus ponderosa P. & C. Lawson) growing in various canopy positions. Daniel et al. (1979) ranked the five conifers according to their tolerance of growing in understory conditions at low light intensity and high root competition, white fir and incense-cedar as tolerant, sugar pine and Douglas-fir as intermediate and ponderosa pine as intolerant. All trees taller than 1.37 m were mapped and measured for stem diameter at breast height, total

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height, height to crown base, height to greatest crown width, bark thickness and 5-year height growth. Height growth was determined from internodal growth of the past 5 years when visible or calculated from breast height age and site index equations (Biging and Wensel, 1985). We assumed acrotony in the terminal branching pattern of incense-cedar and determined terminal growth by counting the last five consecutive growth modules. Trees were assigned to upper, middle and lower canopy layers according to relative canopy height. Sapwood radius and 5-year radial increment were calculated as the arithmetic mean of two measurements from separate increment cores taken a breast height (1.37 m), or at crown base on trees where the base of the live crown was below breast height. Projected leaf area, the vertical projection of all needle silhouettes, was estimated for each tree using prediction equations developed by Gersonde et al. (2004). Leaf area prediction followed the pipe model theory (Shinozaki et al., 1964; Waring et al., 1982) and assumed that cross-sectional area of the water conducting sapwood below the crown was proportional to the projected foliage area of the tree. Because the leaf area prediction models had a zero intercept, we used prediction equations using sapwood area at crown base for all trees with base of the live crown from below breast height to 2 m height, and prediction equations using sapwood area at breast height for all other trees. Site index for each species was calculated from height–age relationships of trees that showed no periods of suppressed growth in their tree ring pattern and site index equations for Sierra Nevada mixed-conifers (Biging and Wensel, 1985). When suitable site trees were not available due to heart rot or evidence of past suppression, conversion factors for site index were used following Wensel (1997). 2.2. Light capture model We used the light model tRAYci (Brunner, 1998) to calculate incident and absorbed light for each tree crown. Tree crowns were characterized as threedimensional foliage shells with a foliage-free space around the stem and homogeneous foliage density. Crown radii were measured in cardinal directions, and crown shape was estimated for the upper and lower crown, divided at the height of the greatest crown

width. Vertical thickness of the foliage envelope was estimated for the upper and lower crown following Brunner (1998). For a detailed description of this crown representation, see MacFarlane et al. (2003) or Gersonde et al. (2004). The tRAYci model uses Bougeur’s law, applied to light attenuation through a foliated canopy, to calculate the percent of above canopy light (PACL) at any point in the canopy space. Light absorption was calculated as: APACL ¼ PACLð1
expð
0:5  LAD  PATHÞÞ; where APACL is the absorbed light and PACL is the incident light as percent of above canopy light, LAD the leaf area density (m2/m3) of the foliated crown envelope and PATH is the path length (m) of individual light rays through the foliated canopy space. Though the total number of sample points used to estimate mean values for incident and absorbed light varied with crown projection area, a minimum of 20 point light calculations were made on crowns of smaller understory trees. All light values represent the percent of above canopy light calculated over the entire growing season. Average growing season at Blodgett Forest Research Station (BFRS, 2003) was estimated to begin May 1 and end on August 31. The beginning of the growing season in the Sierra Nevada is correlated with snowmelt and threshold temperatures for bud break; the end of the growing season is correlated with vapor pressure deficit (Royce and Barbour, 2001). To account for the effect of climatic variability on growing season length between sample sites, we calculated cumulative radiation (W/m2) and VPD for each site using the MTCLIM (Running et al., 1987) model and long-term data from BFRS. The MTCLIM model considers site differences between the meteorological base station (BFRS) and the sample site, including elevation, latitude, average precipitation, aspect and slope. Beginning of the growing season relative to BFRS (May 1) was determined for individual sample sites when the same cumulative radiation was reached. The end of the growing season was determined when the same cumulative VPD was reached as calculated for August 31 at BFRS. The proportion of diffuse radiation to total radiation was set at 25% for all sample sites. To minimize edge effects on light calculations, we used the torsional edge correction in tRAYci to multiply the rectangular

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sample plots eight times around the mapped plot. Finally, a weighted leaf area was calculated as WLA = meanAPACL  PLA, by multiplying the mean APACL of an individual crown by the total projected leaf area (PLA) determined from leaf area prediction equations. WLA combines the amount of light absorbed by a tree crown during the growing season and the total foliage area of the tree (PLA) and can be used as a competition index that integrates inter-tree competition for resources (Brunner and Nigh, 2000). The relationship between bole volume increment and WLA is expected to change with relative canopy position and would indicate changes in light use efficiency (LUE) with relative tree size. Trees were excluded from the analysis for two reasons: (1) if the minimum value for PACL calculations was zero because a section of the foliated crown space overlapped with the stem space of another tree and (2) if a tree was located directly at the plot boundary, resulting in possible errors of light calculation due to inaccurate canopy representation. Stem volume growth of individual trees was calculated from past 5-year radial increment, 5-year height increment and taper equations for Sierra Nevada mixed-conifers (Wensel and Olson, 1995) and expressed as 5-year volume increment (m3 5 years
1). For trees with crown base below breast height stem form was assumed to be conical. For trees with crown base above breast height but below the range of DBH used in mixed-conifer taper models, stem form was considered cylindrical from the ground to breast height and conical above. Growing space efficiency (GE) was calculated as stem volume increment per unit leaf area (dm3 m
2 5 years
1). 2.3. Analytical approach Preliminary data analysis showed non-linear trends in tree volume growth as a function of increasing leaf area. To model stem volume growth, five non-linear models were selected based upon their properties and successful use in previous studies (Table 2); a power model had been used in several studies (Seymour and Kenefic, 2002) and indicates monotonic increasing, decreasing or linear relationships depending on the value of the exponential parameter; the two-parameter exponential model also forces the relationship through

99

Table 2 Models tested to predict volume increment (Vinc) as a function of predicted leaf area or weighted leaf area (LA) No.

Model form

Model type

[1] [2]

Vinc ¼ b1 LAb2 Vinc ¼ b1 ð1
expð
b2 LAÞÞ

[3] [4]

b3 Vinc ¼ b1 bLA 2 LA Vinc ¼ b1 ð1
expð
b2 LAÞÞb3

[5]

Vinc ¼ b1 ð1
expð
ðLA=b2 Þb3 ÞÞ

Power model Two-parameter exponential model Hoerl model Chapman-Richards model Weibull model

the origin but has a different shape; the Hoerl model (Daniel and Wood, 1980) provides a combination of power and exponential model, and can follow exponential increasing, maximum and declining patterns; the Chapman-Richards model has a sigmoid form; the Weibull model had been used in three previous studies modeling volume increment (Roberts and Long, 1992; Gilmore and Seymour, 1996; Seymour and Kenefic, 2002). Models for stem volume increment (Vinc) were fit for each species using nonlinear least squares regression with either projected leaf area or weighted leaf area as independent variables. Models were evaluated by their residual error, the distribution of the residuals and an Akaike Information Criterion (AIC, Anderson et al., 2000). AIC calculates the likelihood of a model given the data and includes a penalty for extra model parameters. The AIC values were rescaled so that the model with the lowest AIC had the value of zero, Di = AICi
minAIC. The Di values are interpreted as the plausibility of a model, with larger values being less plausible. A transformation of wi = exp(
1/2 Di) provides the likelihood of the model given the data and is normalized so that the wi values sum to 1. The Akaike weights (wi) can be interpreted as approximate probabilities that model i is in fact the best model in the set of models under consideration (Anderson et al., 2000). Boundary line analysis was used to describe the relationship between PACL and PLA. This approach has been used to determine the limiting effects of an environmental variable on the response variable (Webb, 1972; Lark, 1997). Equations were fitted to a subset of points (95th percentile) that constitute the upper boundary of the two-dimensional dataset. This

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upper boundary represents the maximum response to a potentially limiting factor. Data points below the boundary line were assumed to be limited by other factors. Boundary line analysis does not take into account interactions between limiting factors and only applies to additive effects of independent variables.

3. Results 3.1. Volume increment and projected leaf area The 11 sample stands provided a range of stand structures (Table 1) and composition in which trees were sampled in a wide size range (Table 3) and various canopy positions, leading to great differences in stem volume increment. While incense-cedar and white fir occurred in the understory of most stands, ponderosa pine, sugar pine and Douglas-fir occurred in the understory of stands with lower stand volume (Table 1). The mid-canopy and overstory layers were composed of mixed-species in all stands. All species showed a positive non-linear relationship between projected leaf area and stem volume increment (Fig. 1). Of the five non-linear models tested, sigmoidal models had a greater likelihood (wi), given the data for most species (Table 4). The sigmoid shape indicates exponentially increasing Vinc with PLA in small trees, and monotonic declining Vinc in larger trees. The Hoerl, Chapman-Richards and Weibull models showed little differences in model fit despite differences in model form, and have little relative differences in relative Akaike weights (wmax/wi). Only

for the ponderosa pine dataset did the two-parameter exponential model have a high likelihood (wi = 0.2099) similar to sigmoidal models, which indicates that the initially exponential increase in Vinc with PLA was relatively small. Sugar pine reached the highest volume increment (2.66 m3 5 years
1) followed by ponderosa pine and Douglas-fir. The highest projected leaf area values were also observed in sugar pine (1629 m2) followed by white fir (1282 m2) and Douglas-fir (1039 m2). Parameter statistics for the models having the greatest likelihood are given in Table 5. Because of the limited sample of large trees, prediction of trees above 600 m2 PLA is connected with high uncertainty. Overall, residual errors for Vinc were greater for those species that showed high volume increment for individual trees (ponderosa pine and sugar pine). For incense-cedar, the selected model shows an asymptotic development over the sample range (Fig. 1). 3.2. Volume increment and weighted leaf area Predictive models for Vinc performed better when weighted leaf area was used as independent variable as compared to PLA for all species except Douglas-fir (Table 4). For Douglas-fir, all models using PLA as an independent variable result in lower residual errors. The differences, however, were small and more pronounced in models with greater relative likelihood (wmax/wi). The sigmoidal models performed better on data for incense-cedar, sugar pine and white fir, while the two-parameter exponential model had the highest likelihood for the weighted Douglas-fir data

Table 3 Range of tree heights (m) by species and sample stand Stand

Douglas-fir

Incense-cedar

Ponderosa pine

Sugar pine

White fir

B210 B80 CA1 E1 E2 E3 M1 M2 M3 M4 M5

9.2–38.5 1.4–45.5 – – 11.3–40.4 – 4.08–14.1 – – 5.9–17.5 5.9–44.2

1.2–37.8 1.3–30.5 3.7–16.6 2.5–48.7 39.3–49.4 4.5–47.9 0.8–32.7 1.3–30.9 2.5–20 13.9–32.6 6.3–14.4

26.2–38.1 1.4–43.9 1.02–48.8 40.1–60.9 – 13–35.5 1.3–49.2 4.5–47.7 18.7–48.7 20.1–48.5 10.6–47.5

18.3–46 1.4–46.1 12.4–35.6 27.3–50.6 – 5.7–62.7 0.8–18.6 4.6–12.4 2.8–50.2 4.7–47.8 14–48

1.9–41.2 1.2–43.3 1.1–46.6 2.8–19.1 4.9–59.6 1.8–37.1 1.3–20.8 1.2–27.1 5.4–29 6.1–27.4 10–43.3

R.F. Gersonde, K.L. O’Hara / Forest Ecology and Management 219 (2005) 95–108

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Fig. 1. Tree volume increment (Vinc) as a function of projected leaf area (PLA, open circles, dashed line) and weighted leaf area (WLA, filled circles, solid line) for five conifer species; model forms and parameter values are given in Tables 2 and 5: (a) Douglas-fir; (b) incense-cedar; (c) ponderosa pine; (d) sugar pine; (e) white fir.

(wi = 0.3530), and the power model had the highest likelihood for ponderosa pine (wi = 0.4024). The exponential parameter b2 (0.6896) in the power model for ponderosa pine indicates monotonically declining growth efficiency with increasing WLA. For these two species, the relationship between weighted leaf area and Vinc did not show the initial exponential increase and inflexion point as observed with projected leaf area as independent variable. Models of sigmoidal form had higher likelihood for all species except

Douglas-fir: a Weibull model had the highest likelihood for incense-cedar (wi = 0.6383) and white fir (wi = 0.4139), and a Hoerl model was selected for the sugar pine data (wi = 0.5720). For these species, the relative distances in Akaike weights (wi) between power and exponential models and sigmoidal models were relatively large, indicating exponential increase in Vinc with WLA for small trees. Parameter statistics for the best models are given in Table 5. The sigmoidal shape of the WLA models (Fig. 1) was less

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Table 4 Evaluation of predictive models for volume increment from projected leaf area and weighted leaf area using Akaike Information Criterion (AIC) Species

Model

Projected leaf area AIC
343.13
341.23
360.18
358.79
360.42

Weighted leaf area wmax/wi

wi

RMSE


5

7.5  10 2.9  10
5 0.3808 0.1898 0.4293

3

5.7  10 1.5  10 4 1.127 2.262 1

0.0702 0.0713 0.061 0.0617 0.0609

Douglas-fir (n = 65)

[1] [2] [3] [4] [5]

Incense-cedar (n = 252)

[1] [2] [3] [4] [5]


1418
1439.9
1450.9
1452.8
1452.2

1.3  10
8 0.0007 0.183 0.4664 0.3499

3.6  10 7 627.377 2.548 1 1.333

0.0598 0.0582 0.0559 0.0557 0.0557

Ponderosa pine (n = 275)

[1] [2] [3] [4] [5]


1078.1
1091.1
1091.4
1091.7
1091.5

0.0003 0.2099 0.2466 0.2855 0.2577

8.9  10 2 1.36 1.158 1 1.108

0.1403 0.1376 0.1367 0.1366 0.1367

Sugar pine (n = 148)

[1] [2] [3] [4] [5]

2.4  10
14 7.0  10
7 0.3133 0.2724 0.4143

1.7  10 13 5.9  10 5 1.322 1.521 1

0.1536 0.1438 0.1248 0.1249 0.1245

White fir (n = 272)

[1] [2] [3] [4] [5]

1.3  10
7 0.0227 0.4228 0.2528 0.3016

3.2  10 6 18.613 1 1.672 1.402

0.0735 0.0714 0.0694 0.0695 0.0695


552.47
586.86
612.89
612.61
613.45
1418.2
1442.3
1448.1
1447.1
1447.5

AIC
280.57
314.11
314.05
313.82
278.36

wi

wmax/wi
8

RMSE 7

1.8  10 0.353 0.3416 0.3053 6.1  10
9

1.9  10 1 1.033 1.156 5.8  10 7

0.0705 0.0717 0.071 0.0711 0.0956


1372.5
1443.6
1447.2
1456.6
1457.8

1.9  10
19 5.2  10
4 0.0032 0.358 0.6383

3.3  10 18 1.2  10 3 2  10 2 1.783 1

0.0452 0.0385 0.0381 0.0373 0.0372


1065.6
1051.4
1064.1
1064.2
1064.3

0.4024 3.3  10
4 0.1947 0.1956 0.207

1 1.2  10 3 2.067 2.057 1.944

0.1354 0.1391 0.1355 0.1355 0.1355

4.5  10
13 0.0722 0.572 0.1372 0.2186

1.3  10 12 7.926 1 4.169 2.616

0.1406 0.1166 0.1145 0.1157 0.1153

3.3  10
3 7.1  10
5 0.2725 0.3103 0.4139

1.3  10 2 5.8  10 3 1.519 1.334 1

0.0633 0.0643 0.062 0.062 0.0619


539.33
590.94
595.08
592.22
593.16
1350.4
1342.7
1359.3
1359.5
1360.1

Model forms are given in Table 2; wi—Akaike weight, wmax/wi—relative weight, RMSE—residual mean squared error.

pronounced than for models using PLA as independent variable. 3.3. Growth efficiency Changes in GE with increasing leaf area were calculated by dividing the best models for Vinc by leaf area and plotting the results as a function of leaf area. The resulting patterns for GE as a function of PLA showed a peaking relationship (Fig. 2). Among the observed species, the intolerant ponderosa pine had the highest growth efficiency (2.62 dm3 m
2 5 years
1), and the model predicted a maximum GE at 202 m2 PLA. In contrast, the models for shadetolerant incense-cedar and white fir showed the lowest GE (0.87 and 1.43 dm3 m
2 5 years
1, respectively), which were reached at higher leaf area values (227 and

342 m2). The Douglas-fir model reached a GE of 1.46 dm3 m
2 5 years
1 at 567 m2 PLA and the GE model for sugar pine had a maximum (2.07 dm3 m
2 5 years
1) at a PLA value of 628 m2. These two species, while intermediate in maximum GE, peak relatively late. Light use efficiency was calculated as Vinc/WLA (Brunner and Nigh, 2000) and plotted against PLA to express changes with increasing crown size. All species showed the high LUE at low PLA values and generally decreasing LUE with increasing PLA (Fig. 3). Trees with PLA values below 100 m2 had the greatest variability in LUE. When trees were assigned to canopy layers according to relative canopy height, trees in mid-canopy positions (approximately, 10–25 m total height) showed significantly higher LUE values ( p = 0.05) than trees in lower and upper

R.F. Gersonde, K.L. O’Hara / Forest Ecology and Management 219 (2005) 95–108

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Table 5 Parameter statistics for volume increment models using projected leaf area (PLA) and weighted leaf area (WLA) Species

Projected leaf area

Weighted leaf area

Model

Parameter

Mean

Standard error

p-Value

Model

Parameter

Mean

Standard error

p-Value

Douglas-fir

[5]

b1 b2 b3

1.5308 670.8320 1.5111

0.1766 91.2936 0.1115

<0.0001 <0.0001 <0.0001

[2]

b1 b2

3.4818 0.0009

1.4672 0.0004

0.0210 0.0458

Incense-cedar

[4]

b1 b2 b3

0.3636 0.0063 2.2086

0.0220 0.0011 0.3953

<0.0001 <0.0001 <0.0001

[5]

b1 b2 b3

0.3400 80.4556 1.3313

0.0138 6.4177 0.0898

<0.0001 <0.0001 <0.0001

Ponderosa pine

[4]

b1 b2 b3

2.0833 0.0020 1.2273

0.2724 0.0005 0.1165

<0.0001 0.0001 <0.0001

[1]

b1 b2

0.0248 0.6895

0.0030 0.0221

<0.0001 <0.0001

Sugar pine

[5]

b1 b2 b3

2.5989 809.1520 1.4435

0.1297 57.4966 0.0679

<0.0001 <0.0001 <0.0001

[3]

b1 b2 b3

0.0034 0.9992 1.0773

0.0009 0.0001 0.0527

0.0003 <0.0001 <0.0001

White fir

[3]

b1 b2 b3

0.0004 0.9993 1.2449

0.0001 0.0001 0.0676

0.0043 <0.0001 <0.0001

[5]

b1 b2 b3

1.5672 488.9151 0.7960

0.3044 188.2424 0.0456

<0.0001 0.0100 <0.0001

Models forms are given in Table 2.

canopy layers (Table 6). These differences were not significant for incense-cedar. Analysis of variance was used to quantify the effect of canopy layers on LUE. Means of canopy layers were compared using the Tuckey test for unequal sample sizes (Zar, 1999). Canopy layers accounted for 1–45% of the variability in LUE.

Fig. 2. Growth efficiency as a function of projected leaf area for individual species; DF: Douglas-fir, IC: incense-cedar, PP: ponderosa pine, SP: sugar pine, WF: white fir.

4. Discussion The results of this study demonstrate patterns of growth in vertically structured canopies of Sierra Nevada mixed-conifer forests. Each species was found in a range of canopy positions and light environments. This situation made comparison of species-specific growth patterns possible and shows GE over a wide range of tree size and light environments. The models for volume increment (Vinc) and PLA had sigmoid shapes, showed exponential increase of Vinc with the PLA for small trees (<100 m2 PLA, Fig. 1) and decreasing Vinc with increasing PLA for larger trees. This pattern that was less pronounced for the intolerant ponderosa pine than for other species (Fig. 1). Since small trees generally grew in the partial shade of higher canopy strata, it was assumed that their gain in productivity would be driven by improvements in resource environment and that higher GE would occur in mid-canopy trees of intermediate size. This pattern was consistent among the observed species in multiaged stands. Stands with heterogeneous canopies and diverse tree sizes exhibit continuous light gradients throughout the canopies that result in improved light resource conditions with relative canopy height (Gersonde et al., 2004). Here,

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Fig. 3. Light use efficiency (LUE) plotted against projected leaf area (PLA) for individual mixed-conifer species: (a) Douglas-fir; (b) incensecedar; (c) ponderosa pine; (d) sugar pine; (e) white fir. Trees are assigned to canopy layers according to relative canopy height.

Table 6 Mean light use efficiency (LUE = Vinc/WLA) for individual canopy layers (mean and S.E.) (dm3 m
2 5 years
1; canopy layers were assigned in the field according to relative canopy height) Canopy layer

Upper

Middle

Lower

R2

p-Value

Douglas-fir Incense-cedar Ponderosa pine Sugar pine White fir

2.41 2.72 6.32 3.77 3.30

7.07 2.77 10.31 5.08 7.73

1.33 2.62 8.25 3.35 4.47

0.45 0.01 0.13 0.16 0.17

<0.0001 0.53 <0.0001 <0.0001 <0.0001

(0.13) (0.27) (0.26) (0.15) (0.22)

(0.91) (0.18) (0.62) (0.29) (0.63)

(0.19) (0.29) (0.72) (0.28) (0.31)

ANOVA was used to quantify the effect (R2 and p-values for F-test) of canopy layers on LUE.

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crown expansion is accompanied by increasing Vinc due to improved light resource conditions. However, when changes in light conditions were accounted for by calculating LUE using WLA, it appeared that average efficiency of trees in mid-canopy positions was still higher. Our results show that other factors than improved light conditions contribute to the pattern of GE with increasing PLA in multiaged stands. Roberts et al. (1993) had conceptualized that the patterns of GE development depend on stand structure and the resulting light environments within the canopy. They observed tolerant subalpine fir growing in heterogeneous canopies to exhibit a peak in GE in mid-canopy positions, and postulated that intolerant species growing in homogeneous stands would show continuously declining GE. While this argument was based on single-species stands, our example of multiaged, mixed-species stands demonstrates that patterns of GE for intolerant species can exhibit a peak in lower leaf area values. Tree species in boreal forests react differently to the interaction of tree height and light environment (Claveau et al., 2002). While shade-tolerant Abies and Picea species showed changes in diameter growth with height and changing light, Pinus species in boreal forests showed less variation in growth and morphological response due to light environment. Diameter growth of intolerant boreal species, less than 4 m tall, was mainly driven by tree height. Our results in the Sierra Nevada also indicate that young, shade-tolerant trees experiences greater changes in GE due to light environment than shade-intolerant species. Although shade-tolerant white fir and incense-cedar exhibited initial exponential growth with size in the understory, intolerant ponderosa pine showed a very steep increase in growth and high GE below 100 m2 PLA (Fig. 2). Models for sugar pine and Douglas-fir showed an intermediate increase in GE with PLA and reached their maximum later than other species. This slower increase in GE indicated a greater plasticity in stem volume growth under limited light environments, while higher maximum GE could reflect an adaptation to high light environments. The latter two species appear intermediate in both traits. Such differences in growth plasticity have been described in playing a key role in the performance of Douglas-fir and lodgepole pine (Chen et al., 1996). A shift in allocation from

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belowground structures to crown expansion in sapling size trees and to woody tissue in pole size trees has been shown to occur with ponderosa pine (Grulke and Retzlaff, 2001) and would explain the initial increase in growth efficiency and the peak in intermediate canopy positions of pole size trees. Such a shift in allocation is expected due to increase in xylem production with continuous height growth and requirements for mechanical support (Cannell and Dewar, 1994). Although we cannot demonstrate a similar pattern for other mixed-conifer species, our results on changes in GE with increasing PLA suggest that a shift in allocation towards woody tissue occurs later in species that are intermediate or tolerant to shade. Using weighted leaf area to model Vinc in multiaged stands enabled us to account for variable light resource conditions and the differences in leaf area density among the observed species. Following the approach by Brunner and Nigh (2000) who weighted leaf area of individual trees by the average amount of light absorbed by the crown, the efficiency of a tree growing in shade is changed due to limited light resources and the amount of leaf area available to absorb radiation. This approach incorporates the ability of shadetolerant species to absorb more light due to higher leaf area density. The initially slow increase in Vinc was reduced to smaller trees when WLA was used as independent variable (Fig. 1) and indicates that trees in partially shaded understory conditions produce stem volume more efficiently when relative light conditions were considered. Plots of LUE versus PLA (Fig. 3) demonstrate this pattern but also show an increase in LUE from small understory trees to mid-canopy trees with increasing PLA. This trend was not significant for incense-cedar and is probably due to the subjective differentiation into canopy layers be relative canopy height and the slower growth dynamic of this species. The highest variability in LUE occurred with trees below 200 m2 PLA, growing in the lower and midcanopy layers. Apparently, these trees experience competitive interactions that are not reflected in WLA but have an effect on growth efficiency. Dividing trees into canopy layers explained some of the variation (Table 5) in LUE, but further investigation is warranted. Overall, these results can be used to incorporate competition for light resources into the concept of growing space allocation for multiaged

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stands. Growing space allocated to lower canopy strata could be evaluated with respect to horizontal canopy structure and the resulting light resource conditions for those trees. The resulting model could differentiate between growing conditions in stem-wise mixtures versus group selection and would be of particular advantage for modeling mixed-species stands where changes in stand structure might influence the competitive advantage of species and stand dynamics. GE has been used to express the vigor of whole stands or individual trees because it relates to the carbon status of the tree (Waring et al., 1980; Waring and Pitman, 1983). It is assumed that secondary growth has a lower allocation priority than primary growth and respiration (Waring and Schlesinger, 1985). Once higher priorities are satisfied, the amount of secondary growth can serve as an indicator of tree vigor. Although using GE as an index for tree vigor might be useful for an individual species, it does not apply to comparison between species because of differences in biomass allocation and differences in wood-specific gravity between species. In a comparative study of Norway spruce and Scott’s pine, O’Hara et al. (1999) showed that Norway spruce maintained more leaf area than Scott’s pine in shaded and open grown conditions while maintaining similar volume growth rates, resulting in lower GE for Norway spruce. This, however, did not indicate lower vigor, but different biomass allocation patterns. Differences in leaf area and stem wood production among the tree species in our study reflect those findings. The lower GE of shade-tolerant white fir and incense-cedar probably reflect species-specific differences in biomass partitioning, when compared with ponderosa pine and sugar pine. A lower canopy position in vertically structured stands with multiple age classes does not necessarily equate with a suppressed crown class, as might be the case in single-species even-aged stands. For instance, Reid et al. (2004) observed higher GE in suppressed lodgepole pines compared to other crown classes. While suppressed lodgepole pine showed lower volume increment and lower vigor, it was not expressed in lower GE. Differences in patterns of GE found between species might be explained by the amount of leaf area a tree maintains, given a certain light environment. Observations in mixed-conifer stands show that tree species differ in the amount of leaf area they maintain in limited light environments. Having more leaf area under shaded

conditions can help maintaining a positive carbon balance in limited resource conditions (Lusk, 2002), and could be seen as a life history trait of shade-tolerant species. Boundary line analysis of PLA as a function of PACL showed that incense-cedar and white fir maintained significantly more PLA than ponderosa pine at relative light levels of 50% (Fig. 4), with Douglas-fir and sugar pine in intermediate positions (Gersonde, 2003). A change in biomass allocation under shaded conditions would also change GE while allocating resources to other plant compartments. Such differences in allocation patterns among species growing in mixed stands has implications for forest stand dynamics, in particular, if trees grow up in the resource limited conditions under an existing forest canopy. Species with lower GE and high plasticity would be able to persist under limited resource conditions while recruitment into upper canopy strata of species with high GE and low plasticity would be tied to improvement of light resources with increasing tree size. The observed differences in GE have implications for management of mixed-species and multiaged stands. Species mixture alone can affect total stand GE depending on the proportion of species with high potential GE, such as ponderosa pine and sugar pine (Fig. 2). These stands, however, do not necessarily lead to maximum productivity, as intolerant species might require lower stand density to achieve high GE. Silvicultural treatments of mixed-species stands can ensure high growth efficiency for individual stand components and systems that maintain high levels of productivity over time. For example, pine species in the

Fig. 4. Maximum projected leaf area maintained by different species at 50 PACL, mean and 95% confidence interval of boundary line analysis.

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Sierra Nevada would benefit from early thinning due to an early peak in GE at low leaf area values, while shadetolerant species provide more flexibility with regard to cutting cycle length, stand density or partial shading. A stand composed of older cohorts of pine species with an understory of shade-tolerant fir and incense-cedar could have higher productivity as a single-species stand. Species with a relatively late peak in GE (sugar pine) could be retained during stand regeneration cuts and thus contribute longer to stand productivity.

5. Conclusions The Sierra Nevada mixed-conifer species showed differences in patterns of volume increment and growth efficiency with increasing leaf area. High Vinc and GE were associated with species of low tolerance to shade, while shade-tolerant species showed a greater response in GE to changing light conditions. These results demonstrated that patterns of GE can be used to quantify differences in shade tolerance between species growing in multiaged mixed stands. Using WLA to describe the effect of local light environment on GE allowed us to quantify competitive relationships between trees in different canopy layers, because it accounted for differences in leaf area between trees and the amount of absorbed light. Shade-tolerant trees were found to maintain more leaf area under shaded conditions than shade-intolerant species, leading to differences in GE between species. Such differences do not equate to lower vigor but are important life history traits that have consequences for growth in limited light environments. Light use efficiency was highest in mid-canopy positions for most species, however, our results show that other factors besides light environment appear to play a role in the development of GE in multiaged stands. The predictive models we developed for bole volume increment as a function of leaf area relate productivity to occupied growing space and can be used in predictive models of multiaged, mixed-species stands.

Acknowledgements We thank the staff and management of Blodgett Forest Research Station for providing research support

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and data access. Funding for this project was provided by Sierra Pacific Industries Inc. and the Agricultural Experiment Station of the University of California. This study was part of the dissertation research of Rolf Gersonde at the University of California, Berkeley.

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