The influence of canopy gaps on overstory tree and forest growth rates in a mature mixed-age, mixed-species forest

Forest Ecology and Management 196 (2004) 351–366

The influence of canopy gaps on overstory tree and forest growth rates in a mature mixed-age, mixed-species forest Brian S. Pedersen*, Jessica L. Howard1 Department of Environmental Studies, Dickinson College, Carlisle, PA 17013, USA Received 9 September 2003; received in revised form 21 March 2004; accepted 31 March 2004

Abstract The death of overstory trees creates gaps in forest canopies. These canopy gaps have positive impacts on forests, including enhancing species diversity. The relative contributions to canopy gap closure made by understory trees within gaps and overstory trees at gap edges determines the future structure and species composition of a forest. Most studies of tree growth responses to gaps have focused on understory trees or canopy expansion by overstory trees. Here we focus on the stem radial growth rates of overstory trees and forest growth rates, measured as stand basal area increment. Our study area was a mature mixed-age, mixed-species deciduous forest in south-central Pennsylvania, USA. A hierarchical regression analysis found that gap-edge trees
20 cm dbh (diameter at breast height, 1.3 m) had 26% higher stem radial growth rates than comparable trees not located at gap edges (P ¼ 0:004). Our hypothesis that smaller overstory trees would experience a greater growth benefit at gap edges was marginally supported (P ¼ 0:06). A tree’s position north or south of a gap did not influence its growth response to the gap. The results suggest that overstory trees make an important contribution to canopy gap closure. Canopy gaps reduced the area occupied by overstory trees by 16%. But based on our regression model of stem radial growth rates, nearly two-thirds of the stand basal area increment lost because of gaps was offset by the enhanced growth of trees at gap edges (considering trees
20 cm dbh only). A simple, spatially-explicit process model of tree and forest growth in relation to gaps supported this finding. These results demonstrate that the benefits of canopy gaps come at a cost in forest growth rates that is considerably less than the gap area indicates. # 2004 Elsevier B.V. All rights reserved. Keywords: Deciduous forest; Forest growth model; Stand basal area increment; Stem radial growth rate; Tree-ring

1. Introduction The sizes and species of trees in a forest determine forest attributes such as the habitats available for other

*

Corresponding author. Tel.: þ1-717-245-1897; fax: þ1-717-245-1971. E-mail address: [email protected] (B.S. Pedersen). 1 Present address: 7710 Marshall Heights Ct., Falls Church, VA 22043, USA.

organisms, value of the timber, quality of the aesthetic and recreational experiences, and susceptibility of the forest to stresses and disturbances (Oliver and Larson, 1990; Yahner, 2000; Sharpe et al., 2003). In mature forests, the death of a large, overstory tree creates a gap in the forest canopy and provides an opportunity for substantial future changes in the sizes and species of trees (Brokaw, 1982). Consequently, understanding the formation and closure of canopy gaps is essential for effective forest management (Runkle, 1991; Coates and Burton, 1997).

0378-1127/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2004.03.031

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The sizes and species of trees in a future forest are determined by the mode of canopy gap closure. Resources for tree growth are more abundant in gaps, both above and below ground (Canham et al., 1990; Wilczynski and Pickett, 1993). Understory trees located within a gap can exploit these resources to enhance their growth rates (Canham, 1988) and grow into the forest overstory, contributing to closure of the gap (Valverde and Silvertown, 1997). But canopy gaps are typically closed by the combination of trees growing up from the understory (closure from below) and overstory trees expanding their crowns laterally into a gap (closure from the side; Runkle and Yetter, 1987). If closure from below dominates, the future overstory will include more small trees and may have a different species composition than the previous overstory (Whitmore, 1989). If closure from the side is substantial, then the future overstory will include more large trees (Nelson, 1955) and there will be less change in species composition. The mode of canopy gap closure is influenced by factors such as gap size and orientation, how and when a canopy gap formed, gap microsite characteristics, and the tree and other plant species present in the gap (Veblen, 1992). Past studies of the gap closure process have focused on the growth response of understory trees to gaps (e.g., Canham, 1988; Tryon et al., 1992; Ashton and Larson, 1996; Poulson and Platt, 1996; Wu et al., 1999) and the horizontal growth of overstory tree crowns into gaps (e.g., Trimble and Tryon, 1966; Hibbs, 1982; Young and Hubbell, 1991; Runkle, 1998; Muth and Bazzaz, 2002). However, understanding gap closure and its consequences for forests also requires understanding how the stem radial growth rates of overstory trees respond to gaps. Stem radial growth rates are an integrative measure of tree vigor and tree response to the environment (Pedersen, 1998), and cause changes in stem diameter, the most commonly measured characteristic of tree size (Avery and Burkhart, 1994). The frequency distribution of stem diameters is a fundamental descriptor of forests that serves as an indicator of forest attributes (e.g., Loewenstein et al., 2000; Kangas and Maltamo, 2003; Sarkkola et al., 2003). Individual-based forest simulation models, which are widely used to study the influence of environmental factors on forests and to support forest management, are typically based on tree stem diameter (Bugmann, 2001).

There are few reports of the stem radial growth response of overstory trees to gaps. Poage and Peart (1993) found that overstory American beech (Fagus grandifolia Ehrh.) at gap edges did not have higher stem radial growth rates than trees representative of their entire sample area. Wardman and Schmidt (1998) found that overstory Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco.) at gap edges had larger stem diameters, indicative of higher stem radial growth rates because they studied a singleage, single-species forest. Two reports describe stem radial growth rate increases resulting from the disease-induced decline of neighboring trees. Aughanbaugh (1935) found that overstory trees of 10 species experienced substantial increases in stem radial growth rates during and after the decline of American chestnut (Castanea dentata [Marsh.] Borkh.). DiGregorio et al. (1999) found that overstory sugar maple (Acer saccharum Marsh.) located at the edge of gaps formed by declining American beech had 8% higher stem radial growth rates. But these latter two cases involve a thinning process rather than the typical process of canopy gap formation (Aughanbaugh, 1935). Thinning removes trees from throughout a stand, with a preference for particular sizes and species (Sharpe et al., 2003). A number of researchers (e.g., Cutter et al., 1991; Miller, 1997; Pape, 1999) have described increases in the stem radial growth rates of overstory trees following thinning treatments. The stem radial growth response of overstory trees to canopy gaps can be influenced by several factors. Below ground competition from understory trees and other plants growing within gaps may limit the growth response of overstory trees to gaps (Campbell et al., 1998). When a gap forms, smaller overstory trees at the gap edge may experience a relatively greater increase in access to light, as compared to larger overstory trees, and so may exhibit a stronger growth response to the gap (Muth and Bazzaz, 2002). In addition, larger trees at a gap edge may be less physiologically capable of responding to the increased resources available at a gap edge and so may not respond with higher growth rates (Oliver and Larson, 1990). In northern latitudes, overstory trees located on the north edge of a gap will receive more light than those located on the south edge and may show a stronger growth response to the gap-edge

B.S. Pedersen, J.L. Howard / Forest Ecology and Management 196 (2004) 351–366

environment, as has been reported for understory trees in gaps (Poulson and Platt, 1989). To evaluate the factors influencing the response of overstory trees to gaps in a mature mixed-age, mixed-species forest, we tested three hypotheses: (1) Overstory trees located at gap edges will have higher stem radial growth rates than comparable trees not located at gap edges. (2) The growth rate benefit of being located at a gap edge will be greater for smaller overstory trees than for larger overstory trees. (3) The growth rate benefit of being located at a gap edge will be greater for overstory trees located on the north side of a gap than for comparable trees located on the south side of a gap. We applied the tree-level growth rate results to determine the influence of canopy gaps on forest-level growth rates. While canopy gaps have positive effects on forest attributes, such as species diversity (Greenberg and Lanham, 2001; McCarthy, 2001; Schumann et al., 2003), the presence of a gap represents the absence of one or more growing overstory trees. As the proportion of forest area occupied by gaps increases, the forest growth rate would be expected to decrease. However, higher growth rates for overstory trees located at gap edges would partially compensate for the forest growth lost as a result of gaps. We quantified the extent of that compensation as stand basal area increment.

2. Methods 2.1. Study area We studied a portion (4.5 ha) of a mixed-age forest stand of the red oak-mixed hardwood type (Fike, 1999) in south-central Pennsylvania, USA (408170 1000 N latitude, 778170 4500 W longitude). Characterizing the structure and species composition of this forest was part of this research, as explained below. This upland stand is on the lower slope of a north-facing ridge, with slopes of 10–208 and elevations of 230–260 m. The soil is a Typic Fragiudult (very stony silt loam derived from sandstone and shale) which has a moderate water holding capacity and is strongly to extremely acid (Zarichansky, 1986).

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The study area is in the privately-owned Florence Jones Reineman Sanctuary (FJRS), a 1377 ha preserve established in 1965. Hunting is prohibited and the preserve is heavily impacted by deer herbivory (Pedersen and Wallis, 2004). Since the preserve’s establishment, the study area has not been subject to timber management; prior to establishment, FJRS was subject to selective logging (personal communication, David B. Steckel, Natural Lands Trust, Media, Pennsylvania). Historically, the study area is likely to have experienced anthropogenic disturbances similar to those of other forests in the region including: repeated clearcutting or selective logging since the 18th century; intentionally and accidentally set fires prior to the 20th century, and effective fire suppression since; and introduction of the chestnut blight fungus and gypsy moth (Ruffner and Abrams, 1998; Yahner, 2000). 2.2. Sampling and measurements 2.2.1. Gaps We identified all canopy gaps (sensu Runkle, 1991) intersecting two parallel line transects (870 m total length, 50 m apart), using tree height to distinguish between the overstory trees that form the forest canopy and define gap edges, and the understory trees growing below the forest canopy and within gaps. Overstory trees were those >2/3 the height of the surrounding canopy and understory trees were those <2/3 the height of the surrounding canopy, a definition consistent with criteria reviewed in Runkle (1992). To accurately project the location of canopy gap boundaries on the forest floor, we used an instrument with bubble levels to determine the zenith (Densitometer, Geographic Resource Solutions, Arcata, California). We quantified the proportion of line transect length intersecting the gaps. The areas of the identified canopy gaps were approximated as ellipsoids (Runkle, 1992). We delineated the gap axes, the longest line segment within each canopy gap and then the longest line segment orthogonal to the first. The intersection of these axes is the gap centroid. We also delineated the expanded gap, the polygon bounded by the stems of the overstory trees defining the canopy gap (Runkle, 1992). For the tree growth rate analysis, the gap-edge sample initially consisted of the 152 trees
20 cm diameter at breast height (dbh, 1.3 m) that bordered

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the 14 identified gaps (an additional eight trees bordering the gaps were <20 cm dbh). All trees in the gapedge sample were classified as being on the north or south side of a gap relative to the gap centroid. Gap ages were estimated from the current condition of dead trees
20 cm diameter that were rooted or formerly rooted within the expanded gaps (not all diameter measurements could be made at breast height, depending on tree decomposition and mode of death). State of decomposition of these likely gapmakers was rated on a 0–5 scale (e.g., 0 ¼ leaves present, 5 ¼ main trunk gone and only fragments of tree base remain [McCune and Henckel, 1993]). We approximated the years since tree death from the stateof-decomposition ratings using a regression relationship developed for forests in the Midwestern USA (Pedersen and McCune, 2002). 2.2.2. Null gap Lieberman et al. (1989), recognizing that a forest cannot simply be divided into gap and non-gap environments, defined the term null gap to refer to the forest overall. To quantify the stand basal area and tree density of the null gap, we applied a plotless sampling method (second closest individual estimator [Engeman et al., 1994]) at 10 m intervals along four parallel line transects (including the two transects used for gap sampling; 1820 m total length, 25 m apart). All trees
5 cm dbh were considered. We determined if these trees were growing at a gap edge or in a gap. For the tree growth rate analysis, the null-gap sample initially consisted of the 93 trees selected by the plotless sampling that were
20 cm dbh, the same size criterion applied for the gap-edge sample. The non-gap sample initially consisted of the 43 trees in the null-gap sample that were not growing at a gap edge. 2.2.3. Tree growth rates and sample sizes Two cores were removed from the sample trees at breast height, perpendicular to the slope (or direction of tree lean, if any). The cores were air-dried, mounted, and sanded with progressively finer abrasives until annual growth ring boundaries and other ring features were clearly visible with a stereo microscope. We cross-dated (Fritts and Swetnam, 1989) and measured ring widths for the most recent 10 complete growing seasons (1990–1999) to the nearest 0.01 mm (Velmex stage, Acu-Rite encoder, and Metronics

readout from Velmex, Bloomfield, New York; and Measure J2X software from Voortech Consulting, Holderness, New Hampshire). Rings were cross-dated using narrow ring widths (notably for the drought years 1988 and 1991 [unpublished data, Pennsylvania State Climatologist, University Park, Pennsylvania]) and, when available, species-specific ring features (e.g., a light-colored ring in 1995 for many yellowpoplar [Liriodendron tulipifera L.]). Annual ringwidth measurements of cores from the same tree were averaged. Trees were eliminated from the initial samples for three reasons (Table 1). First, the non-gap sample includes only trees <60 cm dbh so we excluded trees
60 cm dbh from the gap-edge and null-gap samples to insure a balanced comparison of growth rates. Second, some cores could not be cross-dated or measured with confidence, were damaged during preparation, or were lost. The remaining trees in the three samples were represented by at least 1.8 cores/tree. Third, the gap-edge and null-gap samples include trees represented twice in these samples because the trees were selected twice by the sampling procedures. Only the unique trees were included in the initial statistical analysis. Table 1 Sample sizes (number of trees; all
20 cm dbh) Criteria

Identified during sampling (initial samples) <60 cm dbh Growth rate measurement availableb Unique

Sample Gap-edge

Null-gap

Non-gapa

152

93

43

141 139c,d

90 85c,e

43 39

130

84

39

The sample sizes for the hierarchical regression model are in bold face and the samples for the reparameterized regression model are italicized. The criteria for eliminating trees from the samples are explained in the text. Some trees were included more than once in a sample or were included in more than one sample (see footnotes) to insure sample representativeness (see text for explanation). a A subset of the null-gap sample. b At least one core per tree could be measured and cross-dated. c Includes nine trees common to these two samples because these trees were selected by both the gap and null-gap sampling procedures. d Includes nine trees represented twice. e Includes one tree represented twice.

B.S. Pedersen, J.L. Howard / Forest Ecology and Management 196 (2004) 351–366

2.3. Analysis 2.3.1. Tree growth rates We initially compared the growth rates of trees in the gap-edge and non-gap samples using hierarchical regression analysis, a hypothesis-based approach (Tabachnick and Fidell, 1989). The dependent variable was 1990–1999 stem radial growth rate. To identify independent variables for the regression model, we first determined if any difference in growth rates could be attributed to dbh. Second, we determined if any remaining difference in growth rates could be attributed to tree taxon (minor taxa were combined; Table 2). Third, we determined if any remaining difference in growth rates was due to trees’ being in the gap-edge or non-gap sample. Finally, we determined if any remaining difference in growth rates Table 2 Tree taxonomic groups for the growth rate analysis and relative stand basal area for trees
5 cm dbh (null gap) Taxon

Considered separately Birch, sweet (Betula lenta L.) Hickory (Carya Nutt.)a Locust, black (Robinia pseudoacacia L.) Maple (Acer L.)b Oak (Quercus L.)c Yellow-poplar (Liriodendron tulipifera L.)

Relative stand basal area (proportion) 0.152 0.125 0.075 0.200 0.125 0.231

Combined into the minor taxonomic group 0.080 Ash (Fraxinus L.)d Beech, American (Fagus grandifolia Ehrh.) Hemlock, eastern (Tsuga canadensis [L.] Carr.) Sassafras (Sassafras albidum [Nutt.] Nees) Tupelo, black (Nyssa sylvatica Marsh.) Common and scientific names follow Harlow et al. (1996). Six additional taxa were not included in the growth rate analysis because all individuals were <20 cm dbh (relative stand basal area for these trees was 0.011): American basswood (Tilia americana L.), cherry (Prunus L.), flowering dogwood (Cornus florida L.), slippery elm (Ulmus rubra Muˆ hl.), eastern hophornbeam (Ostrya virginiana [Mill.] K. Koch), and witch-hazel (Hamamelis virginiana L.). a Includes shagbark hickory (Carya ovata [Mill.] K. Koch). b Predominantly red maple (Acer rubrum L.), but also Norway maple (A. platanoides L.) and striped maple (A. pensylvanicum L.). c Includes chestnut oak (Quercus prinus L.), northern red oak (Q. rubra L.), and white oak (Q. alba L.). d Predominantly white ash (Fraxinus americana L.).

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was due to a difference in the relationship between growth rate and dbh between the gap-edge and nongap samples, and gap-edge trees’ being located on the north or south edge of a gap. This hierarchical approach is hypothesis-based in that we sought the most likely explanation for differences in tree growth rates (viz., tree dbh and taxon) before testing our hypotheses. In this hierarchical regression model, tree dbh was a continuous variable (dbh). Indicator variables, which take the value 0 (false) or 1 (true; Neter et al., 1989), represented taxonomic groups (e.g., birch?), sample (gap-edge?), and location (north?). The product of two variables, dbhgap-edge?, represented the interaction between tree dbh and sample. Forward variable selection (Neter et al., 1989) was used to select statisticallysignificant variables (a ¼ 0:05) at the stage in the hierarchy where these variables could enter into the regression equation. Growth rate data were log-transformed. Residuals were examined to verify that the final model satisfied the assumptions underlying regression analysis. We also examined Mahalanobis and Cook’s distances to identify outliers and insure that no data points were disproportionately influential (Tabachnick and Fidell, 1989; Norusˇis, 1992). The regression analysis was performed with SPSS/PCþ, Version 5.0 (Chicago, Illinois). Following development of the hierarchical regression model, we reparameterized the model using the null-gap sample instead of the non-gap sample to provide a comparison between the growth rates of gap-edge trees and trees representing the forest overall. In developing this reparameterized regression model, we included the 10 trees represented more than once in the gap-edge and null-gap samples so the model would represent the gap-edge and null-gap trees in the study area (i.e., sampling with replacement [Zar, 1996]; Table 1). For the same reason, we also included the nine trees common to the gap-edge and null-gap samples. 2.3.2. Forest growth rates We applied the hierarchical regression model and our data on the structure and species composition of the study area’s forest to calculate stand basal area increment (bai) for 1990–1999. Determining the effect of canopy gaps on stand bai required that we calculate stand bai for three ‘‘forests’’. We refer to the study area

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that we characterized (null gap) as the gap-plus forest because it has gaps and the gap-edge trees may have higher growth rates than non-gap trees. The hypothetical gap-minus forest is the same as the gap-plus forest except that gap-edge trees have the same growth rates as non-gap trees. The hypothetical gapless forest is the same as the gap-plus forest except that all gaps were filled with trees representative of the null gap (so there are no gap-edge trees). For the gap-plus forest, we computed stem radial growth rates by applying the hierarchical regression model. Trees were divided into (1) the taxonomic groups with distinct growth rates identified by the hierarchical regression analysis; (2) 10–5 cm dbh classes; (3) gap-edge or non-gap; and (4) tree location north or south of the gap centroid. For all trees in a dbh class, we applied the dbh corresponding to the mean tree basal area of that class (e.g., 22.6 cm dbh for trees in the 20.0–24.9 cm dbh class). The results were converted to individual tree bai assuming a bark factor of 0.92 (ratio of diameter inside the bark to the diameter outside the bark; Wenger, 1984) and that all trees had a circular cross-section. We then summed the individual tree bai values for each category, weighting by the stem density for each taxonomic group and dbh class, and by the proportion of trees for the corresponding taxonomic group and dbh class that were gap-edge or non-gap and north or south of the gap centroid. For the gap-minus forest, we repeated the gap-plus calculations assuming that all trees had the growth rates of non-gap trees. For the gapless forest, we ‘‘filled’’ the canopy gaps. Canopy gap fraction is the proportion of forest area occupied by canopy gaps. So we repeated the gap-plus calculations assuming that stem density for each taxonomic group and dbh class was 1=½ð1 ðcanopy gap fractionÞ times greater than for the gap-plus forest and that all trees had the growth rates of non-gap trees. To support the empirical analysis and generalize the effects of gaps on stand bai, we used spreadsheet software to develop a simple, spatially-explicit process model of forest growth rates based on individual tree growth rates. The model has 10,000 cells arranged in a 100 100 grid. A cell may contain one or no trees, determined stochastically. The probability that a cell does not contain a tree is the canopy gap fraction. Trees in cells are defined as being gap-edge or non-gap

(a)

(b) Fig. 1. Portion of process model structure. Cells may contain a tree (gray shading) or represent a canopy gap (no shading). Closed circles indicate gap-edge trees (which may experience a growth benefit) and open circles indicate trees not at a gap edge. We considered two spatial relationships: (a) each cell has four neighbors (up, down, left, and right) and (b) each cell has eight neighbors (up, down, left, right, and the four cells on the grid diagonals).

trees, depending on whether or not they neighbor a cell without a tree. We considered two spatial relationships between cells. Each grid cell may have four neighboring cells (left, right, up, or down) or eight neighboring cells (left, right, up, down, and the four cells on the grid diagonals; Fig. 1). Non-gap trees have a bai of 1 (arbitrary units). Gap-edge trees can experience a bai growth benefit; for example, a 5% growth benefit corresponds to a gap-edge tree bai of 1.05. The model grid is surrounded by trees so there are no gaps at the edge of the simulated forest. This stochastic model was run 10 times for each of a range of canopy gap fractions and bai growth benefits for gap-edge trees.

3. Results 3.1. Tree growth rates Based on the hierarchical regression analysis, we found support for our first hypothesis: the 1990–1999 radial stem growth rate of gap-edge trees was significantly greater than for comparable non-gap trees (P ¼ 0:004, variable: gap-edge?; Table 3). Support for our second hypothesis was marginal, but consistent with the hypothesis that smaller trees experience a

B.S. Pedersen, J.L. Howard / Forest Ecology and Management 196 (2004) 351–366

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Table 3 Regression models Stage

Independent variable

Hierarchical model: gap-edge and non-gap samples Pa

DR2b

0.0062

0.000

0.200

0.0085

0.000

0.3073 0.1162

0.000 0.010

0.330 0.012

0.3255 0.0947

0.000 0.070

0.1006

0.004

0.023

0.0604

0.026

Regression coefficient 1

dbh (cm)c

2

yellow-poplar? locust?

3

gap-edge?

Intercept R2model R2adjusted N (trees)

Reparameterized model: gap-edge and null-gap samples

0.9364 (P ¼ 0.000) 0.564 (P ¼ 0.000) 0.553 169

Regression coefficient

Pa

0.8675 (P ¼ 0.000) 0.524 (P ¼ 0.000) 0.518 224

The dependent variable is the log-transformed 1990–1999 stem radial growth rate at breast height (mm/decade). Independent variables are listed by their stage of possible entry into the hierarchical model. A ‘‘?’’ denotes an indicator variable that takes the value 0 (false) or 1 (true). Independent variables not selected for the hierarchical model: birch? (P ¼ 0:560), hickory? (P ¼ 0:130), maple? (P ¼ 0:926), oak? (P ¼ 0:107), dbhgap-edge? (P ¼ 0:060), and north? (P ¼ 0:456; P-values are for the end of the stage in the hierarchy when the variable could have entered the model). a Statistical significance of regression coefficient in model shown. b Increase in regression model R2 due to the addition of the corresponding independent variable. c Measured during the 2000 growing season.

greater growth benefit from their position at a gap edge than larger trees (P ¼ 0:060; variable: dbh gapedge?). We did not find support for our third hypothesis: the location of gap-edge trees relative to the gap centroid did not influence their growth rates (P ¼ 0:456; variable: north?). The hierarchical regression model, including only parameters significant at a ¼ 0:05, explains more than half the variance in tree growth rates (R2 ¼ 0:564, P ¼ 0:000; Table 3). Because growth rates were logtransformed, the effect of the indicator variables on growth rate may be expressed on a relative basis. The growth rates of gap-edge trees were 26% greater than those of comparable non-gap trees, a difference that applies to all dbh’s (20.0–59.9 cm) and taxonomic groups (Fig. 2a). By comparison, the model-predicted growth rates of 40 cm dbh trees were 33% greater than those for 20 cm dbh trees. The growth rates for all locust (Robinia pseudoacacia L.) were significantly lower (P ¼ 0:010) and growth rates for all yellow-poplar were significantly higher (P ¼ 0:000) than those of all other taxonomic groups (Table 3; Fig. 2a). Reparameterizing the initial model with the null-gap sample instead of the non-gap sample showed

that the previously-selected independent variables were statistically significant (a ¼ 0:05), except that locust growth rates were only marginally distinct (P ¼ 0:070; Table 3; the sign of the marginally-significant regression parameter was consistent with the hierarchical regression model). The reparameterized regression model indicates that the growth rates of trees at gap edges were 15% greater than those representing the forest overall (Fig. 2b). Because the samples used for the regression models are from a mixed-age, mixed-species forest, the samples differ in how trees are distributed by dbh and taxon (Fig. 3). However, these differences are not responsible for the results. Because the regression models included independent variables representing dbh and taxonomic groups, the models account for the influence of these factors. For example, the gap-edge sample has a lower proportion of birch than the nongap sample (Fig. 3a). If birches had lower growth rates than the other taxonomic groups, then this could contribute to a finding that gap-edge trees had higher growth rates than non-gap trees. But birch trees were not found to have growth rates that were significantly different from the other taxonomic groups (p ¼ 0:560; Table 3).

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(a)

(b)

Fig. 2. Regression models of growth rates of (a) gap-edge and non-gap trees (hierarchical model) and (b) gap-edge and null-gap trees (reparameterized model). Triangles represent yellow-poplar, squares represent locust ((a) only), and circles represent all other taxonomic groups. Open symbols represent gap-edge trees and the closed symbols represent (a) non-gap trees and (b) null-gap trees. The dashed lines show the predicted growth rates for trees represented by open circles and the solid lines show the predicted growth rates for trees represented by closed circles. While all data points are shown, the lines show the regression model results which are based on the trees <60 cm dbh (see text for explanation). Vertical arrows indicate growth rate differences of the taxonomic groups with significantly different growth rates (a ¼ 0:05).

Gap-edge tree growth rates were greater than nongap tree growth rates for most taxonomic groups (Fig. 4). Taxonomic-group-specific differences were calculated after applying the dbh regression coefficient from the hierarchical regression model to account for dbh (Table 3). We present the taxo-

nomic-group-specific results only to indicate the consistency of the response to the gap-edge environment across taxonomic groups. Because of the limited sample sizes for some taxonomic groups, the taxonomic-group-specific results should be interpreted with caution.

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(a)

359

(b)

Fig. 3. Proportion of trees by taxonomic group and dbh class within the samples used for the (a) hierarchical regression model and (b) reparameterized regression model. The white bars represent the gap-edge samples and the gray bars represent the (a) non-gap sample and (b) null-gap sample. Portions of bars filled with parallel lines represent trees 20.0–29.9 cm dbh, unfilled portions represent trees 30.0– 39.9 cm dbh, and portions filled with cross-hatching represent trees 40.0–59.9 cm dbh. Sample sizes are given in Table 1.

3.2. Stand and gap characteristics For the null gap trees
5 cm dbh, stand basal area was 17:6 3:5 m2/ha and tree density was 306 43 stems/ha (95% confidence intervals, computed by bootstrapping with 10,000 iterations [Manly, 1998]). Six of 17 tree genera accounted for over nine-tenths of the stand basal area (birch, hickory, locust, maple, oak, and yellow-poplar; Table 2). The median dbh of the 25 null-gap trees with the largest dbh’s was 49.2 cm and the median height of the five tallest null-gap trees was 29.2 m (based on height measurements of every fifth null-gap tree). Canopy gap fraction was 0.16, whether computed as the proportion of line transect length intersecting canopy gaps or using an estimator designed to offset the bias in favor of identifying larger gaps (Runkle, 1992). The median area of the 14 canopy gaps was 91 m2 (range: 4–1042 m2) and the median area of the 14 expanded gaps was 227 m2 (range: 56–1524 m2). The median number of gap-edge trees
20 cm dbh per gap was 9.5 (range: 5–31). Based on the initial null-gap sample (93 trees; Table 1), the proportion of trees
20 cm dbh in the study area that were located at

the edge of at least one gap was 0:54 0:11 (95% confidence interval based on the binomial distribution [Zar, 1996]). The median number of gapmakers per gap was 3 (range: 1–13) and the median age of the gapmakers was approximately 25 years. For 13 of the 14 gaps, the age of the gaps was at least 14 years, based on the age of the oldest gapmaker in each gap; the age of the other gap was 8 years. 3.3. Forest growth rates Relative to the stand bai for the actual, gap-plus forest (3.55 m2/hadecade), the stand bai for the hypothetical gapless forest was 6% higher (3.76 m2/ hadecade) and the stand bai for the hypothetical gapminus forest was 11% lower (3.16 m2/hadecade). These results indicate that of the stand bai lost because of gaps (½gapless stand bai ½gap-minus stand bai ¼ 0:60 m2/hadecade), nearly two-thirds was made up for by the increased growth of gap-edge trees (½gap-plus stand bai ½gap-minus stand bai ¼ 0:39 m2/hadecade). The results are based on the final hierarchical regression model (Table 3), the

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Fig. 4. Taxonomic-group-specific differences in growth rates between gap-edge, non-gap, and null-gap trees (corrected for differences in dbh with the hierarchical regression model). Black bars represent differences of gap-edge trees relative to non-gap trees (samples used for the hierarchical regression model) and white bars represent differences of gap-edge trees relative to nullgap trees (samples used for the reparameterized regression model). The asterisk (*) indicates that the non-gap sample did not include oaks so no comparison is possible.

dbh-specific tree densities for the taxonomic groups with distinct growth rates (as determined by the hierarchical regression model), and dbh- and taxonomic-group-specific data on the proportion of trees at gap edges (Fig. 5). The influence of tree size on the gap-edge growth benefit and tree position relative to the gap centroid were not considered because these factors were not statistically significant (a ¼ 0:05). The forest growth rate results are limited to trees
20 cm dbh and are based on extrapolating the hierarchical regression model for the small proportion of trees 60.0–69.9 cm dbh (Fig. 5a). Using the process model, we determined stand bai as a function of gap-edge growth benefits that are comparable to those found by the statistical analysis and for (hypothetical) higher, lower, and no growth benefits (Fig. 6a). The process model is based on tree bai while the hierarchical regression model of tree growth rates was based on stem radial growth rate. However, a relative growth benefit for gap-edge trees is nearly the same whether expressed on a radial or

basal area basis. This is because bai is essentially a rectangle, the thickness of the radial growth increment, wrapped around a tree’s circumference (inside the bark). For example, if a 30 cm dbh tree has a 26% greater radial growth rate when it is located at a gap edge (as was determined by the hierarchical regression analysis), then it has a 24% greater bai (this calculation assumes the radial growth rate predicted by the hierarchical regression model [Table 3], a bark factor of 0.92 [as above], and a circular tree cross-section). As expected, the process model indicates that stand bai is greater when gap-edge trees experience a growth benefit (Fig. 6a). Under some model conditions, stand bai is greater for a stand with gaps than for a stand without gaps (i.e., stand bai > 10,000). When gap-edge trees experience a growth benefit, stand bai is greater if cells have eight neighbors rather than four. This is consistent with the model’s result that the proportion of trees neighboring a gap is greater if cells have eight neighbors, rather than four (Fig. 6b). In our study area, canopy gap fraction was 0.16 and the proportion of trees neighboring a gap was 0.54 (see above). The process model indicates that for a canopy gap fraction of 0.16, the proportion of trees neighboring a gap is 0.50 and 0.75 for four and eight neighbors per cell, respectively (Fig. 6b). This suggests that the effective number of neighbors per tree in our study area is approximately four (the effective number of neighbors per tree is not equivalent to the number of overstory trees per gap; see Fig. 1). The process model results are consistent with the stand bai values calculated for the study area. With four neighbors per tree, a canopy gap fraction of 0.16, and a bai growth benefit for gap-edge trees of 25%, the model indicates that stand bai will be 0.95 that of an otherwise equivalent forest without gaps (Fig. 6a). We calculated the stand bai for our forest to be 0.94 that of an equivalent forest without gaps ([gap-plus stand bai]/[gapless stand bai]; see above).

4. Discussion 4.1. Tree growth rates While the samples used for the two regression models are not independent, the relationship between the models’ results increases our confidence in the

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(a)

(b) Fig. 5. Structure and species composition of the study area forest (null gap) for calculating stand basal area increment. (a) Tree density by taxonomic group and dbh class. (b) Proportion of trees at gap edges by taxonomic group and dbh class. Black bars represent locust, gray bars represent yellow-poplar, and white bars represent all other taxa. The proportions of trees at gap edges were computed for pooled dbh classes to insure sufficient sample sizes to calculate a meaningful proportion.

results. When we compared a gap-edge sample to the non-gap sample, we found a 26% difference in growth rates (Fig. 2a), and when we compared a gap-edge sample to the null-gap sample, we found a 15% difference in growth rates (Fig. 2b). That approximately two-fold difference in results is consistent with the null-gap sample having approximately equal numbers of non-gap and gap-edge trees (Table 1). In addition, the two regression models identified similar influences of dbh on growth rate and similar differences in the growth rates of locust and yellow-poplar (Table 3). The clear lack of a difference in the growth rates of overstory trees on the north versus south side of a gap (P ¼ 0:456) may be due to biology or methodology. In contrast to our expectations, Trimble and Tryon (1966) observed higher rates of horizontal crown expansion by overstory trees on the south edge of a gap. Similarly, Ashton and Larson (1996) observed higher rates of understory tree growth on the south

edge of a gap. (Both studies were conducted in the northern hemisphere.) The advantage of greater incident light on the north edge of a gap may be more than offset by higher rates of evaporative soil water and transpiration losses. However, our method of assigning overstory trees to the north or south side of a gap may not accurately reflect the exposure of their crowns to the sun. We based this classification on the location of tree stems (at breast height) relative to gap centroids, without considering crown asymmetries, leaning stems, or oddly-shaped gaps, factors that also determine crown exposure to light (Runkle, 1992; Muth and Bazzaz, 2003). That we found significantly higher growth rates for yellow-poplar and significantly lower growth rates for locust is consistent with other reports on the relative growth rates of these species (Boring and Swank, 1984; Beck, 1990; Huntley, 1990). Trimble and Tryon (1966) reported a species difference in the rate of overstory tree crown expansion into gaps. But we

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(a)

(b) Fig. 6. Results of the process model. (a) Relative stand bai as a function of canopy gap fraction probability and four values of the bai growth benefit for trees located at a gap edge. (b) Proportion of trees located at the edge of a gap as a function of canopy gap fraction probability. Solid lines represent the case of four neighbors per cell and dashed lines represent the case of eight neighbors per cell (Fig. 1). Results were computed for canopy gap fraction probabilities of 0.00, 0.05, 0.10, 0.15, and 0.20. Circles indicate values for the study area. For (a), relative 95% confidence intervals (not shown) are < 0.3% of the mean values shown. For (b), relative 95% confidence intervals (not shown) are < 1.6% of the mean values shown.

could not statistically evaluate taxa-specific responses of stem radial growth rates to gaps given the sample sizes and number of taxa in the samples (Tables 1 and 2, Fig. 4). In future analyses, it may be possible to further quantify the influence of gaps on overstory tree growth rates. We only classified trees as being located at the edge of at least one gap or not being located at a gap edge. Quantifying the degree of gap-edge influence on a tree, for example, as the proportion of crown cir-

cumference bordering a gap, may better explain variations in the growth rates of gap-edge trees. Our analysis was based on cumulative tree growth rates during the interval 1990–1999. However, some trees in the gap-edge samples may not have been at gap edges throughout this period so the growth rate results are conservative. The state of decomposition of the gapmakers suggests that 13 of the 14 gaps formed prior to 1990, but 11 of the gaps contained multiple gapmakers meaning these gaps may have expanded

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since their formation. Even once an overstory tree becomes a gap-edge tree, there may be a time lag before there is a growth response to the new environment, as observed for understory trees following release from suppression (Wright et al., 2000). The growth response of overstory trees to gaps may also vary in the years following gap formation (Valverde and Silvertown, 1997) and may depend on the rate at which a gap formed (e.g., a gapmaker may be killed suddenly by wind or slowly by disease [Krasny and Whitmore, 1992]). The finding that gap-edge trees had 26% higher growth rates than non-gap trees may represent the upper limit of the effect of canopy gaps on growth. Overstory trees in the study area are likely to have little below ground competition from understory trees in the gaps because of extreme deer herbivory (Pedersen and Wallis, 2004). The density of understory trees 0.0–9.9 cm dbh was less in the 14 expanded gaps (82 stems/ha) than for the null gap (116 stems/ha; Pedersen and Wallis, 2004). This is contrary to the expectation of higher understory tree stem density in gaps, an expectation supported by the findings of Clebsch and Busing (1989) and Are´ valo and Ferna´ ndez-Palacios (1998). The positive response of stem radial growth rates of overstory trees to canopy gaps is likely to have several effects on forest dynamics. Given the typical correlation between dbh and crown area (O’Brien et al., 1995; Bragg, 2001), the increased stem radial growth rates of gap-edge overstory trees implies increased rates of horizontal crown growth. As a result, smaller canopy gaps will tend to close from the sides and the effective area of larger gaps that contributes to understory regeneration will be smaller. In addition, because halving gap size more than halves the additional light available in a gap (for smaller gaps; Gray et al., 2002), gap closure from the sides will have a disproportionate, negative effect on the contribution of gaps to light availability in the forest understory. The higher growth rates of overstory trees may also increase below ground competition within gaps, inhibiting the growth of understory trees and other vegetation in gaps (Oliver and Larson, 1990; Mu¨ ller and Wagner, 2003). Together, these effects of gap closure from the side will inhibit the closure of gaps from below, minimizing changes in the sizes and species of overstory trees. However, the contributions of overstory trees to gap

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closure are ultimately limited by the ability of tree to support elongated branches and survive with horizontally-asymmetrical crowns (Young and Hubbell, 1991). The crown asymmetry resulting from gaps can increase the rate of tree and branch mortality, and gap formation (Young and Perkocha, 1994); however, Runkle and Yetter (1987) did not find this to be the case. 4.2. Forest growth rates Our results on forest-level growth rates and canopy gaps are similar to those of Wardman and Schmidt (1998) who reported that gaps did not reduce stand bai in a single-age, single-species forest. Consequently, these authors argued that gaps should be incorporated into managed forests because gaps contribute to stand structural diversity and wildlife habitat. Others have noted additional positive impacts of gaps on managed forests including species diversity, coarse woody debris, soil fertility, and aesthetics (Bradshaw, 1992; Coates and Burton, 1997; Quine et al., 1999). However, because trees growing at gap edges have deeper and broader crowns (Muth and Bazzaz, 2002), these trees may have more and heavier branches that can reduce their economic value (Wenger, 1984). The process model provides a means to generalize the influence of canopy gaps at the tree-level to the forest-level. In this model, the proportion of trees neighboring a gap is based on a random distribution of cells that do not contain trees. If overstory tree mortality is more or less likely for trees neighboring an existing gap, then the spatial distribution of gaps is not random and this will influence the proportion of trees at gap edge (Fig. 6b). Runkle and Yetter (1987) found that mortality rates for gap-edge trees were the same as for trees overall; however, Young and Perkocha (1994) found that gap-edge trees had higher mortality rates. Poorter et al. (1994) reported that gaps were randomly distributed (consistent with Runkle and Yetter (1987)) or clustered (consistent with Young and Perkocha (1994)).

5. Conclusions We found that overstory trees at gap edges had 26% higher stem radial growth rates than comparable trees

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not located at canopy gap edges. Tree size or position relative to a gap did not explain observed differences in stem radial growth rates. The positive growth response of overstory trees to canopy gaps is expected to limit the role of understory tree growth in gap closure and inhibit changes in the sizes and species of trees in a forest. The higher growth rates of gapedge trees offset nearly two-thirds of the stand basal area increment lost as a result of the absence of overstory trees in canopy gaps, a result that was supported by a process model. This finding indicates that the positive contributions of canopy gaps to forests do not necessitate a sacrifice in forest growth rate equal to the canopy gap fraction. In addition to determining if these findings apply in other forests, we suggest that future research consider whether forest simulation models exhibit the growth response to canopy gaps that we observed.

Acknowledgements We are grateful to Angela Wallis, Mark Kauffman, Sarah Pears, Nick Skowronski, and Tim Frontz of Dickinson College for their essential contributions. We thank Dave Steckel, Jim Thorne, and Lee Shull of the Natural Lands Trust for supporting our work at the Florence Jones Reineman Sanctuary. Karl Kleiner of York College of Pennsylvania provided helpful ideas and reviewed a preliminary draft. This work was funded by grants from Dickinson College, including Whitaker Summer Student/Faculty Research Experiences in the Natural Sciences and Mathematics grants.

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