A method for quantifying vertical forest structure

A method for quantifying vertical forest structure

Forest Ecology and Management 104 Ž1998. 157–170 A method for quantifying vertical forest structure Penelope A. Latham ) , Hans R. Zuuring, Dean W. C...

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Forest Ecology and Management 104 Ž1998. 157–170

A method for quantifying vertical forest structure Penelope A. Latham ) , Hans R. Zuuring, Dean W. Coble School of Forestry, UniÕersity of Montana, Missoula, MT 59812, USA Received 5 March 1997; accepted 18 August 1997

Abstract Vertical forest structure is an attribute of forests that is of interest to many disciplines and is consistently discussed in the context of ecosystem management. The vertical stratification of tree crowns is a forest attribute that influences both tree growth and understory community structure. Therefore, it should be considered when making management decisions that affect the structure of stands. However, current methods of quantifying vertical structure are either arbitrarily-defined and do not represent natural stratification patterns of stands or forests, or are too time consuming for landscape analyses. The program, TSTRAT, was developed to place trees into vertical strata in a structural classification of forest vegetation developed for the Inland Northwest ŽUSA.. The primary classification criteria were cover types and classes of stand development described by structural criteria. The TSTRAT algorithm defines strata on the basis of an assumption related to a competition cut-off point among tree crowns in a given area. The predicted strata assignments of trees closely approximated vertical strata that were visually identified, in addition to those identified through cluster analysis. TSTRAT assigns each tree to a stratum, produces various descriptive statistics by vertical stratum, and quantifies overstory tree species diversity and inequality of tree heights. Because TSTRAT simulates the natural vertical arrangement of tree crowns, it is potentially useful in identifying strata that are biologically-related to processes that determine natural vertical stratification patterns. q 1998 Elsevier Science B.V. Keywords: Vertical stratification; Forest structure; Ecosystem management; Competition; Overstory diversity; Size inequality; Gini coefficient; Shannon–Wiener diversity index

1. Introduction Effective forest management depends upon the ability of land managers to objectively quantify biologically-significant attributes of forest stands. The vertical distribution of tree canopies is an attribute of forest structure that is important for managing forest resources as diverse as wildlife, hydrologic response, aesthetics, tree growth and yield ŽO’Hara et al., )

Corresponding author. Tel.: q1-406-243-4325; fax: q1-406243-6656; e-mail: [email protected]

1995., fire hazard, and susceptibility to insects or disease. The arrangement and vertical distribution of leaf area on tree crowns changes during stand development because of competition, tree mortality, the initiation of new understory trees, and the growth of previously suppressed trees. In addition, herbivory, spatial heterogeneity, environmental factors, and disturbance contribute to the complex vertical and horizontal structural patterns that develop in forest canopies ŽOliver and Larson, 1996.. Structural changes that result in differences in the amount and distribution of leaf area Žand cover. in stands affect

0378-1127r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 1 1 2 7 Ž 9 7 . 0 0 2 5 4 - 5

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stand functions such as photosynthesis and respiration ŽWaring and Schlesinger, 1985, p. 220., tree growth ŽO’Hara, 1988, 1989; Smith and Long, 1989; Arbaugh and Peterson, 1993., suitability for wildlife ŽHunter, 1990; Morrison et al., 1992., and understory plant diversity ŽLatham, 1996, Chap. 3.. The stratification patterns of individual overstory trees affect the canopy gap structure which in turn determines the distribution of light and precipitation received by subordinate trees and understory plants ŽAnderson et al., 1969, Cannell and Grace, 1993.. For example, Tamai Ž1976., using hemispherical photography in a spatially uniform Chamaecyparis obtusa plantation, found that sunflecks correlated with gaps near the zenith were due to gaps in individual tree crowns and in inter-tree spaces, but gaps that occurred in the middle to low angular heights were primarily due to the occurrence of inter-tree spaces. Forest stands with greater vertical stratification would substantially alter sunflecks that occurred in the middle to low angular height range. Other studies have found that the gap structure of western Cascade forests was correlated with stand age, disturbance history, and site conditions ŽBradshaw and Spies, 1992., that vertical stand structure affects the structure and composition of understory communities ŽHarcombe and Marks, 1977, Alaback and Juday, 1989., and that developmental changes in forest canopies can be associated with distinct changes in the amount and distribution of understory biomass among life forms ŽAlaback, 1982.. Both the prevalence of canopy openings and canopy type have been correlated with different degrees of understory development in stands of similar ages ŽStewart, 1988.. Therefore, the gap structure of overstory canopies can be expected to affect the development of understory diversity and biodiversity in general. The gap structure of forest canopies is affected by a variety of factors ranging from spatial position of the nearest trees and stand density to the arrangement of needles on tree branches, the arrangement of branches on trees, needle morphology and needle orientation ŽCaldwell, 1987; Hutchings and de Kroon, 1994.. The vertical position of needles, leaf area, and canopy cover is intimately associated with these factors, but few studies have quantified vertical stratification ŽMorrison et al., 1992, p. 127.. The vertical

tree stratification program, TSTRAT, was developed to quantify the vertical aspect of stand structure. It is not expected that the number of vertical strata will be sufficient by itself to describe stand structures. For example, at fine scales of analysis, additional attributes which describe stand density, crown dimensions, or needle morphology may also be needed depending upon the objectives for describing the stand ŽLatham, 1996, Chap. 1.. In other cases, the coefficient of variation of tree heights or the inequality of tree heights Žalso calculated by TSTRAT., may be a more useful statistic than the absolute number of vertical tree strata. The more closely the methodologies developed to quantify structural characteristics of plant communities simulate natural structures, the more closely they can be expected to represent functional changes in those communities and ecosystems. Distinct differences in vertical stand structure were also hypothesized to occur in the stages of stand development identified by Oliver Ž1981. and expanded by O’Hara et al. Ž1996.. The stages identified by O’Hara et al. Ž1996. include stand initiation, stem exclusion-closed, stem exclusion-open, understory reinitiation, young multi-strata, old forest multi-strata, and old forest single-stratum. The different structural patterns observed result from the physical and temporal distribution of tree canopies Žby cohort. in the stand and how resources are distributed among different cohorts. For example, O’Hara’s Ž1996. quantification of leaf area by cohort in multi-aged ponderosa pine stands is an indication of vertical canopy structure. The differences in vertical stand structure associated with cohorts occur at a relatively coarse scale of resolution Žthe mid- or forest scale. and are related to the prevalence of minor disturbances in the stand, population processes such as self-thinning ŽOliver and Larson, 1996., and autogenic changes that occur in trees as they age ŽRyan et al., 1997.. However, differences in vertical structure between structural classes are often difficult to determine in stands where the dominant overstory trees are shade tolerant species and continuous vertical stratification develops. The continuous vertical strata may develop from multiple fine-scale disturbances, extended periods of stand initiation, or extreme patterns of crown differentiation ŽLatham, 1996.. In other cases, it may be difficult to distinguish differences in patterns of

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vertical stratification because stands are in transition between structural stages. In the Inland Northwest, the Northern Region of the USDA Forest Service conducted the Columbia River Basin Ecosystem Management Analysis from 1994–1996. The purpose of this analysis was to develop a scientifically sound, ecosystem-based strategy for managing all lands administered by the Forest Service or the Bureau of Land Management in the basin ŽUSDA Forest Service, 1996.. The structural classes defined by O’Hara et al. Ž1996. were used as a base layer in the landscape analysis to identify current patterns of stand development, and to predict change over time in several associated forest resources. The scientific assessments were conducted concurrently by both the Forest Service and independent researchers, for example, the forest structural classification was quantified by Latham Ž1996. using discriminant analysis. Because the discriminant functions had not yet been developed which would place the initial stands into a structural class, the classes were initially defined by the Forest Service using a preliminary key to the structural classes developed by Latham and Brewer Žunpublished. in conjunction with a method developed by Stage et al. Ž1996. for determining the number of vertical strata in a stand. Stage used the empirical growth and yield model FVS ŽStage, 1973., formerly known as PROGNOSIS, to quantify the number of vertical strata ŽWykoff et al., 1982.. Traditional growth and yield models like FVS can be used to predict tree growth Žand height. over time; however, they do not define discrete canopy layers important for structural definitions. Since FVS did not explicitly model different patterns of vertical stratification, Stage et al. Ž1996. assumed that different cohorts of trees would be distinguished by relatively large differences between the canopy base of a previous cohort and the top of the canopy of a subsequent cohort. Therefore, they focused on canopy gaps to place trees into vertical strata. The initial tree lists were then projected in FVS to generate estimates of tree growth during stand development. These estimates were subsequently used in CRBSUM ŽKeane et al., 1996., a model of forest ‘succession,’ to model forest vegetation change through the structural classes. One of the primary problems with this method was that it was difficult to determine

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stratification patterns for the many stands that did not develop gaps between strata. While there is no a priori reason that projected tree lists cannot be collapsed into discrete layers or strata rather than remain as continuous elements, no single method was available to simulate natural stratification patterns in forests with both types of tree canopy stratification. GSV ŽMilner and Coble, 1995., a mechanistic process-based forest growth model, is the only model known to us that specifically identifies vertical strata to more accurately represent photosynthesis and estimate growth. However, vertical canopy strata in GSV are arbitrarily-defined ŽMilner and Coble, 1995., and do not necessarily represent the ‘natural’ patterns of vertical stratification resulting from stand development ŽOliver, 1981; O’Hara et al., 1996.. In order to quantify differences in vertical stand structure for multiple resource objectives, a flexible methodology was needed that could be applied across scales of analysis. The primary objectives of this analysis were: 1. to develop a method of simulating and quantifying the vertical stratification of forest trees which could be used to identify stages of stand development for both stand level Žfine-scale. and forest level analyses Žmid-scale., and 2. to test the ability of the methodology to represent actual vertical stratification by comparing the vertical structure simulated with TSTRAT to ‘natural’ groupings of trees by height identified by cluster analysis. We also wanted to determine the significance of using vertical strata as a predictor variable in the fine-scale discriminant function developed to distinguish between stem exclusion-closed and understory reinitiation in the Columbia River Basin structural classification. Finally, we were interested in determining the strength of the relationship between vertical stratification and the structure of the understory plant communities.

2. Methods TSTRAT was developed to simulate natural stratification patterns resulting from processes that occur during stand development. It provides a way of collapsing trees into discrete strata or canopy layers using basic tree measurement data and is particularly

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useful in plots which do not leave gaps between canopy layers. The algorithm determines a vertical height cut-off point and assigns trees to strata depending on the relative position of shorter trees to the height cut-off points. Data to develop the vertical stratification algorithm were obtained from 16 research plots used to develop the fine-scale discriminant function that quantified structural differences between stem exclusion-closed and understory reinitiation in the CRB structural classification. The data were collected on 0.04-ha plots in interior Northern Rocky Mountain forests around Missoula, Montana in western larch ŽSAF 212., Douglas-fir ŽSAF 210., and lodgepole pine ŽSAF 218. cover types ŽEyre, 1980. having a mixture of species. These cover types occurred in Douglas-fir Ž Pseudotsuga menziesii var. glauca wBeissn.x Franco. and grand fir Ž Abies grandis wDougl.x Forbes. climax tree series. Western larch Ž Larix occidentalis Nutt.., Douglas-fir Ž Pseudotsuga menziesii var. glauca wBeissn.x Franco., lodgepole pine Ž Pinus contorta var. latifolia Engelm.., Engelmann spruce Ž Picea engelmannii Parry., ponderosa pine Ž Pinus ponderosa Dougl.., grand fir Ž Abies grandis wDougl.x Forbes., and subalpine fir Ž Abies lasiocarpa wHook.x Nutt.. were the major tree species that occurred on the plots. The stem-mapped plots were established in relatively even-aged natural stands originating from fire around 1900 in which no subsequent management activities had occurred. This age period was selected to increase the likelihood that the plots sampled would be in either stem exclusion-closed or understory reinitiation. In this way, structural differences could be examined for plots that were close in age but had developed different numbers of cohorts. The mean age at tree base on the 0.04-ha plots ranged from 62 to 114 yrs. The plots ranged in stocking from 23.2 to 63.4 m2 barha. The number of live trees ranged from 667 to 2,076 per hectare. Species, dbh, height, height-tobase of live crown, crown ratio, crown class, and snag quality were recorded for all trees G 7.6 cm dbh. Smaller size classes were sampled on 0.008-ha nested plots. The modal crown ratio of trees G 7.6 cm dbh was 30%. The plots were assigned to a structural class by using graphs of height–age growth trajectories obtained by stem analysis of trees on the 0.008-ha plots and by using age-class distributions.

Large gaps in the age-classes indicated the presence of a new cohort of understory trees and the onset of understory reinitiation. Cover types were determined using basal area by tree species according to Eyre Ž1980.. 2.1. The stratification algorithm TSTRAT uses basic tree data that includes species, height, crown ratio, and diameter at breast height. The TSTRAT algorithm defines multiple cut-off points based on tree heights and crown lengths and assigns individual trees to vertical strata depending on the relative position of tree crowns to these height cut-off points. Descriptive statistics for mean diameter at breast height, total tree height, height-to-base of live crown, and basal area are summarized by stratum. A tree’s competition zone was defined as the area of the crown where the majority of photosynthesis occurs. In this case, it was defined as the top 60% of the tree crown. A height cut-off point resulted, below which little photosynthesis was assumed to occur. We reasoned that competition would occur when the primary photosynthetic area of nearby tree crowns were positioned within the same vertical space. These interacting trees could potentially affect the acquisition of light by the most important photosynthetic area of an individual tree’s crown Žin several ways not limited to shading.. As a result, either height suppression or height growth might occur depending upon the physiological condition and spatial position of the tree in the canopy. The height cut-off values were based on an adaptation of competition evaluation points defined in other studies Že.g., Biging and Dobbertin, 1995. and the observation of tree crown relationships in the study area. Before applying the stratification algorithm, the tree records were sorted in descending order by height and crown length, so that for trees of equivalent height, the tree with the longest crown was considered first. Then, under the assumption that competition to stay in an advantageous position for the acquisition of light is greatest in the top 60% of the tree crown, the height value for the competition cut-off point per stratum would be 0.40 ) CL q HBLC starting with the tallest tree that had the longest crown for that tree height ŽCL s crown length, HBLCs height-to-base of the live

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Fig. 1. Diagram showing the use of a competition coefficient of 0.4 to calculate the competition cut-off height value. ‘Open’ trees are the trees used to compute the height cut-off value.

crown.. All trees with heights that equaled or exceeded the competition cut-off height were placed in the same stratum. When a tree height was less than the cut-off height, a new cut-off height value was calculated based on the tallest remaining tree with the longest crown for that tree height, until all the trees were accounted for or until some pre-defined lower limit for strata definition was reached ŽFig. 1..

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Horizontal spatial location is not included in the algorithm. The TSTRAT algorithm is most appropriately applied at the plot level, so that trees are spatially ‘near’ each other as opposed to being applied to entire stands. One approach to representing the vertical stratification of a ‘stand’ would be to classify several plots and assign the stand a strata value based on the majority strata value. Alternatively, administrative boundaries could be redrawn to represent areas with similar numbers of vertical strata or to represent similar structural classes. Two main indices are calculated by TSTRAT as alternative measures of vertical stand structure: the coefficient of variation of tree heights and the Gini coefficient of inequality applied to tree heights. The Shannon–Wiener diversity index was calculated to quantify differences in tree species diversity and then tested in the discriminant analysis to determine its potential for use as a surrogate for other more difficult to obtain measures of vertical structure ŽLatham, 1996.. Spearman rank correlation coefficients were calculated to quantify the association between the Shannon–Wiener diversity index and the other measures of vertical structure quantified by TSTRAT. 1. The coefficient of variation of tree heights was calculated according to Sokal and Rohlf Ž1981.: CV s Ž s.d.rX . 100 where s.d.s the standard deviation.

Table 1 Comparison of program features in the FORTRAN version for DOS and the Microsoft EXCEL 5.0 spreadsheet version of the stratification program, TSTRAT TSTRAT program features

FORTRAN

EXCEL

Allows user to define species up to a maximum of 30 Places each tree in a stratum Allows the definition of a lower limit for strata identification Ždefault s 0. Allows the user to define the competition cut-off point Ždefaults 0.4. Calculates descriptive statistics per stratum Defines and displays strata cut-offs Calculates the Gini coefficient of inequality for tree heights Calculates the coefficient of variation for tree heights Calculates the Shannon–Wiener diversity index for tree species Output to two separate output files Self-contained output goes to other spreadsheet pages Sorting routine which reduces formatting time for data input Heightrdiameter error trapping Provides a profile of tree structure with tree crowns and boles color differentiated Processes multiple plots at a time

X X X X X X X X X X y y X y X

No limit X X X X X X X X y X X y X y

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Table 2 Chi-square values and associated probabilities for the hypothesis tests comparing the results of the vertical stratification algorithm to those of the cluster analysis Plot number

N

% Misclassification

Chi square test statistic

P-value

11 15 16 19 22 23 30 33 34 36 38 39 40 46 47 50

47 65 46 84 32 47 27 31 40 31 34 69 60 73 63 32

12.8 6.1 10.9 6.0 6.2 17.0 11.1 25.8 7.5 12.9 0 13.0 18.3 12.3 4.8 9.4

0.702 1.243 1.463 3.793 0.533 1.057 0.335 4.909 1.444 1.714 0.000 9.024 4.054 1.25 0.524 0.577

0.873 0.537 0.691 0.435 0.912 0.788 0.846 0.086 0.486 0.634 1.000 0.061 0.542 0.87 0.971 0.448

a

Combined strata P-value

0.854

0.584 0.042 a 1.000 0.277

Significantly different Ž a s 0.05..

2. The Gini coefficient ŽWeiner and Solbrig, 1984; Dixon et al., 1987. is a measure of inequality which can be applied to plant heights as follows: n 1 GC s Ž 2 i y n y 1. Xi Ý Ý Xi Ž n y 1. 1 where Ý X i s Xn as given in Dixon et al. Ž1987. and i s the rank of a tree in ascending order. It is the

arithmetic average of the absolute values of the differences in some metric, e.g., tree height, between all pairs of individuals. The Gini coefficient has a minimum value of 0 when all the measurements are equal and a theoretical maximum of 1.0 in an infinite population in which all measurements but one have a value of 0: the ultimate in inequality. Weiner and Solbrig Ž1984. recommend using a measure of in-

Fig. 2. Dendrogram of cluster analysis for plot 38. Euclidean distances appear along the y-axis. Values listed next to ‘CL’ and ‘ST’ at the bottom of the diagram represent strata assignments made from the cluster analysis and stratification program, respectively. Tree numbers correspond to those on the vertical stratification graph.

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equality rather than a measure of skewness as an indicator of size hierarchies that develop in plant populations because of one-sided competition. 3. The Shannon–Wiener diversity index quantifies tree species diversity in the plots ŽMagurran, 1988.: HX s yÝ pi lnpi where pi s the proportion of trees Žpercent of individuals. in the ith species. Counts of tree species were selected to calculate the index instead of basal area by species because the use of basal area would exclude the occurrence of smaller trees on a plot. The Shannon–Wiener index is one of the most widely used measures of diversity and is based on both species richness and evenness. An advantage of using this index is that its distributional properties have

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been examined, and if the index is calculated for a number of samples, the indices themselves will be normally distributed and can be compared using parametric statistics. Two versions of TSTRAT were developed: a DOS-resident FORTRAN program which allows multiple plots to be evaluated at a time and a VISUAL BASIC FOR APPLICATIONS program which evaluates and graphs individual plots in a Microsoft EXCEL 5.0 spreadsheet environment. Program features for the two versions are listed in Table 1. 2.2. Analysis Cluster analysis was performed in SYSTAT version 5.0 ŽWilkinson et al., 1992. using heights of all trees greater than 7.6 cm dbh. The Furthest Neighbor

Fig. 3. Tree strata predicted by TSTRAT for plot 38. Vertical bars represent individual trees. Darkened upper portions indicate crown length. Strata are delineated by lines at the competition cut-off heights. Tree numbers appear slightly to the left of the corresponding bar. S1, S2, S3, S4 are stratum labels.

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method was used as the clustering criterion and Euclidean distance as the measure of inter-object distance. Results of the analysis were treated as a surrogate for the natural stratification pattern of the measured plots. Other variables were initially considered such as crown length, height-to-base of live crown, and the height value for the competition cut-off point; however, these often resulted in inappropriate clusters being defined for the purpose of identifying vertical strata. For example, trees with similar crown lengths might be grouped together even though they had very dissimilar heights. Euclidean distance performed better than similarity measures in grouping tree heights. This may be because similarity criteria have more difficulty identifying clusters that are not spherical ŽDillon and Goldstein, 1984.. Although Euclidean distance has been criticized because it is affected by scale ŽDillon and Goldstein, 1984; Ludwig and Reynolds, 1988., all measurements for this analysis were on the same scale, i.e., values of tree heights. Consequently, scale invariance was not an issue. Clusters of trees belonging to a stratum were identified by comparing the results of the cluster analysis to a graph of trees on the plot. The trees were displayed in the order in which they were recorded Žclockwise from north.. The crown lengths

and boles were color differentiated. The largest groups suggested by the cluster analysis that could visually be identified on the graph were selected as ‘natural groupings’ and all trees in a group were given a stratum label, e.g., 1, 2, 3, etc. Each tree was also given a stratum label corresponding to the stratum assigned by TSTRAT. The proportions of trees in the vertical strata generated by TSTRAT were compared to those obtained from the cluster analysis using a chi-square test statistic. The hypotheses tested for each stratum were : H 0 :PObserved strata ŽCluster. s PPredicted strata ŽTSTRAT. and H 1:Not H 0 . The desired outcome was that the proportion of trees in the strata derived by both methods would be similar. Before conducting the chi-square test for each of the plots, a stratum was combined with an adjacent stratum if fewer than five trees were present ŽKoopmans, 1987.. Following cluster analysis and stratum assignment, the number of strata per plot were used as an independent variable with other structural criteria in the discriminant analysis to quantify the CRB finescale structural classification ŽLatham, 1996, Chapter 1.. The same variable was also used as part of a canonical correspondence analysis to examine the relationship of overstory structure to the structure of the understory communities ŽLatham, 1996, Chap. 3..

Fig. 4. Dendrogram of cluster analysis for plot 33. Euclidean distances appear along the y-axis. Values listed next to ‘CL’ and ‘ST’ at the bottom of the diagram represent strata assignments made from the cluster analysis and stratification program, respectively. Tree numbers correspond to those on the vertical stratification graph.

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3. Results Vertical stratification patterns for fourteen of the sixteen plots were highly similar Ž a s 0.05. ŽTable 2.. Plots 33 and 39 were not significantly different, but were much less similar to the cluster analysis strata than the other plots. When strata were combined for plot 33, the p-value dropped to 0.042 indicating a significant difference. The average error rate for TSTRAT was 10.88% Žs.d. 5.95%.. Five plots were affected by low cell frequencies: 16, 30, 33, 34, and 36. Combining strata had a variable affect on the probability values associated with the chi-square test statistic causing them to

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decrease for three plots and increase for the other two. The greatest increase occurred for plot 34 where the p-value rose dramatically from 0.486 to 1.000. Three strata were identified for plot 34 and within those strata only three trees were ‘misidentified’ by the TSTRAT program. The two merged strata were the ones containing the misidentified trees, thus eliminating any existing differences and making the frequency distributions exactly equal. The reverse situation occurred with plot 36, the plot with the greatest decrease in p-value. Four strata were identified for this plot. Strata 3 and 4 had few observations, but were identical for both distributions. Upon merging them with stratum 2, all cells that had identical

Fig. 5. Tree strata predicted by TSTRAT for plot 33. Vertical bars represent individual trees. Darkened upper portions indicate crown length. Strata are separated by lines at the competition cut-off heights. Tree numbers appear slightly to the left of the corresponding bar. S1, S2, S3 are stratum labels. Numbers over the bars indicate the stratum assignment of trees in the cluster analysis that were ‘misclassified’ by the TSTRAT program.

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Table 3 Spearman rank correlation coefficients between the Shannon–Wiener diversity index and other measures of vertical stand structure Structural index

Stem exclusion ŽS–W index.

Understory reinitiation ŽS–W index.

Combined stages ŽS–W index.

No. of vertical strata CV for tree height Gini coefficient for tree height

y0.846 0.436 0.436

0.866 0.8 0.8

y0.288 0.5 0.515

proportions were eliminated, thereby decreasing the probability that the two distributions were from the same population. 3.1. Plot 38 and plot 33: dendrograms and Õertical stratification graphs (TSTRAT) Plots 38 and 39 represent the extremes in stratification success. Plot 33, a close second to plot 39 in its dissimilarity to the cluster analysis, was selected for discussion over plot 39 because of its relatively short tree list and corresponding clarity in graphing. Dendrograms present the results of the cluster analyses ŽFigs. 2 and 4.; vertical stratification graphs present the results obtained using TSTRAT ŽFigs. 3 and 5.. The stratification algorithm identified the same tree strata assignments for plot 38 as were identified using cluster analysis ŽFigs. 2 and 3.. Discrete clusters corresponding to strata groups were identified at the division that was 2nd from the top Žcorresponding to Euclidian distances of 41.0 for strata 1 and 2 and 21.0 for strata 3 and 4.. Clusters for plot 33 ŽFig. 4. were also identified at the division point that was second from the top Žcorresponding to a Euclidean distance of 36.0 for strata 1 and 2. and resulted in eight trees being misclassified. Group 3 was identified at the highest division ŽEuclidean distances 73.0.. In order to duplicate the vertical stratification computed by the TSTRAT program, stratum 2 would have been identified at tree 509 rather than at tree 511. While it was not possible to identify clusters at the second division for all of the plots because some canopy structures were more complex, no clusters were identified below the third division from the bottom. 1 1 Divisions have been identified as if they occurred from the top down for ease of discussion, but hierarchical clustering in SYSTAT actually occurs from the bottom up.

The correlation analysis indicated strong associations between the Shannon–Wiener diversity index and the other measures of vertical structure when the analysis was done by structural class ŽTable 3.. In stem exclusion, the S–W index was strongly but negatively associated with the number of vertical tree strata. This association was reversed in understory reinitiation. The S–W index was more closely associated with the other indices of vertical structure in understory reinitiation than in stem exclusion. In the CRB fine-scale discriminant analysis ŽLatham, 1996., the number of vertical tree strata was consistently important in the models used to quantify overstory structure and was significantly different between the structural classes stem exclusion and understory reinitiation ŽMann–Whitney UStatistic for the null hypothesis of no difference between classes: 42.5, p s 0.074, n s 16, a s 0.10.. In the canonical correspondence analysis, the number of vertical tree strata was strongly correlated with the composition and structure of the understory communities. Pearson’s correlation coefficient and Kendall’s tau between the number of vertical strata and the first ordination axis were y0.865 and y0.695, respectively using PC-ORD ŽMcCune, 1993..

4. Discussion The vertical stratification algorithm in TSTRAT satisfactorily reflected the stratification of the plots as they were represented by the results of the cluster analyses. In addition, the strata defined made sense upon visual inspection. The trees that appeared the most ‘out of place’ were usually ones that were very near the height values of the competition cut-off points, and generally, were the trees that were misclassified. Occasionally though, as with plot 33, there was another stratification pattern that could occur as easily as the one determined by TSTRAT.

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However, the purpose of the algorithm was to place tree crowns into strata that reflect competition processes in the plot. In closed canopy forests, light is particularly limiting. It was assumed that other factors affecting tree growth were integrated by canopy development and height growth of the trees ŽOliver and Larson, 1996; Oliver, 1992; Perry, 1994.. In actuality, competition in plant communities is rarely monothetic. The development of vegetation is a dynamic process involving resource trade-offs with interactions between aboveground and belowground resource capture, and allogenic factors ŽTilman, 1988; Cannell and Grace, 1993; Oliver and Larson, 1996.. If the tree strata assignments for plot 33 are examined from the perspective of their ability to interfere with light capture by other trees, only trees 508, 513, and 544 in stratum 1 appear questionable. A modification to the algorithm might include a certain percentage above the competition cut-off point which the height of a subordinate tree must exceed before it is assigned to that stratum. The utility of the TSTRAT algorithm may partially be associated with the growth response of trees to the varying spectral quality of light associated with the presence of nearby trees in forest understories, particularly, for shade-intolerant species. Most plants respond to shade by increasing the allocation of photosynthates to and within shoots in such a way as to compensate for a reduction in light. Some aspects of this photomorphogenetic response are triggered not by the reduction in light per se but by a shift in the spectrum ŽCannell and Grace, 1993.. Vegetation shadelight having a reduced ratio of redrfar-red light has been shown to affect the photomorphogenetic response of plants receiving the altered redrfar-red light ratios ŽCaldwell, 1987; Cannell and Grace, 1993.. Although little work has been done with trees, and the response tends to be greater for hardwood species than for conifers ŽKimmins, 1987., this response has been demonstrated in Pinus radiata D. Don ŽCaldwell, 1987. and tropical tree seedlings ŽKwesiga and Grace, 1986.. Ballare´ et al. Ž1990. found that a plant did not have to be overtopped by another to detect its presence. This interesting result implies that a plant may avoid competition by increasing extension growth when another plant is detected nearby ŽCannell and Grace, 1993.. If leaves or needles at the top of a tree’s crown are

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already saturated with light, side shade may have a significant affect on vertical stratification. Although this is only one aspect of the complex interactions affecting plant growth in forest understories, species-specific responses to altered redrfar-red ratios, influenced by other trees nearby, have the potential to affect stratification patterns of forest stands. While heuristically useful, the assumptions implicit in the development of the TSTRAT algorithm have yet to be verified. Further research is required to determine what biological relationships do in fact exist. The height cut-off point used in the TSTRAT algorithm is consistent with the occurrence of the maximum amount of foliage area and mass by relative crown depth identified in other studies ŽMaguire and Bennett, 1996.. In a review of competition indices, Biging and Dobbertin Ž1995. evaluated crown-based indices Žrepresenting crown volume, crown cross-sectional area, and crown surface area. in growth models at a percent of a subject tree’s height. The competition indices were incorporated into species-specific growth models to evaluate the effect on reduction of the mean square error ŽMSE. in diameter squared growth and height growth equations. The best results were obtained at 66% and 75% of the subject tree’s height for ponderosa pine and at 50% and 66% of the subject tree’s height for white fir. The point representing 66% of a tree’s height was a fairly consistent indicator of a lower limit for competition in Biging and Dobbertin’s data. Moreover, they found that reduction of the MSE when using different types of competition indices was minor compared to selection of the evaluation height, and that the spatial location of trees was less important than expanding the number of trees that might affect the outcome of competition. Biging and Dobbertin’s Ž1995. data were collected in the mixed conifer forest type in northern California and included ponderosa pine Ž Pinus ponderosa Doug.., coastal Douglas-fir Ž Pseudotsuga menziesii var. menziesii wMirbelx Franco., white fir Ž Abies concolor Gord. and Glend.., red fir (Abies magnifica A. Murr.., and sugar pine Ž Pinus lambertiana Dougl... The modal crown ratio in this species mixture was 50%. The authors point out that two-thirds of the crown length from the top of the tree coincided with

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Table 4 Mean competition cut-off height values and competition heights as a percent of total tree height by cover type Cover type

Mean competition height Žm.

Competition height as % of tree height

Lodgepole pine Western larch Douglas-fir

18 16.4 14.9

87.4% 84.9% 61.1%

66% of tree height for their data. The competition cut-off height corresponding to the condition where competition occurs in the upper 66% of the tree crown would be 0.33 ) CL q HBLC. While it is difficult to define an exact point of influence for use in a competition index, it appears that the empirically derived competition cut-off height corresponding to 0.4 ) CL q HBLC Žor simply a competition coefficient of 0.4. may be related to the greater percentage of shade-intolerant species in the Montana data set. The mean competition height values for three cover types as a percent of total tree height were calculated for comparison with Biging and Dobbertin’s data ŽTable 4.. The cover types were defined by a dominant species but were not pure. Biging and Dobbertin’s evaluation heights were 50% to 66% for white fir Ža shade-tolerant species. and 66% to 75% for ponderosa pine Ža relatively shade-intolerant species.. In the Montana data, the competition cut-off heights for the two shade-intolerant cover types, western larch and lodgepole pine, were not only greater than for Douglas-fir, a mid-range shade-tolerant species, but they occurred higher in the canopy. The competition cut-off height values identified in this study are probably not appropriate for all data sets given differences in shade tolerance of the component tree species. Therefore, the competition cutoff value can be specified by the user in TSTRAT. A competition cut-off algorithm of 0.5 ) CL q HBLC was initially tried and rejected for the Montana data. A competition cut-off algorithm - 0.4 ) CL q HBLC was not tested based on observation of the relative positions of tree crowns in the data set; however, it is possible that it may work as well. Controlled experiments to determine the onset of height growth associated with the percentage of crown overlap by surrounding trees are needed to provide the biological foundation for acceptance of this conceptually derived algorithm.

Despite the lack of experimental data, the number of vertical strata identified by TSTRAT was shown to be important in several contexts. The strata identified were similar to those recognized using cluster analysis. The correlation analysis performed between the number of vertical strata, the coefficient of variation of tree heights, the Gini coefficient of inequality of tree heights, and overstory species diversity indicated the presence of very strong relationships among these indices. The number of vertical strata was an essential variable in several fine-scale discriminant models developed for the CRB structural classification and was strongly related to the structure of the understory communities. In this analysis, as in other analyses of overstory structure and understory diversity associated with the CRB structural classification ŽLatham, 1996., previously unrevealed ecological differences appear when analyses are separated by stage of stand development Žstructural class.. During stem exclusion, a period of strong competition, the number of vertical strata appeared to be related to crown differentiation patterns among a fewer number of successful competitor species. During understory reinitiation, the association between the Shannon–Wiener index and the number of vertical strata was equally as strong as during stem exclusion. However, following the selfthinning that occurs during understory reinitiation, vertical stratification patterns are apparently associated with the occurrence of additional species in the understory rather than suppression of equal-aged trees.

5. Conclusion The vertical stratification of tree canopies and its association with differences in stand development is an attribute of forest structure that has not been incorporated into forest management planning, yet

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the analyses conducted in this research have indicated the importance of this forest attribute. The TSTRAT algorithm is potentially useful in a variety of management or research-oriented applications where definition of vertical strata is desired, e.g., aesthetic value of forests, structure related to wildlife habitat, fire and forest health risk assessments, and ecological analyses related to biodiversity. From a broader perspective, the number of vertical strata that develop in forests is an emergent characteristic of natural stands related to differences in species composition, competitive relationships, environmental constraints, and disturbance. At a time when the number of unmanaged stands is becoming increasingly limited, it is important to quantify characteristics describing forest structures that result from natural processes of stand development in order to provide base-line conditions from which to monitor change. TSTRAT 2 provides a way of reproducing and quantifying vertical stand stratification patterns and allows users to view a simplified representation of overstory stand structure.

Acknowledgements Financial support was provided for this project by the Northern Region of the USDA Forest Service in conjunction with the Columbia River Basin Eastside Ecosystem Assessment. We are particularly indebted to Kevin O’Hara for helpful comments on the manuscript and for sharing his ideas about vertical structure with us. The useful comments of two anonymous reviewers greatly improved the manuscript, and were truly appreciated. Thanks also to Ellen Voth for her assistance with graphics and program development.

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2 The FORTRAN and EXCEL 5.0 versions of TSTRAT are available from the principal author upon request.

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