A quantitative technique for the identification of canopy stratification in tropical and temperate forests

doi:10.1016/S0378-1127(99)00118-8

Forest Ecology and Management

Volume 127, Issues 1–3, 1 March 2000, Pages 77-86

https://doi.org/10.1016/S0378-1127(99)00118-8 Get rights and content

Abstract

Canopy stratification is one of the oldest concepts in tropical forest ecology. However, there has been considerable debate over the existence and identification of strata. Much of the confusion arises from the differing definitions of strata (i.e. vertical stratification of phytomass, individual crowns, or species) and the methods used to evaluate them (e.g. profile diagrams). In this paper, a quantitative technique for identifying stratification of individual tree crowns in the forest canopy is presented. Strata are identified by comparing sorted tree heights to a moving average of height at the base of the live crown. Height and crown measurements were obtained from 21 published profile diagrams of forests, representing many biogeographic regions and covering a wide variety of forest types. The technique provides an objective measure of canopy strata allowing for a valid comparison of stratification between the different profile diagrams. Neither the original author's estimates of strata nor the number of strata detected by the quantitative technique support the premise that tropical forests have more strata than temperate forests. With the sole exception of a mono-layered European Douglas-fir plantation, all forests in this study had two or three layers.

Introduction

Canopy stratification is one of the oldest concepts in tropical forest ecology, dating as far back as the early 19th century (Richards, 1996). Nonetheless, there has been considerable debate regarding the existence and measurement of strata in the forest (Richards, 1996; Smith, 1973; Whitmore, 1985). Some authors have found canopy strata in forests they studied (e.g. Davis and Richards, 1933; Ashton and Hall, 1992); others have not (e.g. Mildbraed, 1922; Paijmans, 1970); while some authors have cryptically suggested that whether canopy strata exist or not, the concept of stratification is a useful organizational tool for the study of the vertical distribution of plants and animals (e.g. Halle et al., 1978).

Perhaps the most important sources of confusion regarding the nature of stratification are its definition and the relatively subjective methods traditionally used to identify it. The term `stratification' has been used to characterize three distinct, though closely allied, phenomena (Smith, 1973): vertical stratification of phytomass (e.g. Ashton and Hall, 1992), vertical stratification of individual crowns (e.g. Grubb et al., 1963), and vertical stratification of species (e.g. Oliver, 1978). Strata may exist by one definition, but not another. For example, phytomass may be stratified in a forest even if individual crowns are not; or, individual crowns of the same species may be found in different strata.

The oldest and most widely used method to study stratification is the profile diagram, which was introduced to the literature by Watt (1924)in a study of beech forests in England. Davis and Richards (1933)were the first to apply the profile diagram technique to a tropical forest. A profile diagram is created by establishing a plot (usually 40–70 m by 10 m wide, although this may vary depending on tree density), measuring the height, the crown length, and the crown width for all trees, and later converting these measurements to a scale drawing of the plot seen in profile. From the diagram one can visually assess whether or not strata exist. In some cases, histograms of height class or phytomass have supplemented profile diagrams (e.g. Grubb et al., 1963; Ashton and Hall, 1992). Confirmation of the presence of strata from profile diagrams or histograms of height or phytomass is visual and qualitative. Grubb et al. (1963), discussing the lowland rain forest of Ecuador, claimed that the number of strata in a given forest was more a matter of `personal preference' than objective criteria.

Ashton and Hall (1992)presented the first quantitative measure of stratification, the stratification index. The stratification index is the ratio of phytomass in the height class with the greatest amount of phytomass to that of the height class with the least amount. The resultant number provides a normalized index of stratification that can be compared among stands. However, the stratification index does not identify how many strata exist, where they are found in the vertical profile of the stand, nor which trees are found in which strata. In addition, Ashton and Hall's stratification index requires measures of individual tree crown width, a relatively time-consuming procedure in dense tropical forests.

Recently, Latham et al. (1998)proposed a quantitative model, TSTRAT, for identifying stratification within stands. Their methodology was developed to facilitate structural classification of temperate conifer forests of the Inland Northwest region of the USA (Montana, Idaho, Oregon, and Washington). TSTRAT estimates the number of strata in a given stand using individual tree height and live crown ratio data. The trees are sorted by height and crown ratio and the upper 60% of the tallest tree crown—described as the competition zone (Latham et al., 1998)—is used as the basis of inclusion for the first strata. All trees with heights greater than or equal to the lower limit of this competition zone are included in the first stratum. The tallest tree not included in the first stratum is used as the guide for inclusion in the next stratum, and so on, until all trees have been assigned to strata. While this approach provides a repeatable estimate of the number of strata and requires only height and live crown ratio measures, we believe that the number of strata may often be overestimated. The causes of this bias are considered in the discussion.

In this paper, we present a simple quantitative technique for identifying stratification of individual tree crowns (Smith, 1973). We have adopted this definition of stratification in developing the technique because of the relative ease and accuracy of measuring individual crowns vs. the distribution of phytomass, and because it permits comparison of patterns of stratification among forests of differing species composition.

The stratification algorithm identifies discontinuities in the vertical distribution of crowns by comparing the height of a tree (HT) to the mean height of the base of the live crown (HBLC) of all taller trees (McCarter et al., 1996). The algorithm proceeds by the following steps:

1.
Sort the trees by HT and HBLC in descending order.
2.
Beginning with the tallest tree (t₁), calculate the mean HBLC [for t₁, mean HBLC = HBLC (t₁), for later trees within the same stratum mean HBLC is the mean HBLC of all preceding trees].
3.
Compare the height of the next tallest tree [HT(t₂)] plus the constant of overlap (k_o) to the mean HBLC. [The constant, k_o, defines a threshold distance between the mean HBLC and HT(t₂) (see Section 1.3.]
4.
If HT(t₂) + k_o is greater than the mean HBLC, then t₂ is in the same stratum as t₁. The mean HBLC is recalculated using t₁ and t₂.
5.
If HT(t₂) + k_o is less than the mean HBLC, then t₂ is in a stratum below t₁. The calculation of mean HBLC is reinitialized beginning with t₂, ignoring HBLC values from the preceding stratum.
6.
The decision rules (steps 4 and 5) are repeated for all trees in the plot.

To evaluate and parameterize the algorithm we used tree height and crown length data obtained from profile diagrams in the published literature, supplemented by our own unpublished data (Table 1). The data represent a wide range of forest types (both temperate and tropical), species compositions, and stand structures. The sole criterion for inclusion of a profile diagram was a minimum of 30 visible trees. Each profile diagram was enlarged with a photocopying machine to facilitate measurement. Height and HBLC were measured for each tree in the profile diagram for which both the top and bottom of the crown were visible. This criterion excluded between 10% and 20% of the trees in the profile diagrams. A detailed evaluation of several profile diagrams found neither systematic exclusion of trees in particular strata nor a bias toward missing crown tops or crown bottoms. The stratification algorithm was run for the data obtained from each profile diagram and the number of predicted strata was then compared to the original author's estimates.

We performed a sensitivity analysis of the constant k_o to determine a standard value that could be used when comparing stratification in different stands. For each profile diagram the constant, k_o, was evaluated using both simple distance measures and percentages of the maximum height of the stand. The distance measures ranged from the height of the tallest tree for each stand to −1 × (the height of the tallest tree). The height ratios ranged from −100% to 100% of the height of the tallest tree in the stand. The range of distance values for k_o are plotted against the number of strata detected for each profile diagram in Fig. 1 (the results from the height ratio values for k_o were nearly identical and are not shown). To estimate the `best-fit' value for the parameter k_o, we used the sum of squares method (Neter et al., 1989) as follows: $Error = ∑ i=1 n (S_{obs} −S_{est})^{2}$ where S_obs is the strata observed by the original authors, S_est the strata detected by the algorithm for each value of k_o, and n the number of profile diagrams.

The `best-fit' value of k_o is that value which minimizes the error estimate.

To illustrate the results of the stratification algorithm, we have included a profile diagram (Fig. 2; Paijmans, 1970) and a graph of the output from the stratification analysis (Fig. 3). Note that in Fig. 3 the discontinuities in the mean HBLC at trees 6 and 15 are the beginning of new layers.

Section snippets

Results and discussion

The goodness-of-fit profile for k_o (Fig. 4) shows that a value of 1.5–2.0 m overlap in the stratification algorithm resulted in the minimum estimation error. Above k_o = 5 m, the number of strata in all forests becomes asymptotic at one stratum (Fig. 1). When k_o = −10 m, the number of strata in each stand approaches the number of trees included in the stand analysis (Fig. 1). Of the values for k_o that we tested in each profile diagram, k_o = 1.5 m routinely identified levels of stratification consistent

Conclusion

Profile diagrams have been the standard means of identifying stratification in forest canopies, yet they have three principal drawbacks as tools for analyzing stratification, namely, their interpretation is subjective, they are labor-intensive, and spatially restrictive. The approach for identifying stratification described here liberates researchers from all three problems. The algorithm is objective, allowing for a valid comparison of stratification between forest plots. Because a drawing of

Acknowledgements

We would like to thank Mark Ashton, Peter Ashton, Gordon Orians, and Jim McCarter for helpful comments on earlier drafts of the manuscript. This work was supported by the Landscape Management Project under the supervision of Chad Oliver. Copies of the stratification algorithm are available from the Landscape Management System web site¹.

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A quantitative technique for the identification of canopy stratification in tropical and temperate forests

Abstract

Introduction

Section snippets

Results and discussion

Conclusion

Acknowledgements

For. Ecol. Manage.

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J. Ecol.

The Mora forests of Trinidad, British West Indies

J. Ecol.

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J. Ecol.

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