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Analysing structural diversity in two temperate forests in northeastern China
Forest Ecology and Management xxx (2013) xxx–xxx
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Analysing structural diversity in two temperate forests in northeastern China Ruiqiang Ni a, Yeerjiang Baiketuerhan b, Chunyu Zhang a, Xiuhai Zhao a,⇑, Klaus von Gadow c a
Key Laboratory for Forest Resources & Ecosystem Processes of Beijing, Beijing Forestry University, Beijing 100083, China College of Forestry and Horticulture, Xinjiang Agricultural University, Urmqi 830052, China c Faculty of Forestry and Forest Ecology, Georg-August-University Göttingen, Büsgenweg 5, D-37077 Göttingen, Germany b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Spatial structure Second order statistics Nearest neighbour statistics Bivariate mixtures
a b s t r a c t This contribution presents an analysis of the structural diversity in two temperate forest ecosystems in northeastern China, based on two large contiguous observational studies covering an area of 5.2 ha (260 200 m2) each. The total number of living trees in the conifer and broad-leaved forest (CBF) study area is 2927 per ha, comprising 37 species and 21 genera. The old growth forest (OGF) study area has 2276 trees per ha, including 22 species and 13 genera. Tree species are classified according to their community status as mature and immature canopy, subcanopy and shrub. A clustering process based on two distinct communities of the bivariate dbh/height distributions is used to differentiate between mature and immature canopy species. Numerical analysis is based on these four distinct cohorts. Despite advances in remote sensing, mapped tree data in large observation windows are very rare. Thus, we are able to use methods for analysing forest structure which are suitable for both, unmapped and mapped data. The two data sets are unique in that all (approximately) 27,000 tree heights are available. Accordingly, it was possible to fit bimodal height distributions and bivariate mixed dbh/height distributions to almost all individual species that were represented by sufficiently large numbers. Methods of second order statistics (SOC), including marked point statistics as well as nearest neighbor statistics (NNS) based on nearest neighbourhood structure units are also presented, including bivariate mixtures of the NNS attributes ‘‘mingling’’ and ‘‘dominance’’. Mark correlations were investigated for several marks, including diameters, heights and nearest neighbor statistics. Finally, we discuss the most important results and motivate the need for detailed assessments in large contiguous field plots. The literature on spatial statistics is often rather technical, and there is relatively little exchange between mathematicians developing the theory and ecologists who have interesting data from observational studies, such as presented in this contribution. Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved.
1. Introduction Structure is a fundamental notion referring to patterns and relationships within a more or less well-defined system. Important theoretical concepts relating to biological structures include selforganisation which involves regeneration, tree mortality and a variety of interactions between individual plants. The properties of a particular forest ecosystem, including biomass production, biodiversity and the quality of ecosystem services, are determined to a large degree by its structure. Trees propagate, grow and die, but they are sessile, bound to one specific location. Forest regeneration, growth and mortality generate very specific structures. Specific structures in turn, generate particular processes of growth and ⇑ Corresponding author. Address: Forest College in Beijing Forestry University, No. 35 Qinghua East Road, Haidian District, Beijing 100083, China. E-mail addresses: [email protected] (R. Ni), [email protected] (Y. Baiketuerhan), [email protected] (C. Zhang), [email protected] (X. Zhao), kgadow@ gwdg.de (K. von Gadow).
regeneration. The production and dispersal of seeds and the associated processes of germination, seedling establishment and survival are important factors of plant population dynamics and structuring (Harper, 1977). Thus, structure is not only the result of past developments, but also the starting point for future dynamics. ‘‘Forest structure’’ usually refers to the way in which the attributes of trees are distributed within a forest. Associated with a specific forest structure is some degree of heterogeneity or richness which we call diversity. In a forest ecosystem, diversity does, however, not only refer to species richness, but to a range of phenomena that determine the heterogeneity within a community of trees, including the diversity of tree sizes and tree locations. New analytical tools used in geostatistics, point process statistics, and random set statistics allow more detailed research of the interaction between spatial patterns and biological processes. Some data are continuous, like wind, temperature and precipitation. They are measured at discrete sample points and continuous information is obtained by spatial interpolation, for example by using
0378-1127/$ - see front matter Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.foreco.2013.10.012
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx
Kriging techniques (Pommerening, 2008). Where objects of interest can be conveniently described as single points, e.g. tree locations, methods of point process statistics are useful. Of particular interest are the second-order characteristics (SOC) which were developed within the theoretical framework of mathematical statistics and then applied in various fields of research, including forestry (Møller and Waagepetersen, 2007; Illian et al., 2008). Examples of SOC’s in forestry applications are Ripley’s K- and Besag’s L-function, pair- and mark correlation functions and mark variograms. SOC’s describe the variability and correlations in marked and non-marked point processes. Functional second-order characteristics depend on a distance variable r and quantify correlations between all pairs of points with a distance of approximately r between them. This allows them to be related to various ecological scales (Pommerening, 2002). The scientific literature abounds with studies of diameter distributions of even-aged monocultures. Other structural characteristics of a forest which are important for analysing disturbances are a group which Pommerening (2008) calls nearest neighbor summary statistics (NNSS). In this contribution we are using the term nearest neighbor statistics (abbreviated to NNS). NNS methods assume that the ecosystem is a mosaic of neighborhood groups and that the spatial structure of a forest is largely determined by the distribution of neighborhood characteristics. NNS methods have important advantages over classical spatial statistics, including low cost field assessment and cohort-specific structural analysis. Trees need not be mapped (which is usually expensive) and neighborhood statistics may be assessed in routine forest inventories without additional cost, which is one of the important practical advantages of using NNS (Gadow et al., 2012). Despite advances in remote sensing and other assessment technologies, mapped tree data are often not available, except in specially designed research plots. Forest inventories tend to provide tree data samples in small spatial observational windows. Thus, in the overwhelming number of cases, the amount of data and their spatial range is too limited to use SOC methods. The objective of this contribution is to compare the results of a structural analysis in a multi-species temperate forest based on two large observational study areas with mapped tree locations. In contrast to traditional approaches which are usually limited to numerical analysis, this study attempts to refer to a biological basis where tree species are identified according to their specific social status within the community. The quantitative analysis is then based on distinct social cohorts. 2. Data and methods This section describes the data sets and methods. The methods are grouped into two categories. One group applies to unmapped, the other to mapped tree data. Often, tree locations are not mapped, but the tree attributes, e.g. species, dbh’s and heights, are available. Mapped data in two large observation windows are available. Thus it is possible to use second order characteristics (SOC’s) which may depart from the hypothesis of complete spatial randomness (CSR). Thus, our null hypothesis is that marks are spatially independent. Cumulative characteristics such as the L function or the mark-weighted L functions (Montes et al., 2008) can be used to test such hypotheses. If they are rejected, it makes sense to proceed with an analysis involving SOC’s, such as pair correlation functions or mark variograms. If the hypothesis of mark independence is accepted, it suffices to use nearest neighbor statistics (NNS) (see Illian et al., 2008 for details). 2.1. The data sets This investigation is based on observations collected in a broadleaved Korean pine mixed forest, in the Changbai Nature Reserve in
north-eastern China. The climate in this region has been classified as a continental mountain affected by monsoon climate. The annual average temperature is 3.6 °C, the highest monthly average temperature is 19.6 °C measured in August, and the lowest monthly average temperature is 15.4 °C, measured in January. The average temperature extremes are 32.3 °C and 37.6 °C. The annual mean precipitation is 707 mm, the mean relative humidity 66%. The distribution of the precipitation during the year is relatively uneven. A relatively wet season occurs from June to August, a relatively dry season begins in September and ends in May of the following year. The soil is a brown forest soil and the topography is flat and slightly undulating (Zhang et al., 2010a,b). Both study sites cover an area of 5.2-ha (260 200 m2). The CBF site was established in the summer of 2005, the OGF site in October 2007. Fig. 1 shows the spatial distribution of trees by species, in both plots. The total number of living trees in the CBF plot was 15,221 (i.e. 2927 trees per ha) in 2005, comprising 37 species and 21 genera. The main canopy species are Pinus koraiensis, Tilia amurensis, Quercus mongolica, Fraxinus mandshurica, Acer barbinerve, Acer tegmentosum, Acer mono and Ulmus japonica. The OGF plot had 11,833 trees in 2007 (i.e. 2281 trees per ha), comprising 22 species and 13 genera. The main canopy species in OGF are P. koraiensis, T. amurensis, Abies nephrolepis, A. barbinerve, A. tegmentosum, A. mono and Picea jezoensis. The CBF plot represents a secondary conifer and broadleaved mixed forest (128°07.990 E, 42°20.910 N), the OGF an old growth forest (128°4.5730 E, 42°13.6840 N). The mean elevations of the CBF and OGF plots are 748 and 1042 m, respectively. The topography is almost flat in both study areas, and for this reason topographical effects on the community structure can be neglected (Zhang et al., 2010a,b). 2.2. Species grouping Unmapped tree data are often available or can be obtained at low cost. Therefore, because of their practical relevance, analytical tools that do not depend on mapped tree data are particularly important. Some non-spatial methods are relatively easy to apply, others require advanced methods. An important first step in analysing a forest ecosystem involves classification of tree species on the basis some physical or functional property. Typically, temperate forests display three reasonably well-defined layers of woody vegetation. The tallest trees are the canopy trees which intercept most of the radiation. Directly beneath the canopy there is another layer of woody vegetation, known as the subcanopy layer. Trees forming this cohort typically never reach canopy height. The shrub layer is formed by low woody plants, sometimes with multiple shoots or stems from the base that attain a height at maturity which is usually less than one third of the canopy height. In this study, each of the 51 tree species belongs to one of these cohorts: canopy trees, subcanopy trees and shrubs. This classification, which is straight forward for most species, has been adopted following standard ecological handbooks that describe each species as belonging to one of the three layers (Fu, 1995). The canopy species typically occur in two distinct cohorts which can be identified by a suitable clustering approach. We used a bivariate mixed normal distributions of tree diameter and height to identify the two clusters (see Section 2.3.2 for technical details). Fig. 2 shows the typical two clusters for canopy species using T. amurensis and P. koraiensis as examples, in the CBF and OGF plots. The examples show that the relationship between dbh’s and heights is quite different between the mature and immature canopy trees. The trees in the immature canopy-tree cluster of the two canopy species are suppressed, they have small crowns and a bigger height/dbh ratio. The mature canopy-tree cluster has large crowns and a smaller height/dbh ratio. Before reaching
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx
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Fig. 1. Spatial distribution of trees in the two field studies. The CBF plot (left) has 37, OGF (right) 22 species. The species are identified by color; dbh’s are scaled to observed values. The species abbreviations are explained in Appendix A.
Fig. 2. Examples of two clusters for Tilia amurensis (left) and Pinus koraiensis (right), identified by the bivariate dbh/height distributions in the CBF and OGF study areas, respectively.
the canopy, the height/dbh ratio of the immature canopy species considerably exceeds that of the bigger individuals. While the canopy species are growing in the understorey, their height growth seems to be more important than their diameter growth. The same phenomenon has been observed in European beech forests (Zucchini et al., 2001). Thus, the canopy species belong to two distinct cohorts which can be identified using a suitable clustering approach. The growing sites are similar, but CBF represents a secondary forest heavily disturbed by timber harvesting while OGF represents an undisturbed climax community. Based on these observations, we further subdivide canopy trees into large (dbh P 25 cm) and small (dbh < 25 cm) individuals to identify their specific status within the system. The subcanopy species are characterized by a single cluster. We thus identify four distinct tree cohorts and designate them using Roman numerals, as follows: Cohort
I
II
III
IV
Definition Mature Immature Subcanopy Shrubs canopy trees canopy trees trees (dbh P 25 cm) (dbh < 25 cm)
Population density is sometimes expressed by the number of individuals. But the number of trees per unit area is not a useful measure of population density because it does not incorpo-
rate tree size. Therefore, we use the sum of the cross-sectional areas of all trees, expressed in m2 per hectare, which is known as the basal area (G). The distribution of basal area by species groups indicates the relative area occupancy of the four cohorts. The average ratios of height (m)/dbh (cm) for the canopy species in cohort I are 0.53 and 0.49 in CBF and OGF respectively. The corresponding ratios in cohort II are 1.01 and 0.93. 2.3. Frequency distributions of tree attributes 2.3.1. Height distributions Altogether 15,221 and 11,833 tree heights were measured in the CBF and OGF study areas, respectively. Such a large number of heights is rarely available for research and consequently, the non-spatial analysis will concentrate on the tree heights. The tree height distributions were usually found to exhibit a bimodal shape. For this reason, the mixtools package of the R comprehensive network is used (Benaglia et al., 2009). The mixture density is given by FðxÞ ¼ k1 F 1 ðxÞ þ k2 F 2 ðxÞ; where k1 and k2 represent the proportions of the two probability density functions F1 and F2. 2.3.2. Bivariate mixtures Previous studies did reveal that the relationship between tree diameters and heights is rather different in small and big canopy
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx
30 cm
10 cm 20 cm
i
50 cm
Fig. 3. Left: example of a neighborhood structural unit (left) with different species, tree sizes and a specific spatial arrangement. Right: a hypothetical forest may be seen as a mosaic of neighborhood structure units (NSU) and an example of a sampling scheme to assess the distributions of structural attributes.
species. These differences are revealed by a mixture of two bivariate normal distributions of dbh and height. Using this approach, we denote f(d,h) the bivariate probability density function of tree dbh and tree height and propose the following mixture model:
f ðd; hÞ ¼ a n1 ðd; hÞ þ ð1 aÞ n2 ðd; hÞ
ð1Þ
where a, a parameter in the interval (0, 1), determines the proportion of trees belonging to each of the two component bivariate normal distributions n1(d,h) and n2(d,h). The parameters of nj(d,h) are the expectations ldj, lhj; the variances r2dj and r2hj , and the correlation coefficient qj, j = 1,2. For further details refer to Zucchini et al., 2001. It is possible, of course to improve the fit by using a mixture of three or more distributions instead of just two. However, the field observations do not reveal persuasive biological grounds for believing that the populations comprise three or more distinct subpopulations. The parameters are estimated using the mclust library of the R statistical software (Fraley et al., 2012). 2.4. Nearest neighbour statistics Nearest neighbor statistics (NNS) are based on the assumption that the spatial structure of a forest is determined by the distribution of specific structural relationships within neighborhood groups of trees. A forest is composed of n-tree ‘‘neighborhood structural units’’ (NSU’s, Fig. 3). The distribution of the NSU-attributes permits a detailed analysis of the forest as a whole. Nearest neighbor statistics have important advantages over classical spatial statistics, including low cost of field assessment and cohort-specific structural analysis (a cohort refers to a group of reference trees that share common attributes, e.g. species or size class). NSU’s may be homogenous or inhomogenous consisting of trees that belong to a variety of species, spatial arrangements and size classes (Gadow et al., 2012). The degree of homogeneity within a particular NSU may be described by a set of three variables of identical scale. Each may assume values in the interval (0, 1). These variables are known as Species Mingling (M), Dominance (U) and uniform angle index (W). 2.4.1. Species mingling One neighborhood structural unit consists of a reference tree1 and its n nearest neighbors. Species mingling (Gadow, 1993; Füldner, 1995; Pommerening, 2002), is defined as follows:
Mi ¼
4 1X vj 4 j¼1
with
vj ¼
1; j not the same species as i 0; otherwise
ð2Þ
1 In spatial statistics the terms ‘‘point related’’ and ‘‘test location’’ related summary characteristics are sometimes used (Pommerening, 2008; Illian et al., 2008).
The variable mingling is thus defined as the proportion of the four nearest neighbours that differ from the reference tree in terms of the species. Values range between 0 (only one species) and 1, when every neighbour belongs to a different species than the reference tree (e.g. Mi = 0.5 in Fig. 3). The distribution of the Mi values, in conjunction with the relative species proportions, allows an assessment of the spatial diversity within a forest. 2.4.2. Dominance The variable dominance (U) is a spatially explicit measure of the relative dominance of the reference tree within an n-tree NSU. It is calculated according to Eq. (3) (Hui et al., 1998).
Ui ¼
4 1X vj 4 j¼1
with
vj ¼
1; j is smaller than i 0; otherwise
ð3Þ
Dominance, like mingling, may assume values between 0 and 1 and gives the proportion of the four nearest neighbour trees that are smaller than the reference tree (e.g. Ui = 0.25 in Fig. 3, assuming that the dbh of tree i is also 20 cm). 2.4.3. The uniform angle index The uniform angle index (W) concept is based on the classification of the angles aij (once again, i refers to the reference tree and j to the neighbors) between the vectors pointing away from the reference tree i to its neighbors j (Gadow et al., 1998) as shown in Fig. 3.
Wi ¼
4 1X mjk with 4 j¼1
mjk ¼
1; ajk < a0 and 0 6 W i 6 1 0; otherwise
ð4Þ
The basic idea of uniform angle concept is to compare the angles aij with an appropriate reference angle a0, which is chosen so that it yields an easily remembered number for the mean W in the case of a Poisson forest. In the case of the 4-tree sample the appropriate angle a0 was chosen as 72° which should produce a mean value W ¼ 0:5. Thus Wi is defined as the fraction of the angles aij which are smaller than the standard angle a0 (e.g. Wi = 0.25 in Fig. 3, assuming that only one angle is smaller than the standard). Consequently 0 6 W i 6 1 (note that when aij exceeds 180° , then aij is equal to 360 minus aij.). Small values of Wi correspond to a regular neighbourhood of tree i, while values of Wi close to 1 correspond to the case where the n neighbours of i appear in a cluster of trees close together. The same tendency is true for the mean W and we have W-regular < W -random < W-cluster. The Mean Directional index, which is more closely related to classical ideas of directional statistics (Upton and Fingleton, 1989), exploits the directional information given by the reference tree i and its n nearest neighbours in another way than the uniform angle index. The basic idea is similar, but we prefer to use the
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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uniform angle index because the numerical results correspond with Mingling and Dominance. 2.4.4. Eliminating edge effects To eliminate the edge effect and improve the accuracy of the estimates we implemented in our Mi, Ui, and Wi calculations the nearest neighbour edge correction method proposed by Pommerening and Stoyan (2006). This edge correction evaluates individually for each tree whether all n nearest neighbours are truly located within the window of observation and eliminates all trees for which this is not the case. 2.5. Scale-dependent spatial analysis Scale dependent spatial analysis evaluates textures at different scales, i.e. not only short-range but also long-range. This requires large observational studies with mapped trees. 2.5.1. Marked point process Let us consider a quantitative mark such as tree dbh, tree height or mingling. In this case, the mark correlation function kf(r) is a tool for analysing the spatial mark structure. Let kf(r) be the mean value of a suitable ‘‘test’’ function f dependent on the marks. Important ‘‘test’’ functions are f1(m1,m2) = m1m2 or f2(m1,m2) = 1/2(m1-m2)2, where mi is the mark of the point in the i-disc. Note that kf(r) is only defined if in both discs there is a point of the point process. The mean value in the case of f1, kf(r), denoted by kmm(r), is usually divided by the squared mean mark l2 giving the mark correlation function kmm(r) = kmm(r)/l2. The mark correlation function denotes independent marks when kmm(r) = 1 for all r; kmm(r) > 1 indicates positive mark correlation, whilst kmm(r) < 1 implies mark inhibition. The corresponding mean based on f2, i.e. kf2(r), is usually called mark variogram (Cressie, 1993; Stoyan et al., 1995; Stoyan and Wälder, 2000). This function describes the differences of the mark at the intertree distance r. When r is small, it provides information about tree-to-tree interactions. If r is large, it describes the influence of environmental factors such as soil, humidity and altitude (Stoyan and Penttinen, 2000). The mark correlation function has been applied to forestry problems by several authors (Penttinen et al., 1992; Gavrikov et al., 1993; see also Comas and Mateu, 2007, who provide an estimator of this function). 2.5.2. Software The methods described above were implemeted using the Comprehensive R Archive Network (R Development Core Team, 2012), the spatstat (Baddeley and Turner, 2005) and mixdist (Macdonald and Du, 2008) packages were used in this study.
3. Results 3.1. Density by species groups The basal areas are useful for evaluating the plot densities for biologically relevant cohorts. The total basal areas in the CBF and OGF study areas are 33.7 and 56.3 m2/ha respectively. Their distributions by tree cohorts are quite different in the two study areas, as shown in Fig. 4. OGF has more than twice the basal area in the mature canopy species when compared with CBF and only 60% of the basal area in the immature canopy species. CBF in turn has almost three times the density in the subcanopy species when compared with OGF. OGF has a considerably greater shrub density (A. barbinerve) than CBF.
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3.2. Frequency distributions of tree attributes 3.2.1. Height distributions Fig. 5 shows the bimodal distributions of tree heights in the CBF and OGF study areas. In the CBF plot, 71% of the trees have heights with a mean value of 5.4 m while 29% of the heights have a mean of 15.5 m. At a first glance, the OGF study area exhibits a similar two-component height structure. Both distributions in the two plots are separated at a height of approximately 12 m. This same separating height in both plots is interesting because the OGF canopy considerably exceeds that of CBF. The bigger cohort in OGF has a mean of 20.4 m which considerably exceeds that of the corresponding CBF mean by 5 m. In addition, there is a second peak of tree heights around 25 m in OGF. 3.2.2. Bivariate mixtures Fig. 6 presents graphs of two bivariate mixtures involving dbh and height in the two study areas. The selected canopy species which show the typical two clusters are Populus davidiana in CBF and P. koraiensis in OGF. The dbh/height ratio’s of the understorey cluster of the two canopy species is much greater than the respective ratio’s of the dominant clusters. The graphical representation of the bivariate mixtures allows a better interpretation of the structural peculiarities of particular species and species groups. The shapes depicted in Fig. 6 are typical for many canopy species. Most subcanopy species and shrubs, however, show bivariate dbh/height distributions that are characterized by a single cluster. 3.3. Nearest neighbour statistics For all species correlation coefficients were calculated for mingling-dominance, mingling-uniform angle index and dominanceuniform angle index. The results are presented in Table 1. The correlations are an indication of the strength of the linear relationship between pairs of the three nearest neighbour statistics. Most correlations are significant or highly significant. The highest correlations are found between mingling and dominance. These are positive in the case of the canopy species (Piko and Tima) and all species combined, but negative in the two shrub species (Acba and Acuk). The canopy species (Piko and Tima) are often larger trees compared with the surrounding neighbors of other species. Thus, the individuals have high mingling ususally have stronger dominance. In particular, the canopy species (Piko and Tima) in the OGF plot were more significantly dominant than that in the CBF plot. Accordingly, the shrub tree speices have high mingling was depressed by the larger neighbors so that have weaker dominance. In the meanwhile, the uniform angle index was not significant relative with the dominance in general. The remaining correlations are less obvious. Bivariate graphs of species mingling and dominance are presented in Fig. 7 for the canopy species T. amurensis and the shrub species A. barbinerve. Most T. amurensis trees have high mingling and dominance values. Since most of the trees of this species have larger diameter. It ususally occurs in neighborhoods where they are dominant and at the same time surrounded by trees of other species. This feature is even more distinct in the OGF area. While the shrub species A. barbinerve, on the other hand, often grows in clusters so that exhibits low mingling and dominance. For this reason, it occurs in a wide variety of M/U combinations. 3.4. Scale-dependent spatial analysis The mark correlation function of a marked point process X is a measure of the dependence between the marks of two points of the
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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Fig. 4. Basal areas by species cohorts identified by Roman numerals (I, II, III, IV) and different shading of columns.
Fig. 5. Bimodal Weibull distribution of all tree heights greater than 3 m in the CBF (left) and OGF (right) study areas. The parameters of the mixed Weibull distribution are shown below the graphs, where p refers to the tree number proportions and mu and sigma to the means and standard deviations respectively.
Fig. 6. Graphic representation of two bivariate mixtures involving dbh and height (left: Populus davidiana in CBF; right Pinus koraiensis in OGF).
process at distance r. Mark correlations were investigated for several marks, including diameters, heights and nearest neighbor statistics. The mark correlation function Kmm(r), is based on a null model of random labelling of marks across fixed locations of trees. Kmm(r) = 1 means that the ratio of observed labelling to random labelling is equal to one. A value of Kmm(r) < 1 indicates mutual inhibition, Kmm(r) > 1 mutual attraction (see Law et al., 2009; Eckel et al., 2012). For small distance values r the estimated functions for T. amurensis are running below the acceptance interval in both plots, which means that at close range the correlation between pairs of the same dbh are less than would be expected (Fig. 8). In other words, the large individual of the species has less frequency of large conspecific neighbors. T. amurensis shows mutual inhibi-
tion at 0–25 m scales in the CBF plot, while it does at 0–5 m scales in the OGF. It is probably for that the OGF plot has more large individuals of this species than in the CBF plot (Fig. 1). The NNS marks of close neighbors are, however, not independent of each other. For very small r, individual i and individuals j can be nearest neighbors of each other and share other neighbors. This may be statistically improper and therefore it was decided to not pursue this particular anaysis further.
4. Discussion Important ecosystem functions, and the potential and limitations of human use are defined by the structure of a forest
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx Table 1 Correlation coefficients for the three nearest neighbour statistics for six species in the CBF and OGF plots. M: mingling, U:dominance, W: uniform angle index. Group
Species
Canopy
Piko Tiam Acps Acte Acba Acuk Total
Subcanopy Shrub
CBF
OGF
M-U
M-W
W-U
M-U
M-W
W-U
0.14*** 0.24*** 0.14*** 0.04ns 0.26*** 0.05ns 0.112***
0.01ns 0.04ns 0.1*** 0.12** 0.16*** 0.11ns 0.001***
0.07ns 0.07* 0.01ns 0.05ns 0.04ns 0.00ns 0.047ns
0.38*** 0.45*** 0.07* 0.07ns 0.29*** 0.03ns 0.211***
0.11*** 0.06ns 0.01ns 0.13ns –0.23*** 0.05ns 0.081***
0.15*** 0.09* 0.10** 0.11ns 0.03* 0.10ns 0.104ns
Significance levels indicated as follows: ns P > 0.05. * P < 0.05. ** P < 0.01. *** P < 0.001.
Fig. 7. Bivariate distribution of species mingling and dominance in the two study areas (CBF left and OGF right) for the canopy species Tilia amurensis (1202 trees in CBF and 751 trees in OGF) and the subcanopy species Acer barbinerve (2165 trees in CBF and 1767 trees in OGF).
Tiam OGF
kmm (r)
1.0
0.8
1.4
1.0
kmmobs (r) kmmtheo(r) kmmhi(r) kmmlo(r)
CBF
kmmobs (r) kmmtheo(r) kmmhi(r) kmmlo(r)
0.6
0.6
kmm (r)
1.8
Tiam
0
10
20
r
30
40
50
0
10
20
r
30
40
50
Fig. 8. r-Wise 99% acceptance intervals for the mark correlation function using dbh as marks for Tilia amurensis in the CBF and OGF plots.
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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ecosystem. Spatial patterns affect the competition status, seedling growth and survival and crown formation of forest trees (Moeur, 1993; Pretzsch, 1997). Analysis of the spatial pattern of tree species is important in gaining a better understanding of the underlying ecological processes that control the development of the observed patterns. The spatial patterns of trees and their interactions provide critical information about community structure and species coexistence, and significantly determine reproduction, growth, mortality, dispersal, resource use, gap creation, and understory development (He et al., 1997; Druckenbrod et al., 2005; Wiegand et al., 2007). The vertical and horizontal distributions of tree sizes determine the distribution of micro-climatic conditions, the availability of resources and the formation of habitat niches and thus, directly or indirectly, the biological diversity within a forest community. Spatial structures are of paramount importance in community studies because their presence indicates that some process has been at work to create them (Legendre et al., 2009). Thus, information about forest structure contributes to improved understanding of the history, functions and future development potential of a particular forest ecosystem (Ruggiero et al., 1991; Spies, 1997; Franklin et al., 2002). In addition, and perhaps most importantly, structural data provide an essential basis for the analysis of ecosystem disturbance through selective harvest events. The assessment and analysis of forest structure thus facilitates a comparison between a managed forest and an unmanaged reference ecosystem. An important step in the analysis of a multi-species ecosystem is the grouping of species. We first identified canopy, subcanopy and shrub species and then differentiated between dominant and subdominant canopy species using a clustering process based on a bivariate mixed diameter/height distribution. The height/dbh ratios of the subdominant canopy species significant exceed those of the dominant canopy species. At the community level, the two study areas showed rather distinct structural charateristics. The total basal areas in the CBF and OGF study areas are quite different. With 56.3 m2/ha OGF is very dense compared to the 33.7 m2/ha in the CBF study area. The basal area distributions by tree cohorts are also quite different in the two study areas, as shown in Fig. 4. The bimodal distributions of tree heights are quite similar in shape in the two plots. However whereas the mean heights of the two smaller subpopulations are similar (5.4; 4.9 m), the mean heights of the two bigger subpopulations are quite different (15.5; 20.4), with OGF exceeding the corresponding CBF mean height by 5 m. These differences in the two plots provide further evidence of very different development stages on two similar growing sites. The bivariate mixtures in the two plots are consistent with several previous studies (Weiner et al., 1998; Damgaard et al., 2002), indicating higher allocation to height growth in the early stage of the life history, probably in an attempt to reach the canopy as soon as possible. Later on, diameter growth is more prominent. The same phenomenon has been observed in European beech forests (Zucchini et al., 2001). The correlations between pairs of the three nearest neighbour statistics were positively significant, especially regarding the species mingling and dominance relationships of the canopy species. For the subcanopy and shrub species this relationship was not pronounced. The canopy species T. amurensis in the OGF had stronger dominance than that species in the CBF plot (Fig. 7). It is due to more larger trees in the OGF plot. As an old growth forest, the OGF plot had more percentage of large trees (canopy species) and less percentage of small trees (subcanopy species, shrubs). Shelly (1985) and Hector et al. (1999) point out that individuals compete more intensively with conspecific individuals than with individuals of other species. The mark correlation function demonstrated that the T. amurensis had mutual inhibition at small scale. It
meant that there is not so probably to have several large trees in short distances. It is consistent with the result of large dominance of the species (Fig. 7). In this study, we used several methods to describe and analyse the structural characteristics of two temperate forest communities in northeastern China. In the context of more proportion of canopy species, the OGF plot showed differently in structural diversity on many aspects. It provides further evidence of very different development stages on two similar growing sites, and supplies with guideline for the forest management of different successional stage of forest. Plant community dynamics is driven by spatially-dependent birth, death and growth processes, often embedded in a heterogeneous landscape (Law et al., 2009). It is about the dynamics of multispecies spatial patterns as exemplified by the CBF and OGF observational studies. The spatial dimension is a key component in the study of a forest ecosystem. However, the literature on spatial statistics is often rather technical, and there is relatively little exchange between mathematicians developing the theory and ecologists who have interesting data from observational studies, such as presented in this contribution. Acknowledgements Ding ShengJian, He Huaijiang, Chen BeiBei and Huang Zhen and several others assisted with the field data collection. Zhou HaiCheng and Xia Fucai identified the species. Valuable comments were provided by Wang Jinsong and Gao LuShuang. This research is supported by the National Basic Research Programme of China (973 Programme, 2011CB403203), the 12th five-year National Science and Technology plan of China (2012BAC01B03) and the Program for New Century Excellent Talents in University of Ministry of Education of China [NCET-12-0781].
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.foreco.2013.10.012. References Baddeley, A., Turner, R., 2005. Spatstat: an r package for analyzing spatial point patterns. J. Stat. Softw. 12, 1–42. Benaglia, T., Chauveau, D., Hunter, D.R., Young, D.S., 2009. Mixtools: an r package for analyzing finite mixture models. J. Stat. Softw. 32, 1–29. Comas, C., Mateu, J., 2007. Modelling forest dynamics: a perspective from point process methods. Biom. J. 49, 176–196. Cressie, N., 1993. Statistics for Spatial Data. John Wiley and Sons, New York. Damgaard, C., Weiner, J., Nagashima, H., 2002. Modelling individual growth and competition in plant populations: growth curves of chenopodium album at two densities. J. Ecol. 90, 666–671. Druckenbrod, D.L., Shugart, H.H., Davies, I., 2005. Spatial pattern and process in forest stands within the Virginia piedmont. J. Veg. Sci. 16, 37–48. Eckel, S., Fleischer, F., Grabarnik, P., Schmidt, V., 2012. An investigation on the spatial correlations for relative purchasing power in Baden–Württemberg. Adv. Stat. Anal. 92 (2008), 135–152. Fraley, C., Raftery, A.E., Murphy, T.B., Scrucca, L., 2012. mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597, Department of Statistics, University of Washington. Franklin, J.F., Spies, T.A., Pelt, R.V., Carey, A.B., Thornburgh, D.A., Berg, D.R., Lindenmayer, D.B., Harmon, M.E., Keeton, W.S., Shaw, D.C., 2002. Disturbances and structural development of natural forest ecosystems with silvicultural implications, using Douglas-fir forests as an example. For. Ecol. Manage. 155, 399–423. Fu, P.Y., 1995. Plant Key in Northeastern China (2nd Edition). Science Press, Beijing. Füldner, K., 1995. Strukturbeschreibung von Buchen-EdellaubholzMischwWäldern. Cuvillier Ver-lag, Göttingen (in German). Gadow, K.v., 1993. Zur Bestandesbeschreibung in der Forsteinrichtung. Forst und Holz 48, 602–606 (in German).
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R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx Gadow, K.v., Hui, G.Y., Albert, M., 1998. Das Winkelmass – ein Strukturparameter zur Beschreibung der Individualverteilung in Waldbeständen. Centralblatt für das Gesamte Forstwesen 115, 1–10 (in German). Gadow, K.v., Zhang, C.Y., Wehenkel, C., Pommerening, A., Corral-Rivas, J., Korol, M., Myklush, S., Hui, G.Y., Kiviste, A., Zhao, X.H., 2012. Forest structure and diversity. In: Pukkala, T., Gadow, K.v. (Eds.), Continuous Cover Forestry, Book Series Managing Forest Ecosystems, vol. 23. Springer Science Business, Media B.V., pp. 29–84. Gavrikov, V.L., Grabarnik, P., Stoyan, D., 1993. Trunk-top relations in a Siberian pine forest. Biom. J. 35, 487–498. Harper, J.L., 1977. Population Biology of Plants. Academic Press, London. He, F., Legendre, P., Lafrankie, J.V., 1997. Distribution patterns of tree species in a Malaysian tropical rain forest. J. Veg. Sci. 8, 105–114. Hector, A., Schmid, B., Beierkuhnlein, C., Caldeira, M.C., Diemer, M., Dimitrakopoulos, P.G., Finn, J.A., Freitas, H., Giller, P.S., Good, J., 1999. Plant diversity and productivity experiments in European grasslands. Science 286, 1123–1127. Hui, G.Y., Albert, M., Gadow, K.v., 1998. Das Umgebungsmaß als Parameter zur Nachbildung von Bestandesstrukturen. Forstwisse nschaftliches Centralblatt 117, 258–266 (in German). Illian, J., Penttinen, A., Stoyan, H., Stoyan, D., 2008. Statistical Analysis and Modelling of Spatial Point Patterns. John Wiley, p. 534. Law, R., Illian, J., Burslem, D.F.R.P., Gratzer, G., Gunatilleke, C., Gunatilleke, I., 2009. Ecological information from spatial patterns of plants: insights from point process theory. J. Ecol. 97, 616–628. Legendre, P., Mi, X., Ren, H., Ma, K., Yu, M., Sun, I.F., He, F., 2009. Partitioning beta diversity in a subtropical broad-leaved forest of China. Ecology 90, 663–674. Macdonald, P., Du, J., 2008. Mixdist: finite mixture distribution models. R package version 0.5-2. Moeur, M., 1993. Crown width and foliage weight of northern Rocky Mountain conifers, USDA, Forest Service, Intermountain Forest and Range Experiment Station, Ogden, Utah, Research Paper INT-283, pp. 14. Møller, J., Waagepetersen, R.P., 2007. Modern statistics for spatial point processes. Scand. J. Stat. 34, 643–684. Montes, F., Barbeito, I., Rubio, A., Cañellas, I., 2008. Evaluating height structure in scots pine forests using marked point processes. Can. J. Forest Res. 38, 1924–1934. Penttinen, A., Stoyan, D., Henttonen, H.M., 1992. Marked point processes in forest statistics. Forest Sci. 38, 806–824. Pommerening, A., 2002. Approaches to quantifying forest structures. Forestry 75, 305–324. Pommerening, A., 2008. Analysing and Modelling Spatial Woodland Structure. Habilitationsschrift (DSc dissertation), University of Natural Resources and Applied Life Sciences, Vienna, Austria.
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Forest Ecology and Management journal homepage: www.elsevier.com/locate/foreco
Analysing structural diversity in two temperate forests in northeastern China Ruiqiang Ni a, Yeerjiang Baiketuerhan b, Chunyu Zhang a, Xiuhai Zhao a,⇑, Klaus von Gadow c a
Key Laboratory for Forest Resources & Ecosystem Processes of Beijing, Beijing Forestry University, Beijing 100083, China College of Forestry and Horticulture, Xinjiang Agricultural University, Urmqi 830052, China c Faculty of Forestry and Forest Ecology, Georg-August-University Göttingen, Büsgenweg 5, D-37077 Göttingen, Germany b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Spatial structure Second order statistics Nearest neighbour statistics Bivariate mixtures
a b s t r a c t This contribution presents an analysis of the structural diversity in two temperate forest ecosystems in northeastern China, based on two large contiguous observational studies covering an area of 5.2 ha (260 200 m2) each. The total number of living trees in the conifer and broad-leaved forest (CBF) study area is 2927 per ha, comprising 37 species and 21 genera. The old growth forest (OGF) study area has 2276 trees per ha, including 22 species and 13 genera. Tree species are classified according to their community status as mature and immature canopy, subcanopy and shrub. A clustering process based on two distinct communities of the bivariate dbh/height distributions is used to differentiate between mature and immature canopy species. Numerical analysis is based on these four distinct cohorts. Despite advances in remote sensing, mapped tree data in large observation windows are very rare. Thus, we are able to use methods for analysing forest structure which are suitable for both, unmapped and mapped data. The two data sets are unique in that all (approximately) 27,000 tree heights are available. Accordingly, it was possible to fit bimodal height distributions and bivariate mixed dbh/height distributions to almost all individual species that were represented by sufficiently large numbers. Methods of second order statistics (SOC), including marked point statistics as well as nearest neighbor statistics (NNS) based on nearest neighbourhood structure units are also presented, including bivariate mixtures of the NNS attributes ‘‘mingling’’ and ‘‘dominance’’. Mark correlations were investigated for several marks, including diameters, heights and nearest neighbor statistics. Finally, we discuss the most important results and motivate the need for detailed assessments in large contiguous field plots. The literature on spatial statistics is often rather technical, and there is relatively little exchange between mathematicians developing the theory and ecologists who have interesting data from observational studies, such as presented in this contribution. Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved.
1. Introduction Structure is a fundamental notion referring to patterns and relationships within a more or less well-defined system. Important theoretical concepts relating to biological structures include selforganisation which involves regeneration, tree mortality and a variety of interactions between individual plants. The properties of a particular forest ecosystem, including biomass production, biodiversity and the quality of ecosystem services, are determined to a large degree by its structure. Trees propagate, grow and die, but they are sessile, bound to one specific location. Forest regeneration, growth and mortality generate very specific structures. Specific structures in turn, generate particular processes of growth and ⇑ Corresponding author. Address: Forest College in Beijing Forestry University, No. 35 Qinghua East Road, Haidian District, Beijing 100083, China. E-mail addresses: [email protected] (R. Ni), [email protected] (Y. Baiketuerhan), [email protected] (C. Zhang), [email protected] (X. Zhao), kgadow@ gwdg.de (K. von Gadow).
regeneration. The production and dispersal of seeds and the associated processes of germination, seedling establishment and survival are important factors of plant population dynamics and structuring (Harper, 1977). Thus, structure is not only the result of past developments, but also the starting point for future dynamics. ‘‘Forest structure’’ usually refers to the way in which the attributes of trees are distributed within a forest. Associated with a specific forest structure is some degree of heterogeneity or richness which we call diversity. In a forest ecosystem, diversity does, however, not only refer to species richness, but to a range of phenomena that determine the heterogeneity within a community of trees, including the diversity of tree sizes and tree locations. New analytical tools used in geostatistics, point process statistics, and random set statistics allow more detailed research of the interaction between spatial patterns and biological processes. Some data are continuous, like wind, temperature and precipitation. They are measured at discrete sample points and continuous information is obtained by spatial interpolation, for example by using
0378-1127/$ - see front matter Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.foreco.2013.10.012
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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Kriging techniques (Pommerening, 2008). Where objects of interest can be conveniently described as single points, e.g. tree locations, methods of point process statistics are useful. Of particular interest are the second-order characteristics (SOC) which were developed within the theoretical framework of mathematical statistics and then applied in various fields of research, including forestry (Møller and Waagepetersen, 2007; Illian et al., 2008). Examples of SOC’s in forestry applications are Ripley’s K- and Besag’s L-function, pair- and mark correlation functions and mark variograms. SOC’s describe the variability and correlations in marked and non-marked point processes. Functional second-order characteristics depend on a distance variable r and quantify correlations between all pairs of points with a distance of approximately r between them. This allows them to be related to various ecological scales (Pommerening, 2002). The scientific literature abounds with studies of diameter distributions of even-aged monocultures. Other structural characteristics of a forest which are important for analysing disturbances are a group which Pommerening (2008) calls nearest neighbor summary statistics (NNSS). In this contribution we are using the term nearest neighbor statistics (abbreviated to NNS). NNS methods assume that the ecosystem is a mosaic of neighborhood groups and that the spatial structure of a forest is largely determined by the distribution of neighborhood characteristics. NNS methods have important advantages over classical spatial statistics, including low cost field assessment and cohort-specific structural analysis. Trees need not be mapped (which is usually expensive) and neighborhood statistics may be assessed in routine forest inventories without additional cost, which is one of the important practical advantages of using NNS (Gadow et al., 2012). Despite advances in remote sensing and other assessment technologies, mapped tree data are often not available, except in specially designed research plots. Forest inventories tend to provide tree data samples in small spatial observational windows. Thus, in the overwhelming number of cases, the amount of data and their spatial range is too limited to use SOC methods. The objective of this contribution is to compare the results of a structural analysis in a multi-species temperate forest based on two large observational study areas with mapped tree locations. In contrast to traditional approaches which are usually limited to numerical analysis, this study attempts to refer to a biological basis where tree species are identified according to their specific social status within the community. The quantitative analysis is then based on distinct social cohorts. 2. Data and methods This section describes the data sets and methods. The methods are grouped into two categories. One group applies to unmapped, the other to mapped tree data. Often, tree locations are not mapped, but the tree attributes, e.g. species, dbh’s and heights, are available. Mapped data in two large observation windows are available. Thus it is possible to use second order characteristics (SOC’s) which may depart from the hypothesis of complete spatial randomness (CSR). Thus, our null hypothesis is that marks are spatially independent. Cumulative characteristics such as the L function or the mark-weighted L functions (Montes et al., 2008) can be used to test such hypotheses. If they are rejected, it makes sense to proceed with an analysis involving SOC’s, such as pair correlation functions or mark variograms. If the hypothesis of mark independence is accepted, it suffices to use nearest neighbor statistics (NNS) (see Illian et al., 2008 for details). 2.1. The data sets This investigation is based on observations collected in a broadleaved Korean pine mixed forest, in the Changbai Nature Reserve in
north-eastern China. The climate in this region has been classified as a continental mountain affected by monsoon climate. The annual average temperature is 3.6 °C, the highest monthly average temperature is 19.6 °C measured in August, and the lowest monthly average temperature is 15.4 °C, measured in January. The average temperature extremes are 32.3 °C and 37.6 °C. The annual mean precipitation is 707 mm, the mean relative humidity 66%. The distribution of the precipitation during the year is relatively uneven. A relatively wet season occurs from June to August, a relatively dry season begins in September and ends in May of the following year. The soil is a brown forest soil and the topography is flat and slightly undulating (Zhang et al., 2010a,b). Both study sites cover an area of 5.2-ha (260 200 m2). The CBF site was established in the summer of 2005, the OGF site in October 2007. Fig. 1 shows the spatial distribution of trees by species, in both plots. The total number of living trees in the CBF plot was 15,221 (i.e. 2927 trees per ha) in 2005, comprising 37 species and 21 genera. The main canopy species are Pinus koraiensis, Tilia amurensis, Quercus mongolica, Fraxinus mandshurica, Acer barbinerve, Acer tegmentosum, Acer mono and Ulmus japonica. The OGF plot had 11,833 trees in 2007 (i.e. 2281 trees per ha), comprising 22 species and 13 genera. The main canopy species in OGF are P. koraiensis, T. amurensis, Abies nephrolepis, A. barbinerve, A. tegmentosum, A. mono and Picea jezoensis. The CBF plot represents a secondary conifer and broadleaved mixed forest (128°07.990 E, 42°20.910 N), the OGF an old growth forest (128°4.5730 E, 42°13.6840 N). The mean elevations of the CBF and OGF plots are 748 and 1042 m, respectively. The topography is almost flat in both study areas, and for this reason topographical effects on the community structure can be neglected (Zhang et al., 2010a,b). 2.2. Species grouping Unmapped tree data are often available or can be obtained at low cost. Therefore, because of their practical relevance, analytical tools that do not depend on mapped tree data are particularly important. Some non-spatial methods are relatively easy to apply, others require advanced methods. An important first step in analysing a forest ecosystem involves classification of tree species on the basis some physical or functional property. Typically, temperate forests display three reasonably well-defined layers of woody vegetation. The tallest trees are the canopy trees which intercept most of the radiation. Directly beneath the canopy there is another layer of woody vegetation, known as the subcanopy layer. Trees forming this cohort typically never reach canopy height. The shrub layer is formed by low woody plants, sometimes with multiple shoots or stems from the base that attain a height at maturity which is usually less than one third of the canopy height. In this study, each of the 51 tree species belongs to one of these cohorts: canopy trees, subcanopy trees and shrubs. This classification, which is straight forward for most species, has been adopted following standard ecological handbooks that describe each species as belonging to one of the three layers (Fu, 1995). The canopy species typically occur in two distinct cohorts which can be identified by a suitable clustering approach. We used a bivariate mixed normal distributions of tree diameter and height to identify the two clusters (see Section 2.3.2 for technical details). Fig. 2 shows the typical two clusters for canopy species using T. amurensis and P. koraiensis as examples, in the CBF and OGF plots. The examples show that the relationship between dbh’s and heights is quite different between the mature and immature canopy trees. The trees in the immature canopy-tree cluster of the two canopy species are suppressed, they have small crowns and a bigger height/dbh ratio. The mature canopy-tree cluster has large crowns and a smaller height/dbh ratio. Before reaching
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx
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Fig. 1. Spatial distribution of trees in the two field studies. The CBF plot (left) has 37, OGF (right) 22 species. The species are identified by color; dbh’s are scaled to observed values. The species abbreviations are explained in Appendix A.
Fig. 2. Examples of two clusters for Tilia amurensis (left) and Pinus koraiensis (right), identified by the bivariate dbh/height distributions in the CBF and OGF study areas, respectively.
the canopy, the height/dbh ratio of the immature canopy species considerably exceeds that of the bigger individuals. While the canopy species are growing in the understorey, their height growth seems to be more important than their diameter growth. The same phenomenon has been observed in European beech forests (Zucchini et al., 2001). Thus, the canopy species belong to two distinct cohorts which can be identified using a suitable clustering approach. The growing sites are similar, but CBF represents a secondary forest heavily disturbed by timber harvesting while OGF represents an undisturbed climax community. Based on these observations, we further subdivide canopy trees into large (dbh P 25 cm) and small (dbh < 25 cm) individuals to identify their specific status within the system. The subcanopy species are characterized by a single cluster. We thus identify four distinct tree cohorts and designate them using Roman numerals, as follows: Cohort
I
II
III
IV
Definition Mature Immature Subcanopy Shrubs canopy trees canopy trees trees (dbh P 25 cm) (dbh < 25 cm)
Population density is sometimes expressed by the number of individuals. But the number of trees per unit area is not a useful measure of population density because it does not incorpo-
rate tree size. Therefore, we use the sum of the cross-sectional areas of all trees, expressed in m2 per hectare, which is known as the basal area (G). The distribution of basal area by species groups indicates the relative area occupancy of the four cohorts. The average ratios of height (m)/dbh (cm) for the canopy species in cohort I are 0.53 and 0.49 in CBF and OGF respectively. The corresponding ratios in cohort II are 1.01 and 0.93. 2.3. Frequency distributions of tree attributes 2.3.1. Height distributions Altogether 15,221 and 11,833 tree heights were measured in the CBF and OGF study areas, respectively. Such a large number of heights is rarely available for research and consequently, the non-spatial analysis will concentrate on the tree heights. The tree height distributions were usually found to exhibit a bimodal shape. For this reason, the mixtools package of the R comprehensive network is used (Benaglia et al., 2009). The mixture density is given by FðxÞ ¼ k1 F 1 ðxÞ þ k2 F 2 ðxÞ; where k1 and k2 represent the proportions of the two probability density functions F1 and F2. 2.3.2. Bivariate mixtures Previous studies did reveal that the relationship between tree diameters and heights is rather different in small and big canopy
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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30 cm
10 cm 20 cm
i
50 cm
Fig. 3. Left: example of a neighborhood structural unit (left) with different species, tree sizes and a specific spatial arrangement. Right: a hypothetical forest may be seen as a mosaic of neighborhood structure units (NSU) and an example of a sampling scheme to assess the distributions of structural attributes.
species. These differences are revealed by a mixture of two bivariate normal distributions of dbh and height. Using this approach, we denote f(d,h) the bivariate probability density function of tree dbh and tree height and propose the following mixture model:
f ðd; hÞ ¼ a n1 ðd; hÞ þ ð1 aÞ n2 ðd; hÞ
ð1Þ
where a, a parameter in the interval (0, 1), determines the proportion of trees belonging to each of the two component bivariate normal distributions n1(d,h) and n2(d,h). The parameters of nj(d,h) are the expectations ldj, lhj; the variances r2dj and r2hj , and the correlation coefficient qj, j = 1,2. For further details refer to Zucchini et al., 2001. It is possible, of course to improve the fit by using a mixture of three or more distributions instead of just two. However, the field observations do not reveal persuasive biological grounds for believing that the populations comprise three or more distinct subpopulations. The parameters are estimated using the mclust library of the R statistical software (Fraley et al., 2012). 2.4. Nearest neighbour statistics Nearest neighbor statistics (NNS) are based on the assumption that the spatial structure of a forest is determined by the distribution of specific structural relationships within neighborhood groups of trees. A forest is composed of n-tree ‘‘neighborhood structural units’’ (NSU’s, Fig. 3). The distribution of the NSU-attributes permits a detailed analysis of the forest as a whole. Nearest neighbor statistics have important advantages over classical spatial statistics, including low cost of field assessment and cohort-specific structural analysis (a cohort refers to a group of reference trees that share common attributes, e.g. species or size class). NSU’s may be homogenous or inhomogenous consisting of trees that belong to a variety of species, spatial arrangements and size classes (Gadow et al., 2012). The degree of homogeneity within a particular NSU may be described by a set of three variables of identical scale. Each may assume values in the interval (0, 1). These variables are known as Species Mingling (M), Dominance (U) and uniform angle index (W). 2.4.1. Species mingling One neighborhood structural unit consists of a reference tree1 and its n nearest neighbors. Species mingling (Gadow, 1993; Füldner, 1995; Pommerening, 2002), is defined as follows:
Mi ¼
4 1X vj 4 j¼1
with
vj ¼
1; j not the same species as i 0; otherwise
ð2Þ
1 In spatial statistics the terms ‘‘point related’’ and ‘‘test location’’ related summary characteristics are sometimes used (Pommerening, 2008; Illian et al., 2008).
The variable mingling is thus defined as the proportion of the four nearest neighbours that differ from the reference tree in terms of the species. Values range between 0 (only one species) and 1, when every neighbour belongs to a different species than the reference tree (e.g. Mi = 0.5 in Fig. 3). The distribution of the Mi values, in conjunction with the relative species proportions, allows an assessment of the spatial diversity within a forest. 2.4.2. Dominance The variable dominance (U) is a spatially explicit measure of the relative dominance of the reference tree within an n-tree NSU. It is calculated according to Eq. (3) (Hui et al., 1998).
Ui ¼
4 1X vj 4 j¼1
with
vj ¼
1; j is smaller than i 0; otherwise
ð3Þ
Dominance, like mingling, may assume values between 0 and 1 and gives the proportion of the four nearest neighbour trees that are smaller than the reference tree (e.g. Ui = 0.25 in Fig. 3, assuming that the dbh of tree i is also 20 cm). 2.4.3. The uniform angle index The uniform angle index (W) concept is based on the classification of the angles aij (once again, i refers to the reference tree and j to the neighbors) between the vectors pointing away from the reference tree i to its neighbors j (Gadow et al., 1998) as shown in Fig. 3.
Wi ¼
4 1X mjk with 4 j¼1
mjk ¼
1; ajk < a0 and 0 6 W i 6 1 0; otherwise
ð4Þ
The basic idea of uniform angle concept is to compare the angles aij with an appropriate reference angle a0, which is chosen so that it yields an easily remembered number for the mean W in the case of a Poisson forest. In the case of the 4-tree sample the appropriate angle a0 was chosen as 72° which should produce a mean value W ¼ 0:5. Thus Wi is defined as the fraction of the angles aij which are smaller than the standard angle a0 (e.g. Wi = 0.25 in Fig. 3, assuming that only one angle is smaller than the standard). Consequently 0 6 W i 6 1 (note that when aij exceeds 180° , then aij is equal to 360 minus aij.). Small values of Wi correspond to a regular neighbourhood of tree i, while values of Wi close to 1 correspond to the case where the n neighbours of i appear in a cluster of trees close together. The same tendency is true for the mean W and we have W-regular < W -random < W-cluster. The Mean Directional index, which is more closely related to classical ideas of directional statistics (Upton and Fingleton, 1989), exploits the directional information given by the reference tree i and its n nearest neighbours in another way than the uniform angle index. The basic idea is similar, but we prefer to use the
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uniform angle index because the numerical results correspond with Mingling and Dominance. 2.4.4. Eliminating edge effects To eliminate the edge effect and improve the accuracy of the estimates we implemented in our Mi, Ui, and Wi calculations the nearest neighbour edge correction method proposed by Pommerening and Stoyan (2006). This edge correction evaluates individually for each tree whether all n nearest neighbours are truly located within the window of observation and eliminates all trees for which this is not the case. 2.5. Scale-dependent spatial analysis Scale dependent spatial analysis evaluates textures at different scales, i.e. not only short-range but also long-range. This requires large observational studies with mapped trees. 2.5.1. Marked point process Let us consider a quantitative mark such as tree dbh, tree height or mingling. In this case, the mark correlation function kf(r) is a tool for analysing the spatial mark structure. Let kf(r) be the mean value of a suitable ‘‘test’’ function f dependent on the marks. Important ‘‘test’’ functions are f1(m1,m2) = m1m2 or f2(m1,m2) = 1/2(m1-m2)2, where mi is the mark of the point in the i-disc. Note that kf(r) is only defined if in both discs there is a point of the point process. The mean value in the case of f1, kf(r), denoted by kmm(r), is usually divided by the squared mean mark l2 giving the mark correlation function kmm(r) = kmm(r)/l2. The mark correlation function denotes independent marks when kmm(r) = 1 for all r; kmm(r) > 1 indicates positive mark correlation, whilst kmm(r) < 1 implies mark inhibition. The corresponding mean based on f2, i.e. kf2(r), is usually called mark variogram (Cressie, 1993; Stoyan et al., 1995; Stoyan and Wälder, 2000). This function describes the differences of the mark at the intertree distance r. When r is small, it provides information about tree-to-tree interactions. If r is large, it describes the influence of environmental factors such as soil, humidity and altitude (Stoyan and Penttinen, 2000). The mark correlation function has been applied to forestry problems by several authors (Penttinen et al., 1992; Gavrikov et al., 1993; see also Comas and Mateu, 2007, who provide an estimator of this function). 2.5.2. Software The methods described above were implemeted using the Comprehensive R Archive Network (R Development Core Team, 2012), the spatstat (Baddeley and Turner, 2005) and mixdist (Macdonald and Du, 2008) packages were used in this study.
3. Results 3.1. Density by species groups The basal areas are useful for evaluating the plot densities for biologically relevant cohorts. The total basal areas in the CBF and OGF study areas are 33.7 and 56.3 m2/ha respectively. Their distributions by tree cohorts are quite different in the two study areas, as shown in Fig. 4. OGF has more than twice the basal area in the mature canopy species when compared with CBF and only 60% of the basal area in the immature canopy species. CBF in turn has almost three times the density in the subcanopy species when compared with OGF. OGF has a considerably greater shrub density (A. barbinerve) than CBF.
5
3.2. Frequency distributions of tree attributes 3.2.1. Height distributions Fig. 5 shows the bimodal distributions of tree heights in the CBF and OGF study areas. In the CBF plot, 71% of the trees have heights with a mean value of 5.4 m while 29% of the heights have a mean of 15.5 m. At a first glance, the OGF study area exhibits a similar two-component height structure. Both distributions in the two plots are separated at a height of approximately 12 m. This same separating height in both plots is interesting because the OGF canopy considerably exceeds that of CBF. The bigger cohort in OGF has a mean of 20.4 m which considerably exceeds that of the corresponding CBF mean by 5 m. In addition, there is a second peak of tree heights around 25 m in OGF. 3.2.2. Bivariate mixtures Fig. 6 presents graphs of two bivariate mixtures involving dbh and height in the two study areas. The selected canopy species which show the typical two clusters are Populus davidiana in CBF and P. koraiensis in OGF. The dbh/height ratio’s of the understorey cluster of the two canopy species is much greater than the respective ratio’s of the dominant clusters. The graphical representation of the bivariate mixtures allows a better interpretation of the structural peculiarities of particular species and species groups. The shapes depicted in Fig. 6 are typical for many canopy species. Most subcanopy species and shrubs, however, show bivariate dbh/height distributions that are characterized by a single cluster. 3.3. Nearest neighbour statistics For all species correlation coefficients were calculated for mingling-dominance, mingling-uniform angle index and dominanceuniform angle index. The results are presented in Table 1. The correlations are an indication of the strength of the linear relationship between pairs of the three nearest neighbour statistics. Most correlations are significant or highly significant. The highest correlations are found between mingling and dominance. These are positive in the case of the canopy species (Piko and Tima) and all species combined, but negative in the two shrub species (Acba and Acuk). The canopy species (Piko and Tima) are often larger trees compared with the surrounding neighbors of other species. Thus, the individuals have high mingling ususally have stronger dominance. In particular, the canopy species (Piko and Tima) in the OGF plot were more significantly dominant than that in the CBF plot. Accordingly, the shrub tree speices have high mingling was depressed by the larger neighbors so that have weaker dominance. In the meanwhile, the uniform angle index was not significant relative with the dominance in general. The remaining correlations are less obvious. Bivariate graphs of species mingling and dominance are presented in Fig. 7 for the canopy species T. amurensis and the shrub species A. barbinerve. Most T. amurensis trees have high mingling and dominance values. Since most of the trees of this species have larger diameter. It ususally occurs in neighborhoods where they are dominant and at the same time surrounded by trees of other species. This feature is even more distinct in the OGF area. While the shrub species A. barbinerve, on the other hand, often grows in clusters so that exhibits low mingling and dominance. For this reason, it occurs in a wide variety of M/U combinations. 3.4. Scale-dependent spatial analysis The mark correlation function of a marked point process X is a measure of the dependence between the marks of two points of the
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx
Fig. 4. Basal areas by species cohorts identified by Roman numerals (I, II, III, IV) and different shading of columns.
Fig. 5. Bimodal Weibull distribution of all tree heights greater than 3 m in the CBF (left) and OGF (right) study areas. The parameters of the mixed Weibull distribution are shown below the graphs, where p refers to the tree number proportions and mu and sigma to the means and standard deviations respectively.
Fig. 6. Graphic representation of two bivariate mixtures involving dbh and height (left: Populus davidiana in CBF; right Pinus koraiensis in OGF).
process at distance r. Mark correlations were investigated for several marks, including diameters, heights and nearest neighbor statistics. The mark correlation function Kmm(r), is based on a null model of random labelling of marks across fixed locations of trees. Kmm(r) = 1 means that the ratio of observed labelling to random labelling is equal to one. A value of Kmm(r) < 1 indicates mutual inhibition, Kmm(r) > 1 mutual attraction (see Law et al., 2009; Eckel et al., 2012). For small distance values r the estimated functions for T. amurensis are running below the acceptance interval in both plots, which means that at close range the correlation between pairs of the same dbh are less than would be expected (Fig. 8). In other words, the large individual of the species has less frequency of large conspecific neighbors. T. amurensis shows mutual inhibi-
tion at 0–25 m scales in the CBF plot, while it does at 0–5 m scales in the OGF. It is probably for that the OGF plot has more large individuals of this species than in the CBF plot (Fig. 1). The NNS marks of close neighbors are, however, not independent of each other. For very small r, individual i and individuals j can be nearest neighbors of each other and share other neighbors. This may be statistically improper and therefore it was decided to not pursue this particular anaysis further.
4. Discussion Important ecosystem functions, and the potential and limitations of human use are defined by the structure of a forest
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx Table 1 Correlation coefficients for the three nearest neighbour statistics for six species in the CBF and OGF plots. M: mingling, U:dominance, W: uniform angle index. Group
Species
Canopy
Piko Tiam Acps Acte Acba Acuk Total
Subcanopy Shrub
CBF
OGF
M-U
M-W
W-U
M-U
M-W
W-U
0.14*** 0.24*** 0.14*** 0.04ns 0.26*** 0.05ns 0.112***
0.01ns 0.04ns 0.1*** 0.12** 0.16*** 0.11ns 0.001***
0.07ns 0.07* 0.01ns 0.05ns 0.04ns 0.00ns 0.047ns
0.38*** 0.45*** 0.07* 0.07ns 0.29*** 0.03ns 0.211***
0.11*** 0.06ns 0.01ns 0.13ns –0.23*** 0.05ns 0.081***
0.15*** 0.09* 0.10** 0.11ns 0.03* 0.10ns 0.104ns
Significance levels indicated as follows: ns P > 0.05. * P < 0.05. ** P < 0.01. *** P < 0.001.
Fig. 7. Bivariate distribution of species mingling and dominance in the two study areas (CBF left and OGF right) for the canopy species Tilia amurensis (1202 trees in CBF and 751 trees in OGF) and the subcanopy species Acer barbinerve (2165 trees in CBF and 1767 trees in OGF).
Tiam OGF
kmm (r)
1.0
0.8
1.4
1.0
kmmobs (r) kmmtheo(r) kmmhi(r) kmmlo(r)
CBF
kmmobs (r) kmmtheo(r) kmmhi(r) kmmlo(r)
0.6
0.6
kmm (r)
1.8
Tiam
0
10
20
r
30
40
50
0
10
20
r
30
40
50
Fig. 8. r-Wise 99% acceptance intervals for the mark correlation function using dbh as marks for Tilia amurensis in the CBF and OGF plots.
Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012
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R. Ni et al. / Forest Ecology and Management xxx (2013) xxx–xxx
ecosystem. Spatial patterns affect the competition status, seedling growth and survival and crown formation of forest trees (Moeur, 1993; Pretzsch, 1997). Analysis of the spatial pattern of tree species is important in gaining a better understanding of the underlying ecological processes that control the development of the observed patterns. The spatial patterns of trees and their interactions provide critical information about community structure and species coexistence, and significantly determine reproduction, growth, mortality, dispersal, resource use, gap creation, and understory development (He et al., 1997; Druckenbrod et al., 2005; Wiegand et al., 2007). The vertical and horizontal distributions of tree sizes determine the distribution of micro-climatic conditions, the availability of resources and the formation of habitat niches and thus, directly or indirectly, the biological diversity within a forest community. Spatial structures are of paramount importance in community studies because their presence indicates that some process has been at work to create them (Legendre et al., 2009). Thus, information about forest structure contributes to improved understanding of the history, functions and future development potential of a particular forest ecosystem (Ruggiero et al., 1991; Spies, 1997; Franklin et al., 2002). In addition, and perhaps most importantly, structural data provide an essential basis for the analysis of ecosystem disturbance through selective harvest events. The assessment and analysis of forest structure thus facilitates a comparison between a managed forest and an unmanaged reference ecosystem. An important step in the analysis of a multi-species ecosystem is the grouping of species. We first identified canopy, subcanopy and shrub species and then differentiated between dominant and subdominant canopy species using a clustering process based on a bivariate mixed diameter/height distribution. The height/dbh ratios of the subdominant canopy species significant exceed those of the dominant canopy species. At the community level, the two study areas showed rather distinct structural charateristics. The total basal areas in the CBF and OGF study areas are quite different. With 56.3 m2/ha OGF is very dense compared to the 33.7 m2/ha in the CBF study area. The basal area distributions by tree cohorts are also quite different in the two study areas, as shown in Fig. 4. The bimodal distributions of tree heights are quite similar in shape in the two plots. However whereas the mean heights of the two smaller subpopulations are similar (5.4; 4.9 m), the mean heights of the two bigger subpopulations are quite different (15.5; 20.4), with OGF exceeding the corresponding CBF mean height by 5 m. These differences in the two plots provide further evidence of very different development stages on two similar growing sites. The bivariate mixtures in the two plots are consistent with several previous studies (Weiner et al., 1998; Damgaard et al., 2002), indicating higher allocation to height growth in the early stage of the life history, probably in an attempt to reach the canopy as soon as possible. Later on, diameter growth is more prominent. The same phenomenon has been observed in European beech forests (Zucchini et al., 2001). The correlations between pairs of the three nearest neighbour statistics were positively significant, especially regarding the species mingling and dominance relationships of the canopy species. For the subcanopy and shrub species this relationship was not pronounced. The canopy species T. amurensis in the OGF had stronger dominance than that species in the CBF plot (Fig. 7). It is due to more larger trees in the OGF plot. As an old growth forest, the OGF plot had more percentage of large trees (canopy species) and less percentage of small trees (subcanopy species, shrubs). Shelly (1985) and Hector et al. (1999) point out that individuals compete more intensively with conspecific individuals than with individuals of other species. The mark correlation function demonstrated that the T. amurensis had mutual inhibition at small scale. It
meant that there is not so probably to have several large trees in short distances. It is consistent with the result of large dominance of the species (Fig. 7). In this study, we used several methods to describe and analyse the structural characteristics of two temperate forest communities in northeastern China. In the context of more proportion of canopy species, the OGF plot showed differently in structural diversity on many aspects. It provides further evidence of very different development stages on two similar growing sites, and supplies with guideline for the forest management of different successional stage of forest. Plant community dynamics is driven by spatially-dependent birth, death and growth processes, often embedded in a heterogeneous landscape (Law et al., 2009). It is about the dynamics of multispecies spatial patterns as exemplified by the CBF and OGF observational studies. The spatial dimension is a key component in the study of a forest ecosystem. However, the literature on spatial statistics is often rather technical, and there is relatively little exchange between mathematicians developing the theory and ecologists who have interesting data from observational studies, such as presented in this contribution. Acknowledgements Ding ShengJian, He Huaijiang, Chen BeiBei and Huang Zhen and several others assisted with the field data collection. Zhou HaiCheng and Xia Fucai identified the species. Valuable comments were provided by Wang Jinsong and Gao LuShuang. This research is supported by the National Basic Research Programme of China (973 Programme, 2011CB403203), the 12th five-year National Science and Technology plan of China (2012BAC01B03) and the Program for New Century Excellent Talents in University of Ministry of Education of China [NCET-12-0781].
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Please cite this article in press as: Ni, R., et al. Analysing structural diversity in two temperate forests in northeastern China. Forest Ecol. Manage. (2013), http://dx.doi.org/10.1016/j.foreco.2013.10.012