Tests of Distance-Dependent Competition Indices for Predicting Growth of Japanese Larch Trees

: We examined the usefulness of distance-dependent competition indices for predicting individual tree basal area growth in a mature Japanese larch plantation. Using data from a permanent sample plot, we calculated several traditional distance-dependent competition indices and constructed individual growth prediction models. Results of regression analyses suggested that tree size could explain a large part of variation in tree growth much better than distance-dependent competition indices. We also used local indicators of spatial association to detect “hot spots,” or clusters of similar-sized trees, and “cold spots,” or clusters of trees of varying sizes within sample plots. Relationships between basal area growth and diameter of trees in “hot spots” and “cold spots” were analyzed.


Introduction
Competition among neighboring individuals is one of the most important factors that determine individual tree growth (Tomé and Burkhart, 1989). In many studies, distance-dependent competition indices -which are intended to represent the degree of competition using subject tree size, competitor tree size, and distance to competitor -have been used in analyses (e.g., Daniels, 1976;Lorimer, 1983;Martin and Ek, 1984;Daniels et al., 1986;Tomé and Burkhart, 1989;Dobbertin, 1992, 1995). In some cases, a significant effect of competition on growth has been identified. It has also been shown that distance-dependent competition indices are not so useful for explaining variations in tree growth, in spite of a large effort to calculate these indices. In many cases, initial tree size alone can explain variations in tree growth.
Because the current tree size reflects the cumulative effects of past competition and other environmental factors, there must be a strong correlation between periodic tree growth and initial tree size (Bella, 1971;Lorimer, 1983). However, Bella (1971) showed that the relative importance of competition on growth differs among different size classes within a stand. In addition, Mitsuda et al. (2002) showed that different types of competition indices should be used to predict tree growth for each size class within a stand. These studies suggest the importance of competitive effect represented by competition indices on growth differ among individuals within a stand in relation to the circumstances of each individual tree. Therefore, competition indices based on regression analyses, which treat all trees the same, fail to explain variations in individual tree growth within stands.
Indices representing spatial patterns of tree locations that consider tree size have recently been developed (e.g., Anselin, 1995). Shi and Zhang (2003) applied a group of such indices, which they called Local Indicators of Spatial Association (LISA), to detect local clusters of trees of similar and dissimilar sizes. Within a local cluster of trees of similar size (a "hot spot"), two-sided competition -in which neighboring trees limit each other's access to resources (Schwinning and Weiner, 1998) -should be severe. On the other hand, within a local cluster of trees of dissimilar size (a "cold spot"), one-sided competition -in which larger trees suppress smaller trees -should be severe. Thus, we may be able to reveal differences in the competitive effects on growth by identifying hot spots and cold spots within a stand using LISA.
The objectives of this study were (1) to test distance-dependent competition indices for predicting individual tree basal area growth in a mature Japanese larch plantation and (2) to examine the relative importance of competition on tree growth and how it varies with the spatial distribution of individual trees.

Materials and Methods
The data used in this study was collected in permanent sample plots of a Japanese larch (Larix kaempferi) plantation in Ashoro Research Forest, Kyushu University. Ashoro Research Forest is located from 43º 17' to 43º 19' north latitude and from 143º 29' to 143º 33' east longitude, and its elevation ranges from 100 to 500 m a.s.l. The annual mean temperature and precipitation are about 6 ºC and 800 mm, respectively.  In 1973, trees in the three plots (A, B, and C) were thinned at different intensities; thus, the densities in each stand differ. The stand information of these sample plots is summarized in Table 1. First, we examined the competitive effects on growth using a traditional approach.
We calculated three distance-dependent competition indices-a Horizontal Competition Index (HCI), one-sided Vertical Competition Index (VCI1), and a two-sided Vertical Competition Index (VCI2) (Mitsuda et al., 2002). These indices were calculated as the sums of distance-weighted size ratios (HCI) and the difference (VCI1 and VCI2) between a subject tree (i) and its competitors (j). These methods have been widely used for some time (e.g., Daniels, 1976;Lorimer, 1983;Biging and Dobbertin, 1995;Mitsuda et al., 2002;Yamashita et al., 2006;Kohama et al., 2006) and are defined as follows: where DBH is diameter at breast height, H is tree height, dist ij is distance between the subject tree and competitor, dgl is the difference of ground level between the subject tree and competitor, and C i is a set of competitors of the subject tree i.
We selected all trees within a 3m radius of the subject tree as competitors for calculating HCI and VCI2. Only taller trees within the 3m radius were selected as competitors for the VCI1 calculation. Because we used 3m as the radius for identifying competitors, we excluded edge trees which were located within a 3m buffer from the left, top, and right edges of the plot for subsequent analyses ( Figure   1). We did not set an edge buffer for the lower side because all three plots were adjacent to a forest road where trees did not exist. Trees might be large enough to affect each other over the 3m distance in these plots; however, because we excluded edge trees from the analysis, we used 3m as the radius for identifying competitors to maintain enough trees for additional analyses.
We constructed individual tree annual basal area growth models. First, we used DBH as the sole explanatory variable, then DBH and one of three competition indices as explanatory variables, and finally we examined the competitive effect on tree growth through model selection (see e.g., Burnham and Anderson, 2002).
Because we pooled all the data acquired from the three sample plots and two growth periods for model construction, we included these factors as random variables affecting variations of tree growth in linear mixed-effect models (see. e.g., Faraway, 2006). We set the sample plot factor and growth period factor as random effects assuming normally distributed N(0,σ 2 ). We fitted the following four linear mixedeffect models to the data by the maximum likelihood method, using R (R Development Core Team, 2007) with the lme4 package (Bates, 2007), and compared these linear mixed-effect models using the Bayesian information criterion (BIC) (Schwarz, 1978): [3] where G i is annual basal area growth, α is an intercept, 1 β and 2 β are coefficients of regression, and plot α and period α are random effects of plot and growth period, respectively.
Next, we investigated the relationships between individual tree growth and tree size, and competition indices of trees facing severe competition with neighboring trees. We used the local forms of the Moran coefficient and the Geary ratio as LISA (Shi and Zhang, 2003). The Moran coefficient (MC) is defined as follows: where DBH is plot average DBH. A positive MC value indicates a subject tree is in a cluster of similar size, whereas a negative MC value indicates a subject tree is in a cluster of dissimilar size. In cold spots, the lower negative MC values indicate that both dominant and suppressed trees are in the more severe one-sided competition scenario.
The Geary ratio (GR) is defined as follows: The GR value indicates variance of tree size within a cluster; a lower GR value means less variance of tree size and more severe competition among similar-sized trees.
To extract data acquired from hot and cold spots, we first examined trees with over five competitors, which is larger than the average number of competitors

Results and Discussion
The BIC of the regression model using DBH as the sole explanatory variable (Model 1) was 1607.15, indicating Model 1 is the best fitted of the 4 regression models (Table 2). This result suggests that initial size could explain a large part of the variation in individual tree growth much better than the competition indices.
Model 3, which used DBH and VCI1 as explanatory variables, is the best fitted model that includes the competition index and its BIC was approximately the same suggests that the competition index may not easily explain the variation in individual tree growth. Figure 2 shows a strong relationship between initial DBH and annual basal area growth. Figure 2. Relationshipt between basal area growth and initial DBH As in our study, initial tree size has been accepted as the most effective variable in previous regression analyses. Competition indices have not been accepted, or have provided unsatisfactory explanations of the variation in individual growth in regression models (reviewed by Biging and Dobbertin, 1995). As we mentioned before, the initial tree size reflects the cumulative effects of past competition and other factors. Given that the study site is a mature plantation forest and has not been significantly disturbed for a known period of time, various factors determining individual tree growth could be represented by the actual tree size. Consequently, are competition indices useless for describing individual tree growth?
The coefficients of correlation between annual basal area growth and initial diameter were 0.62, 0.05, and 0.83 for total, hot spot, and cold spot observations, respectively (Table 3 and Figure 3). In cold spots, the coefficient of correlation between basal area and initial diameter increased to 0.83. The correlation between growth and competition indices was also stronger, but its coefficients of correlation showed a weaker relationship than that of initial DBH. Because there are both dominant trees and suppressed trees in cold spots, tree size sufficiently represents superiority over neighboring trees for a dominant tree and inferiority for a suppressed tree. In hot spots, the correlation between basal area growth and initial size become quite weak. In mature undisturbed stands like our study site, where dominant trees and suppressed trees have been fixed through historical competition, it is especially apparent that "big trees grow fast" (Lorimer, 1983). Inoue et al. (2008) showed that volume growth of young Cryptomeria japonica trees depends on tree size before canopy closure and the distance-dependent competition index is far better than actual tree size to describe individual tree volume growth after canopy closure.
They concluded the relative importance of competition increased during the canopy closure process. Nagashima (1999) showed that height growth of Chenopodium album can be predicted using plant size before canopy closure, both size and the competition index can be used at the canopy closure stage, and that plant size can be used from a certain point after canopy closure. These studies suggest that competition among neighboring trees is quite important in young stands in the midst of the canopy closure process. In mature stands where much time has passed since canopy closure, the competitive effect for tree growth becomes relatively unimportant and actual tree size comes to represent competitive status. Lorimer (1983) stated that the high correlation between tree size and growth is, in part, a secondary effect of competition. In this situation, it is difficult to use distancedependent competition indices to predict tree growth, as shown in our results. On the other hand, our results also showed that it may be possible to use distance-dependent competition indices in some situations. Using LISA, we detected clusters of trees where competition among trees of similar or dissimilar size was severe within sample plots. In these clusters, the relative importance of competition on tree growth should be higher and distance-dependent competition indices should logically show somewhat better correlations to tree growth.
Although our study site is in a controlled plantation forest, spatial locations of trees are not uniform and there are some hot spots and cold spots (Figure 1). The spatialsize distribution of individuals affects the stand development through tree competition. This process has recently been intensively studied (e.g., Fajardo and McIntire, 2007). Our results also suggest that the spatial distribution of tree size should be taken into account to describe individual tree growth. In future studies, we should focus on the temporal and spatial changes in the relative importance of competition in individual tree growth. Therefore, we must continue to measure the existing permanent plots and establish new permanent plots. キーワード : 距離従属競争指数, 個体成長, 固定試験地, hot spot, cold spot