The exponential relationships between the reproductive success (including number of fruits and fruit set) and the distance to the nearest male (<i>d</i>₁).

<p>The exponential relationships between the reproductive success (including number of fruits and fruit set) and the distance to the nearest male (<i>d</i>₁).</p

Spatial Characteristics of Tree Diameter Distributions in a Temperate Old-Growth Forest

<div><p>This contribution identifies spatial characteristics of tree diameter in a temperate forest in north-eastern China, based on a fully censused observational study area covering 500×600 m. Mark correlation analysis with three null hypothesis models was used to determine departure from expectations at different neighborhood distances. Tree positions are clumped at all investigated scales in all 37 studied species, while the diameters of most species are spatially negatively correlated, especially at short distances. Interestingly, all three cases showing short-distance attraction of <i>dbh</i> marks are associated with light-demanding shrub species. The short-distance attraction of <i>dbh</i> marks indicates spatially aggregated cohorts of stems of similar size. The percentage of species showing significant <i>dbh</i> suppression peaked at a 4 m distance under the heterogeneous Poisson model. At scales exceeding the peak distance, the percentage of species showing significant <i>dbh</i> suppression decreases sharply with increasing distances. The evidence from this large observational study shows that some of the variation of the spatial characteristics of tree diameters is related variations of topography and soil chemistry. However, an obvious interpretation of this result is still lacking. Thus, removing competitors surrounding the target trees is an effective way to avoid neighboring competition effects reducing the growth of valuable target trees in forest management practice.</p> </div

Pearson's correlations between the coefficient of variation of tree diameters and topographical variables.

<p>^*** indicated a significance at the 0.001 level.</p

Number of stems and sex ratios of <i>Rhamnus davurica</i> in different DBH classes in the 360×660 m research plot, G(P) = G-test results.

<p>Number of stems and sex ratios of <i>Rhamnus davurica</i> in different DBH classes in the 360×660 m research plot, G(P) = G-test results.</p

Path diagramms showing the influence of elevation, local competition from neighboring trees, pollination environment and tree size and on the fruit set of <i>R. davurica</i>.

<p>The arrows define the cause-and-effect relationships in the path diagram for the causal model. Path coefficients are given for each arrow. Female size is expressed as stem diameter (cm) at breast height measured in May 2010. ***p<0.001, **p<0.01, *p<0.05.</p

Spatial characteristics of tree locations and tree <i>dbhs</i> at 0–50 m distances.

<p>Note: L means light; S means shade and M means middle. C means canopy trees and U means understory.</p><p>Spatial point patterns were tested for randomness using the <i>L</i>-function. The spatial characteristics of tree <i>dbhs</i> were analyzed by the homogeneous Poisson (<i>HomP</i>), random labeling (<i>RLM</i>) and heterogeneous Poisson (<i>HetP</i>). Spatial distances at which tree locations show significant aggregation, regularity and randomness are indicated by the symbols “+” in parenthesis in <i>L</i>-function. Spatial distances at which tree locations and tree <i>dbh</i> marks show significant positive, independent and negative correlation are indicated by the symbols “+”, “<i>r</i>” and “−” in parenthesis, respectively.</p

Exemplary results for <i>Syringa reticulata</i> var. <i>amurensis</i> to illustrate the analysis.

<p>Diagram a presents the spatial distribution pattern using the <i>L</i> function. Diagrams b, c and d show the spatial characteristics of the diameter distribution evaluated by the mark correlation function. The significance of a and b was tested by the homogeneous Poisson model, c by the random labeling model, and d by the heterogeneous Poisson model. Dashed lines indicate the confidence envelopes, while solid lines indicate the <i>L</i> or <i>MCF</i> values calculated from the observations. When the solid line was below the lower envelope, inside both envelopes, or above the upper envelope, the pattern was assumed to be significantly regular, spatially random, or significantly aggregated in the <i>L</i>-function analysis. Correspondingly, a solid line above the upper envelope, inside both envelopes, or below the lower envelope, indicates significant positive, independent, or negative correlation of <i>dbh</i> marks in the <i>MCF</i> analysis.</p

Spatial distribution of <i>R. davurica</i> in a 360×660 m research plot in <i>Jiaohe</i> experimental forest in northeastern China in three years.

<p>(a) indicates the distribution in 2010; (b) indicates the distribution in 2011; (c) indicates the distribution in 2012; Squares indicate <i>Rhamnus davurica</i> males; circles indicate females not studied; crosses show females selected for this study. Gray lines show the elevation contours at 5-m intervals.</p

Example of a kernel smoothed intensity map showing the point pattern.

<p>The map colours show the intensities (number of trees per m²) of <i>Syringa reticulata</i> var. <i>amurensis</i> and the elevation contours at 10-m intervals within the 30-ha study area. The unit of the axes is meters.</p

The mortality ratio for males and females in different DBH classes in2011 and 2012.

<p>The mortality ratio for males and females in different DBH classes in2011 and 2012.</p