Importance to assess information regarding density and exhibited spatial patterns of juvenile trees in forests has been emphasized in the thesis. Maintaining composition of forests in order to increase a yield of a timber and increase the income by maintaining a quality of the growing stock is being even more important to support development of impoverished countries. Successful achievement of the sustainable use is also greatly dependent on the quality of collected information regarding renewable resources being the target of the management. Successful forest regeneration is the one of most important preliminary conditions in achieving sustainability of forest management. Appraisal of a success of forest regeneration as well as designs of forest regeneration surveys and interpretation of a collected data, whether imposing natural regeneration, artificial or supplemental planting practices, is the one of most responsible tasks of forest management. An indispensable effort, and a good start in achieving tasks given by principles of the sustainable forest management, is to ensure a success of forest regeneration. Forestry policies in most of the countries, devoted to principles of the sustainable management, are also prescribing the obligatory conduction of forest regeneration surveys. Necessity to evaluating a success of forest regeneration is emphasized for all managed forests. That is of particular importance if a target of management is to maximize benefits and services being provided by forests along to a sustainable utilization of timber.

Field surveys are still the main source of information regarding a success of forest regeneration and in the case where remote sensing is still unable to detect juvenile trees. Assessing only the relative density of juvenile trees, what use to be a practice in most of the forest regeneration surveys, can not be sufficient. Indexing spatial patterns of juvenile trees is also being an elementary measure of a success of forest regeneration. Juvenile trees in forests are likely to exhibiting various spatial patterns. Naturally regenerated juvenile trees are likely to exhibit clustering while artificial or supplemental planting practices can result to regular spatial patterns. Foresters seek for a simple index of the degree of clustering or regularity, being practical to apply in forest regeneration surveys. Total count or mapping positions of juvenile trees is not practically justified in order to indexing their spatial patterns. The use of fixed-area plot sampling in indexing spatial patterns of trees is questionable since the indices are influenced by a size of plots.

Statistical methodology to assessing density and indexing spatial patterns of individual trees in forests is elaborated in the thesis and practical aspects are considered to a great state. The main stress is placed to statistical methods being recognized in the past as rapid approaches in field surveys. Simple measurements of angles between the lines of sight from sampling points to their nearest two neighboring trees, being known as the Mean of Angles method, was proposed by Assuncao (1994) for the use in testing whether trees in forests exhibiting a random spatial pattern. Also being simple to obtain in field, a measurement of distances from sampling points to a given number of the nearest individual trees (c-tree sampling) was proposed in the past to be used in indexing spatial patterns.

To assess relative density of juvenile trees, the conventional practice in forest regeneration surveys is the use of fixed-area plot sampling. These are also used in stratifying forest area by the abundance of juvenile trees; for example, forest stand area being abundant in juvenile trees to that being not regenerated. Besides conventionally used fixed-area plot sampling, c-tree sampling can be used in assessing relative density of trees and it has a potential use in stratifying forest area. On the other hand, c-tree sampling is known as a biased approach in assessing information regarding individual tree parameters; not equal probability of selecting individual trees in clusters. It is also known that c-tree sampling can yield biased density estimates, with the bias dependent on exhibited spatial pattern and the estimator used.

The main given hypothesis of the thesis is that indexing spatial pattern distributions of juvenile trees in forests can serve in choosing an appropriate density estimator for the c-tree sampling approach and thus increase reliability of density estimates. The main objective of the thesis is to propose methodology, being both practical and sufficiently reliable, for the use in forest regeneration surveys and in order to assessing relative density and indexing spatial patterns of juvenile trees. Specific objectives of the thesis include analysis of potential of the arithmetic mean of angles to serve as practical measure of the degree of regularity or clustering. Furthermore, the performance of the best-performed spatial pattern index being proposed by Liu (2001) for the c-tree sampling approach was compared to the index based on the measured angles. Besides objectives relating to indexing spatial patterns of trees, emphasize is given to studying statistical performance of density estimators for c-tree sampling. It was considered use of density estimators being robust and reliable enough to enable they use in forest regeneration surveys. Fixed-area plot sampling was also compared to c-tree sampling by the practical meant of variance, the precision in estimating the density and stratifying the population of naturally regenerated saplings.

Statistical performance of c-tree sampling and the Mean of Angles method was investigated, and hypothesis tested, by conducting simulation studies in point populations having known spatial pattern and density. In general each individual tree in forest can be represented by a point in a plane area. This allows mapping individual tree positions or to mimic real forests by simulating point spatial patterns. In addition to simulating point populations being designated as theoretically most significant, a new methodology being denoted as the "Gap-process" is being introduced in the thesis. This method to simulate clustered point populations may be recognized as a modified Gibbs field process which uses the so-called spatial birth-and-death processes. In ecological terms, the Gap-process can be seen as a disturbance; artificial (for example harvest) or natural (for example damage caused by strong winds, forest fires etc.). The practical applicability of the methodology was tested by mapping naturally regenerated Chamaecyparis saplings sized from 1.5 to 5 m in height and conducting simulation studies at the mapped population. In all simulated point populations, random sampling procedure was conducted. In the mapped population of saplings, along to applying random sampling, systematical sampling was also applied since it can have a practical advantage. That is particularly important in stratifying forest area and in the cases when remote sensing can not detect juvenile trees. The practical meant of variance and the precision in estimating the density of the population of naturally regenerated saplings by fixed-area plot sampling and c-tree sampling was conducted applying the bootstrap statistical technique.

It is concluded that it is not necessary to map positions of juvenile trees in forests and in order to acquire reliable indices of their spatial patterns. A mean of angles can serve as a simple spatial pattern index and its use is recommended to indexing the degree of regularity or clustering of juvenile trees. That is also a practical approach to apply in forest regeneration surveys since the method is simple and robust enough. Moreover, the measurements of angles do not need to be performed with a high precision. On the other hand, applications requiring much reliable indices should consider precise measurement of the angles and relatively large sample along to analyzing its frequency distribution. Higher precision in studying spatial patterns can be also achieved by introducing measurement of distances along to measuring the angles. Moreover, distances between sampling points and trees are dependent upon the relative density of trees and it can be worthwhile to obtaining such measurements. Indices based on measured distances are also applicable to distinguishing between clustered, random and regular populations. In particular, their use can be more practical in testing whether trees in forests are distributed at random, where measuring angles would require a slightly larger sample. However, the use of the distances between sampling points and trees in indexing spatial patterns of trees may not give a reliable insight into the degree of regularity or clustering. Furthermore, an extensive statistical expertise is necessary in order to look beyond these indices, what is clearly not appropriate in supporting practitioners in the field.

The use c-tree sampling in assessing a relative density of juvenile trees is feasible but that requires indexing spatial patterns of trees. It is also necessary to choose an appropriate density estimator. Choosing different density estimators in regard to exhibited spatial pattern distributions enable setting the c to some small value; such as applying a sampling procedure based on measuring distances from sampling points to their second or third nearest tree. Furthermore, these estimators of density need to be robust enough to find a practical use in forest regeneration surveys. It is proposed to use the GM estimator (Trifkovic 2005) in assessing density of trees exhibiting uniformly regular spatial patterns; uniformly regular spatial pattern refer to forest stands where the majority of angles between the lines of sight from random sampling points to their nearest two neighboring trees is larger than 90 degrees and the relative density do not differ significantly. The Pollard estimator (Pollard 1971) is not as robust as estimators accounting for variable circular plot areas but it is appropriate in the case when the trees are distributed uniformly at random.

The (c-1) estimator (Eberhardt 1967) is robust enough to be used in a wide spectrum of clustered spatial distributions. However, it is important to emphasize the finding that the (c-1) estimator is an applicable estimator of density for the cases when frequency distributions of variable circular plot areas (squared plot radiuses) fit the generalized Pareto frequency distribution or the normal frequency distribution. In forest stands having randomly distributed trees, applying c=5 sampling or any higher c value is the most likely to yield frequency distributions of variable circular plot areas fitting the normal frequency distribution; that explains its applicability in the case when the trees are distributed at random. Juvenile trees being naturally regenerated are likely to exhibiting clustered spatial patterns and with clusters being irregular in size and shape. In such populations, applying c=2 sampling was the most likely to yield variable circular plot areas being not significantly different from the generalized Pareto frequency distribution. Furthermore, measured population of naturally regenerated saplings exhibited moderately clustered spatial pattern; spatial pattern being caused by a competition driven change toward randomness and forward to regularity. In such a case, applying the c=3 sampling procedure was the most appropriate. In general, a bias does not increase with the increase in the number of measurements (sample size) and thus increasing the sample size would increase a confidence. Increase in the c value may also increase a reliability of density estimates in populations exhibiting randomness or regularity but a caution is necessary in populations exhibiting clustering. It should be emphasized that increasing the c value in some clustered populations can yield variable circular plots being not significantly different from the exponential frequency distribution. That can still produce relatively high bias, and overestimate the true density, unless deriving a more appropriate density estimator.

The use of c-tree sampling is particularly remarkable in forest regeneration surveys to stratifying forest area where remote sensing can not contribute to a great extent. Especially practical designs are those based on the measurement of distances to second nearest juvenile trees from systematically distributed sampling points. These also can give a greater confidence in stratifying forest area than compared to a conventional practice of applying small sized fixed-area plots.

Methodology based on measuring the angles and the distances to the second nearest trees is recommended for the use in forest regeneration surveys. However, that should not exclude the use of fixed-area plot sampling. In particular that is emphasized when the precision of density estimates is much required. Combined use of plots, distances and angles can even more contribute in assessing a potential of juvenile trees to mature into an ecologically sound and an economically worthwhile forest.

本論文は、森林調査における重要な情報である本数密度を評価するための手法として距離法を取り上げ、森林更新木調査における適応可能性を明らかにすることを目的として、樹木の空間配置と本数密度評価精度の関係を示すとともに、至近木2本の角度を用いて空間配置そのものを評価する方法について、新たな視点を加えて考察したものである。特に、角度を用いた空間配置の分類手法の開発は森林調査における新たな知見として評価することができる。

天然林を管理する上で天然更新木の本数密度を推定することは、その更新方法を評価する上で重要な調査項目である。標準地法は統計的に安定した手法であるが、更新木の空間配置に偏りがある場合には、その精度を維持するために大きな労力を必要とする。これに対して距離法は統計的な安定性は劣るものの、効率性においては標準地法よりも優れており、天然更新木の本数密度推定には実用性が高いとされている。本論文は距離法に焦点をあて、距離法と比較しつつ、その精度と統計的安定性について評価を行い、天然林管理における実用性について考察を加えている。

本論文ではシミュレーションとフィールド調査によって本数密度推定の評価を行っている。シミュレーションではランダム分布の他に規則的な分布と天然林にありがちな集中分布を対象に距離法の精度を評価している。集中分布のパターン化に際して、本論文ではギャッププロセス法という新たな手法を考案し、シミュレーションを行っている。距離法についてはこれまでの先行研究レビューから、本数密度の推定に3種類の代表的な計算方法を選び、それぞれの計算方法について比較し統計的安定性と精度の評価を行っている。その結果、評価対象となる樹木の空間配置パターンによって統計的安定性と精度に違いがあることを明らかにした。すなわち、ランダム分布においては一定水準の精度が確保できるのに対して、集中分布においては本数密度の評価に偏りが生じることを示し、その原因として本数密度評価の基礎となる可変基準円面積の頻度分布によって推定値に偏りが生じることを明らかにした。また、集中分布の空間配置の場合は、カウント木本数を増加させることによって期待される精度向上は、これに要する労力増加の割には小さいことを示した。

次に、本論文では対象木の空間配置パターンを至近木2本のなす角度を用いて推定する方法を示している。これはAssuncao(1994)によって数学的に提案されたアイデアを森林管理の分野に応用したものであり、この分野においては独創的な手法の開発であると評価することができる。シミュレーションによってランダム分布においては至近木2本のなす角度の平均値が90度となり、集中型分布においてはこの平均値が90度以下、規則的な分布においては90度以上となることを明らかにした。さらに、角度の累積頻度分布をパターン化する方法によって、容易に樹木の空間分布を集中分布、規則分布、ランダム分布に類型化できることを示し、シンプルな指標で空間配置を表現することに成功している。

フィールド調査は長野県の赤沢自然休養林内のヒノキ天然林内に設定された、天然更新試験地7.25haにおいて、樹高1.5m以上5m以下の更新木3877本の樹木位置を測定した。この結果、現実林分の天然更新は強い集中分布型を示しているため、標準地法による本数密度の推定では標準地数が十分に確保できない場合に総数において大きく過小評価となることが明らかになった。また、本数密度の高い部分では正しい本数密度を示すのに対して、本数密度の低い部分の評価において、過小評価が著しいことが判った。これに対して距離法では本数密度の低い部分においても適切な密度の評価がなされることが示された。森林管理の実用的な視点にたった場合、天然更新の密な部分よりもむしろ薄い部分の評価を適切に行うことが重要であり、下種伐の効果を評価するためには標準地法よりも距離法の方が適切な本数密度評価方法であることが明らかにされた。

距離法と角度法を組み合わせることによって天然林管理における効率的な更新評価法を提案することが示された。本論文において記述されているようにこの手法は対象となる樹木の空間配置によって本数密度推定に偏りの生じる場合がある。空間配置を正しく知るための指標として角度法が有効であることが明らかにされている。

以上のように、本研究は森林調査における重要な情報である本数密度を評価するための手法である距離法の効果とその限界を明らかにするとともに、現実林分における応用の方法を示したものであり、森林管理の学術分野に貢献するところが大きい。よって審査委員一同は本論文が博士(農学)の学位論文として価値あるものと認めた。