樹型模型分析：量化分析與電腦模擬

Abstract

此次研究的目的主要分三部分。首先，第一部分是完成一個經過調整且配合 3－D 電腦模擬圖的樹型模型（ tree architectural model ）檢索表，在此檢索表中，模型與模型間分類的依據是以電腦模擬幾何參數改變量的多寡為基準。原始電腦程式是 Akio Takenaka （竹中明夫）針對菲島福木（Garcinia subelliptica Meer.）生長模式並以 C ++ 語言所設計。製作檢索表時，僅可能把不僅是結構且外形亦相似的模型置於同一分類層級，主要目標是期望能建立一更合宜且實用的檢索表，以便利實際野外觀察及判斷樹型模型之用。 改變參數即可創造出不同的模型，在模擬模型改變參數的同時，有一件事引起了我的興趣與注意,那便是將 Stone ' s model （史東模型）轉變為 Petit ' s model（彼提德模型）、Scarrone' s model （史凱羅恩模型）轉變為 Fagerlind ' d model （菲傑林德模型）、 Attims ' model （亞提姆斯模型）轉變為 Roux ' s model （魯克斯模型）、Rauh ' s model（羅鄔模型）轉變為 Massart ' s model（馬撒爾特模型）比轉變為其他模型來得容易，反之亦然。基於以上的考量，提出了一個合理的推測，也說是以上所提及的模型，他們兩兩之間相互的關係，就演化及自然選譯的角度看來，可能比我們想像的更為密切。 第二部分是以實際量化分析（ quantitative analysis ）所得的數據及迴歸分析（ regression analysis ）的方式，修正理想模型並模擬出接近現實所觀察的菲島福木。研究中發現菲島福木同一樹冠較中央部分的分枝層，其主側軸具有較長的節間，小側枝分枝數有減少的趨勢。在所有測量的節點，僅有 16 . 6 ％的節點上同時具有第二小側枝。在此同時，較下方的分枝層由於受上方的分枝層遮蔽的結果，會有脫離母體掉落的現象，在本次實驗中亦被觀察到。這些現象及特徵使得菲鳥福木其枝條可以在較受遮陰抑制的情況下，能延展其葉片以利其截取光源，並減少相互間的過度重疊與遮蔽。顯然地，在這個案例中，同一棵樹的同一樹冠中具有彈性的調控以利整體生存的現象，在菲島福木中被表現並觀察得到。 第三也是最後一部分是，關於細葉欖仁（Terminalia boivinii Tul.）的量化描述，並與理論中理想的模型做一比較。細葉欖仁具有很強的側枝優勢（ branch dominance ) , 觀察得知分枝角度 θ1與θ2因分枝級數的增加，而其相互間的差距也有變大的傾向。角度差距增大的現象，被視為是為了維持較大的有效葉面積（ effective leaf area ）之故。每一分枝層平均擁有 3 . 8 個複合分枝軸，其?相當接近理想模型中的?，理想複合分枝軸數是 4－5 。然而相反的，分枝長度比例?與理想模型中能產生最大有效葉面積的? p＝0.615 有一段差距，觀察所得的? p ＝0 . 50 ，接近欖仁樹（T. catappa L . )p＝0.519 ，這個非預期的結果很可能與欖仁具有同樣的理由，其目的是為了能幫助植物產生一分枝長度比例平衡的支持結構，並且製造一有利於葉片分佈的骨架組織。就某些方面來說，建立一穩固的機械性結構似乎比獲得最大有效葉面積來的重要。

The object of this study has been divided into three major parts. Firstly, a modified three-dimensional computer simulated key to architectural models of plants was made, in which the relationships between models depend on amount change of geometric parameters. The original program was coded according to Garcinia subelliptica Merr. in C++ language by Akio Takenaka. I intend to put the familiar models not only in architecture but in shape also as close as possible. The prim object is to bring forward a more convenient and practical way for observing and distinguishing the architectural models of plants. The basic model can be modified by changing parameters to produce new architectural models. During the period of simulating models by changing parameters, there is one special thing intrigue me, that is one can transform Stone’s model into Petit’s model, Scarrone’s model into Fagerlind’s model, Attims’ model into Roux’s model, and Rauh ‘s model into Massart’ s model more easily than any other models. Conversely, it is the same, too. Concluding from the above considerations, I advance a rationalization inference that the correlations between both of them should be closer than any other models more than we can imagine through evolution and natural selection. Secondly, the simulation refined the theoretical model of G . subelliptica Merr. by using actual quantitative values and regression analysis derived from average of real trees. The present study, it was found that longer internode lengths of major limb and reduction in number of twig ‘s branches in the middle tiers within the crown of an individual G. subelliptica Merr.. The second twig was rarely found in this study; it occurred only 16.6% of the total trees observed. Simultaneously, lower branch tiers will be partially shaded by upper branches and fall off also showed down. These features should enable branches of G. subelliptica Merr. which are in conditions of suppression contribute toward to spread their leaves to intercept local light and so avoid too much mutual overlap and shading. Significant, and in this case, true plasticity exists within the crown of a single canopy dominant G. subelliptica Merr. as well. In the third place and lastly, quantitative description of ‘Terminalia boivinii Tul. has been made and compared them with theoretical ones. In T. boivinii Tul. there is a great tendency towards “branch dominance” and the asymmetry of branching (difference between optimal( θ1 &θ2) increase as branch order increases. The growth response of branching angles is regarded as advantageous to maintain a maximum effective leaf area (EA). The observed average number of branch complex for a given tier is 3.8 which approaches theoretical ones’. The value of theoretical one is 4-5. On the contrary, the observed ratios of branch lengths in ‘T boivinii Tul. are far from the theoretical ones’ value p = 0.615 that produce maximal EA. The observed value p = 0.50 which is close to the natural observed value of T.catappa L. p = 0.519. lt’s quite likely that the unexpected result help the stem system to provides the structural support and leaf exposure framework of woody plants just as T. catappa L.. This is not unexpected since engineering principles of branch strength strength and stability would be more important than maximum EA in a branch system in the sight of some situation.