以力學角度探討恐龍與爬蟲類蛋殼的勁度兼論恐龍接觸孵蛋之可能性

Mechanical Analysis of the Eggshell Stiffness in Dinosaurs and Reptiles and Note on the Feasibility of Contact-incubation for Dinosaurs

吳筱柔(Hsiao-Jou Wu)

指導教授 ： 于宏燦

共同指導教授 ： 莊嘉揚(Jia-Yang Juang)

國立臺灣大學/生命科學院/生命科學系/碩士(2021年)

https://doi.org/10.6342/NTU202101823

摘要

現生鳥蛋可被視為一項近乎完美的天然設計，一方面，在孵育期間蛋殼必須具有足夠的堅固度，以承載親鳥坐臥其上的重量 (接觸孵蛋)；另一方面，蛋殼又必須夠脆弱以利雛鳥在孵化時破殼而出。先前跨物種的鳥蛋研究中，已定義無因次參數C，用以量化鳥蛋的堅固程度，並已去除形狀所造成的影響以及重量差異，而此數值在現生鳥類物種間為定值。本研究將此無因次參數C的計算應用至爬蟲類動物與恐龍。

過去對於蛋殼機械性質的研究，僅針對單一類群或物種，且未能將機械性質量化，而關於其他生物性材料的機械性質研究，則會探討其與微結構的關聯性。本研究探討的物種橫跨多種爬蟲類 (龜、鱷及壁虎)，並以無因次參數C與楊氏係數E進行機械性質的量化，也從蛋殼的碳酸鈣含量，和精密儀器 (掃描式電子顯微鏡、電子背向散射繞射) 拍攝結果來討論化學組成及微結構是否影響機械性質。最後結果顯示，爬蟲蛋的無因次參數C平均高於鳥蛋，顯示其較為堅固，然而，爬蟲蛋殼的楊氏係數E與鳥類蛋殼並無明顯差異。而蛋殼組成結果顯示碳酸鈣含量與楊氏係數間具有正相關之趨勢，而結晶組成比較結果中，晶粒尺寸較小的霰石具有較高之無因次參數C，但楊氏係數在兩種結晶組成間並未呈現顯著差異。

本研究亦將實驗方法應用至非鳥類恐龍蛋，以探討非鳥類恐龍採行接觸孵蛋之可能性，利用有限元素法軟體進行蛋殼壓縮模擬，並探討不同恐龍類群間蛋殼的機械性質 (無因次參數C) 差異。另外，本研究也模擬保存較完整的蛋巢標本，包括傷齒龍科 (Troodontidae) 及竊蛋龍科(Oviraptoridae) 的蛋窩，以探討其孵育時的受力情況。文獻與博物館標本之化石蛋殼樣本總數共計105顆蛋，根據模擬結果，我們發現竊蛋龍類 (Oviraptorosauria) 的蛋與現生鳥蛋相比，具有較低的無因次參數C，顯示其較鳥蛋脆弱。而全巢模擬結果中共包含10窩蛋巢，其中傷齒龍整巢的蛋足以共同負載親龍的體重，因此支持傷齒龍可行接觸孵蛋，；此外，因竊蛋龍具有特殊的巢體結構，親龍坐臥其中時獲得額外的地面支撐力，最終力學分析結果顯示竊蛋龍在孵育過程中並不會壓垮巢中任何蛋。

關鍵字

蛋殼 ； 無因次參數 ； 爬蟲蛋 ； 恐龍蛋 ； 接觸孵蛋

並列摘要

An extant avian egg may be regarded as a perfect design by nature. It has to meet contradictory demands: It has to be fragile enough to let the chick out, meanwhile, it has to be stiff enough to bear the load induced by its parents during contact-incubation. In a previous work of our research group on eggshells of over 100 avian species, a dimensionless number C (also called C number) was defined to quantify the shell relative stiffness across a wide range of egg sizes. The dimensionless number C was found to be largely constant among Neornithes. The present study applied the same method to analyze the eggshells of reptiles and dinosaurs.

Most previous studies on eggshell mechanics only focused on single species or taxa and were unable to quantify the numerical value of mechanical properties. As for the research of other biological materials, they usually discuss the relation between microstructure and mechanical properties. The species explored in this study span a variety of reptiles (including turtles, crocodiles, and geckos), and the dimensionless number C and Young’s modulus E are used to quantify the mechanical properties of eggshells. In addition, to discuss whether the chemical composition and microstructure affect the mechanical properties in eggshell, calcium carbonate content, SEM and EBSD images are included in this study. The result shows that the dimensionless number C of reptile eggs is on average higher than that of bird eggs, indicating that reptile eggs are stiffer concerning the egg size. However, Young’s modulus E is an invariant among reptiles and birds. In addition, the result of eggshell chemical composition shows a positive correlation between calcium carbonate content and Young's modulus E. And in the comparison results of the crystalline structure, the higher value of dimensionless number C is found in the aragonite with the smaller grain size. However, in the comparison of Young’s modulus E, there is no significant difference between both structures.

To study the mechanical properties of fossil dinosaur eggs, finite element analysis allowed us to create egg models among dinosaur groups. Besides, to simulate how the eggs deform and break under the contact-incubation scenario, we focused on the clutch specimens with relatively better preservation including troodontid and oviraptorid clutches. A total of 105 eggs from literature and museums were studied. The results show that the dimensionless number C of oviraptorosaurian eggs is lower than that of Neornithes, indicating that they are more fragile than avian eggs. The result from the ten whole clutch simulation supports the hypothesis that troodontid could do contact-incubation, because the troodontid clutch was sufficient to bear the body mass of parents. It also shows that oviraptorid would not break their eggs in the process of incubation due to their unique clutch architecture.

並列關鍵字

eggshell ； dimensionless number ； reptile egg ； dinosaur egg ； contact-incubation

參考文獻

Paganelli, C.V. (1980) The physics of gas exchange across the avian eggshell. American Zoologist. 20: 329-338.

Messens, W., Grijspeerdt, K., and Herman, L. (2005) Eggshell penetration by Salmonella: a review. World's Poultry Science Journal. 61: 71-86.

Graveland, J. and Drent, R. (1997) Calcium availability limits breeding success of passerines on poor soils. Journal of Animal Ecology. 66: 279-288.

Deeming, D.C. (2009) The role of egg turning during incubation. Avian Biology Research. 2: 67-71.

Tyler, G. and Geake, F. (1964) Egg shell strength and its relationship to thickness, with particular reference to individuality in the domestic hen. British Poultry Science. 5: 3-18.