Quantifying Patterns of Morphological Diversity The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Fritz, Joerg. 2013. Quantifying Patterns of Morphological Diversity. Doctoral dissertation, Harvard University. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:11181133 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Quantifying Patterns of Morphological Diversity a dissertation presented by Joerg Fritz to The School of Engineering and Applied Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Applied Mathematics Harvard University Cambridge, Massachusetts August 2013 © 2013 - Joerg Fritz All rights reserved. Thesis advisor: Michael Brenner Joerg Fritz Quantifying Patterns of Morphological Diversity Abstract One of the central questions of biology is how shape is formed by the interaction of gene expression, cell growth and differentiation. The canonical approach to this problem is the detailed study of all these basic processes in a small number of selected model species. In this study we will approach this question from a slightly different perspective, by investigating patterns of diversity in closely related organisms. Can we quantitatively understand these patterns of morphological diversity? In general, this question is even harder to answer than the classical problem described before. Closely related species share many aspects of their developmental program, which constrains the possible morphologies that can develop. In addition, the selective pressures on the morpholgies of closely related species might also be similar, creating an additional mechanism to create patterns of similarity. The relative importance of constraints due to a shared developmental program versus selection in determining patterns of morphology can strongly vary, further complicating matters. However the deemphasis of model species allows usto study asymptotic limits, that is systems where the pattern is nearly totally dominated by one of the above factors. We first investigate the shapes of songbird beaks, and uncover an intriguing pattern where the beak profiles of closely related birds are nearly perfectly approximated as conic sections. Based on this pattern of morphology we determine what features the underlying developmental mechanism of all species must share to produce exactly this pattern, but no other shapes. We uncover a strong constraint on the dynamics of the growth zone of dividing cells that initially shapes the beak in terms of power laws for its size and and movement. In the opposing limit we study a central element of the ascomycete spore shooting mechanism. Apical rings function as natural O-rings that seal of a pressure reservoir, while at the same time minimizing friction for ejected fungal spores. The trade-off between sealing and minimizing friction enforces a highly non-linear optimum ring shape. 90% of real apical ring geometries lie within 2% of this theoretical optimum. iii Contents 1 Introduction and Summary 1 1.1 Songbird beak morphologies . 2 1.2 Fungal Spore shooting apparatus . 3 1.3 The growth speed of lichens . 4 1.4 The interplay between selection and developmental constraints . 5 1.5 The role of boundary layers in shaping biological diversity . 7 1.6 Data analysis versus experiments . 7 2 The morphological diversity of bird beaks 9 2.1 Quantification of beak shape diversity . 11 2.2 Flexibility between shape and aspects of developmental program 17 2.3 Constraints on growth zone dynamics . 23 2.4 Experimental verification . 25 2.5 Summary . 30 3 Boundary layer escape and the ascomycete spore shooting mechanism 32 3.1 Crossing the boundary layer . 33 3.2 Morphological adaptions for boundary layer escape . 37 3.2.1 The spore ejection velocity Vspore ............ 37 3.2.2 The mass to drag ratio m=ξ ................ 38 3.2.3 Fruiting Body Shape L .................. 39 iv 3.3 Apical rings optimize spore dispersal . 42 3.3.1 Optimal lubrication layer thickness . 43 3.3.2 Elastic Deformation of Apical Ring . 45 3.3.3 The fluid layer thickness hƤ ................ 49 3.3.4 Optimality Criterion . 52 3.3.5 Numerical calculation of constants . 54 3.3.6 Testing the prediction with morphological data . 63 3.3.7 Summary . 68 4 The growth speed of crustose and foliose lichens 72 4.1 Diffusion of CO2 around lichen enforces upper limit for growth speed ............................... 74 4.2 Universal growth curve for lichens . 77 4.3 Direct lichen growth speed measurements . 81 4.4 Summary . 81 References 83 A Species List for Beak Shape Study 96 B Selection criteria for apical ring data 102 B.1 Search rules . 102 B.2 Selection Criteria and Measurements of Apical Ring Images . 103 B.3 Selection Criteria for Spore Dimension Measurements . 104 C Species list for apical ring study 105 C.1 Data for Species with Functional Apical Rings . 105 C.2 Data for Species with Non-functional Apical Rings . 110 D Pressure Volume Relation for Ascus 112 v Listing of figures 2.1.1 The phylogenetic structure of beak shapes. 13 2.1.2 The hierarchical collapse of beak shapes under scaling and shear. 15 2.1.3 The basic pattern of beak shape diversity. 16 2.1.4 Polynomial fits for beak shapes. 17 2.2.1 Tholospiza phylogeny and classification of beak shapes. 19 2.2.2 Flexibility of developmental mechanisms. 22 2.3.1 Prediction of growth zone shape and dynamics. 26 2.4.1 Measurement of the“growth zone” in the growing beak. 27 2.4.2 Experimental test of growth zone dynamics. 29 3.1.1 Boundary layer around a fungal sporocarp. 35 3.2.1 Morphological adaptions related to boundary layer escape. 40 3.2.2 Necessary ejection velocity for boundary layer escape. 41 3.3.1 Schematic of fungal spore shooting apparatus . 44 3.3.2 Apical rings before and after spore ejection . 46 3.3.3 Numerical results of elastohydrodynamic calculation . 53 3.3.4 Definition of Lagrangian coordinate system . 55 3.3.5 Final ejection speed as a function of F .............. 58 3.3.6 Contour map of ejection velocity as function of F and G ..... 59 3.3.7 Contour map of ejection velocity as function of F and C ..... 60 3.3.8 Phylogenetic tree highlighting analyzed species . 64 3.3.9 Examples for measured ring dimensions. 66 vi 3.3.10Comparison of theory and real morphological data . 67 3.3.11Data for species with non-functional apical rings . 70 4.1.1 Schematic of lichen growth and flow patterns. 75 4.2.1 Universal lichen growth curve and comparison with experiments. 79 4.2.2 Values of fitting parameters agree with experimental data. 80 A.0.1 Color table for group shapes of bird beaks . 101 C.1.1 Labeled plot for species with functional apical rings . 109 C.2.1 Labeled plot for species with non-functional apical rings . 110 D.0.1 Pressure volume relation for a fungal ascus. 115 vii To all who have either significantly aided or impeded the completion of this thesis. viii Acknowledgments Working on my research and this thesis over the last 4 years has been a great, but pretty often overwhelming, experience. Many of the most valuable things I’ve learned were not what I expected, and had nothing to do with math: working in a team, giving a coherent talk, staying up and working longer than I’ve ever done in my life, teaching more interactively, writing a well-structured paper or generally getting things done and not being perfectionist about everything (…okay, I’m still working on that one). I had a lot of help in all that from Michael Brenner, without a doubt one of the most intuitive, smart and supportive advisors anyone could hope for. During our first meeting he came up with more than 10 different projects on the spot while watching youtube videos about Cordyceps (seriously, google Cordyceps!); this probably counts as one of the most surreal experiences of my life. By now I know this was just par for the course, which probably makes it even more impressive, especially given that these random ideas make up most of my thesis. Thank you for your ideas, support and inspiration, and also for giving me the occasional push in the forward direction. Michael has also fostered the most open, collaborative and friendly research group I could imagine. Some of them have helped tremendously with the science in the thesis. But probably more importantly, many of them have become really good friends. My closest collaboration was with Agnese Seminara who shared my ix interest in mycology, taught me a lot about persistence, creating models, clarity when writing papers and the value of margaritas on Friday evenings. She was also the nucleus for our self-organizing group lunches, where I first met many others of this group. Another notable member of this group was Shreyas Mandre who was always around to give advice, bounce off ideas and teach me about fluid dynamics by not answering my questions. Shreyas and his wife, Radhika Kelkar, were also fantastic friends and neighbors in Peabody Terrace, were we spent many evenings chatting, laughing and cooking Indian food. Tobias Schneider made sure that I didn’t forget all my German, and that I went running at least occasionally. Watching the Ironman Hawaii on the projector in Pierce 306 with Tobias was a real highlight (and next time we do this, we’ll get work done on that day, I’m sure).