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This book contains recent research in mathematical and analytical studies on diatoms. These studies reflect the complex and intricate nature of the problems being analyzed and the need to use mathematics as an aid in finding solutions. Diatoms are important components of marine food webs, the silica and carbon cycles, primary productivity, and carbon sequestration. Their uniqueness as glass-encased unicells and their presence throughout geologic history exemplifies the need to better understand such organisms. Explicating the role of diatoms in the biological world is no more urgent than their role as environmental and climate indicators, and as such, is aided by the mathematical studies in this book.
The volume contains twelve original research papers as chapters. Macroevolutionary science topics covered are morphological analysis, morphospace analysis, adaptation, food web dynamics, origination-extinction and diversity, biogeography, life cycle dynamics, complexity, symmetry, and evolvability. Mathematics used in the chapters include stochastic and delay differential and partial differential equations, differential geometry, probability theory, ergodic theory, group theory, knot theory, statistical distributions, chaos theory, and combinatorics. Applied sciences used in the chapters include networks, machine learning, robotics, computer vision, image processing, pattern recognition, and dynamical systems. The volume covers a diverse range of mathematical treatments of topics in diatom research.
List of Figures xviii
List of Tables xxx
Preface xxxv
Acknowledgments xxxvii
Prologue -- Introductory Remarks xxxix
Part I: Morphological Measurement in Macroevolutionary Distribution Analysis 1
1. Diatom Bauplan, As Modified 2D Valve Face Shapes of a 3D Capped Cylinder and Valve Shape Distribution 3
2. Comparative Surface Analysis and Tracking Changes in Diatom Valve Face Morphology 39
3. Diatom Valve Morphology, Surface Gradients and Natural Classification 81
Part II: Macroevolutionary Systems Analysis of Diatoms 115
4. Probabilistic Diatom Adaptive Radiation in the Southern Ocean 117
5. Cenozoic Diatom Origination and Extinction and Influences on Diversity 159
6. Diatom Food Web Dynamics and Hydrodynamics Influences in the Arctic Ocean 199
Part III: General and Special Functions in Diatom Macroevolutionary Spaces 241
7. Diatom Clade Biogeography: Climate Influences, Phenotypic Integration and Endemism 243
8. Cell Division Timing and Mode of the Diatom Life Cycle 277
9. Diatom Morphospaces, Tree Spaces and Lineage Crown Groups 313
Part IV: Macroevolutionary Characteristics of Diatoms 355
10. Diatom Morphological Complexity Over Time as a Measurable Dynamical System 357
11. Diatom Surface Symmetry, Symmetry Groups and Symmetry Breaking 399
12. Evolvability of Diatoms as a Function of 3D Surface Phenotype 437
Epilogue -- Findings and the Future 475
Index 479
Janice L. Pappas has BA, BS, PhD degrees from the University of Michigan and an MA degree from Drake University. She is a theoretical and mathematical biologist and her work includes studies on diatoms and other organisms in morphometrics, morphogenesis, biological symmetry and complexity, evolutionary processes, and evolutionary ecology. Mathematics used in studies includes stochastic and delay differential and partial differential equations, orthogonal polynomials, differential geometry, probability theory, optimization theory, group theory, machine learning, information theory, and ergodic theory. Some specific studies include Morse theory and morphospace dynamics; fuzzy measures in systematics; vector spaces in ecological analysis; combinatorics and dynamical systems in macroevolutionary processes.
