Mathematical Macroevolution in Diatom Research

MATHEMATICAL MACROEVOLUTION IN DIATOM RESEARCH
 
Buy this book to learn how to use mathematics in macroevolution research and apply mathematics to study complex biological problems.
 
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.
 
Audience
 
Diatom researchers, mathematical biologists, evolutionary and macroevolutionary biologists, paleontologists, paleobiologists, theoretical biologists, as well as researchers in applied mathematics, algorithm sciences, complex systems science, computational sciences, informatics, computer vision and image processing sciences, nanoscience, the biofuels industry, and applied engineering.

List of contents

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
 
1.1 Introduction 3
 
1.1.1 Analytical Valve Shape Geometry 5
 
1.1.2 Valve Shape Constructs of Diatom Genera 8
 
1.2 Methods: A Test of Recurrent Diatom Valve Shapes 10
 
1.2.1 Legendre Polynomials, Hypergeometric Distribution, and Probabilities of Valve Shapes 12
 
1.2.2 Multivariate Hypergeometric Distribution of Diatom Valve Shapes as Recurrent Forms 15
 
1.3 Results 18
 
1.4 Discussion 22
 
1.4.1 Valve Shape Probability Distribution 22
 
1.4.2 Hypergeometric Functions and Other Shape Outline Methods 22
 
1.4.3 Application: Valve Shape Changes and Diversity during the Cenozoic 25
 
1.4.4 Diatom Valve Shape Distribution: Other Potential Studies 25
 
1.5 Summary and Future Research 26
 
1.6 Appendix 26
 
1.7 References 34
 
2 Comparative Surface Analysis and Tracking Changes in Diatom Valve Face Morphology 39
 
2.1 Introduction 39
 
2.1.1 Image Matching of Surface Features 40
 
2.1.2 Image Matching: Diatoms 41
 
2.2 Purpose of this Study 42
 
2.3 Background on Image and Surface Geometry 42
 
2.3.1 The Geometry of the Digital Image and the Jacobian 42
 
2.3.2 The Geometry of the Diatom 3D Surface Model and the Jacobian 45
 
2.3.3 The Image Gradient and Jacobian 46
 
2.4 Image Matching Kinematics via the Jacobian 47
 
2.4.1 Position and Motion: The Kinematics of Image Matching 47
 
2.4.2 Displacement and Implicit Functions 48
 
2.4.3 Displacement and Motion: Position and Orientation 49
 
2.4.4 Surface Feature Matching via the Jacobian 50
 
2.4.5 The Jacobian of Whole Surface Matching 52
 
2.5 Methods 53
 
2.5.1 Fiducial Outcomes of Image Matching of Surface Features 53
 
2.6 Results 54
 
2.6.1 Surface Feature Image Matching and the Jacobian 56
 
2.6.2 Whole Valve Images, Matching of Crest Lines and the Jacobian 60
 
2.6.3 Image Matching of more than Two Images 65
 
2.7 Discussion 71
 
2.7.1 Utility of Jacobian-Based Methods and Image Matching 72
 
2.7.2 The Image Jacobian and Rotation in A Reference Frame: Potential Application to Diatom Images 73
 
2.7.3 Deformation and Registration of Image Surfaces: An Alternative Jacobian Calculation 75
 
2.8 Summary and Future Research 77
 
2.9 References 77
 
3 Diatom Valve Morphology, Surface Gradients and Natural Classification 81
 
3.1 Introduction 81
 
3.2 Purposes of this Study 82
 
3.2.1 The Genus Navicula 83
 
3.3 Methods 84
 
3.3.1 Naviculoid Diatom Surface Analysis 84
 
3.3.2 Gradients of Digital Image Surfaces 84
 
3.3.3 Histogram of Oriented Gradients and Surface Representation 89
 
3.3.4 Application to Diatom Valve Face Digital Images 90
 
3.3.5 Support Vector Regression and Classification 90
 
3.3.6 Using HOG as Combination Gradient Magnitude and Direction Input Data for SVR 91
 
3.3.7 Computational Efficiency and Cost 95
 
3.4 Diatom Valve Surface Morphological Analysis 95
 
3.4.1 SVR Model Fit of Naviculoid Taxa 95
 
3.4.2 Valve Surface Morphological Classification and Regression of Naviculoid Diatoms 96
 
3.5 Results 96
 
3.5.1 HOG Data Analysis 96
 
3

About the author

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.

Summary

MATHEMATICAL MACROEVOLUTION IN DIATOM RESEARCH

Buy this book to learn how to use mathematics in macroevolution research and apply mathematics to study complex biological problems.

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.

Audience

Diatom researchers, mathematical biologists, evolutionary and macroevolutionary biologists, paleontologists, paleobiologists, theoretical biologists, as well as researchers in applied mathematics, algorithm sciences, complex systems science, computational sciences, informatics, computer vision and image processing sciences, nanoscience, the biofuels industry, and applied engineering.

Product details

• Authors: Drake U, Richard Gordon, Pappas, Janice L Pappas, Janice L. Pappas, Janice L. (University of Michigan Pappas, Janice L. Gordon Pappas
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 31.12.2021
• EAN: 9781119749851
• ISBN: 978-1-119-74985-1
• No. of pages: 544
• Series: Diatoms: Biology and Applications
• Subjects: Natural sciences, medicine, IT, technology > Biology > General, dictionaries; Ökologie, Life Sciences, Biowissenschaften, Kieselalgen, Phycology, Algenkunde, Ecology & Organismal Biology, Ökologie u. Biologie der Organismen, Diatomeen, Ökologie / Salzwasser, Marine Ecology