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Mathematical Macroevolution in Diatom Research

By Janice L. Pappas
Series: Diatoms: Biology and Applications
Copyright: 2023   |   Status: Published
ISBN: 9781119750437  |  Hardcover  |  
527 pages | 173 illustrations
Price: $275 USD
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One Line Description
Buy this book to learn how to use mathematics in macroevolution research and apply mathematics to study complex biological problems.

Description
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.

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Author / Editor Details
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.

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Table of Contents
List of Figures
List of Tables
Preface
Acknowledgments
Prologue – Introductory Remarks
Part I: Morphological Measurement in Macroevolutionary Distribution Analysis
1. Diatom Bauplan, As Modified 2D Valve Face Shapes of a 3D Capped Cylinder
and Valve Shape Distribution
1.1 Introduction
1.1.1 Analytical Valve Shape Geometry
1.1.2 Valve Shape Constructs of Diatom Genera
1.2 Methods: A Test of Recurrent Diatom Valve Shapes
1.2.1 Legendre Polynomials, Hypergeometric Distribution, and Probabilities of Valve Shapes
1.2.2 Multivariate Hypergeometric Distribution of Diatom Valve Shapes as Recurrent Forms
1.3 Results
1.4 Discussion
1.4.1 Valve Shape Probability Distribution
1.4.2 Hypergeometric Functions and Other Shape Outline Methods
1.4.3 Application: Valve Shape Changes and Diversity during the Cenozoic
1.4.4 Diatom Valve Shape Distribution: Other Potential Studies
1.5 Summary and Future Research
1.6 Appendix
1.7 References
2. Comparative Surface Analysis and Tracking Changes in Diatom Valve Face Morphology
2.1 Introduction
2.1.1 Image Matching of Surface Features
2.1.2 Image Matching: Diatoms
2.2 Purpose of this Study
2.3 Background on Image and Surface Geometry
2.3.1 The Geometry of the Digital Image and the Jacobian
2.3.2 The Geometry of the Diatom 3D Surface Model and the Jacobian
2.3.3 The Image Gradient and Jacobian
2.4 Image Matching Kinematics via the Jacobian
2.4.1 Position and Motion: The Kinematics of Image Matching
2.4.2 Displacement and Implicit Functions
2.4.3 Displacement and Motion: Position and Orientation
2.4.4 Surface Feature Matching via the Jacobian
2.4.5 The Jacobian of Whole Surface Matching
2.5 Methods
2.5.1 Fiducial Outcomes of Image Matching of Surface Features
2.6 Results
2.6.1 Surface Feature Image Matching and the Jacobian
2.6.2 Whole Valve Images, Matching of Crest Lines and the Jacobian
2.6.3 Image Matching of more than Two Images
2.7 Discussion
2.7.1 Utility of Jacobian-Based Methods and Image Matching
2.7.2 The Image Jacobian and Rotation in A Reference Frame: Potential Application to Diatom Images
2.7.3 Deformation and Registration of Image Surfaces: An Alternative Jacobian Calculation
2.8 Summary and Future Research
2.9 References
3. Diatom Valve Morphology, Surface Gradients and Natural Classification
3.1 Introduction
3.2 Purposes of this Study
3.2.1 The Genus Navicula
3.3 Methods
3.3.1 Naviculoid Diatom Surface Analysis
3.3.2 Gradients of Digital Image Surfaces
3.3.3 Histogram of Oriented Gradients and Surface Representation
3.3.4 Application to Diatom Valve Face Digital Images
3.3.5 Support Vector Regression and Classification
3.3.6 Using HOG as Combination Gradient Magnitude and Direction Input Data for SVR
3.3.7 Computational Efficiency and Cost
3.4 Diatom Valve Surface Morphological Analysis
3.4.1 SVR Model Fit of Naviculoid Taxa
3.4.2 Valve Surface Morphological Classification and Regression of Naviculoid Diatoms
3.5 Results
3.5.1 HOG Data Analysis
3.5.2 Goodness-of-Fit SVR Model Using 4D HOG Data from Naviculoid LMs
3.5.3 SVR of Naviculoid 2D HOG Data
3.5.4 Second Round of SVR Analysis of Remaining Naviculoid 2D HOG Data
3.5.5 Last Round of SVR Analysis of Remaining Naviculoid 2D HOG Data
3.5.6 Classification Results from SVR Analysis of Naviculoid Taxa
3.6 Discussion
3.6.1 Characteristics of SVM and SVR
3.6.2 Advantages in Using HOG Data and SVR
3.6.3 Potential Utility of HOG Data and SVR in Diatom Research
3.7 Summary and Future Research
3.8 References
Part II: Macroevolutionary Systems Analysis of Diatoms
4. Probabilistic Diatom Adaptive Radiation in the Southern Ocean
4.1 Introduction
4.1.1 Diatoms in the SO
4.1.2 Chaetocerotales and Bacillariales Speciation Rates
4.1.3 Chaetocerotales and Bacillariales: Fe, NO3 and SiO2 Availability in the SO
4.1.4 Modeling Diatom Adaptive Radiation
4.2 Purposes of this Study
4.3 Mathematical Modeling of Adaptive Radiation
4.3.1 Quantitative Phenotypic Trait Measurement and Adaptive Radiation
4.3.2 Adaptive Radiation: Implicit Stochastic Models
4.3.3 Adaptive Radiation Models: Time Evolution of a Stochastic System
4.3.4 Adaptive Radiation as an Optimal Control Problem
4.3.5 Exit Probabilities as Boundaries for Completion of Adaptive Radiation
4.3.6 Exit Times for the Adaptive Radiation Process
4.3.7 Adaptive Radiation: A Study of Southern Ocean Diatoms and Niche Filling
4.4 Methods
4.4.1 Niche Filling and Adaptive Radiation
4.5 Results
4.5.1 Ecological Niche Preference, Photosynthesis Efficiency, Nutrient Enrichment or Limitation, and Adaptive Radiation
4.5.2 Ecological Niche Preference and Photosynthesis Efficiency Rankings Representing Niche Filling as Adaptive Radiation
4.5.3 Niche Filling and the Lyapunov modified OU Adaptive Radiation Model
4.6 Discussion
4.6.1 More on Specifications for Adaptive Radiation Modeling
4.6.2 Diatom Adaptive Radiation Short-Term Trends as a Result of Niche Filling in the SO
4.6.3 Other Potential Mathematical Modeling Regimes of Adaptive Radiation
4.7 Summary and Future Directions
4.7.1 Caveats in Adaptive Radiation Studies to be Considered
4.8 References
5. Cenozoic Diatom Origination and Extinction and Influences on Diversity
5.1 Introduction
5.1.1 Cenozoic Diatoms and Environmental Conditions
5.1.2 Diatom Diversity during the Cenozoic
5.1.3 Diversity as a Result of the Frequency of Origination and Extinction Events
5.2 Purposes of this Study
5.3 Methods and Background
5.3.1 Reconstructed Diatom Origination, Extinction and Diversity during the Cenozoic
5.3.2 Cumulative Functions and the Frequency of Cenozoic Origination and Extinction
5.3.3 Origination and Extinction: Heaviside Functions and Switching
5.3.4 Origination and Extinction as a Sequence of Steps and Accumulated Switches during the Cenozoic
5.3.5 Piecewise Continuous Switching via the Laplace Transform of the Heaviside Functions
5.3.6 Overlapping of Origination and Extinction: A Convolution Product
5.3.7 Non-Overlapping Origination and Extinction: A Poisson Process
5.3.8 Test of Switch Reversibility, Cenozoic Events and a Lyapunov Function
5.3.9 Origination and Extinction: Relation to Diversity
5.4 Results
5.4.1 Cumulative Frequency of Cenozoic Diatom Origination and Extinction Events
5.4.2 Switching from Diatom Origination to Extinction over the Cenozoic
5.4.3 Origination and Extinction Sequential Steps and Accumulated Switches during the Cenozoic
5.4.4 Overlapping via a Convolution Product of Origination and Extinction
5.4.5 Origination and Extinction as Poisson Processes
5.4.6 Test of Origination and Extinction Switches: Stochastic or Deterministic Chaos?
5.4.7 Diversity and Its Relation to Origination and Extinction for Cenozoic Diatoms
5.5 Discussion
5.5.1 Diversity and the Effects from Origination and Extinction of Cenozoic Diatoms
5.5.2 Cenozoic Events and Diatom Diversity, Origination and Extinction
5.5.3 Origination and Extinction Related to Diversity: Markov Chain, Martingale, Ergodic Processes, and Lyapunov Functions
5.6 Summary and Future Research
5.7 References
6. Diatom Food Web Dynamics and Hydrodynamics Influences in the Arctic Ocean
6.1 Introduction
6.2 Purposes of this Study
6.3 Background on Arctic Ocean Diatoms
6.3.1 Diatoms and their Relation to Sea Ice
6.3.2 Sea Ice, Upwelling and Diatom Productivity
6.3.3 Diatom Lipid Content as a Proxy for Biomass
6.3.4 Diatom Biomass and the Hydrodynamics of Upwelling
6.4 Lattice Boltzmann Model
6.5 Lattice Boltzmann Model and Hydrodynamics
6.5.1 Upwelling and Buoyancy
6.5.2 Collisions and Streaming Densities of Diatom Genera during Upwelling
6.5.3 Buoyancy and Ice
6.5.4 Upwelling and the Splitting of the Cylindrical Rotation of Currents
6.6 Lattice Boltzmann Model: Diatom Bloom Density, Sea Ice and Upwelling
6.7 Lattice Boltzmann Model: Specifications for Simulation
6.7.1 Overview of 2D LBM with Respect to Diatom Genera Lattice Nodes
6.7.2 Buoyancy, Upwelling and Diatom Blooms in LBM via ρ and u
6.8 Methods
6.9 Results
6.10 Discussion
6.10.1 Arctic Diatom Food Web Dynamics: Other Potential Outcomes
6.10.2 Diatom Blooms: Influences over Time and Space
6.11 Summary and Future Research
6.12 References
Part III: General and Special Functions in Diatom Macroevolutionary Spaces
7. Diatom Clade Biogeography: Climate Influences, Phenotypic Integration and Endemism
7.1 Introduction
7.1.1 Biogeography and Climate
7.1.2 Mapping Biogeographic Patterns
7.1.3 Biogeography as an Optimization Problem
7.1.4 Biogeographic Pattern and Spatial Rate of Change
7.1.5 Biogeography, Phenotypic Integration and Phenotypic Novelty
7.2 Purposes of this Study
7.3 Methods
7.3.1 Freshwater Diatom Dispersal Biogeography and the Traveling Salesman Problem
7.3.2 Freshwater Diatom Biogeographic Patterns with Respect to Climate
7.3.3 Diatom Biogeographic Patterns and Distance Decay
7.3.4 Endemism and Continental Area
7.3.5 Endemism and Dispersal Distance
7.3.6 Endemism, Phenotypic Integration and Phenotypic Novelty: The Raphe
7.4 Results
7.4.1 Clade Shortest Tours from Continent to Continent with Respect to Climate
7.4.2 Magnitude of Clade Tour Stops from Continent to Continent with Respect to Climate
7.4.3 Ecological Similarity, Biogeographical Distribution and Distance Decay
7.4.4 Biogeographical Distribution of Freshwater Diatom Genera
7.4.5 Endemics in each Clade and on each Continent
7.4.6 Phenotypic Integration and Relation to Geographic Distribution
7.5 Discussion
7.5.1 Freshwater Diatom Clade Dispersal and Climate
7.5.2 Distance Decay as the Pattern of Dispersal in Freshwater Diatom Biogeography
7.5.3 Phenotypic Integration and Diatom Biogeography
7.6 Summary and Future Research
7.7 References
8 Cell Division Timing and Mode of the Diatom Life Cycle
8.1 Introduction
8.1.1 Evolution of Diatom Cell Division Dynamics
8.1.2 Diatom Life Cycle as a Dynamical System
8.1.3 Diatom Cell Division and Growth Rate
8.1.4 Diatom Cell Size Diminution during Mitosis
8.1.5 Diatom Cell Division during Meiosis
8.1.6 Diatom Cell Division after Meiosis
8.2 Purposes of this Study
8.3 Background on the Diatom Cell Cycle
8.3.1 Diatom Life Cycle Timing: Stages
8.3.2 Diatom Life Cycle Timing: Switches
8.3.3 Diatom Life Cycle Timing: Cell Behavior
8.4 Modeling the Diatom Life Cycle: Timing of Stages and Switches
8.4.1 Delay Differential Equations
8.4.2 Solutions to DDEs
8.4.3 Mackey-Glass System of DDEs
8.4.4 Mackey-Glass System: Stage 1 of the Diatom Life Cycle
8.4.5 Mackey-Glass System: Stage 2 of the Diatom Life Cycle
8.4.6 Mackey-Glass System: Stages 3 and 4 of the Diatom Life Cycle
8.4.7 Mackey-Glass System: The Diatom Life Cycle Switches
8.5 Methods
8.6 Results
8.7 Discussion
8.7.1 Cell Size Control and the Diatom Cell Cycle Structure
8.7.2 Potential Alterations to the Mackey-Glass System when Applied to the Diatom Life Cycle
8.7.3 Mackey-Glass Systems: Utility and Applications
8.7.4 Potential Additional Analyses of Results from Mackey-Glass Systems
8.8 Summary and Future Research
8.9 References
9. Diatom Morphospaces, Tree Spaces and Lineage Crown Groups
9.1 Introduction
9.1.1 Euclidean Spaces are Subspaces of Hilbert and Banach Spaces
9.1.2 From Geometrical to Topological Spaces as Mathematical Morphospaces
9.2 Occupied and Unoccupied Morphospace
9.3 Purposes of this Study
9.4 Morphospace Structure and Dynamics
9.4.1 Morphospace Networks and All Possible Morphologies
9.4.2 Networks, Hierarchy and Morphospace
9.5 Phylogeny Structure and Phylogenetic Dynamics
9.5.1 Phylogenetic Trees and Mapped Traits
9.5.2 Phylogenetic Trees and the Geometry of Tree Spaces
9.6 Measuring Occupied Morphospace: Clustering Coefficients
9.7 A Brief Background on Diatom Morphospaces
9.8 Mathematical Morphospaces in the Context of a Diatom Phylogeny
9.9 Methods
9.9.1 Input Data for Morphospace Analysis
9.9.2 Diatom Lineage Crown Groups Embedded in a Metric Space
9.9.3 Diatom Submorphospaces Embedded in a Metric Morphospace
9.9.4 Clustering Coefficients as Measures of Occupied Morphospace
9.10 Results
9.11 Discussion
9.11.1 Trees, Networks and Morphospaces
9.11.2 Probabilistic Distances in Lineage Crown Group Morphospace
9.11.3 Diatom Novelties Versus Repetitive Forms in Occupied Morphospace
9.11.4 Diatom Teratologies and Mutagenicities: Influences on Morphology
9.11.5 Understanding Diatom Evolution via Morphospace and Phylogenetic Analyses
9.12 Summary and Future Research
9.12.1 What is Morphological Data?
9.12.2 Tempo and Mode of Phylomorphogenetic Spaces
9.13 References
Part IV: Macroevolutionary Characteristics of Diatoms
10. Diatom Morphological Complexity Over Time as a Measurable Dynamical System
10.1 Introduction
10.1.1 Complexity and Evolution
10.2 Diatom Morphological Complexity
10.3 Purposes of this Study
10.4 Characterizing Morphological Complexity
10.5 Information and Morphology
10.6 Information and Complexity
10.7 Markov Chains and their Properties
10.7.1 Markov Chains and Lyapunov Exponents
10.8 Ergodicity and Chaoticity
10.8.1 Entropy Rates
10.9 Kolmogorov Complexity and Entropy
10.10 Methods
10.10.1 Transition Probability Matrix and Properties of a Markov Chain
10.10.2 Measuring Morphological Kolmogorov Complexity
10.10.3 Diatom Morphological Complexity over Geologic Time and Comparison of Cretaceous and Cenozoic Taxa
10.11 Results
10.12 Discussion
10.13 Summary and Future Research
10.13.1 Is Morphological Complexity Related to Morphological Symmetry?
10.14 References
11. Diatom Surface Symmetry, Symmetry Groups and Symmetry Breaking
11.1 Introduction
11.1.1 Geometry as a Basis for Form, Surfaces and Symmetry
11.1.2 Inverse Functions as a Basis for Symmetry and Stability
11.2 Symmetry of 3D Organismal Surfaces
11.2.1 Shape versus Surface Symmetries
11.2.2 Geometry of Non-Flat 3D Surfaces: Bidirectional Curvature and Its Relation to Twists and Writhes
11.2.3 Knots: Geometry and Topology of Closed Curved Surfaces
11.2.4 From Hyperbolic Geometry and Surfaces to Hyperbolic Knots
11.2.5 Closed Helices, Hyperbolic Knots and Möbius Surfaces
11.3 Symmetry Groups
11.3.1 Diatom Surface Symmetry Groups: Cyclic, Reflective, Dihedral, Glide, Scale, and Knot
11.3.2 States of Symmetry
11.4 Purposes of this Study
11.5 Methods
11.5.1 Systems of Parametric 3D Equations for Exemplar Diatom Surface Models
11.5.2 Symmetry Groups: Cyclic, Reflective, Dihedral, Glide, Scale, and Knot
11.5.3 From Partial Derivatives to Ordinary Derivatives to Assess Stability
11.5.4 Inverse Jacobian Eigenvalues and Surface Symmetry Analysis
11.5.5 Stability and Inverse Jacobian Eigenvalues
11.5.6 Diatom Surface Symmetries and Symmetry Group Assessment
11.5.7 Vegetative Size Reduction and Symmetry Breaking
11.5.8 Relative Stability and Symmetry
11.5.9 Symmetry Gradients
11.6 Results
11.7 Discussion
11.7.1 Diatom Surface Symmetries and the Intricacies of Assessment
11.7.2 More on Diatom Surface Symmetries and Handedness
11.7.3 Diatom Vegetative Reproduction and Symmetry Breaking
11.7.4 Symmetry Breaking, Vegetative Reproduction, Size Reduction, and Stability
11.7.5 Eigenvalues and Variance: Instability and Fluctuating Asymmetry
11.7.6 Symmetry Groups and Evolutionary Dynamics: Symmetry in Diatoms and Adaptation
11.8 Summary and Future Research
11.9 References
12. Evolvability of Diatoms as a Function of 3D Surface Phenotype
12.1 Introduction
12.1.1 3D Surface Properties – An Overview
12.1.2 From Differential Geometry to the Characterization of 3D Surfaces
12.1.3 The Phenotype Characterized via a 3D Surface and Its Geometric Characteristics
12.1.4 From Geometric Phenotype to Evolvability
12.1.5 Evolvability and Phenotypic Novelty
12.1.6 Evolvability and Diatoms
12.1.7 Diatom Exemplar Phenotypic and Valve Plication Characteristics
12.1.8 Diatom Architecture and the Geometric Phenotype
12.2 Purposes of this Study
12.3 Methods
12.3.1 Phenotypic Inertia
12.3.1.1 Measurement of Phenotypic Inertia: Christoffel Symbols
12.3.2 Phenotypic Robustness
12.3.2.1 Measurement of Phenotypic Robustness: the Hessian
12.3.3 Phenotypic Stability
12.3.3.1 Measurement of Phenotypic Stability: the Laplacian
12.3.4 Evolvability of each Diatom Genus: Actinoptychus, Arachnoidiscus and Cyclotella
12.3.5 Evolvability Among Diatom Genera
12.3.6 Contribution of Phenotypic Inertia, Robustness and Stability to Evolvability
12.3.7 Phenotypic Novelty Measurement
12.3.8 Evolvability and Phenotypic Novelty
12.4 Results
12.4.1 Phenotypic Inertia, Robustness and Stability
12.4.2 Evolvability across Genera
12.4.3 Evolvability and the Fitness Function Components of Phenotypic Inertia, Robustness and Stability
12.4.4 Phenotypic Novelty and Comparison to Evolvability
12.5 Discussion
12.6 Summary and Future Research
12.7 References
Epilogue – Findings and the Future
Index
FINAL

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