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El. knyga: Integrated Population Biology and Modeling, Part A

Volume editor (Professor, Medical College of Georgia, USA), Volume editor (University of Hyderabad Campus, India)
  • Formatas: PDF+DRM
  • Serija: Handbook of Statistics
  • Išleidimo metai: 26-Sep-2018
  • Leidėjas: North-Holland
  • Kalba: eng
  • ISBN-13: 9780444640734
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  • Formatas: PDF+DRM
  • Serija: Handbook of Statistics
  • Išleidimo metai: 26-Sep-2018
  • Leidėjas: North-Holland
  • Kalba: eng
  • ISBN-13: 9780444640734
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Integrated Population Biology and Modeling: Part A offers very complex and precise realities of quantifying modern and traditional methods of understanding populations and population dynamics. Chapters cover emerging topics of note, including Longevity dynamics, Modeling human-environment interactions, Survival Probabilities from 5-Year Cumulative Life Table Survival Ratios (Tx+5/Tx): Some Innovative Methodological Investigations, Cell migration Models, Evolutionary Dynamics of Cancer Cells, an Integrated approach for modeling of coastal lagoons: A case for Chilka Lake, India, Population and metapopulation dynamics, Mortality analysis: measures and models, Stationary Population Models, Are there biological and social limits to human longevity , Probability models in biology, Stochastic Models in Population Biology, and more.

  • Covers emerging topics of note in the subject matter
  • Presents chapters on Longevity dynamics, Modeling human-environment interactions, Survival Probabilities from 5-Year Cumulative Life Table Survival Ratios (Tx+5/Tx), and more
Contributors xv
Preface xvii
Section I Cellular Population Dynamics
1 Population Dynamics and Evolution of Cancer Cells
3(34)
Ignacio A. Rodriguez-Brenes
Dominik Wodarz
1 Introduction
3(3)
2 Evolutionary Dynamics of Escape From Tissue Homeostasis
6(6)
2.1 Mathematical Models of Tissue Homeostasis
6(2)
2.2 Evolutionary Dynamics of Feedback Escape
8(2)
2.3 Feedback, Stem Cell Enrichment, and Drug Resistance
10(2)
3 Telomeres and the Evolutionary Potential of Cells
12(7)
3.1 Replicative Limits and Cellular Hierarchy
12(3)
3.2 Replicative Limits and Precancerous Mutations
15(2)
3.3 Replicative Limits in a Growing Cell Population
17(2)
4 Dynamics of Therapy Responses and Resistance Evolution
19(9)
4.1 Dynamics Underlying Chemoprevention With Aspirin
24(4)
5 Conclusions
28(1)
References
28(9)
2 Stochastic and Deterministic Modeling of Cell Migration
37(56)
Enrico Gavagnin
Christian A. Yates
1 Introduction
38(4)
2 Cell Motility
42(20)
2.1 Connecting Stochastic and Deterministic Models of Cell Movement
42(15)
2.2 Higher Dimensions
57(2)
2.3 Higher Order Closure Approximations
59(3)
3 Model Extensions
62(23)
3.1 Cell Proliferation
63(5)
3.2 Cell Interactions
68(9)
3.3 Crowing Domains
77(5)
3.4 Persistence of Motion
82(3)
4 Conclusion
85(1)
References
86(7)
3 Data-Driven Mathematical Modeling of Microbial Community Dynamics
93(38)
Shinji Nakaoka
1 Introduction
93(1)
2 Microbial Community Profiling
94(2)
3 Mechanistic Modeling Approach
96(14)
3.1 Derivation of Specific LV Systems
98(2)
3.2 Generalized Lotka--Volterra Equations
100(2)
3.3 Data Fitting
102(8)
4 Data-Driven Approach
110(16)
4.1 Attractor Reconstruction From Time-Series Data
112(14)
5 Conclusion
126(2)
Acknowledgments
128(1)
References
128(3)
4 Reaction--Diffusion Kinetics in Growing Domains
131(24)
Carlos Escudero
Santos Bravo Yuste
Enrique Abad
Felipe Le Vot
1 Introduction
132(1)
2 Diffusion on a Uniformly Growing Domain
133(8)
2.1 Langevin Equation
133(2)
2.2 Fokker--Planck Equation
135(6)
3 Encounter-Controlled Annihilation: Mean-Field Theory
141(3)
4 Exact Solution for Encounter-Controlled Annihilation
144(4)
5 Conclusions and Outlook
148(1)
Acknowledgments
149(1)
References
150(5)
Section II Insect Experiments to Human Demographic Theories
5 The Life Table Population Identity: Discovery, Formulations, Proof, Extensions, and Applications
155(32)
James R. Carey
Sarah Silverman
Ami S.R. Srinivasa Rao
1 Introduction
155(1)
2 Brouard's Theorem
156(2)
2.1 Background
157(1)
2.2 Equality of Life-Lived and Life-Left Pyramids
157(1)
3 Discovery of Carey's Equality
158(9)
3.1 Background and Motivation
158(2)
3.2 Framing the Concept
160(1)
3.3 Simulation Studies
160(2)
3.4 Construction of a Heuristic Life Table
162(2)
3.5 Visualization
164(3)
4 Formulations
167(2)
4.1 Model 1: Equality of Age Structure and Death Distribution
167(1)
4.2 Model 2: Theorem of Life Lived and Life Left
167(2)
5 A Proof
169(1)
6 Extensions
170(4)
6.1 Death Cohort Equal Birth Cohort
170(2)
6.2 Equality in Stable Populations
172(1)
6.3 Nonstationary/Nonstable Populations
173(1)
7 Applications: Residual Demography in Medfly Populations
174(6)
7.1 Medfly Population Seasonal Trends in Mean Age
175(4)
7.2 Age-Structure Estimation
179(1)
8 Relevance and Implications for Future Studies
180(3)
8.1 Human Evolution
181(1)
8.2 Historical Demography
181(1)
8.3 Demographic Principles
182(1)
8.4 Replacement-Level Populations in the 21st Century
182(1)
8.5 Future world
183(1)
9 Conclusions
183(1)
Acknowledgments
183(1)
References
183(4)
6 Stochastic Modeling of Some Natural Phenomena: A Special Reference to Human Fertility
187(88)
Ram Chandra Yadava
1 Introduction
187(4)
1.1 Model Building
190(1)
1.2 The Qualities of a Model Builder
190(1)
1.3 Uses of Mathematical Models
191(1)
2 Models Based on Bernoulli Trials
191(27)
2.1 Bernoulli Trials and Related Distributions
191(1)
2.2 Binomial Distribution
192(1)
2.3 Geometric Distribution
192(1)
2.4 Negative Binomial Distribution
193(1)
2.5 Applications of Binomial, Geometric, and Negative Binomial Distributions in Human Reproduction Process
194(3)
2.6 Some Extended Distributions
197(7)
2.7 Stopping Rule and Sex Ratio at Birth
204(1)
2.8 Binomial Distribution as a Number of Male Births out of n Births: A Caution
205(3)
2.9 Sex Ratio at Birth Under Sex-Selective Abortions
208(3)
2.10 A Modified Form of Binomial Distribution
211(4)
2.11 A Probability Model for Time of First Conception/Birth
215(1)
2.12 Time Between Consecutive Births (Interlive Birth Interval or Closed Birth Interval)
216(1)
2.13 A Probability Model for Number of Births for Migrated Couples
217(1)
3 Poisson, Exponential, and Gamma Distributions as Continuous Analog of Binomial, Geometric, and Negative-Binomial Distributions
218(10)
3.1 Poisson Distribution
218(3)
3.2 An Alternative Way for Finding pk(t): The Use of Gamma Distribution
221(1)
3.3 A Probability Model for Number of Complete Conceptions in Time Interval (0, T)
222(2)
3.4 Exponential Distribution as Continuous Analog of Geometric Distribution
224(1)
3.5 A Probability Model for Time of First Birth
224(1)
3.6 A Probability Model for Time of First Birth Accounting for Adolescent Sterility
225(1)
3.7 Menstruating Interval Under Nonuse of Contraception
225(3)
4 A Parity-Dependent Model for Number of Births and Its Application
228(12)
5 Equilibrium Birth Process
240(9)
6 Distribution Function and Its Use in Computation of Certain Parameters
249(3)
7 Use of [ 1 --- F(x)] in Computation of Certain Parameters of Interest
252(12)
7.1 Prevalence/Incidence Mean
252(2)
7.2 Estimation of Mean PPA Using Prevalence/Incidence Method
254(1)
7.3 Application for Computation of Mean Duration of Breastfeeding
255(1)
7.4 Estimation of Parity Progression Ratios and IPPR From Open and Closed Birth Interval Data
255(9)
8 Use of Mathematical Models: Some Examples
264(9)
8.1 Better Understanding
264(1)
8.2 Getting Estimates of Parameters
265(1)
8.3 Testing Adequacy of Model
265(2)
8.4 Impact of Alternations in Parameters
267(1)
8.5 Explaining Apparent Inconsistencies
267(6)
Acknowledgments
273(1)
References
273(1)
Further Reading
274(1)
7 Two Decades of Drosophila Population Dynamics: Modeling, Experiments, and Implications
275(40)
Sutirth Dey
Amitabh Joshi
1 Introduction
276(3)
2 The Laboratory Ecology of Drosophila
279(1)
3 The Drosophila Model: The Importance of Larval and Adult Food Levels
280(2)
4 Larval vs Adult Food Levels and the Dynamics of Small Drosophila Populations
282(2)
5 Effects of Immigration on Small Population Constancy and Persistence
284(2)
6 Synchrony and Asynchrony in Metapopulations
286(6)
7 Stabilizing Small Populations
292(5)
7.1 Stabilizing Spatially Unstructured Populations
293(3)
7.2 Stabilizing Spatially Structured Populations
296(1)
8 The Devil in the Details
297(1)
9 Life History, Competitive Ability, and the Evolution of Population Stability
298(6)
10 Conclusions
304(11)
Acknowledgments 306(1)
References 306(309)
Section III Complex Environmental and Biogeochemical Dynamics
8 The Environmental Kuznets Curve Fails in a Globalized Socio-Ecological Metapopulation: A Sustainability Game Theory Approach
315(28)
Tamer Oraby
Chris T. Bauch
Madhur Anand
1 Introduction
316(3)
2 Methods
319(8)
2.1 Game Description
319(6)
2.2 Ecosystem Services Impacts and the Cost of Abatement
325(2)
2.3 Nash Equilibrium
327(1)
3 Results
327(8)
3.1 Intrinsic Problem
327(3)
3.2 Extrinsic Problem
330(1)
3.3 Intrinsic--Extrinsic Problem
330(3)
3.4 Sensitivity Analysis
333(2)
4 Discussion
335(1)
5 Conclusion
336(1)
References
336(7)
9 Integrated Approach for Modeling Coastal Lagoons: A Case for Chilka Lake, India
343(62)
S.R.V. Prasad Bhuvanagiri
Srinivasu Pichika
Raman Akkur
Kalavati Chaganti
Rakhesh Madhusoodhanan
Sarada Varma Pusapati
1 Introduction
344(1)
2 Study Area
345(2)
3 Sampling Methods and Analysis
347(13)
3.1 Sampling Methods
347(1)
3.2 Salinity Measurements and Local Weather Data
347(1)
3.3 Data Analysis
348(1)
3.4 Hydrobiology
348(12)
4 Ecosystem Modeling
360(1)
5 3D Description of Chilka Lagoon
361(20)
5.1 The Algorithm
363(1)
5.2 Algorithm Implementation
363(3)
5.3 Inferences From 3D Visualization
366(2)
5.4 Hydro-Environmental Findings
368(4)
5.5 Water and Salt Budgets for Chilka
372(9)
6 Dissolved Oxygen Dynamics
381(14)
6.1 Abstract Mathematical Model for DO Dynamics
384(1)
6.2 Development of Biogeochemical Model for DO in Lake Chilka
385(6)
6.3 Sensitivity Analysis
391(1)
6.4 Model Calibration and Validation
392(1)
6.5 Influence of Individual Plankton Groups on the DO Dynamics
393(2)
7 Conclusions
395(1)
Acknowledgments
396(1)
References
396(4)
Further Reading
400(5)
Section IV Measures of Mortality and Stochastics
10 Measures and Models of Mortality
405(38)
Vladimir Canudas-Romo
Stefano Mazzuco
Lucia Zanotto
1 Mortality Measures
405(11)
1.1 Life Tables
406(1)
1.2 Life Expectancy: Period vs Cohort
407(3)
1.3 Period-Cohort Measures: CAL and TCAL
410(3)
1.4 Mean, Median, Modal, and Maximum Ages at Death
413(1)
1.5 Variability of Age at Death
414(2)
2 Mortality Models
416(18)
2.1 Gompertz
417(3)
2.2 Gamma-Gompertz
420(3)
2.3 Logistic
423(2)
2.4 (Generalized) Extreme-Value
425(2)
2.5 Siler
427(2)
2.6 Mixture
429(4)
2.7 Heligman--Pollard Model
433(1)
3 Estimation Methods
434(6)
References
440(3)
11 Stochastic Population Models
443(38)
John Fricks
Ephraim Hanks
1 Introduction
443(2)
2 Markov Population Models
445(16)
2.1 Definition and Representations
445(9)
2.2 Numerical Methods and Large-Sample Approximations
454(7)
3 Inference for Well-Mixed Population Processes
461(5)
3.1 Inference for Directly Observed Population Processes
461(1)
3.2 Inference for Discrete-Time Observations With Measurement Error
462(1)
3.3 Example: Simulated Birth--Death Process
463(3)
4 Spatial Population Processes
466(11)
4.1 Large-N Limits of Spatial Birth--Death Processes
468(1)
4.2 Spatial Diffusion From Spatial Birth--Death Processes
469(2)
4.3 Inference on Spatial Birth Death Process Parameters
471(2)
4.4 Example: Simulated Spatial Population Process
473(4)
5 Conclusions
477(1)
References
478(3)
12 Survival Probabilities From 5-Year Cumulative Life Table Survival Ratios (Tx+5/Tx): Some Innovative Methodological Investigations
481(64)
Subrata Lahiri
1 Introduction
482(18)
1.1 Some Preliminary Concepts and Definitions
482(1)
1.2 Types of Life Table
483(1)
1.3 Needs, Importance, and Uses of Life Tables
484(6)
1.4 Life Table Based on Age-Return Only
490(7)
1.5 Old-Age Mortality
497(2)
1.6 Mortality Models
499(1)
1.7 Recent Contributions of Arni S. R. Srinivasa Rao and James R. Carey on Stationary Population and Other Related Issues
500(1)
2 A New Methodology for Life Table Construction at Ages 5 and Above From 5-Year Cumulative Life Table Survival Ratios (Tx+5/Tx) by Lahiri
500(19)
2.1 Introduction
500(2)
2.2 Methodology: Analytical Approaches
502(17)
3 Summary and Conclusions
519(3)
3.1 Some Specific Observations and Direction for Future Research
521(1)
Acknowledgments
522(1)
Appendix A Analytical Justification for the Algebraic Chain Relationship (Formula 3 or 4 in the Text) Between the Two Consecutive spx's Under Conventional Approximation for 5LX From lx
522(1)
Appendix B Some Issues Related to the Fixation of T(i)w and Invariant Properties of 5S(i)(w--5)+, 5E(i)w--5, and 5p(i)w--5 Over Iterations Under Approach-II for Life Table Construction
523(1)
Invariant Properties of 5S(i)(w--5)+, 5E(i)w--5, and 5p(i)w--5 Over Iterations
524(1)
Appendix C Mathematical Proof of Convergence of the Iterative Procedure for Constructing Adult Abridged Mortality or Life Table From Cumulative Life Table Survival Ratios
525(6)
Appendix D Tabular Calculations
531(8)
Main Text References
539(3)
Suggested Reading
542(3)
Section V Human Inequality Measures and Well Being
13 Methods of Measuring Human Well-being and Human Development
545(32)
Udoy Saikia
Gouranga Dasvarma
James Chalmers
1 Aims and Purpose
546(1)
2 Identifying the Statistical Problem
546(1)
3 Recent Developments in the Search for Innovations
547(1)
4 Unsupported Assumptions About the Existing Metric
548(1)
5 The Linkage of Process Data With Subjectivity
548(1)
6 Innovations in the Human Development Index System
549(2)
7 Subjective/Processual Breakthrough in the GNH System
551(1)
8 Introduction to Flinders University Innovation
552(1)
9 Quantifying Human Development: The Case of Timor-Leste 2016-17
553(1)
10 Calculation of HDI and GDI
554(1)
10.1 Data and Methods
554(1)
11 Calculation of HDI and GDI and Their Components for the Total Population
555(9)
11.1 Components of HDI
555(7)
11.2 HDI and Gender Development Index for the Youth (Population Aged 15-34 Years)
562(2)
12 Gender Development Index for the Youth
564(1)
13 Quantifying Human Well-being: The Case of Assam Well-being Survey 2015
565(1)
14 What Would a Well-being Index Do?
566(1)
15 How Is "Well-being" Defined in a Well-being Index?
566(1)
16 The Dimensions of Well-being Are Interconnected
567(1)
17 Key Steps in Preparing a Well-being Index
567(1)
18 Measuring Human Well-being in Assam, India
568(3)
19 What Are the Main Uses of a Well-being Index?
571(1)
Appendix: Methodology of Measuring Subjective Well-being
571(3)
References
574(1)
Further Reading
575(2)
14 A Bio-Demographic Perspective on Inequality and Life Expectancy: An Analysis of 159 Countries for the Periods 1970-90 and 1990-2010
577(38)
David A. Swanson
Lucky M. Tedrow
1 Introduction
578(3)
2 Data and Methods
581(3)
3 Results
584(3)
3.1 Changes in Life Expectancy and Differences Among the SES Quartiles
584(3)
3.2 Changes in SES
587(1)
4 Discussion
587(4)
5 Concluding Remarks
591(2)
Appendix
593(18)
References
611(2)
Further Reading
613(2)
Index 615
Arni S.R. Srinivasa Rao works in pure mathematics, applied mathematics, probability, and artificial intelligence and applications in medicine. He is a Professor at the Medical College of Georgia, Augusta University, U.S.A, and the Director of the Laboratory for Theory and Mathematical Modeling housed within the Division of Infectious Diseases, Medical College of Georgia, Augusta, U.S.A. Previously, Dr. Rao conducted research and/or taught at Mathematical Institute, University of Oxford (2003, 2005-07), Indian Statistical Institute (1998-2002, 2006-2012), Indian Institute of Science (2002-04), University of Guelph (2004-06). Until 2012, Dr. Rao held a permanent faculty position at the Indian Statistical Institute. He has won the Heiwa-Nakajima Award (Japan) and Fast Track Young Scientists Fellowship in Mathematical Sciences (DST, New Delhi). Dr. Rao also proved a major theorem in stationary population models, such as, Rao's Partition Theorem in Populations, Rao-Carey Theorem in stationary populations, and developed mathematical modeling-based policies for the spread of diseases like HIV, H5N1, COVID-19, etc. He developed a new set of network models for understanding avian pathogen biology on grid graphs (these were called chicken walk models), AI Models for COVID-19 and received wide coverage in the science media. Recently, he developed concepts such as Exact Deep Learning Machines”, and Multilevel Contours” within a bundle of Complex Number Planes.

book Ancient Inhabitants of Jebel Moya” published by the Cambridge Press under the joint authorship of Rao and two anthropologists. On the basis of work done at CU during the two year period, 1946-1948, Rao earned a Ph.D. degree and a few years later Sc.D. degree of CU and the rare honor of life fellowship of Kings College, Cambridge.

He retired from ISI in 1980 at the mandatory age of 60 after working for 40 years during which period he developed ISI as an international center for statistical education and research. He also took an active part in establishing state statistical bureaus to collect local statistics and transmitting them to Central Statistical Organization in New Delhi. Rao played a pivitol role in launching undergraduate and postgraduate courses at ISI. He is the author of 475 research publications and several breakthrough papers contributing to statistical theory and methodology for applications to problems in all areas of human endeavor. There are a number of classical statistical terms named after him, the most popular of which are Cramer-Rao inequality, Rao-Blackwellization, Raos Orthogonal arrays used in quality control, Raos score test, Raos Quadratic Entropy used in ecological work, Raos metric and distance which are incorporated in most statistical books.

He is the author of 10 books, of which two important books are, Linear Statistical Inference which is translated into German, Russian, Czec, Polish and Japanese languages,and Statistics and Truth which is translated into, French, German, Japanese, Mainland Chinese, Taiwan Chinese, Turkish and Korean languages.

He directed the research work of 50 students for the Ph.D. degrees who in turn produced 500 Ph.D.s. Rao received 38 hon. Doctorate degree from universities in 19 countries spanning 6 continents. He received the highest awards in statistics in USA,UK and India: National Medal of Science awarded by the president of USA, Indian National Medal of Science awarded by the Prime Minister of India and the Guy Medal in Gold awarded by the Royal Statistical Society, UK. Rao was a recipient of the first batch of Bhatnagar awards in 1959 for mathematical sciences and and numerous medals in India and abroad from Science Academies. He is a Fellow of Royal Society (FRS),UK, and member of National Academy of Sciences, USA, Lithuania and Europe. In his honor a research Institute named as CRRAO ADVANCED INSTITUTE OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE was established in the campus of Hyderabad University.