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El. knyga: Integrated Population Biology and Modeling Part B

Volume editor (University of Hyderabad Campus, India), Volume editor (Professor, Medical College of Georgia, USA)
  • Formatas: EPUB+DRM
  • Serija: Handbook of Statistics
  • Išleidimo metai: 05-Feb-2019
  • Leidėjas: North-Holland
  • Kalba: eng
  • ISBN-13: 9780444641533
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  • Formatas: EPUB+DRM
  • Serija: Handbook of Statistics
  • Išleidimo metai: 05-Feb-2019
  • Leidėjas: North-Holland
  • Kalba: eng
  • ISBN-13: 9780444641533
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Integrated Population Biology and Modeling: Part B, Volume 40 offers very delicately complex and precise realities of quantifying modern and traditional methods of understanding populations and population dynamics, with this updated release focusing on Prey-predator animal models, Back projections, Evolutionary Biology computations, Population biology of collective behavior and bio patchiness, Collective behavior, Population biology through data science, Mathematical modeling of multi-species mutualism: new insights, remaining challenges and applications to ecology, Population Dynamics of Manipur, Stochastic Processes and Population Dynamics Models: The Mechanisms for Extinction, Persistence and Resonance, Theories of Stationary Populations and association with life lived and life left, and more.

  • Studies human and animal models that are studied both separately and throughout chapters
  • Presents a comprehensive and timely update on integrated population biology
Contributors xiii
Preface xv
Section VI Agent Based Models, Capture-Recapture Methods and Multi-Species Mutualism
1 An Agent-Based Model of the Spatial Distribution and Density of the Santa Cruz Island Fox
3(30)
Shelby M. Scott
Casey E. Middleton
Erin N. Bodine
1 Introduction
4(3)
2 Incorporating GIS Data into an ABM
7(4)
2.1 GIS Data Types
7(2)
2.2 Projections and Coordinate Systems for GIS Data
9(2)
3 Model Description
11(12)
3.1 Overview
11(2)
3.2 Design Concepts
13(4)
3.3 Details
17(6)
4 Results
23(6)
4.1 Results of Model Analysis Without Golden Eagle Predation
23(3)
4.2 Model Results with Golden Eagle Predation
26(3)
5 Conclusions and Discussion
29(1)
Acknowledgments
30(1)
Appendix
30(1)
Supplemental Resources
30(1)
References
30(3)
2 Capture-Recapture Methods and Models: Estimating Population Size
33(52)
Ruth King
Rachel McCrea
1 Introduction
33(3)
2 Closed Population Capture-Recapture Studies
36(15)
2.1 Simple Beginnings: Lincoln-Petersen Estimator
36(4)
2.2 Multiple Capture Occasions
40(11)
3 Heterogeneity
51(23)
3.1 Unobserved Heterogeneity
53(4)
3.2 Observed (Time-Invariant) Heterogeneity
57(6)
3.3 Time-Varying Observed Individual Heterogeneity
63(11)
4 Open Populations
74(3)
5 Discussion
77(3)
References
80(5)
3 Mathematical Modeling of Multispecies Mutualism: From Particular Models Toward a Generalization of the Concept
85(48)
Paul Georgescu
Daniel Maxin
Laurentiu Sega
Hong Zhang
1 Introduction
86(1)
2 Mutualism Within the Framework of a General Model
87(5)
2.1 Mechanisms Behind Mutualisms
87(1)
2.2 To Be or Not to Be Independent
88(1)
2.3 The Generalization Paradigm
89(3)
3 Modeling Considerations: From Specific Models to a More General Framework
92(7)
3.1 The Lotka-Volterra Legacy
92(2)
3.2 Saturating Functional Responses and More General Frameworks
94(2)
3.3 An Unlikely Marriage: Two-Sex Reproduction in the Mutualistic Framework
96(2)
3.4 Getting Away From the Logistic Growth: Allee Effects
98(1)
4 Two-Dimensional Models: A Stability Analysis
99(16)
4.1 Stability Results Using the LaSalle Invariance Principle
101(3)
4.2 Stability Results Using the Dulac Criterion: Threshold-Like Parameters
104(6)
4.3 Examples
110(5)
5 n-Dimensional Models: Boundedness and Unboundedness
115(12)
5.1 A Generic Framework
116(2)
5.2 Boundedness vs Unboundedness: A Tale of n Parameters
118(1)
5.3 Particular Growth Conditions: A Single Parameter to Rule Them All
119(2)
5.4 Mutualism as Reduction of Mortality for the Benefiting Species
121(2)
5.5 Mutualism as a Positive Contribution to the Fertility Rate of the Benefiting Species
123(2)
5.6 Which Species Is Responsible for Unboundedness?
125(2)
6 Final Considerations
127(1)
Acknowledgment
128(1)
References
129(4)
Section VII Stochastic Complexity and Structural Dynamics
4 Stochastic Models for Structured Populations
133(24)
Shripad Tuljapurkar
David Steinsaltz
1 Introduction
133(2)
2 Introduction: Population Dynamics in a Constant Environment
135(2)
3 Structured Populations in Stochastic Environments
137(12)
3.1 The Environment
137(2)
3.2 Population Dynamics
139(5)
3.3 Limiting Distributions
144(1)
3.4 A Key Limit: Stochastic Growth Rate
145(4)
4 Stochastic Growth Rate: Small-Noise Approximation
149(2)
5 Stochastic Growth Rate: Derivatives
151(2)
5.1 Derivatives With Respect to Vital Rates
152(1)
5.2 Derivatives With Respect to Transition Matrix Elements
153(1)
6 Discussion
153(1)
References
154(3)
5 Studying Complexity and Risk Through Stochastic Population Dynamics: Persistence, Resonance, and Extinction in Ecosystems
157(38)
Anuj Mubayi
Christopher Kribs
Viswanathan Arunachalam
Carlos Castillo-Chavez
1 Introduction
157(8)
1.1 Definitions
160(2)
1.2 Examples of Basic Stochastic Processes
162(3)
2 Persistence in Stochastic Models
165(10)
2.1 Stochastic Logistic Growth Model for a Single Population Species
166(1)
2.2 Quasi-Stationarity (QSD) of a Birth-Death Process
167(2)
2.3 Stochastic Model for Interacting Population Species: Native and Invading Species
169(2)
2.4 Stochastic Model for Heterogeneity in Population of a Single Type of Cells
171(4)
3 Types of Stochasticity and Extinction in Stochastic Models
175(5)
3.1 Time to Extinction of a Birth-Death Process
175(1)
3.2 The Role of Stochasticity and Heterogeneity on Extinction Risk
176(4)
4 Oscillations and Resonance in the Stochastic Models
180(5)
4.1 Sustained Oscillations via Coherence Resonance
180(2)
4.2 Sustained Oscillations via Stochastic Resonance
182(3)
5 Computational Stochastic Approaches
185(5)
5.1 Agent-Based Models and Parameter Estimation as Emergent Behavior
185(3)
5.2 Algorithms for Simulating Stochastic Models
188(2)
6 Conclusion
190(1)
References
190(5)
6 Analyzing Variety of Birth Intervals: A Stochastic Approach
195(92)
Ram Chandra Yadava
Piyush Kant Rai
1 Introduction
195(5)
1.1 Heterogeneity and Selection
198(1)
1.2 Variety of Birth Intervals
198(2)
2 Impact of Heterogeneity on Distributions of Duration Variables
200(15)
2.1 Selection Bias in Postpartum Amenorrhea Period From Follow-Up Studies and Its Adjustment
200(8)
2.2 Estimating Birth Interval Characteristic of Women
208(4)
2.3 Impact of Heterogeneity on Time of First Conception
212(3)
3 Sampling Frame as a Determinant of Duration Variable
215(58)
3.1 Usual Closed Birth Interval vs Most Recent Closed Birth Interval
215(27)
3.2 Most Recent Closed Birth Interval Assuming ith Order Births to Be Uniformly Distributed Over Time
242(8)
3.3 Closed Birth Interval vs Straddling Birth Interval
250(4)
3.4 Open Birth Interval
254(11)
3.5 Forward Birth Interval
265(7)
3.6 Interior Birth Interval
272(1)
4 Analyzing Consecutive Closed Birth Intervals: A Correlation Analysis
273(7)
4.1 Consecutive Closed Birth Intervals
273(3)
4.2 Application of the Analysis on NFHS-2 Data
276(4)
References
280(7)
Section VIII GWAS, Species Divergence and Bayesian Item Response Theory
7 Detection of Quantitative Trait Loci From Genome-Wide Association Studies
287(68)
David A. Spade
1 Introduction
287(1)
2 SNP Data and Data Preparation
288(13)
2.1 Description of the Data
288(1)
2.2 Methods of Phasing
289(12)
3 Working Example
301(1)
4 Nontree-Based Methods of GWAS Analysis
301(14)
4.1 Single-Marker Association
302(5)
4.2 Haplotype Association Mapping
307(7)
4.3 Regression-Based Methods of QTL Detection
314(1)
5 Tree-Based Methods for Phased Data
315(27)
5.1 Perfect Phylogeny Construction
315(4)
5.2 QBlossoc
319(3)
5.3 Models of Allele Substitution
322(3)
5.4 Likelihood Score Approach
325(11)
5.5 Bayesian SNP Detection
336(6)
6 Tree-Based GWAS Analysis From Unphased Genetic Data
342(5)
6.1 Local Semiperfect Phylogeny Construction
343(2)
6.2 Determination of Significance
345(2)
7 Conclusion
347(1)
References
348(5)
Further Reading
353(2)
8 Bayesian Item Response Theory for Cancer Biomarker Discovery
355(50)
Katabathula Ramachandra Murthy
Salendra Singh
David Tuck
Vinay Varadan
1 Introduction
356(2)
2 Item Response Theory
358(10)
2.1 Introduction
358(1)
2.2 Dichotomous Models
359(3)
2.3 Polytomous Models
362(6)
3 Biomarker Information Function
368(8)
3.1 One Parameter Logistic
369(1)
3.2 Two Parameter Logistic
369(1)
3.3 Three Parameter Logistic
369(1)
3.4 Graded Response Model
370(2)
3.5 Partial Credit Model
372(2)
3.6 Rating Scale Model
374(2)
4 Bayesian Frame Work for IRT models
376(3)
4.1 Markov Chain Monte Carlo Methods (MCMC)
377(1)
4.2 Model Selection
378(1)
5 Experimental Study
379(18)
5.1 Model Selection
379(1)
5.2 Biomarker Selection
379(12)
5.3 Applications of IRT in Cancer Research
391(6)
6 Future Developments of IRT in Biological Modelling
397(1)
7 Stan Codes for IRT Models
398(1)
Three-Parameter Logistic
398(1)
Graded Response
399(2)
References
401(4)
9 Effects of Phenotypic Plasticity and Unpredictability of Selection Environment on Niche Separation and Species Divergence
405(30)
Narayan Behera
1 Introduction
406(4)
2 Model
410(8)
2.1 Life Cycle
410(2)
2.2 Model Specification
412(4)
2.3 Computer Simulation
416(2)
3 Results
418(7)
3.1 Haploid Population With Single Gaussian Food Supply
418(3)
3.2 Haploid Population With Double Gaussian Food Supply
421(2)
3.3 Diploid Population Having Additive Allelic Effect Gene Interaction and Double Food Supply
423(2)
4 Discussion
425(4)
References
429(2)
Further Reading
431(4)
Section IX Aging and Age-Structured Population Dynamics
10 Theory and Applications of Backward Probabilities and Prevalences in Cross-Longitudinal Surveys
435(52)
Nicolas Brouard
1 Backward Probabilities Estimated From Chained Labor Force Surveys
437(20)
1.1 Probability or Forward Probability
437(2)
1.2 Backward Probability
439(3)
1.3 Markov Chains and Strong Ergodicity
442(10)
1.4 Weak Ergodicity
452(2)
1.5 Backward Prevalence of a Specific Cohort
454(3)
1.6 Forward Prevalence of a Specific Cohort
457(1)
2 Backward Probabilities With Transient States and an Absorbing State
457(27)
2.1 Chaining Forward for a Specific Cohort
460(6)
2.2 Chaining Backward for a Specific Cohort
466(12)
2.3 Some Estimations of Backward Prevalences
478(4)
2.4 Limitations Concerning the Estimation of Forward and Backward Prevalences
482(1)
2.5 Perspectives Concerning the Estimation of Backward Prevalences
483(1)
3 Conclusion
484(1)
Acknowledgments
485(1)
References
485(2)
11 Behavior of Stationary Population Identity in Two-Dimensions: Age and Proportion of Population Truncated in Follow-up
487(14)
Arni S.R. Srinivasa Rao
James R. Carey
1 Introduction
487(2)
2 Structure of the Two-Dimensional Captive Cohort
489(2)
3 Truncation of the Follow-up Data of Captive Cohorts
491(1)
4 Captive Population Age Structure, Truncation, and Partition Functions
492(6)
4.1 Time Left for a Captive Cohort and Right Truncation
493(5)
5 Discussion
498(1)
6 Conclusions
499(1)
References
499(1)
Further Reading
500(1)
12 Demographic Situation of Manipur, India
501(50)
Moirangthem Hemanta Meitei
1 Outline
501(12)
1.1 The Origin of Communities in Manipur
507(1)
1.2 Manipur at Crossroad
508(5)
2 Demographic Composition of Manipur
513(26)
2.1 Demographic Indicators
524(1)
2.2 Mortality Situation in Manipur
524(7)
2.3 Fertility in Manipur
531(5)
2.4 Migration
536(3)
3 Age Composition
539(7)
3.1 Future Trajectory of Population
541(5)
References
546(1)
Further Reading
547(4)
Section X Collective Behaviors in Ecology
13 Deriving Mesoscopic Models of Collective Behavior for Finite Populations
551(44)
Jitesh Jhawar
Richard G. Morris
Vishwesha Guttal
Nomenclature
552(1)
1 Introduction
552(1)
2 Background
553(4)
3 Mesoscopic Description of a Pairwise Binary-Choice Model
557(13)
3.1 The Model
557(2)
3.2 Constructing Mesoscopic SDEs
559(7)
3.3 Characterizing Mesoscopic Dynamics
566(3)
3.4 Results for the Pairwise Pairwise Interaction Model
569(1)
4 Ternary Interaction Model for Binary Choice
570(7)
4.1 Constructing a Mesoscopic SDE for the Ternary Interaction Model
571(3)
4.2 Characterizing Mesoscopic Dynamics
574(1)
4.3 Results for the Ternary Interaction Model
574(3)
5 Discussion
577(4)
5.1 Comparison of System-Size Expansion With Chemical Langevin Approach
577(1)
5.2 Multiplicative Noise at Mesoscopic Scales
578(1)
5.3 Extensions and Concluding Remarks
579(2)
5.4 Resources
581(1)
Acknowledgments
581(1)
Appendices
581(9)
Appendix A The Chemical Langevin Equation
581(3)
Appendix B Pairwise Interaction Model in Two Spatial Dimensions
584(1)
B.1 van Kampen's System-Size Expansion of Transition Rates
584(1)
B.2 Chemical Langevin Approach
586(4)
References
590(5)
14 Collective Behavior and Ecology
595(32)
Glenn R. Flierl
1 Introduction
595(1)
2 Individual-Based Models
596(5)
2.1 Dispersion/Diffusion
597(1)
2.2 Taxis
598(3)
2.3 Kinesis
601(1)
3 Collective Behavior (Using IBMs)
601(1)
3.1 Schooling
601(1)
4 Fokker-Planck Equation
602(8)
4.1 Common Behavior
603(3)
4.2 Steady Solutions
606(4)
5 Collective Behavior (Using FP)
610(4)
6 Collective Behavior and Ecology
614(11)
6.1 One Variable
615(3)
6.2 Two-Variables
618(7)
7 Concluding Remarks
625(1)
Acknowledgments
626(1)
References
626(1)
Further Reading
626(1)
Index 627
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.

C. R. Rao is a world famous statistician who earned a place in the history of statistics as one of those who developed statistics from its adhoc origins into a firmly grounded mathematical science.”

He was employed at the Indian Statistical Institute (ISI) in 1943 as a research scholar after obtaining an MA degree in mathematics with a first class and first rank from Andhra University in1941 and MA degree in statistics from Calcutta University in 1943 with a first class, first rank, gold medal and record marks which remain unbroken during the last 73 years.

At the age of 28 he was made a full professor at ISI in recognition of his creativity.” While at ISI, Rao went to Cambridge University (CU) in 1946 on an invitation to work on an anthropometric project using the methodology developed at ISI. Rao worked in the museum of archeology and anthropology in Duckworth laboratory of CU during 1946-1948 as a paid visiting scholar. The results were reported in the 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.