A biologist's guide to mathematical modeling in ecology and evolution:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton ; Oxford
Princeton University Press
2007
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| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references |
| Physical Description: | X, 732 Seiten Illustrationen, Karten |
| ISBN: | 0691123446 9780691123448 |
Staff View
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| 245 | 1 | 0 | |a A biologist's guide to mathematical modeling in ecology and evolution |c Sarah P. Otto and Troy Day |
| 264 | 1 | |a Princeton ; Oxford |b Princeton University Press |c 2007 | |
| 300 | |a X, 732 Seiten |b Illustrationen, Karten | ||
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| 650 | 4 | |a Écologie - Modèles mathématiques | |
| 650 | 4 | |a Évolution (Biologie) - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Ökologie | |
| 650 | 4 | |a Ecology |x Mathematical models | |
| 650 | 4 | |a Evolution (Biology) |x Mathematical models | |
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| adam_text | A BIOLOGIST S GUIDE TO MATHEMATICAL MODELING IN ECOLOGY AND EVOLUTION
SARAH P. OTTO AND TROY DAY UNIVSR?.LTATS- UND LENDER BIBLIOLHEK
DARMSTADT BIBLIOTHEK BIOTOGI§ PRINCETON UNIVERSITY PRESS PRINCETON AND
OXFORD CONTENTS PREFACE IX CHAPTER 1: MATHEMATICAL MODELING IN BIOLOGY 1
1.1 INTRODUCTION 1 1.2 HIV 2 1.3 MODELS OF HIV/AIDS 5 1.4 CONCLUDING
MESSAGE 14 CHAPTER 2: HOW TO CONSTRUCT A MODEL 17 2.1 INTRODUCTION 17
2.2 FORMULATE THE QUESTION 19 2.3 DETERMINE THE BASIC INGREDIENTS 19 2.4
QUALITATIVELY DESCRIBE THE BIOLOGICAL SYSTEM 26 2.5 QUANTITATIVELY
DESCRIBE THE BIOLOGICAL SYSTEM 33 2.6 ANALYZE THE EQUATIONS 39 2.7
CHECKS AND BALANCES 47 2.8 RELATE THE RESULTS BACK TO THE QUESTION 50
2.9 CONCLUDING MESSAGE 51 CHAPTER 3: DERIVING CLASSIC MODELS IN ECOLOGY
AND EVOLUTIONARY BIOLOGY 54 3.1 INTRODUCTION 54 3.2 EXPONENTIAL AND
LOGISTIC MODELS OF POPULATION GROWTH 54 3.3 HAPLOID AND DIPLOID MODELS
OF NATURAL SELECTION 62 3.4 MODELS OF INTERACTIONS AMONG SPECIES 72 3.5
EPIDEMIOLOGICAL MODELS OF DISEASE SPREAD 77 3.6 WORKING
BACKWARD*INTERPRETING EQUATIONS IN TERMS OF THE BIOLOGY 79 3.7
CONCLUDING MESSAGE 82 PRIMER 1: FUNCTIONS AND APPROXIMATIONS 89 PL.L
FUNCTIONS AND THEIR FORMS 89 PI.2 LINEAR APPROXIMATIONS 96 PI.3 THE
TAYLOR SERIES 100 CHAPTER 4: NUMERICAL AND GRAPHICAL TECHNIQUES*
DEVELOPING A FEELING FOR YOUR MODEL 110 4.1 INTRODUCTION 110 4.2 PLOTS
OF VARIABLES OVER TIME 111 4.3 PLOTS OF VARIABLES AS A FUNCTION OF THE
VARIABLES THEMSELVES 124 VL CONTENTS 4.4 MULTIPLE VARIABLES AND
PHASE-PLANE DIAGRAMS 133 4.5 CONCLUDING MESSAGE 145 CHAPTER 5:
EQUILIBRIA AND STABILITY ANALYSES- ONE-VARIABLE MODELS 151 5.1
INTRODUCTION 151 5.2 FINDING AN EQUILIBRIUM 152 5.3 DETERMINING
STABILITY 163 5.4 APPROXIMATIONS 176 5.5 CONCLUDING MESSAGE 184 CHAPTER
6: GENERAL SOLUTIONS AND TRANSFORMATIONS* ONE-VARIABLE MODELS 191 6.1
INTRODUCTION 191 6.2 TRANSFORMATIONS 192 6.3 LINEAR MODELS IN DISCRETE
TIME 193 6.4 NONLINEAR MODELS IN DISCRETE TIME 195 6.5 LINEAR MODELS IN
CONTINUOUS TIME 198 6.6 NONLINEAR MODELS IN CONTINUOUS TIME 202 6.7
CONCLUDING MESSAGE 207 PRIMER 2: LINEAR ALGEBRA 21 4 P2.1 AN
INTRODUCTION TO VECTORS AND MATRICES 214 P2.2 VECTOR AND MATRIX ADDITION
219 P2.3 MULTIPLICATION BY A SCALAR 222 P2.4 MULTIPLICATION OF VECTORS
AND MATRICES 224 P2.5 THE TRACE AND DETERMINANT OF A SQUARE MATRIX 228
P2.6 THE INVERSE 233 P2.7 SOLVING SYSTEMS OF EQUATIONS 235 P2.8 THE
EIGENVALUES OF A MATRIX 237 P2.9 THE EIGENVECTORS OF A MATRIX 243
CHAPTER 7: EQUILIBRIA AND STABILITY ANALYSES*LINEAR MODELS WITH MULTIPLE
VARIABLES 254 7.1 INTRODUCTION 254 7.2 MODELS WITH MORE THAN ONE DYNAMIC
VARIABLE 255 7.3 LINEAR MULTIVARIABLE MODELS 260 7.4 EQUILIBRIA AND
STABILITY FOR LINEAR DISCRETE-TIME MODELS 279 , 7.5 CONCLUDING MESSAGE
289 CHAPTER 8: EQUILIBRIA AND STABILITY ANALYSES- NONLINEAR MODELS WITH
MULTIPLE VARIABLES 294 8.1 INTRODUCTION 294 8.2 NONLINEAR
MULTIPLE-VARIABLE MODELS 294 8.3 EQUILIBRIA AND STABILITY FOR NONLINEAR
DISCRETE-TIME MODELS 316 8.4 PERTURBATION TECHNIQUES FOR APPROXIMATING
EIGENVALUES 330 8.5 CONCLUDING MESSAGE 337 CONTENTS VII CHAPTER 9:
GENERAL SOLUTIONS AND TRANFORMATIONS* MODELS WITH MULTIPLE VARIABLES 347
9.1 INTRODUCTION 347 9.2 LINEAR MODELS INVOLVING MULTIPLE VARIABLES 347
9.3 NONLINEAR MODELS INVOLVING MULTIPLE VARIABLES 365 9.4 CONCLUDING
MESSAGE 381 CHAPTER 10: DYNAMICS OF CLASS-STRUCTURED POPULATIONS 386
10.1 INTRODUCTION 386 10.2 CONSTRUCTING CLASS-STRUCTURED MODELS 388 10.3
ANALYZING CLASS-STRUCTURED MODELS 393 10.4 REPRODUCTIVE VALUE AND LEFT
EIGENVECTORS 398 10.5 THE EFFECT OF PARAMETERS ON THE LONG-TERM GROWTH
RATE 400 10.6 AGE-STRUCTURED MODELS*THE LESLIE MATRIX 403 10.7
CONCLUDING MESSAGE 418 CHAPTER 11: TECHNIQUES FOR ANALYZING MODELS WITH
PERIODIC BEHAVIOR 423 11.1 INTRODUCTION - 423 11.2 WHAT ARE PERIODIC
DYNAMICS? 423 11.3 COMPOSITE MAPPINGS 425 11.4 HOPF BIFURCATIONS 428
11.5 CONSTANTS OF MOTION 436 11.6 CONCLUDING MESSAGE 449 CHAPTER 12:
EVOLUTIONARY INVASION ANALYSIS 454 12.1 INTRODUCTION 454 12.2 TWO
INTRODUCTORY EXAMPLES 455 12.3 THE GENERAL TECHNIQUE OF EVOLUTIONARY
INVASION ANALYSIS 465 12.4 DETERMINING HOW THE ESS CHANGES AS A FUNCTION
OF PARAMETERS 478 12.5 EVOLUTIONARY INVASION ANALYSES IN
CLASS-STRUCTURED POPULATIONS 485 12.6 CONCLUDING MESSAGE 502 PRIMER 3:
PROBABILITY THEORY 513 P3.1 AN INTRODUCTION TO PROBABILITY 513 P3.2
CONDITIONAL PROBABILITIES AND BAYES THEOREM 518 P3.3 DISCRETE
PROBABILITY DISTRIBUTIONS 521 P3.4 CONTINUOUS PROBABILITY DISTRIBUTIONS
536 P3.5 THE (INSERT YOUR NAME HERE) DISTRIBUTION 553 CHAPTER 13:
PROBABILISTI C MODELS 567 13.1 INTRODUCTION 567 13.2 MODELS OF
POPULATION GROWTH 568 13.3 BIRTH-DEATH MODELS 573 13.4 WRIGHT-FISHER
MODEL OF ALLELE FREQUENCY CHANGE 576 13.5 MORAN MODEL OF ALLELE
FREQUENCY CHANGE 581 13.6 CANCER DEVELOPMENT 584 VIII CONTENTS 13.7
CELLULAR AUTOMATA*A MODEL OF EXTINCTION AND RECOLONIZATION 591 13.8
LOOKING BACKWARD IN TIME*COALESCENT THEORY 594 13.9 CONCLUDING MESSAGE
602 CHAPTER 14: ANALYZING DISCRETE STOCHASTIC MODELS 608 14.1
INTRODUCTION 608 14.2 TWO-STATE MARKOV MODELS 608 14.3 MULTISTATE MARKOV
MODELS 614 14.4 BIRTH-DEATH MODELS 631 14.5 BRANCHING PROCESSES 639 14.6
CONCLUDING MESSAGE 644 CHAPTER 15: ANALYZING CONTINUOUS STOCHASTIC
MODELS* DIFFUSION IN TIME AND SPACE 649 15.1 INTRODUCTION 649 15.2
CONSTRUCTING DIFFUSION MODELS 649 15.3 ANALYZING THE DIFFUSION EQUATION
WITH DRIFT 664 15.4 MODELING POPULATIONS IN SPACE USING THE DIFFUSION
EQUATION 684 15.5 CONCLUDING MESSAGE 687 EPILOGUE: THE ART OF
MATHEMATICAL MODELING IN BIOLOGY 692 APPENDIX 1: COMMONLY USED
MATHEMATICAL RULES 695 AL.L RULES FOR ALGEBRAIC FUNCTIONS 695 A1.2 RULES
FOR LOGARITHMIC AND EXPONENTIAL FUNCTIONS 695 A1.3 SOME IMPORTANT SUMS
696 A1.4 SOME IMPORTANT PRODUCTS 696 A1.5 INEQUALITIES 697 APPENDIX 2:
SOME IMPORTANT RULES FROM CALCULUS 699 A2.1 CONCEPTS - 699 A2.2
DERIVATIVES 701 A2.3 INTEGRALS 703 1 A2.4 LIMITS 704 APPENDIX 3: THE
PERRON-FROBENIUS THEOREM 709 A3.1: DEFINITIONS 709 A3.2: THE
PERRON-FROBENIUS THEOREM 710 APPENDIX 4: FINDING MAXIMA AND MINIMA OF
FUNCTIONS 713 A4.1 FUNCTIONS WITH ONE VARIABLE 713 A4.2 FUNCTIONS WITH
MULTIPLE VARIABLES 714 APPENDIX 5: MOMENT-GENERATING FUNCTIONS 717 INDEX
OF DEFINITIONS, RECIPES, AND RULES 725 GENERAL INDEX 727
|
| adam_txt |
A BIOLOGIST'S GUIDE TO MATHEMATICAL MODELING IN ECOLOGY AND EVOLUTION
SARAH P. OTTO AND TROY DAY UNIVSR?.LTATS- UND LENDER BIBLIOLHEK
DARMSTADT BIBLIOTHEK BIOTOGI§ PRINCETON UNIVERSITY PRESS PRINCETON AND
OXFORD CONTENTS PREFACE IX CHAPTER 1: MATHEMATICAL MODELING IN BIOLOGY 1
1.1 INTRODUCTION 1 1.2 HIV 2 1.3 MODELS OF HIV/AIDS 5 1.4 CONCLUDING
MESSAGE 14 CHAPTER 2: HOW TO CONSTRUCT A MODEL 17 2.1 INTRODUCTION 17
2.2 FORMULATE THE QUESTION 19 2.3 DETERMINE THE BASIC INGREDIENTS 19 2.4
QUALITATIVELY DESCRIBE THE BIOLOGICAL SYSTEM 26 2.5 QUANTITATIVELY
DESCRIBE THE BIOLOGICAL SYSTEM 33 2.6 ANALYZE THE EQUATIONS 39 2.7
CHECKS AND BALANCES 47 2.8 RELATE THE RESULTS BACK TO THE QUESTION 50
2.9 CONCLUDING MESSAGE 51 CHAPTER 3: DERIVING CLASSIC MODELS IN ECOLOGY
AND EVOLUTIONARY BIOLOGY 54 3.1 INTRODUCTION 54 3.2 EXPONENTIAL AND
LOGISTIC MODELS OF POPULATION GROWTH 54 3.3 HAPLOID AND DIPLOID MODELS
OF NATURAL SELECTION 62 3.4 MODELS OF INTERACTIONS AMONG SPECIES 72 3.5
EPIDEMIOLOGICAL MODELS OF DISEASE SPREAD 77 3.6 WORKING
BACKWARD*INTERPRETING EQUATIONS IN TERMS OF THE BIOLOGY 79 3.7
CONCLUDING MESSAGE 82 PRIMER 1: FUNCTIONS AND APPROXIMATIONS 89 PL.L
FUNCTIONS AND THEIR FORMS 89 PI.2 LINEAR APPROXIMATIONS 96 PI.3 THE
TAYLOR SERIES 100 CHAPTER 4: NUMERICAL AND GRAPHICAL TECHNIQUES*
DEVELOPING A FEELING FOR YOUR MODEL 110 4.1 INTRODUCTION 110 4.2 PLOTS
OF VARIABLES OVER TIME ' 111 4.3 PLOTS OF VARIABLES AS A FUNCTION OF THE
VARIABLES THEMSELVES 124 VL CONTENTS 4.4 MULTIPLE VARIABLES AND
PHASE-PLANE DIAGRAMS 133 4.5 CONCLUDING MESSAGE 145 CHAPTER 5:
EQUILIBRIA AND STABILITY ANALYSES- ONE-VARIABLE MODELS 151 5.1
INTRODUCTION 151 5.2 FINDING AN EQUILIBRIUM 152 5.3 DETERMINING
STABILITY 163 5.4 APPROXIMATIONS 176 5.5 CONCLUDING MESSAGE 184 CHAPTER
6: GENERAL SOLUTIONS AND TRANSFORMATIONS* ONE-VARIABLE MODELS 191 6.1
INTRODUCTION 191 6.2 TRANSFORMATIONS 192 6.3 LINEAR MODELS IN DISCRETE
TIME 193 6.4 NONLINEAR MODELS IN DISCRETE TIME 195 6.5 LINEAR MODELS IN
CONTINUOUS TIME 198 6.6 NONLINEAR MODELS IN CONTINUOUS TIME 202 6.7
CONCLUDING MESSAGE 207 PRIMER 2: LINEAR ALGEBRA 21 4 P2.1 AN
INTRODUCTION TO VECTORS AND MATRICES 214 P2.2 VECTOR AND MATRIX ADDITION
219 P2.3 MULTIPLICATION BY A SCALAR 222 P2.4 MULTIPLICATION OF VECTORS
AND MATRICES 224 P2.5 THE TRACE AND DETERMINANT OF A SQUARE MATRIX 228
P2.6 THE INVERSE 233 P2.7 SOLVING SYSTEMS OF EQUATIONS 235 P2.8 THE
EIGENVALUES OF A MATRIX 237 P2.9 THE EIGENVECTORS OF A MATRIX 243
CHAPTER 7: EQUILIBRIA AND STABILITY ANALYSES*LINEAR MODELS WITH MULTIPLE
VARIABLES 254 7.1 INTRODUCTION 254 7.2 MODELS WITH MORE THAN ONE DYNAMIC
VARIABLE 255 7.3 LINEAR MULTIVARIABLE MODELS 260 7.4 EQUILIBRIA AND
STABILITY FOR LINEAR DISCRETE-TIME MODELS 279 , 7.5 CONCLUDING MESSAGE
289 CHAPTER 8: EQUILIBRIA AND STABILITY ANALYSES- NONLINEAR MODELS WITH
MULTIPLE VARIABLES 294 8.1 INTRODUCTION 294 8.2 NONLINEAR
MULTIPLE-VARIABLE MODELS 294 8.3 EQUILIBRIA AND STABILITY FOR NONLINEAR
DISCRETE-TIME MODELS 316 8.4 PERTURBATION TECHNIQUES FOR APPROXIMATING
EIGENVALUES 330 8.5 CONCLUDING MESSAGE 337 CONTENTS VII CHAPTER 9:
GENERAL SOLUTIONS AND TRANFORMATIONS* MODELS WITH MULTIPLE VARIABLES 347
9.1 INTRODUCTION 347 9.2 LINEAR MODELS INVOLVING MULTIPLE VARIABLES 347
9.3 NONLINEAR MODELS INVOLVING MULTIPLE VARIABLES 365 9.4 CONCLUDING
MESSAGE 381 CHAPTER 10: DYNAMICS OF CLASS-STRUCTURED POPULATIONS 386
10.1 INTRODUCTION 386 10.2 CONSTRUCTING CLASS-STRUCTURED MODELS 388 10.3
ANALYZING CLASS-STRUCTURED MODELS 393 10.4 REPRODUCTIVE VALUE AND LEFT
EIGENVECTORS 398 10.5 THE EFFECT OF PARAMETERS ON THE LONG-TERM GROWTH
RATE 400 10.6 AGE-STRUCTURED MODELS*THE LESLIE MATRIX 403 10.7
CONCLUDING MESSAGE 418 CHAPTER 11: TECHNIQUES FOR ANALYZING MODELS WITH
PERIODIC BEHAVIOR 423 11.1 INTRODUCTION - 423 11.2 WHAT ARE PERIODIC
DYNAMICS? 423 11.3 COMPOSITE MAPPINGS 425 11.4 HOPF BIFURCATIONS 428
11.5 CONSTANTS OF MOTION 436 11.6 CONCLUDING MESSAGE 449 CHAPTER 12:
EVOLUTIONARY INVASION ANALYSIS 454 12.1 INTRODUCTION 454 12.2 TWO
INTRODUCTORY EXAMPLES 455 12.3 THE GENERAL TECHNIQUE OF EVOLUTIONARY
INVASION ANALYSIS 465 12.4 DETERMINING HOW THE ESS CHANGES AS A FUNCTION
OF PARAMETERS 478 12.5 EVOLUTIONARY INVASION ANALYSES IN
CLASS-STRUCTURED POPULATIONS 485 12.6 CONCLUDING MESSAGE 502 PRIMER 3:
PROBABILITY THEORY 513 P3.1 AN INTRODUCTION TO PROBABILITY 513 P3.2
CONDITIONAL PROBABILITIES AND BAYES' THEOREM 518 P3.3 DISCRETE
PROBABILITY DISTRIBUTIONS 521 P3.4 CONTINUOUS PROBABILITY DISTRIBUTIONS
536 P3.5 THE (INSERT YOUR NAME HERE) DISTRIBUTION 553 CHAPTER 13:
PROBABILISTI C MODELS 567 13.1 INTRODUCTION " 567 13.2 MODELS OF
POPULATION GROWTH 568 13.3 BIRTH-DEATH MODELS 573 13.4 WRIGHT-FISHER
MODEL OF ALLELE FREQUENCY CHANGE 576 13.5 MORAN MODEL OF ALLELE
FREQUENCY CHANGE 581 13.6 CANCER DEVELOPMENT 584 VIII CONTENTS 13.7
CELLULAR AUTOMATA*A MODEL OF EXTINCTION AND RECOLONIZATION 591 13.8
LOOKING BACKWARD IN TIME*COALESCENT THEORY 594 13.9 CONCLUDING MESSAGE
602 CHAPTER 14: ANALYZING DISCRETE STOCHASTIC MODELS 608 14.1
INTRODUCTION 608 14.2 TWO-STATE MARKOV MODELS 608 14.3 MULTISTATE MARKOV
MODELS 614 14.4 BIRTH-DEATH MODELS 631 14.5 BRANCHING PROCESSES 639 14.6
CONCLUDING MESSAGE 644 CHAPTER 15: ANALYZING CONTINUOUS STOCHASTIC
MODELS* DIFFUSION IN TIME AND SPACE 649 15.1 INTRODUCTION 649 15.2
CONSTRUCTING DIFFUSION MODELS 649 15.3 ANALYZING THE DIFFUSION EQUATION
WITH DRIFT 664 15.4 MODELING POPULATIONS IN SPACE USING THE DIFFUSION
EQUATION 684 15.5 CONCLUDING MESSAGE 687 EPILOGUE: THE ART OF
MATHEMATICAL MODELING IN BIOLOGY 692 APPENDIX 1: COMMONLY USED
MATHEMATICAL RULES 695 AL.L RULES FOR ALGEBRAIC FUNCTIONS 695 A1.2 RULES
FOR LOGARITHMIC AND EXPONENTIAL FUNCTIONS 695 A1.3 SOME IMPORTANT SUMS
696 A1.4 SOME IMPORTANT PRODUCTS 696 A1.5 INEQUALITIES 697 APPENDIX 2:
SOME IMPORTANT RULES FROM CALCULUS 699 A2.1 CONCEPTS - 699 A2.2
DERIVATIVES 701 A2.3 INTEGRALS 703 1 A2.4 LIMITS 704 APPENDIX 3: THE
PERRON-FROBENIUS THEOREM 709 A3.1: DEFINITIONS 709 A3.2: THE
PERRON-FROBENIUS THEOREM 710 APPENDIX 4: FINDING MAXIMA AND MINIMA OF
FUNCTIONS 713 A4.1 FUNCTIONS WITH ONE VARIABLE 713 A4.2 FUNCTIONS WITH
MULTIPLE VARIABLES 714 APPENDIX 5: MOMENT-GENERATING FUNCTIONS 717 INDEX
OF DEFINITIONS, RECIPES, AND RULES 725 GENERAL INDEX 727 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Otto, Sarah P. 1967- Day, Troy 1968- |
| author_GND | (DE-588)132966867 (DE-588)132966883 |
| author_facet | Otto, Sarah P. 1967- Day, Troy 1968- |
| author_role | aut aut |
| author_sort | Otto, Sarah P. 1967- |
| author_variant | s p o sp spo t d td |
| building | Verbundindex |
| bvnumber | BV023029386 |
| callnumber-first | Q - Science |
| callnumber-label | QH541 |
| callnumber-raw | QH541.15.M3 |
| callnumber-search | QH541.15.M3 |
| callnumber-sort | QH 3541.15 M3 |
| callnumber-subject | QH - Natural History and Biology |
| classification_rvk | SK 970 WC 7000 WI 1500 WI 2050 |
| classification_tum | BIO 175f BIO 130f BIO 105f |
| ctrlnum | (OCoLC)65065577 (DE-599)BVBBV023029386 |
| dewey-full | 577.01/5118 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 577 - Ecology |
| dewey-raw | 577.01/5118 |
| dewey-search | 577.01/5118 |
| dewey-sort | 3577.01 45118 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| discipline_str_mv | Biologie Mathematik |
| format | Book |
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| id | DE-604.BV023029386 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:16:22Z |
| indexdate | 2024-07-09T21:09:21Z |
| institution | BVB |
| isbn | 0691123446 9780691123448 |
| language | English |
| lccn | 2006044774 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016233294 |
| oclc_num | 65065577 |
| open_access_boolean | |
| owner | DE-20 DE-29T DE-M49 DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-703 DE-188 |
| owner_facet | DE-20 DE-29T DE-M49 DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-703 DE-188 |
| physical | X, 732 Seiten Illustrationen, Karten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Princeton University Press |
| record_format | marc |
| spelling | Otto, Sarah P. 1967- Verfasser (DE-588)132966867 aut A biologist's guide to mathematical modeling in ecology and evolution Sarah P. Otto and Troy Day Princeton ; Oxford Princeton University Press 2007 X, 732 Seiten Illustrationen, Karten txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references Écologie - Modèles mathématiques Évolution (Biologie) - Modèles mathématiques Mathematisches Modell Ökologie Ecology Mathematical models Evolution (Biology) Mathematical models Ökologie (DE-588)4043207-5 gnd rswk-swf Evolution (DE-588)4071050-6 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s Ökologie (DE-588)4043207-5 s DE-604 Evolution (DE-588)4071050-6 s Day, Troy 1968- Verfasser (DE-588)132966883 aut http://www.loc.gov/catdir/enhancements/fy0704/2006044774-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0704/2006044774-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0708/2006044774-t.html Table of contents only HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016233294&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Otto, Sarah P. 1967- Day, Troy 1968- A biologist's guide to mathematical modeling in ecology and evolution Écologie - Modèles mathématiques Évolution (Biologie) - Modèles mathématiques Mathematisches Modell Ökologie Ecology Mathematical models Evolution (Biology) Mathematical models Ökologie (DE-588)4043207-5 gnd Evolution (DE-588)4071050-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4043207-5 (DE-588)4071050-6 (DE-588)4114528-8 |
| title | A biologist's guide to mathematical modeling in ecology and evolution |
| title_auth | A biologist's guide to mathematical modeling in ecology and evolution |
| title_exact_search | A biologist's guide to mathematical modeling in ecology and evolution |
| title_exact_search_txtP | A biologist's guide to mathematical modeling in ecology and evolution |
| title_full | A biologist's guide to mathematical modeling in ecology and evolution Sarah P. Otto and Troy Day |
| title_fullStr | A biologist's guide to mathematical modeling in ecology and evolution Sarah P. Otto and Troy Day |
| title_full_unstemmed | A biologist's guide to mathematical modeling in ecology and evolution Sarah P. Otto and Troy Day |
| title_short | A biologist's guide to mathematical modeling in ecology and evolution |
| title_sort | a biologist s guide to mathematical modeling in ecology and evolution |
| topic | Écologie - Modèles mathématiques Évolution (Biologie) - Modèles mathématiques Mathematisches Modell Ökologie Ecology Mathematical models Evolution (Biology) Mathematical models Ökologie (DE-588)4043207-5 gnd Evolution (DE-588)4071050-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Écologie - Modèles mathématiques Évolution (Biologie) - Modèles mathématiques Mathematisches Modell Ökologie Ecology Mathematical models Evolution (Biology) Mathematical models Evolution |
| url | http://www.loc.gov/catdir/enhancements/fy0704/2006044774-b.html http://www.loc.gov/catdir/enhancements/fy0704/2006044774-d.html http://www.loc.gov/catdir/enhancements/fy0708/2006044774-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016233294&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ottosarahp abiologistsguidetomathematicalmodelinginecologyandevolution AT daytroy abiologistsguidetomathematicalmodelinginecologyandevolution |