Chance in biology : using probability to explore nature /

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Through the application of probability theory, this text makes predictions about how plants and animals work in a stochastic universe. It uses real-world examples, numerous illustrations and chapter summaries.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Denny, Mark W., 1951- (Autor), Gaines, Steven, 1951- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, ©2000.
Temas:
Biomathematics.
Probabilities.
Biomathématiques.
Probabilités.
probability.
NATURE > Reference.
SCIENCE > Life Sciences > Biology.
SCIENCE > Life Sciences > General.
Biological sciences.
Statistics & probability.
Applied mathematics.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine derived contents note: Table of contents for Chance in biology : using probability to explore nature / Mark Denny and Steven Gaines.
  • Bibliographic record and links to related information available from the Library of Congress catalog
  • Information from electronic data provided by the publisher. May be incomplete or contain other coding.
  • Preface xi
  • 1 The Nature of Chance 3
  • 1.1 Silk, Strength, and Statistics 3
  • 1.2 What Is Certain?7
  • 1.3 Determinism versus Chance 8
  • 1.4 Chaos 9
  • 1.5 A Road Map 11
  • 2 Rules of Disorder 12
  • 2.1 Events, Experiments, and Outcomes 12
  • 2.1.1 Sarcastic Fish 13
  • 2.1.2 Bipolar Smut 14
  • 2.1.3 Discrete versus Continuous 17
  • 2.1.4 Drawing Pictures 18
  • 2.2 Probability 19
  • 2.3 Rules and Tools 20
  • 2.3.1 Events Are the Sum of Their Parts 20
  • 2.3.2 The Union of Sets 21
  • 2.3.3 The Probability of a Union 23
  • 2.3.4 Probability and the Intersection of Sets 24
  • 2.3.5 The Complement of a Set 25
  • 2.3.6 Additional Information and Conditional Probabilities 27
  • 2.3.7 Bayes' Formula 29
  • 2.3.8 AIDS and Bayes' Formula 30
  • 2.3.9 The Independence of Sets 32
  • 2.4 Probability Distributions 34
  • 2.5 Summary 37
  • 2.6 Problems 37
  • 3 Discrete Patterns of Disorder 40
  • 3.1 Random Variables 40
  • 3.2 Expectations Defined 42
  • 3.3 The Variance 46
  • 3.4 The Trials of Bernoulli 48
  • 3.5 Beyond 0 's and 1 's 50
  • 3.6 Bernoulli = Binomial 51
  • 3.6.1 Permutations and Combinations 53
  • 3.7 Waiting Forever 60
  • 3.8 Summary 65
  • 3.9 Problems 66
  • 4 Continuous Patterns of Disorder 68
  • 4.1 The Uniform Distribution 69
  • 4.1.1 The Cumulative Probability Distribution 70
  • 4.1.2 The Probability Density Function 71
  • 4.1.3 The Expectation 74
  • 4.1.4 The Variance 76
  • 4.2 The Shape of Distributions 77
  • 4.3 The Normal Curve 79
  • 4.4 Why Is the Normal Curve Normal?82
  • 4.5 The Cumulative Normal Curve 84
  • 4.6 The Standard Error 86
  • 4.7 A Brief Detour to Statistics 89
  • 4.8 Summary 92
  • 4.9 Problems 93
  • 4.10 Appendix 1:The Normal Distribution 94
  • 4.11 Appendix 2:The Central Limit Theorem 98
  • 5 Random Walks 106
  • 5.1 The Motion of Molecules 106
  • 5.2 Rules of a Random Walk 110
  • 5.2.1 The Average 110
  • 5.2.2 The Variance 112
  • 5.2.3 Diffusive Speed 115
  • 5.3 Diffusion and the Real World 115
  • 5.4 A Digression on the Binomial Theorem 117
  • 5.5 The Biology of Diffusion 119
  • 5.6 Fick's Equation 123
  • 5.7 A Use of Fick's Equation: Limits to Size 126
  • 5.8 Receptors and Channels 130
  • 5.9 Summary 136
  • 5.10 Problems 137
  • 6 More Random Walks 139
  • 6.1 Diffusion to Capture 139
  • 6.1.1 Two Absorbing Walls 142
  • 6.1.2 One Reflecting Wall 144
  • 6.2 Adrift at Sea: Turbulent Mixing of Plankton 145
  • 6.3 Genetic Drift 148
  • 6.3.1 A Genetic Diffusion Coefficient 149
  • 6.3.2 Drift and Fixation 151
  • 6.4 Genetic Drift and Irreproducible Pigs 154
  • 6.5 The Biology of Elastic Materials 156
  • 6.5.1 Elasticity Defined 156
  • 6.5.2 Biological Rubbers 157
  • 6.5.3 The Limits to Energy Storage 161
  • 6.6 Random Walks in Three Dimensions 163
  • 6.7 Random Protein Con .gurations 167
  • 6.8 A Segue to Thermodynamics 169
  • 6.9 Summary 173
  • 6.10 Problems 173
  • 7 The Statistics of Extremes 175
  • 7.1 The Danger of Cocktail Parties 175
  • 7.2 Calculating the Maximum 182
  • 7.3 Mean and Modal Maxima 185
  • 7.4 Ocean Waves 186
  • 7.5 The Statistics of Extremes 189
  • 7.6 Life and Death in Rhode Island 194
  • 7.7 Play Ball!196
  • 7.8 A Note on Extrapolation 204
  • 7.9 Summary 206
  • 7.10 Problems 206
  • 8 Noise and Perception 208
  • 8.1 Noise Is Inevitable 208
  • 8.2 Dim Lights and Fuzzy Images 212
  • 8.3 The Poisson Distribution 213
  • 8.4 Bayes' Formula and the Design of Rods 218
  • 8.5 Designing Error-Free Rods 219
  • 8.5.1 The Origin of Membrane Potentials 220
  • 8.5.2 Membrane Potential in Rod Cells 222
  • 8.6 Noise and Ion Channels 225
  • 8.6.1 An Electrical Analog 226
  • 8.6.2 Calculating the Membrane Voltage 227
  • 8.6.3 Calculating the Size 229
  • 8.7 Noise and Hearing 230
  • 8.7.1 Fluctuations in Pressure 231
  • 8.7.2 The Rate of Impact 232
  • 8.7.3 Fluctuations in Velocity 233
  • 8.7.4 Fluctuations in Momentum 235
  • 8.7.5 The Standard Error of Pressure 235
  • 8.7.6 Quantifying the Answer 236
  • 8.8 The Rest of the Story 239
  • 8.9 Stochastic Resonance 239
  • 8.9.1 The Utility of Noise 239
  • 8.9.2 Nonlinear Systems 242
  • 8.9.3 The History of Stochastic Resonance 244
  • 8.10 Summary 245
  • 8.11 A Word at the End 246
  • 8.12 A Problem 247
  • 8.13 Appendix 248
  • 9 The Answers 250
  • 9.1 Chapter 2 250
  • 9.2 Chapter 3 256
  • 9.3 Chapter 4 262
  • 9.4 Chapter 5 266
  • 9.5 Chapter 6 269
  • 9.6 Chapter 7 271
  • 9.7 Chapter 8 273
  • Symbol Index 279
  • Author Index 284
  • Subject Index 286
  • Library of Congress subject headings for this publication: Biomathematics, Probabilities.

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