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Chance in Biology : Using Probability to Explore Nature - Mark W. Denny

Chance in Biology

Using Probability to Explore Nature


Published: 23rd September 2002
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Life is a chancy proposition: from the movement of molecules to the age at which we die, chance plays a key role in the natural world. Traditionally, biologists have viewed the inevitable "noise" of life as an unfortunate complication. The authors of this book, however, treat random processes as a benefit. In this introduction to chance in biology, Mark Denny and Steven Gaines help readers to apply the probability theory needed to make sense of chance events--using examples from ocean waves to spiderwebs, in fields ranging from molecular mechanics to evolution.

Through the application of probability theory, Denny and Gaines make predictions about how plants and animals work in a stochastic universe. Is it possible to pack a variety of ion channels into a cell membrane and have each operate at near-peak flow? Why are our arteries rubbery? The concept of a random walk provides the necessary insight. Is there an absolute upper limit to human life span? Could the sound of a cocktail party burst your eardrums? The statistics of extremes allows us to make the appropriate calculations. How long must you wait to see the detail in a moonlit landscape? Can you hear the noise of individual molecules? The authors provide answers to these and many other questions.

After an introduction to the basic statistical methods to be used in this book, the authors emphasize the application of probability theory to biology rather than the details of the theory itself. Readers with an introductory background in calculus will be able to follow the reasoning, and sets of problems, together with their solutions, are offered to reinforce concepts. The use of real-world examples, numerous illustrations, and chapter summaries--all presented with clarity and wit--make for a highly accessible text. By relating the theory of probability to the understanding of form and function in living things, the authors seek to pique the reader's curiosity about statistics and provide a new perspective on the role of chance in biology.

"An excellent introduction to the uses of probability theory for a reader who is more familiar with biology than with mathematics ... Denny and Gaines have done a valuable service to biologists who are interested in a quantitative approach to life sciences."--Paul Janmey, Nature Cell Biology "A lively, well-written text... A student who reads this book closely will come away with a much deeper appreciation for the universality of diffusion mechanics in science, the deep connections between the distributions central to inferential statistics, the importance of extreme events and how to deal with them analytically, and, most importantly, the power and limitations inherent in the underpinning of the inferential statistics that the student has learned elsewhere."--Mark R. Patterson, American Scientist "This is a fantastic book. Indeed, one would be hard-pressed to find a more readable and lucid introduction to probability theory."--Gary B. Gillis, Journal of Experimental Biology

Prefacep. xi
The Nature of Chancep. 3
Silk, Strength, and Statisticsp. 3
What Is Certain?p. 7
Determinism versus Chancep. 8
Chaosp. 9
A Road Mapp. 11
Rules of Disorderp. 12
Events, Experiments, and Outcomesp. 12
Sarcastic Fishp. 13
Bipolar Smutp. 14
Discrete versus Continuousp. 17
Drawing Picturesp. 18
Probabilityp. 19
Rules and Toolsp. 20
Events Are the Sum of Their Partsp. 20
The Union of Setsp. 21
The Probability of a Unionp. 23
Probability and the Intersection of Setsp. 24
The Complement of a Setp. 25
Additional Information and Conditional Probabilitiesp. 27
Bayes' Formulap. 29
AIDS and Bayes' Formulap. 30
The Independence of Setsp. 32
Probability Distributionsp. 34
Summaryp. 37
Problemsp. 37
Discrete Patterns of Disorderp. 40
Random Variablesp. 40
Expectations Definedp. 42
The Variancep. 46
The Trials of Bernoullip. 48
Beyond 0's and 1'sp. 50
Bernoulli = Binomialp. 51
Permutations and Combinationsp. 53
Waiting Foreverp. 60
Summaryp. 65
Problemsp. 66
Continuous Patterns of Disorderp. 68
The Uniform Distributionp. 69
The Cumulative Probability Distributionp. 70
The Probability Density Functionp. 71
The Expectationp. 74
The Variancep. 76
The Shape of Distributionsp. 77
The Normal Curvep. 79
Why Is the Normal Curve Normal?p. 82
The Cumulative Normal Curvep. 84
The Standard Errorp. 86
A Brief Detour to Statisticsp. 89
Summaryp. 92
Problemsp. 93
Appendix 1: The Normal Distributionp. 94
Appendix 2: The Central Limit Theoremp. 98
Random Walksp. 106
The Motion of Moleculesp. 106
Rules of a Random Walkp. 110
The Averagep. 110
The Variancep. 112
Diffusive Speedp. 115
Diffusion and the Real Worldp. 115
A Digression on the Binomial Theoremp. 117
The Biology of Diffusionp. 119
Fick's Equationp. 123
A Use of Fick's Equation: Limits to Sizep. 126
Receptors and Channelsp. 130
Summaryp. 136
Problemsp. 137
More Random Walksp. 139
Diffusion to Capturep. 139
Two Absorbing Wallsp. 142
One Reflecting Wallp. 144
Adrift at Sea: Turbulent Mixing of Planktonp. 145
Genetic Driftp. 148
A Genetic Diffusion Coefficientp. 149
Drift and Fixationp. 151
Genetic Drift and Irreproducible Pigsp. 154
The Biology of Elastic Materialsp. 156
Elasticity Definedp. 156
Biological Rubbersp. 157
The Limits to Energy Storagep. 161
Random Walks in Three Dimensionsp. 163
Random Protein Configurationsp. 167
A Segue to Thermodynamicsp. 169
Summaryp. 173
Problemsp. 173
The Statistics of Extremesp. 175
The Danger of Cocktail Partiesp. 175
Calculating the Maximump. 182
Mean and Modal Maximap. 185
Ocean Wavesp. 186
The Statistics of Extremesp. 189
Life and Death in Rhode Islandp. 194
Play Ball!p. 196
A Note on Extrapolationp. 204
Summaryp. 206
Problemsp. 206
Noise and Perceptionp. 208
Noise Is Inevitablep. 208
Dim Lights and Fuzzy Imagesp. 212
The Poisson Distributionp. 213
Bayes' Formula and the Design of Rodsp. 218
Designing Error-Free Rodsp. 219
The Origin of Membrane Potentialsp. 220
Membrane Potential in Rod Cellsp. 222
Noise and Ion Channelsp. 225
An Electrical Analogp. 226
Calculating the Membrane Voltagep. 227
Calculating the Sizep. 229
Noise and Hearingp. 230
Fluctuations in Pressurep. 231
The Rate of Impactp. 232
Fluctuations in Velocityp. 233
Fluctuations in Momentump. 235
The Standard Error of Pressurep. 235
Quantifying the Answerp. 236
The Rest of the Storyp. 239
Stochastic Resonancep. 239
The Utility of Noisep. 239
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691094946
ISBN-10: 0691094942
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 312
Published: 23rd September 2002
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.5 x 15.2  x 1.91
Weight (kg): 0.43