Chance in Biology

by Denny, Mark; Gaines, Steven

• ISBN13: 9780691094946
• ISBN10: 0691094942
• Edition: Reprint
• Format: Paperback
• Copyright: 2002-09-03
• Publisher: Princeton Univ Pr

Summary

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.

Table of Contents

Preface	xi
The Nature of Chance	3	(9)
Silk, Strength, and Statistics	3	(4)
What Is Certain?	7	(1)
Determinism versus Chance	8	(1)
Chaos	9	(2)
A Road Map	11	(1)
Rules of Disorder	12	(28)
Events, Experiments, and Outcomes	12	(7)
Sarcastic Fish	13	(1)
Bipolar Smut	14	(3)
Discrete versus Continuous	17	(1)
Drawing Pictures	18	(1)
Probability	19	(1)
Rules and Tools	20	(14)
Events Are the Sum of Their Parts	20	(1)
The Union of Sets	21	(2)
The Probability of a Union	23	(1)
Probability and the Intersection of Sets	24	(1)
The Complement of a Set	25	(2)
Additional Information and Conditional Probabilities	27	(2)
Bayes' Formula	29	(1)
AIDS and Bayes' Formula	30	(2)
The Independence of Sets	32	(2)
Probability Distributions	34	(3)
Summary	37	(1)
Problems	37	(3)
Discrete Patterns of Disorder	40	(28)
Random Variables	40	(2)
Expectations Defined	42	(4)
The Variance	46	(2)
The Trials of Bernoulli	48	(2)
Beyond 0's and 1's	50	(1)
Σ Bernoulli = Binomial	51	(9)
Permutations and Combinations	53	(7)
Waiting Forever	60	(5)
Summary	65	(1)
Problems	66	(2)
Continuous Patterns of Disorder	68	(38)
The Uniform Distribution	69	(8)
The Cumulative Probability Distribution	70	(1)
The Probability Density Function	71	(3)
The Expectation	74	(2)
The Variance	76	(1)
The Shape of Distributions	77	(2)
The Normal Curve	79	(3)
Why Is the Normal Curve Normal?	82	(2)
The Cumulative Normal Curve	84	(2)
The Standard Error	86	(3)
A Brief Detour to Statistics	89	(3)
Summary	92	(1)
Problems	93	(1)
Appendix 1: The Normal Distribution	94	(4)
Appendix 2: The Central Limit Theorem	98	(8)
Random Walks	106	(33)
The Motion of Molecules	106	(4)
Rules of a Random Walk	110	(5)
The Average	110	(2)
The Variance	112	(3)
Diffusive Speed	115	(1)
Diffusion and the Real World	115	(2)
A Digression on the Binomial Theorem	117	(2)
The Biology of Diffusion	119	(4)
Fick's Equation	123	(3)
A Use of Fick's Equation: Limits to Size	126	(4)
Receptors and Channels	130	(6)
Summary	136	(1)
Problems	137	(2)
More Random Walks	139	(36)
Diffusion to Capture	139	(6)
Two Absorbing Walls	142	(2)
One Reflecting Wall	144	(1)
Adrift at Sea: Turbulent Mixing of Plankton	145	(3)
Genetic Drift	148	(6)
A Genetic Diffusion Coefficient	149	(2)
Drift and Fixation	151	(3)
Genetic Drift and Irreproducible Pigs	154	(2)
The Biology of Elastic Materials	156	(7)
Elasticity Defined	156	(1)
Biological Rubbers	157	(4)
The Limits to Energy Storage	161	(2)
Random Walks in Three Dimensions	163	(4)
Random Protein Configurations	167	(2)
A Segue to Thermodynamics	169	(4)
Summary	173	(1)
Problems	173	(2)
The Statistics of Extremes	175	(33)
The Danger of Cocktail Parties	175	(7)
Calculating the Maximum	182	(3)
Mean and Modal Maxima	185	(1)
Ocean Waves	186	(3)
The Statistics of Extremes	189	(5)
Life and Death in Rhode Island	194	(2)
Play Ball!	196	(8)
A Note on Extrapolation	204	(2)
Summary	206	(1)
Problems	206	(2)
Noise and Perception	208	(42)
Noise Is Inevitable	208	(4)
Dim Lights and Fuzzy Images	212	(1)
The Poisson Distribution	213	(5)
Bayes' Formula and the Design of Rods	218	(1)
Designing Error-Free Rods	219	(6)
The Origin of Membrane Potentials	220	(2)
Membrane Potential in Rod Cells	222	(3)
Noise and Ion Channels	225	(5)
An Electrical Analog	226	(1)
Calculating the Membrane Voltage	227	(2)
Calculating the Size	229	(1)
Noise and Hearing	230	(9)
Fluctuations in Pressure	231	(1)
The Rate of Impact	232	(1)
Fluctuations in Velocity	233	(2)
Fluctuations in Momentum	235	(1)
The Standard Error of Pressure	235	(1)
Quantifying the Answer	236	(3)
The Rest of the Story	239	(1)
Stochastic Resonance	239	(6)
The Utility of Noise	239	(3)
Nonlinear Systems	242	(2)
The History of Stochastic Resonance	244	(1)
Summary	245	(1)
A Word at the End	246	(1)
A Problem	247	(1)
Appendix	248	(2)
The Answers	250	(29)
Chapter 2	250	(6)
Chapter 3	256	(6)
Chapter 4	262	(4)
Chapter 5	266	(3)
Chapter 6	269	(2)
Chapter 7	271	(2)
Chapter 8	273	(6)
Symbol Index	279	(5)
Author Index	284	(2)
Subject Index	286