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 eventsusing 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 nearpeak 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 realworld examples, numerous illustrations, and chapter summariesall presented with clarity and witmake 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.

Front Matter Front Matter (pp. ivi) 
Table of Contents Table of Contents (pp. viix) 
Preface Preface (pp. xi2) 
1 The Nature of Chance 1 The Nature of Chance (pp. 311)Spider silk is an amazing material. Pound for pound it is four times as strong as steel and can absorb three times as much energy as the kevlar from which bulletproof vests are made (Gosline et al. 1986). Better yet, silk doesn’t require a blast furnace or a chemical factory for its production; it begins as a viscous liquid produced by small glands in the abdomen of a spider, and is tempered into threads as the spider uses its legs to pull the secretion through small spigots. Silk threads, each a tenth the diameter of a human hair, are woven...

2 Rules of Disorder 2 Rules of Disorder (pp. 1239)The theory of probability is a formal branch of mathematics with elegant theorems, complicated proofs, and its own book of jargon. Despite these potential obstacles, people use probability informally nearly every day. When we play games, decide what to wear by glancing at the morning sky, or pick the route we will take to get across town during rush hour, we often rely on crude perceptions of probability to make decisions in the face of uncertainty. Even the most mathphobic individuals occasionally use elementary aspects of probability theory to guide their actions. Unfortunately, such primitive applications of probability are often...

3 Discrete Patterns of Disorder 3 Discrete Patterns of Disorder (pp. 4067)In the last chapter we developed a number of rules to help us explore chance events. All of these rules were devised to allow us to enumerate the probability distribution for a random experiment. By being able to list all of the possible outcomes of an experiment and to associate each outcome with a probability, we have an invaluable tool; as we will see, knowledge about probability distributions allows us to solve many types of problems. But there is one issue that challenges our arsenal of techniques—large sample spaces. We have focused so far on relatively simple experiments with...

4 Continuous Patterns of Disorder 4 Continuous Patterns of Disorder (pp. 68105)Life is not always discrete. As a result, there are many circumstances in biology in which the outcome of an experiment does not readily correspond to an integer value. For example, when two lions fight for a prey item, the approach we have taken so far is to assume that one predator wins (and therefore is free to consume the entire prey), while the other loses and gets nothing. In reality, it is quite possible for each predator to make off with a fraction of the kill. Two arms and a leg might amount to 36% of the overall calories...

5 Random Walks 5 Random Walks (pp. 106138)In this chapter and the next we make our first practical, scientific use of the probability distributions introduced in chapters 3 and 4. We will show you how the binomial and normal distributions can be used to explain phenomena as farranging as molecular diffusion and the rates at which phytoplankton are mixed in tropical lagoons, how the genetic composition of a population can drift across generations, and why your arteries are rubbery. All of these subjects depend on the statistics ofrandom walks. We begin with a discussion of molecular diffusion.
It is commonly understood that heat is a form...

6 More Random Walks 6 More Random Walks (pp. 139174)In the last chapter, we explored random walks in the context of molecular diffusion, and confined our discussion to cases of motion along a single axis. But these simple examples are merely an hors d’ouevre to the rich banquet of biological problems that can be addressed using the concepts of random motion. In this chapter, we will examine two of these: the question of how long it takes an object to bump into the edge of its environment, and the question of why rubber is elastic. In the process we will expand our understanding of random walks to include motion...

7 The Statistics of Extremes 7 The Statistics of Extremes (pp. 175207)In this chapter we follow yet another strange example of a random walk to see where it will lead. Eventually, after wandering through the risks of cocktail parties and ocean waves, we will arrive at a branch of statistics that deals with the extremes of nature, society, and technology. What is the oldest age to which a human being will ever live? Is there ever likely to be another 0.400 hitter in major league baseball? How likely is it that a jet engine will flame out on your next trip to Chicago? When we finish this chapter we will be...

8 Noise and Perception 8 Noise and Perception (pp. 208249)Biologists are accustomed to dealing with random fluctuations. The size of a population may fluctuate, the physical environment varies through time, and (being complex creatures) both plants and animals exhibit behaviors that can appear to be stochastic. In many of these cases, it is possible to cling to the hope that if we knew just a little bit more about how the population, environment, or organism worked, we could predict the fluctuations that now appear random. There are aspects of life, however, where random behavior, what we will callnoise, is unavoidable. In this chapter we will expand our repertoire...

9 The Answers 9 The Answers (pp. 250274)1. Enumerate the sample space. There is only one gesture in which all five fingers are folded; similarly, there is only one gesture in which all fingers are raised. There are five gestures in which a single finger is raised and (through a consideration of the complement of each gesture) five in which a single finger is folded. With a bit of fiddling you should be able to convince yourself that there are ten different gestures in which two fingers are raised and three folded and another ten in which three are raised and two folded. In all, there are...

Literature Cited Literature Cited (pp. 275278) 
Symbol Index Symbol Index (pp. 279283) 
Author Index Author Index (pp. 284285) 
Subject Index Subject Index (pp. 286291)