Chance in Biology

  • M. Denny &
  • S. Gaines
Princeton University Press · December 2000 Hardback £24.95/$39.50

Most biologists' professional dealings with probability are likely to be limited to the P value hovering above data points as a statistical test for real differences. Typically, this probability is calculated by a software package, and its origins are lost in the mists of a mostly forgotten course in statistics, or never learned at all. In descriptive biological research, calculating probabilities has no apparent use, whereas in other fields, such as clinical studies, it is so important that it is better left to professional statisticians than to those who do the experiments.

As interdisciplinary work continues to grow, especially in areas in which biology or biomedicine is fused with physics and engineering, a quantitative approach to biological experiments is likely to become more common. Although investigators who are trained primarily in physical sciences have a variety of accessible texts from which to learn biological sciences, those who cross disciplines in the other direction often have a harder time and fewer resources. This book by Mark Denny and Steven Gaines is an excellent introduction to the uses of probability theory for a reader who is more familiar with biology than with mathematics.

One of the strengths of this book is that the authors clearly recognize the difficulty of re-familiarizing the reader with mathematical ideas that may be dormant, but which can be put to use surprisingly easily. The book will probably be of most use to readers who have had at least some exposure to calculus, but the authors have worked hard to remind the reader of basic equations and methods, often in amusing and informative prose. However, there is no compromise here in deriving, completely when possible, the most important equations. A good feature of many derivations is a patient narrative style that stops to consider key features that can assist the reader's intuition.

The first half of the book is an introduction to the basic ideas of probability and statistical analysis, using examples that reflect the authors own specializations in marine biology and biomaterials. The early chapters are engaging and slow-paced. Some of this material is likely to be familiar, but the presentation is somewhat like an informal discussion, so even the standard ideas are a surprisingly pleasant read. An important part of each chapter is a selection of problems. These are designed not to intimidate and are often entertaining, such as the assignment to calculate the probability of inadvertently making an obscene hand gesture when randomly waving to people with unknown customs. Equally important are the answers, which are thorough enough to be a useful guide even when the problems become more difficult. This section ends with a “brief detour to statistics”, which introduces basic concepts as well as important theorems and equations such as the central limit theorem, the binomial equation, the forms of common probability densities and much more. As a reward for following the examples, one also learns many wonderful facts, such as the time it takes for a photon to travel from the centre to the surface of the sun, or why survivors of shipwrecks seldom survive a swim to the shore.

The real beauty of the book is found in the second half, in which the authors “return to our mission.....to apply the theory of probability in a predictive fashion to biology”. Here, by putting to use the formalism and ideas developed in the first half, the usefulness of thinking about probability is demonstrated for a range of problems in biology. Examples from population dynamics, genetics, biopolymer mechanics, environmental studies, sensory perception and other areas are illuminated by straightforward application of the basics learned in the previous portion of the book. This is not a matter of using statistics to analyse data, but rather of seeing the implications of a set of results and beginning to infer the basic rules that govern seemingly random complex behaviours. A good deal of attention is devoted to random walks, and their application to phenomena as diverse as entropic elasticity, survival of predator and prey, and genetic drift. These examples nicely show how such disparate events can be understood by their common underlying processes and by extension of the common, and often surprisingly simple, mathematics that describes them.

As is probably inevitable in a work that touches on many different fields, not everything will be immediately understandable, and some amount of jargon is present, usually in areas that are more closely related to biology than to probability theory. This is a minor concern and unlikely to lead to any real confusion, but some passages such as “many benthic animals have planktonic larvae” will be wonderfully opaque to many readers.

In short, Denny and Gaines have done a valuable service to biologists who are interested in a quantitative approach to life sciences. Being biologists themselves, the authors have an excellent perception of what makes entry into a standard presentation of statistics and probability such an unappealing prospect, and the humour and clarity of the text does a good deal to lower the energy barrier to making the effort. However, as the authors point out, there is no free ride here, and the value of this book will depend on how much effort readers choose to make in using the new tools with which they are presented.