Lilliputians and gorillas pit weights to learn size isn't everything

This is a book with a text that works on many levels, making it relevant to anyone with a professional or academic interest in biology. At the core of the narrative is the belief that there will be a unifying theory for biology in the same way that there is a unifying theory for physics. This belief is based in part on the argument that because all biology is just chemical reactions and because chemistry is just a molecular manifestation of the laws of physics and because these laws are just mathematics, then all biology can be reduced to and explained by mathematical formulas. It is claimed by some, among them Immanuel Kant, that only if biology can stand up to mathematical scrutiny can it move from science to a Science.

John Whitfield accepts that for many biologists mathematics is not their strength, and many will find In the Beat of a Heart challenging for this very reason. However, it is good for any scientist to have his or her most cherished beliefs questioned.

Among the mathematical models reviewed in this book are the fractal network theory, allometry, neutral ecology and the 1/4 power laws. Allometry was described by Julian Huxley, an icon for every biologist, as the most useful theory in biology. An example of the 1/4 power laws is the fact that fluid transport in a plant is proportional to the mass of the plant raised to the power of 3/4. It is easy to see how this might be because biology cannot ignore the laws of physics and in particular the rules of fluid dynamics.

Likewise, Kleiber's law states that metabolic rate = constant x mass 3/4. Although this was first proposed in 1932, it actually got its first airing in 1699 in Gulliver's Travels when Gulliver met the Lilliputians. The little people's king allocated Swift's hero a daily food allowance that was the equivalent to the daily intake of 1,724 of the king's subjects. If a Lilliputian was the same size as Gulliver's index finger, then Gulliver was 26 times taller than a Lilliputian and thus weighed 17,600 times (26³) more than the same Lilliputian. Since 1,724 is 17,600 raised to the power of 0.76, Kleiber's law must be true.

A further theme of this book is that understanding the flow and allocation of energy lies at the heart of understanding biodiversity. Many of these potentially unpalatable models and theories have been devised by biologists who hanker after the precision of physics. Lord May of Oxford, a physicist turned biologist, considers this to be the view of biologists who do not have the faintest clue about what physics is really like. A very important message to emerge from this book is that scientists in all disciplines would gain a great deal from listening to and talking to each other far more than they do at present.

Some passages are disturbing. It is claimed, for example, that the services provided by wildlife are worth $33 trillion (£17.8 trillion) a year. Just the fact that someone felt that any price could be put on the biology without which we are dead is staggering and depressing. Likewise, the suggestion that ecologists need never do any field work is as silly as it was in the 17th century when Robert Morrison (professor of botany at Oxford University) accused John Ray (the greatest English natural historian) of studying botany more in the closet than in the field. Ray's insightful biological observations were, in fact, based on a great deal of field work.

It may be claimed that mathematical models are useful, especially when they fail in interesting ways. Biology is all about change. This is either a delightful challenge or an irritating problem, depending on whether you are a biologist or career researcher. For many biologists, making mathematical models to explain and predict biology is like trying to nail jelly to a wall. I once asked a very wise professor, with 60 years' research under his belt, why a plant produced flush foliage. He paused and then replied that, in his opinion, plants rarely do anything for one reason but normally for half a dozen at least. This makes building mathematical models very difficult.

It might be claimed that physicists and mathematicians take up mathematical modelling of biology because ultimately the only really interesting science explains the world as it relates to humans. This book also shows clearly how science is an entirely human construct. Without humans, there would be no science.

In the Beat of a Heart provides a fascinating insight into how science is done. When Whitfield travels to Costa Rica, the prose becomes Brysonesque. When he describes the teaching of Robert MacArthur as leaving the students feeling that not only were things suddenly much clearer but also that they themselves were suddenly much cleverer, we will all remember particularly gifted teachers in our past. MacArthur was the first person to use the broken-stick methodology to explain the abundance of different species that demonstrates a hollow-curve distribution. The broken stick has now been replaced by the broken-tree model, because as we all know life is a tree not a stick.

Any contemporary account of biology always ends up contemplating the future and in particular the problems associated with conserving our biological heritage. One of the most pressing problems is the control of alien invasive plant species. As this is nigh impossible, prediction of potential perpetrators is a much preferred option. Sadly, this is as difficult as controlling established species.

Models here would be very useful, but as yet there is nothing. However, one model has thrown an interesting light on human behaviour in the developed world. It has been shown that energy consumption, body mass and birth rates are proportional until you examine the situation in the US. There women use as much energy as a (theoretical) 30-tonne gorilla. As Whitfield says, this gives the reader a good idea why some humans have had such a profound effect on their environment.

Timothy Walker is director, Oxford University Botanic Garden.