Acta Biotheoretica 42: 85-87, 1994. 9 1994 KluwerAcademic Publishers. Printed in the Netherlands.

REVIEWS Paul Doucet and Peter B. Sloep: Mathematical Modeling in the Life Sciences. Ellis Horwood, New York etc., 1992, (Series: Mathematics and Its Applications), 490 + xiv pp.,ISBN 0-13-562000-7 Cloth, 0-13-562018-X Paper. This is a delightful book, well-written, balanced and inspiring. As the preface explains, the aim of the book is to provide the material for a general basic course devoted to the art of applying mathematics, as a language rather than a bag of tricks, in the life sciences. Much attention is given to the ideas, concepts and methods from the theory of dynamical systems, but statistics, computer simulation and methodological considerations are certainly not forgotten as one can infer from the following list of chapter titles: 1. Processes and differential equations; 2. Differential equations and difference equations; 3. Computer simulation; 4. Compartment systems; 5. Dynamic Systems; 6. State space analysis and stability; 7. Linear systems; 8. Using graphs; 9. Curve fitting; 10. Probability: an introduction; 11. Stochastic models; 12. Statistical inference; 13. Working with models; 14. Constructing models; 15. Chemical kinetics; 16. Physiological control; 17. Growth; 18. Population dynamics; 19. Fishery; 20. Mathematical notions and techniques. To obtain some impression of the didactical quality, without suffering too much from my own prejudices, I concentrated on chapter 12, statistical inference, since I have no teaching or other experience with this subject. I found the exposition very clear, with new ideas introduced at a pleasant pace and deliberate pitfalls to keep students alert. Concepts and methods are introduced in the context of examples, next scrutinised to see what is really essential and then general conclusions are stated at the end. The aim is insight, not easy recipes. There are a couple of exercises and for most of these answers are given at the end of the book. The same attitude, be pragmatic but strive for insight, characterizes chapter 13 on methodological issues. After all this praise, it's time to say a few words about what the book does NOT offer. The attention is restricted to relatively elementary tools (the Laplace transform in Chapter 7 is a bit of an exception). No linear algebra (the authors claim that they made up for this by means of the Laplace transform is not really warranted). A definition and examples of null isoclines, but no Poincar&Bendixson theory. So it is doubtful whether a student who has mastered this book will be able to make a phase plane analysis of a relatively simple prey-predator model. No partial differential equations, so no continuum models. (In the preface the authors say that, in their opinion, partial differential equations and linear algebra should be the first mathematical subjects to be treated in a follow-up course.) A second point concerns the conclusions that should follow at the end of a modelling exercise, i.e. the interpretation of the results in biological (or medical or whatever) terms. The authors certainly pay attention to this, but still I missed something. In an attempt to describe clearly what this was, I then realised that I also missed something in the methodological Chapter 13. What is emphasized there is that a theoretical hypothesis leads to predictions that can be tested, and therefore falsified. But what about ecological models

86 that are used as theoretical experiments to help us to make little steps on our long way in unravelling the complicated network of relationships between mechanisms at the individual level and phenomena at the population level? Hopefully the joint effort of many scientists over a long period will finally lead to testable predictions. Meanwhile one has to use models to sharpen and scrutinise our intuition, to explore possibilities, to structure our thinking, .... It then becomes crucial to formulate what conclusions follow, via an analysis of a model, from the assumptions that have been made. Students need training to learn to compare one model with another, rather than with reality. In this respect the book could have offered more. The book is certainly written with much care. It is therefore surprising that there are many (in general innocent) misprints, the funniest of which I found on page 292 where it is stated that "we cannot never be sure of the truth of empirical claims". Other small points of criticism concern: the derivation, on pages 24 and 25, of the variation - of - constants formula by a mathematical trick, rather than on the basis of the interpretation; on page 1 the authors say that they want "a description which could explain the exponential curve" (their emphasis), but I cannot understand what 'explain' means here?; the rather formal exposition of scaling in section 14.4, which may give students the idea that it is much more difficult than it actually is. The book is very well suited for a course. But it is a fact of life that teachers often want to compose their own course. Even for those the book has much to offer, both in the form of ready material and in the form of inspiration for a didactical approach. In conclusion: highly recommended. Odo Diekmann CWI, Amsterdam

Mae-Wan Ho: The Rainbow and the Worm; the Physics of Organisms. Singapore, New Yersey, London, Hong Kong, World Scientific, 1993, ix + 202 pp., ISBN 981-02-1486-3; 981-02-1487-1 (pbk). The most fascinating chapter of this book is, in my eyes, the one on biophotons. These are photons emitted by living organisms spontaneously or, with increased intensity, after exposure to light. The patterns of stimulated emission of, for instance, early fruitfly embryos strongly suggest the photons to be emitted coherently, as in a very weak (multimode) laser. This phenomenon touches closely on the problem of biological individuality. In the author's words: "These observations are consistent with the idea that the living system is one coherent 'photon field' which is bound to living matter" (p. 126). To physicist Fritz Popp they are diagnostic. Even more exciting is the phenomenon of 'super-delayed photon emission' displayed exclusively by synchronously-developing groups of embryos. The observations suggest that this "results from cooperative interactions among embryos within the entire population so that most if not all embryos are emitting light simultaneously" (p. 130). In other words, the embryos together form one coherent system. This is, I think, the most direct evidence to date showing that individual animals can in fact act together as one single system. The tendency to do so must be deeply ingrained in the individual. I have expressed that as the self-and-congener cognitive structure of the

87 individual (Kortmulder, 1986; Kortmulder and Sprey, 1990). This implies that the individual is to a certain degree structured as series of reflections in tailors' mirrors. Only in this way they can easily naturally 'resonate' with each other. Such a concept is in agreement with the necessity of a, quite restricted, early exposure to and interaction with another animal for the healthy development of the individual and with the 'catastrophic' change in behaviour on meeting a real congener in adult life. A.D.F. Addink (pers. comm.) has found that goldfish and other vertebrates maintain elevated stress levels when shut in a calorimeter chamber alone. Company of conspecifics releases stress immediately. Recently, Kortmulder and Feuth-de Bruijn (1993) have demonstrated that two fish interacting in territorial fashion act as one dynamical system with phase transitions and a critical point. Macroscopic coherence is the main theme in the authors quest about Schr6dinger's question: "What is life?" She seems to have put her stakes on quantum coherence as an explanation, and the experiments on coherent photon emission described above certainly provide a strong argument. Yet, I wonder whether the observations might allow other explanations; for instance if it is not the photons themselves that are coherent, but the underlying processes producing them. After all, that "very weak laser" has not (yet?) been observed directly; its existence is being deduced from the timing patterns of photon emission. Critical point phenomena associated with phase transitions and dissipative structures are likely candidates (Prigogine and Stengers, 1984; Kortmulder and Feuth-de Bruijn, 1993). On the other hand, suggesting alternative interpretations in an off-hand manner may do paltry justice to the whole of the argument, since the author does deal with these examples and since there is a high degree of coherence in the whole of the book. Indeed, seeing the importance of the issue and the wide scope of her enquiry, it will be very worthwhile to check for consistency step by step. The book has not made me dream, as held out in prospect by a rather silly back-cover text. However, Ho certainly makes a good case for hers. It is said that Kekul6 dreamed the essence of the chemical structure of aromatic substances before he was able to conceive of a theory. Like Kekul6's, Ho's dreams are about things going round in cycles. "Let us learn to dream!" Kekul6 said, as the story goes. Ho has learned not only to dream, but also how to digest, how to filter, process and criticise them, without throwing the baby out with the bath-water. This is more than can be said of most of us, particularly those who adhere to a strict 19th century mechanicistic or utilitarian standpoint without recognising the dream in it. Besides, Ho's dreams are perhaps a little bit more graceful and they may allow for just that little bit more hope as for the future of mankind and life on this planet.

References Kortmulder, K. (1986). The congener; a neglected area in the study of behaviour. Acta Biotheor. 35: 39-67. Kortmulder, K. and Th.E. Sprey (1990). The connectedness of all that is alive and the grounds of congenership. Rivista di Biologia - Biology Forum 83: 107-127. Kortmulder, K. and E. Feuth-de Bruijn (1993). On some generative orders of behaviour. Acta Biotheor. 41: 329-344. Prigogine, I. and I. Stengers (1984) Order out of Chaos. London, Fontana. Koenraad Kortmulder Ethology Section IEEW University of Leiden