Mathematical Ideas in Biology by J. Maynard SmithReview by: Mark WilliamsonJournal of Animal Ecology, Vol. 38, No. 3 (Oct., 1969), p. 796Published by: British Ecological SocietyStable URL: http://www.jstor.org/stable/3056 .

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796 Reviews

price-after all there are 686 pages, and none of the authors wastes any space-or by the reference in the preface to a companion volume, still in the press, supplementing this one.

R. A. HINDE

J. Maynard Smith (1968). Mathematical Ideas in Biology. Pp. viii +152; text-figures. London: Cambridge University Press. 30s (hard-back); 12s (paper-back).

The aim of this book is 'to show that mathematical reasoning is sometimes illuminating in biology'. The wide range of examples discussed certainly show that mathematics is useful in many parts of biology, and that many different mathematical techniques are worth knowing. The topics include the consequences of scale, the genetics of families, natural selection, target theory, the control of muscular movement and of protein synthesis, and morphogenesis, as well as two chapters on population regulation. There is deliberately no treatment of statistics, but there is some discussion of problems in probability including conditional and inverse probabilities.

Each chapter is concerned to show both how to formulate a problem in mathematical terms, and how to solve the equations that result. There are appendices giving, in outline, the formal mathematics of the exponential function, complex numbers, differentiation and integration, and other topics. Most of the text relates to recurrence relations, differential equations and probability.

All the chapters contain some points of interest to ecologists, but the two on population regula- tion, namely chapter 2 (generations separate) and chapter 3 (generations not separate), deal with ecological problems at length. Most of the discussion is of problems of equilibria and their stability, and the nature of oscillations about them. Rather few examples are given, and they are not tied very closely to the theory.

Each chapter ends with problems for the reader, and these relate well to the text. There is a slip in at least one of the answers given, but more interestingly, one problem has lead to a dispute between mathematicians in Nature. As might be expected in a book dedicated to J. B. S. Haldane, the treatment is very confident. This should be helpful, as many biologists would benefit from using mathematics more confidently and boldly.

MARK WILLIAMSON

C. W. Stortenbeker (1967). Observations on the Population Dynamics of the Red Locust, Nomadacris septemfasciata (Serville), in its Outbreak Areas. Pp. viii + 118; 20 text- figures. Agricultural Research Reports 694 ITBON Mededeling Nr. 84. Wageningen: Centre for Agricultural Publications and Documentation. Price Dfl. 15.00.

The author worked with the International Red Locust Control Service centred at Abercorn, Zambia, from 1958 to 1964. He was part of the team studying the red locust in the neighbourhood of Lake Rukwa in western Tanzania where land temporarily flooded in the rains provides grass- land in the dry season which is very suitable for the mass breeding of this species of locust. The young adults mature at the start of the following wet season and oviposit. The red locust has produced serious outbreaks three times in the last century, but is now carefully watched at Rukwa and incipient outbreaks are destroyed with insecticide.

An understanding of population dynamics requires census information from which the causes of death and changes in reproductive success can be assessed. For locusts this is notoriously difficult; the outstanding feature of this work is that it set out to provide life-table figures and to a considerable extent succeeded. The basic difficulty was the patchy locust distribution over the various suitable areas, which altogether amounted to about 850 square miles; various ingenious methods of sampling were used. The study of oviposition was simplified by controlled burning so that favourable oviposition sites were created. The eggs were then sampled and the resulting hoppers were followed to assess the mortality factors operating over each age interval. The main predators on the first- and second-instar hoppers are thought to be asilid flies and dragonflies. Having estimated the hopper mortality per 1000 yd2/day ( Y), the hopper density (x1) and the pre- dator density (x2) a relationship of the form

Y = -75+0-02x1+25x2

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