Models in Ecology by J. Maynard SmithReview by: M. P. HassellJournal of Animal Ecology, Vol. 44, No. 1 (Feb., 1975), pp. 344-345Published by: British Ecological SocietyStable URL: http://www.jstor.org/stable/3872 .

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344 Reviews

M. S. Mani (Ed.) (1974). Ecology and Biogeography in India. Monographiae Biologicae Vol. 23. Pp. xx+774; 163 figures; 75 monochrome photographs; 2 maps. W. Junk, The Hague. Price Dutc'> Guilders 190.

The Indian sub-continent must bid fair to being the naturalist's paradise, in spite of the better reputation of tropical countries made more famous by the great Victorians. Opening this volume and seeing, side by side, the burning, flat, southern plains, the lush Western Ghats and the stark Himalayas brings back all the wonder, even after a quarter of a century. Nevertheless, the most abiding impression left by the book is its weight; not because it contains nothing else, but because nearly 800 pages of Dr Junk's clay-laden paper is a lot to handle.

There are chapters on topography, geology and climate, the flora and phytogeography by regions. Then comes a fascinating account by Parmanand Lal of the very varied tribal com- munities which form a small, but not in general diminishing, percentage of the total population. In contrast, the chapter by A. K. Mukherjee on the vanishing larger fauna is sad. It is followed by a general ecology of the vertebrates and then the biogeography of termites, butterflies Diptera, fishes, Amphibia, reptiles and mammals. Finally a series of five regional biogeographies and a summary chapter, on biogeographical evolution.

Professor Mani, now Emeritus, is, of course, an entomologist and this book is not only edited by him, he has also written eleven of the twenty-four chapters. This is in line with his past enormous industry. Inevitably the book has its bad patches: I counted 177 proper names of insects or places on one page. To someone who has collected, for example, the butterflies of India and whose latent interest is readily aroused, it is amazing how dull some zoo-geography can be when it is in the in-between stage; no longer enthusiastic description and not yet succinct, well-digested, summary.

Fortunately not all the book is like that. L. R. TAYLOR

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Reviews 345

That it should be chosen as the concluding chapter is strange; it would be more aptly placed after Chapter 6 (migration), leaving the- book to end on the evolution of ecosystem stability.

Maynard Smith has wherever possible drawn on unpublished works of his own, which tend to be the most thought-provoking parts of the book. For example, Chapter 3 contains a new analyti- cal model for competition in Nicholson's blowflies; one that elegantly shows how the delays due to developmental time result in the observed oscillations. Chapter 6 has an intriguing analysis of some effects of migration on stability of a predator-prey interaction in a patchy environment. This, however, would have gained considerably by closer reference to previous discussion. One model, for instance, allows four patterns of migration: (1) prey leaving patches with abundant prey, (2) prey leaving patches with abundant predators, (3) predators leaving patches with abundant predators and (4) predators leaving patches with few prey. Maynard Smith concludes that such behaviour tends to synchronize neighbouring patches and will not contribute to stability. Yet in Chapter 4 we saw how predator interference, which leads to behaviour (3) above, can stabilize an interaction, and it is known that predator aggregation at high prey densities, resulting from behaviour (4), can also contribute to stability. Chapter 10 has an interesting sec- tion on the stability of models with three levels (top predators, intermediate predators and prey) with systematic links between. The conclusion is that competition between the prey destabilizes the system, while competition for prey by the predators is stabilizing. Why this should be so is unclear.

In several places Maynard Smith has strongly stressed the effects of age structure and time delays on stability. Indeed this guides the organization of the first parts of the book. Thus, instead of grouping predator-prey interactions together, we move from instantaneous models of predation, to time delays in single-species models, to discrete predator-prey models. This is followed by inter-species competition and then back to predator-prey migration models. A more logical plan would have been to consider firstly the logistic model, followed by delayed feed- back models in a single-species system (e.g. Nicholson's blowfles). Predator-prey interactions could then be grouped together and followed by interspecific competition.

With such correct stress on the importance of time delays, it is surprising that Maynard Smith has been led into making some general statements that only result from the inadequacies of the differential models considered. Thus in Chapter 2 appear the statements that proportional refuges for prey have no effect on stability, while a fixed number of refuges contribute to stability. This is true of the Lotka-Volterra equations. But in any discrete difference model, such as the Nicholson- Bailey model or its more complex descendants, both kinds of refuge can stabilize with the fixed number of refuges having the greater effect.

Similarly, in Chapter 5, Maynard Smith states that while predator-prey interactions can cause oscillations, 'competitive interactions do not produce oscillations'. This again is true of the Lotka-Volterra competition equations, with their basis in the logistic. Introduce time delays, however, as occur in the real world, and the complete range of exponential damping, oscillatory damping or stable limit cycle behaviour as found in predator-prey models are possible.

There are other more minor criticisms. For instance, in Chapter 4 it is stated that 'unlike insect host parasitoid systems, most of the predation [by warm-blooded predators] occurs between breeding seasons when prey recruitment cannot replace losses'. Surely this is no different to the univoltine insect whose immature stages are parasitized and recruitment awaits the following year. There are several places in the book where more attention should have been paid to the presentation of equations. For example, equations 7(a) and 7(b) contain different symbols for the intrinsic rate of increase, and the symbol b in equation 7(a) is only defined in the next section. In the same chapter, Holling's disc equation (eqn 16) is followed by no explanation that a is the 'attack coefficient' and b is the 'handling time'.

The book is not designed as a basic student's text, but should be useful to research workers and advanced students in ecology. Strangely, it requires many more ecological than mathematical skills of the reader since much background information is omitted and some of the important biological assumptions within different models remain implicit. It is up to the reader to sort them out. Treated as a whole the book shows well how simple models can lead to stimulating ideas in population and ecosystem dynamics. Their confirmation must await the accumulation of data.

M. P. HASSELL

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