Bulletin of Mathematical Biology Vol. 52, No. 4, pp. 583-596, 1990. Pergamon Press pie. Printed in Great Britain. Society for Mathematical Biology

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Evolution of Life Histories of Mammals." Theory and Pattern, Mark S. Boyce (ed.). Yale University Press, New Haven CT, 1988. $45.00 (cloth), 373 pp.

It sometimes takes a second look at familiar situations to bring an awareness of their puzzling eccentricity. So it is with the relation between ecological theory and the natural historical case studies with which most ecologists occupy most of their effort. These studies are ostensibly motivated by theoretical issues, so we might blithely assume that the empirical work is intended to test the theories, according to the classical view of the scientific method. But when we ask just what is being tested, and how is it being tested, the matter becomes awkward.

The areas of theory in ecology comprise sets of assumptions, constituting idealized representations of the system, from which conclusions are deduced by mathematical manipulation. It obviously does not make much sense to attempt to test the validity of mathematics with the sparse and noisy biological data which inevitably are our lot. But it does not make much sense, either, to invest in testing the validity of the assumptions of the theoreticians' models in any strict sense, for we know they are not strictly true. In any practically observable natural setting, the assumptions of theory are bound to be violated grossly: things assumed constant are not, all other things are not equal, and it is not feasible to collect data over a broad enough domain to expect that the departures from the assumptions will cancel out in the aggregate. Further, owing to the practical difficulty of directly measuring the quantities central to the theory, surrogate variables are substituted; and often, in order to limit the number of things which must be measured, the analysis of an empirical study will add even more assumptions to the original theory, so that one study's control variable is another's constraint, and vice versa. What are we to make of all this?

The book under present review, "Evolution of Life Histories of Mammals", edited by Mark S. Boyce, sent me off on this fugue of introspection. With the one exception of a pre-eminently abstract chapter, by William M. Schaffer (on the nature of chaotic dynamics in some representations of density dependent one- and many-species systems), the book's chapters are concerned with natural historical observations. These are variously, intensive studies of a species, comparisons of subpopulations within a species, comparisons among species within a small phylogenetic group, comparisons of species grouped according to major phylogenetic assemblages, and comparisons of species

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across all taxa for which data could be found, looking for pattern in the relations of rates such as mortalities and fecundities. Studies of this sort are familiar enough. But what is the point of the focus on "mammals" in this book? Does this provide some organizing principle that will illuminate the relation of these empirical studies to the body of life history theory which they cite?

The curious thing is that the book does not identify any life history pattern, as encapsulated in a schedule of mortality and fecundity, that is really unique to mammals. On the contrary, mammals exhibit a range of life histories that span an enormous spectrum, which includes some patterns rather like those of quite disparate life forms. So the life histories of mammals do not pose more, or less, of a question, or any different question, than other life histories.

Perhaps the organizing principle has nothing to do with life history theory, and instead originates in the happenstance that a number of scientists have the experience, expertise and interest for accumulating natural historical observa- tions on mammals, and they find it congenial to get together from time to time in order to swap accounts. Incidentally, none of this is to be taken lightly, as the dedication necessary to obtain these hard-won data is considerable, and the results unquestionably are fascinating regardless of their relation to theory.

Indeed, it is the particularity, the diversity, and the detail which make up much of the charm of natural historical facts. But as these facts accumulate, their sheer mass may become daunting. In this circumstance, the role for theory can be as a conceptual framework within which the threatening mud slide of facts may at least be organized and categorized on a basis that appears more comprehensive than would compiling an encyclopedia along, for example, taxonomic lines. From this perspective then, there really is no test of the theory. It is simply a matter of wondering whether the theory, not withstanding its over-simplifications, offers a satisfactory cataloguing device for the facts, not withstanding their obvious violations of the assumptions of the theory, and turning a blind eye to the complications. In other words, if its work, fine; and if it doesn't work, no hard feelings.

The irony of this picture, if it is correct, is that when the attempt is made to apply life history theory to the facts, the quantity of facts is found wanting, even though it was a perceived surfeit of facts that may have prompted the turn to theory in the first place. I will explain the deficit in a moment.

The body of mathematical models and theorems known as life history theory is a comparatively successful area of mathematical biology. The bulk of its mathematical machinery has been directed at, and has adequately addressed, the core problem: relating the multitude of age- and stage-specific traits in a life history to a scalar objective function (the measure of fitness), and constructing a formalism to solve in a limited way for the "optimal" life history (the life history which maximizes the fitness measure in a constant environment).

There is one theoretical loose end: how to characterize the measure of fitness,

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and how to maximize it, when the environment, including the effects of population density, is not constant. As to whether this is a big loose end or a little loose end, the jury is still out.

It would be a little loose end, if it turns out that the existing constant- environment theory is an adequate local approximation for the global fluctuating-environment phenomenon, where the trade-offs between adap- tations to various environmental states are governed by a reasonably simple rule, such as maximizing the weighted geometric mean local fitness over all states, weighting by the respective frequency of those states, with perhaps some correction for serial correlation in states and for the effect of that correlation on the expected age distribution on entering each respective state. It would be a big loose end, if it turns out that there is substantially more to it than this.

The present collection actually does not have much to say, in a theoretical vein, about this loose end. Boyce, in his overview chapter, says that it is an important problem, but has little more to offer. Schaffer, in the speculative conclusion to his chapter on chaos, suggests that the loose end is a big one, since optimizing over a chaotic, but deterministic, trajectory is quite beyond the reach of available methods, and so it possibly belongs in a realm of theory quite unlike anything we now have. In the next sentence, however, Schaffer sows the seeds of a, counter-argument that is at least as plausible. Quite possibly evolution is almos t as incapable as we are at carrying out such an optimization: in other words, if deterministic chaos is from randomness, with modest amounts the theory of optimizing in the face of a enough, thank you.

practically impossible to distinguish of data of modest accuracy, perhaps random environment will serve well

Returning now to the promise of that portion of life history theory which I alleged was successful, why couldn't this serve as a cornucopia of testable hypotheses? The problem is that this theory holds out the provocation of explaining and predicting evolutionary optimality; but optimality of a life history (or of any other strategy) is judged relative to the possible set of available alternative life histories, and while we can readily observe the strategy that has evolved, the full details of the possible set are obscured by a veil of both theoretical and practical difficulties. In a hypothetical case, where the heavens opened, the angels sang, and the configuration of the possible set were given, the present theory would be adequate, I believe, to predict, for a constant environment, the optimal life history, which might then be compared to evolution's solution. But without knowledge of the possible set, the theory cannot specify the optimum.

The panoply of comparative methods in empirical life history studies are attempts to square this particular circle, but I fear they fall short of being truly persuasive. Comparisons between species just reveal a collection of optima from different respective possible sets of physiological and genetic resources.

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Comparisons of subpopulations within a species just reveal the optima from the different phenotypic possible sets realized under the different environments experienced by the respective subpopulations. Studies of the variations among individuals within a population mostly reveal the perturbations to an optimum phenotype resulting from developmental circumstances and accidents of recombination; and besides there is the old sample-size problem of estimating fitness characters on individuals who only die once. None of this really reveals the possible set. A serious attempt to do so will have to be an undertaking on a scale that dwarfs the sorts of projects that we are accustomed to in evolutionary ecology; and I can't imagine what agency would be prepared to fund it on this scale.

And so, the pile of facts turns out to be too small by a wide margin. No doubt it is possible to be more optimistic about all this, but I don't know that the grounds are compelling.

In the meanwhile, the book edited by Boyce, is well-written and well-edited, and full of extremely interesting chapters about the life histories of mammals. I especially enjoyed a magisterial summary by Andrew T. Smith of the life histories of pikas, and an insightful comparison of marsupial and eutherian reproductive rates by John F. Eisenberg. Many of the other chapters also describe twists and turns of real life histories which suggest intriguing theoretical issues that would be fun to pursue someday, if we ever could get the necessary data.

DANIEL GOODMAN Biology Department

Montana State University Bozeman, MT 59717, U.S.A.

Population Harvesting: Demographic Models of Fish, Forest, and Animal Resources (Monographs in Population Biology, Vol. 27), Wayne M. Getz and Robert G. Haight. Princeton University Press, Princeton, NJ, 1989. $45.00 (cloth), $15.95 (paper), 391 pp.

Until recent years researchers and managers in the fields of forestry and fisheries have tended to inhabit separate intellectual worlds, in spite of the many common features of their disciplines. Both, for example, deal with the economic utilization of biologically renewable resources and as such do (or at least should) draw on principles and ideas from the disciplines of economics