Charnov, E. L. 1993; Life History Invariants. Oxford University Press, Oxford. xv + 167 pp., £13.50 (pbk). ISBN: 0‐19‐854072‐8 (cloth). ISBN: 0‐19‐854071‐X (paper).

Abstract

There is an enormous literature that examines the allometric relationship log(y) = c + b log(x), where a and b are constants.This literature tends to focus on the slope b.In his book, Life History Invariants, Charnov seeks those relationships in which b is f 1 and then asks how the intercept c varies.Thus, the central interest in this book is the equation y = cx, rearranged as c = y/x, where x and y are some life history characteristics and c is a constant.Thus, for example, c could be sex ratio, the ratio annual clutch size/adult mortality rate or the ratio clutch size/age at maturity.The book is divided into six major chapters: 1) the evolution of the sex ratio, 2) alternative life histories, 3) the evolution of life history characteristics in indeterminate growers, 4) the evolution of life history traits in determinate growers, 5) population dynamics and 6) senescence.No significant new results are presented, the book being an overview of papers previously authored by Charnov.However, it brings this body of work together within a particular framework.It is this framework that is the central motivation of the book.The most important question that arises when considering a particular way of viewing the world is "does the change in perspective give us new insights into the phenomena under study.7".In some cases Charnov does demonstrate that his approach opens novel avenues of analysis, but in others I was not convinced that the approach produced new insights.This is most obvious in the case of the evolution of sex ratio and sex allocation (chapters 2-3).Charnov has made some extremely insightful advances in this area, and these two chapters summarize part of this work.But I cannot see how an emphasis on "symmetry"or "dimensionless numbers" in any way helps me understand more clearly these phenomena than the original approach that focussed on the phenomena themselves.The approach is, however, very useful in the analysis of the evolution of life history traits in indeterminate (chapter 4) and determinate growers (chapter 5).Chapter 4 proceeds from the general growth function, 1, = 1, (1 -e-kx), where 1, is length at age x, 1, the asymptotic length and k is a constant.It has long been known that in fish the ratios lx/la and M/k, where M is mortality rate, are more or less constant for populations within a species and for species within a taxonomic family.Charnov reviews these data, noting both the general agreement in fish and the existence of data that do not conform.Additional data from aquatic invertebrates and reptiles also suggest a rough constancy in the aforementioned ratios.Following this review Charnov presents a theoretical justification for these observations.His argument is based on three assumptions:1) that R, is a suitable fitness measure, 2) that the reproductive value at the age of maturity, V(u), is a power function of the length at maturity (V(a) cc l,P), where p is a constant, 3) there is a trade-off between 1, and k, this trade-off being described by the power function, 1, cc k -h, where h is a constant.From these assumptions Charnov shows how the ratios k/M and 1,/l, are related to the power function exponents h and p.There is