The book is a collection of chapters on various mathematical aspects of population models. According to the introduction, it arose out of a colloquium on the dynamics of populations, held in Amsterdam in 1983. The volume covers a very wide area of mathematical population theory. Some of the chapters are original papers or reviews of original sources, many others contain purely expository (even textbook) material.
Part A, titled ”Mathematical models for physiologically structured populations: a systematic exposition”, follows a monograph style. It is written by the editors and Hejmans and summarizes, in principle, the immense material published previously by these authors and their collaborators. Chapter I, by the editors, provides an introduction to population models, through three examples, the invertebrate functional response, the size dependent reproduction in ectothermic animals and the cell size distribution.
Chapter II, by the second editor, is devoted to the dynamics of cell populations described by partial differential equations, based on the linear operator semi-group approach. Basic concepts and results of operator semi-group theory are summarized and applied to the investigation of balanced exponential growth generated by mathematical models
Chapter III, by the editors, concerns model building for structured populations, again in the form of partial differential equations. The considerations include mass balances, the delta-functions formalism, limiting processes and other topics (with relevant results from the calculus in an appendix).
Chapter IV, by the editors, is devoted to age-dependence. Besides known results of the linear theory, with the renewal equation as the main tool, certain extensions, both linear and nonlinear, are treated. In Chapter V, by H. J. A. M. Heijmans, the dynamics of the age size-distribution of a cell population is investigated, using the abstract renewal equation in the operator space.
Finally, chapter VI, by the second editor and H. J. A. M. Heijmans (with some contributions by F. van den Bosch), is devoted to nonlinear models. A uniform bibliography and an index of examples are a useful addition to Part A of the book.
Part B, about one-third of the volume, is much more inhomogeneous. Its title, ”From physiological ecology to population dynamics: a collection of papers” is consistent with its contents. Twelve papers are grouped into five ”topics”, individuals and laboratory populations, field populations, cell populations, numerical approaches, and analytical approaches. Despite independent interest of these contributions, it is impossible to characterize them in this short review.