Complex population dynamics. A theoretical/empirical synthesis.

*(English)*Zbl 1062.92077
Monographs in Population Biology 35. Princeton, NJ: Princeton University Press (ISBN 0-691-09021-1/pbk). xvii, 450 p. (2003).

This is an inspiring book on mathematical models of population dynamics any researcher and serious student of the field must read. It attempts to arrive at some basic principles based on empirical evidence and translate them into mathematical models and, in so doing, build a theory of population dynamics, a real theoretical/empirical synthesis as claimed in the subtitle. Real case studies are used to illustrate the making of models. Alternative models are used to test alternative ecological theories or explanatory mechanisms of the observed dynamical behaviour of the ecosystem. This is clearly the way to built a mature predictive scientific theory. Although some of the ideas and methods may be controversial and there is a lot of ground still to be covered, this is a serious attempt in the right direction.

A major concern is the cause of the observed oscillations in many trophic systems. One of the interesting ideas one can find here is the concept of first and second order oscillations and how to distinguish between them by looking at data. Among the exploratory data analysis techniques used for this (nonlinear) time-series data, I found particularly interesting the partial rate correlation function (an alternative to the classical autocorrelation and partial autocorrelation functions), which is particularly adapted to dynamical models of population dynamics.

Part I is on Theory (chapter titles: Introduction; Population dynamics from first principles; Single-species populations; Trophic interactions; Connecting mathematical theory to empirical dynamics). Part II is on Data (chapter titles: Empirical approaches – an overview; Phenomenological time-series analysis; Fitting mechanistic models), and Part III treats Case Studies (chapter titles: Larch budmoth; Southern pine beetle; Red grouse; Voles and other rodents; Snowshoe hare; Ungulates; General conclusions). The book ends with a good Glossary, References and an Index.

A major concern is the cause of the observed oscillations in many trophic systems. One of the interesting ideas one can find here is the concept of first and second order oscillations and how to distinguish between them by looking at data. Among the exploratory data analysis techniques used for this (nonlinear) time-series data, I found particularly interesting the partial rate correlation function (an alternative to the classical autocorrelation and partial autocorrelation functions), which is particularly adapted to dynamical models of population dynamics.

Part I is on Theory (chapter titles: Introduction; Population dynamics from first principles; Single-species populations; Trophic interactions; Connecting mathematical theory to empirical dynamics). Part II is on Data (chapter titles: Empirical approaches – an overview; Phenomenological time-series analysis; Fitting mechanistic models), and Part III treats Case Studies (chapter titles: Larch budmoth; Southern pine beetle; Red grouse; Voles and other rodents; Snowshoe hare; Ungulates; General conclusions). The book ends with a good Glossary, References and an Index.

Reviewer: Carlos A. Braumann (Évora)