Modelling fluctuating populations.

*(English)*Zbl 0593.92013
A Wiley-Interscience Publication. Chichester etc.: John Wiley & Sons. XIII, 379 p. (1982).

This book is intended as a ”do-it-yourself” manual to enable readers of widely varying levels of mathematical sophistication to formulate, analyse and interpret their own population models. One of four primary aims is to help reverse the increasing division of population biologists into those who possess mathematical self-confidence and those who do not.

For the initially less adept reader whose confidence increases after working through the more elementary material and for those readers who are already mathematically practised, we have set out in chapters 3 and 5 some considerably more challenging deterministic material and in chapters 6 and 7 give an extensive discussion of the state of the art in stochastic modelling. To assist in the learning process at all levels, each chapter in which new techniques are introduced is provided with a set of problems, many of which are based on models recently published in the population-biology literature.

Despite the heated philosophical debate which re-emerges from time to time over the role which mathematics ought to play in the life sciences, we believe that mathematical modelling should be judged on the same grounds as any other scientific tool, namely on what it can deliver.

We thus conclude with three detailed case studies (Chapters 8, 9, and 10) drawn from our own research experience, in which we discuss not only the practical use of the analytic techniques described in the earlier parts of the book, but also the equally vital phases of model formulation and final interpretation. We lay particular emphasis in this section on the testing and verification of our models, and have therefore chosen as our examples laboratory populations which are sufficiently carefully controlled and closely documented for detailed model testing to be a practicable proposition.

For the initially less adept reader whose confidence increases after working through the more elementary material and for those readers who are already mathematically practised, we have set out in chapters 3 and 5 some considerably more challenging deterministic material and in chapters 6 and 7 give an extensive discussion of the state of the art in stochastic modelling. To assist in the learning process at all levels, each chapter in which new techniques are introduced is provided with a set of problems, many of which are based on models recently published in the population-biology literature.

Despite the heated philosophical debate which re-emerges from time to time over the role which mathematics ought to play in the life sciences, we believe that mathematical modelling should be judged on the same grounds as any other scientific tool, namely on what it can deliver.

We thus conclude with three detailed case studies (Chapters 8, 9, and 10) drawn from our own research experience, in which we discuss not only the practical use of the analytic techniques described in the earlier parts of the book, but also the equally vital phases of model formulation and final interpretation. We lay particular emphasis in this section on the testing and verification of our models, and have therefore chosen as our examples laboratory populations which are sufficiently carefully controlled and closely documented for detailed model testing to be a practicable proposition.

##### MSC:

92D25 | Population dynamics (general) |

92-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology |

92D40 | Ecology |

92-02 | Research exposition (monographs, survey articles) pertaining to biology |