Review: This is the fourth edition of a text that aims to put maths and statistics at the heart of ecological understanding. For those upgrading from previous editions its key change is in species diversity. For those new to the book, read on.

The idea for the book came from the author's realisation that although there were numerous texts on ecology there were very few that looked at ecology from the point of quantitative analysis. Since, he argued, this was at the heart of much of modern ecology there was a need for an introduction (the primer of the title) to basic maths and statistics. In part this makes ecological models easier to understand; in part it should allow better models to be made because more students would be exposed to mathematical thinking (that this is the fourth edition suggests there is a need). Chapter 1 starts with one of the most basic ecological ideas - population growth. Starting with a simple equation and gradually increasing complexity, the reader is shown how variations on this theme can result in different population results. After showing the results of some population models the chapter ends with a series of questions to work through. This basic structure of increasing complexity, examples and test questions is repeated for subsequent chapters. From the basic population model, the work moves on to consider logistic growth. The lack of limits that underpinned the earlier population equations are replaced by those considering the more realistic limiting factors. Theoretical arguments are backed up by a series of actual cases. Chapter three adds age structures and survivorship curves to the mix. This is followed by discussing changes caused by migration between discrete populations. Up to this point the focus has been on the single population or at least species. Chapter five starts a second phase in this discussions with the consideration that there are always going to be other species involved. We start with the effects of competition and the variations with the Lotka-Volterra equation. Chapter six moves on to predation which has the classic snowshoe hare/lynx example but which also explores some of the important variations on the basic model. Keeping with the multi-species theme but adding the influence of the physical environment, the next chapter looks at the mathematics of island biogeography. Arguably one of the key elements because of its use in conservation the reader can explore both the maths involved as well as some field examples. Chapter 8 examines the role of, principally, Markov models and their use in understanding the concept of succession. Finally, the new work on species diversity is outlined where both maths and models are used to discuss and explore the key concepts. The text is completed with a section on answers to the set questions and a glossary.

This is a text that requires some level of mathematics - calculus and matrices would be key as well as some basic grounding in statistics. Having said that the book is at pains to explain the various steps as it goes along so even if the maths are weak the understanding can still be there. Usefully, each chapter has a decent discussion on the various assumptions that are made about the models. This can be as useful as the models themselves because it is often the unspoken assumptions that are the key to understanding the model's strengths and weaknesses. Overall, a very useful text which should be a companion alongside broader ecology texts as a reminder of the significance that maths has for today's ecology students.