Review: Despite the importance of mathematics and statistics in ecology it still remains one of the more difficult areas to teach. It's hard to see why since most people who take advanced courses have the ability to handle abstract concepts by definition. Perhaps it's the way that we get into the subject. With this end in mind, two texts have been juxtaposed in the review system giving this reviewer a chance to see two very different approaches to the topic.

In this text (see here for the other), the author argues that what is needed is a descriptive guide to numbers so that people gain an appreciation of the background to the work. If this is true then it follows that subsequent work will be more accurate and use better mathematical and statistical models. The first chapter aims to highlight why we need maths and why it's important. One element here is the need for a rigorous method - the scientific method - which is described in detail in chapter two. Once data have been collected they need to be displayed which is where chapter three's data display ideas come in. Chapter four changes direction with a look at experimental design and the traps we need to be aware of. Up to this point, most of the discussion is about getting a strong foundation for the data from which further analysis can proceed. Starting with chapter five, the move is towards examining the ways we can deal with data to better understand any trends etc. One of the first ideas you'd need to note is whether the data show any real trend or feature - significance in statistical testing - which is what chapter five deals with. However, good a test we are only ever going to look at a portion of the data and so chapter six outlines the ways in which we can consider sampling and the types of tests we can use. Chapter seven moves on to examine the normal distribution and the tests we can use to compare population and sample means. This is followed by a brief overview of errors and their impact upon the results. One of the most important measures in ecology is the degree to which populations vary from each other. There are numerous tests but analysis of variance is the key. Here, we study the ways in which our samples might vary with changing factors. Chapter 9 to 11 take a different number of factors and show us how we can get the right statistical measure for our results. There's also a discussion about the various traps that we can fall into. One point noted in chapter 12 is the range of tests available (with the concomitant need to choose the right one). Part of this range is seen in the discussions in chapters 12 and 13 which examine more detailed tests such as transformations and nested ANOVA. Chapter 14 looks in a different direction when it studies correlation and regression, a topic expanded by the next chapter which considers some of the more advanced ideas. Chapters 16 to 18 change direction again in looking at non-paramtric statistics i.e. those whose population parameters are not known (as against the previous tests where this was established). Chapter 19 focusses on choosing the right test which leaves a final chapter to argue for a sound ethical way of carrying out research.

This is an interesting text in many ways. This reviewer is not convinced that it has completely argued its case but it has put forward a good deal of useful information. The information is there but the organisation can leave the reader puzzled. Had the text started with choosing tests and the ethics and details behind decision making then it would have given the reader a sounder footing. Then , it would be possible to describe the range of tests sound in the knowledge that the basic philosophy had been covered. Despite that, this is a useful text not least because of its constant reminder to the scientists to get help, to consider alternatives and to plan. It is very unlikely that any one text will serve all our needs for mathematics and statistics (and this text does have a good bibliography and recommendations for texts) so readers should consider this as a good introduction to thinking and planning.