**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.