*Population Genetics*covers all the standard material of an introductory population genetics text but really is concise, coming in at just over two hundred pages.

It is illustrated with examples and case studies drawn from nine classic papers from the 1950s through 1980s. Gillespie doesn't treat the history of population genetics himself, but finding and reading these papers — not all, unfortunately, freely available online — gives a good feel for how the theory was developed. There's some mention of outstanding questions, but the attention is on "that part of population genetics that is central and incontrovertible".

Gillespie finds room for a decent range of problems, closely integrated into the text and directly supporting it, and even for solutions to maybe half of these. Python is used wherever programming is involved.

The approach is mathematical but never gets hung up on completeness, with some resort to "proof by reference". As Gillespie says, "the real work of theoretical population genetics is not in the mathematics but in the models". He does makes some use of simulations, but shies away from the "gruesome prospect" of ugly mathematics. So the usual simplifications are made: when it comes to quantitative genetics, for example, norms of reaction get a passing mention and then genetic-environmental covariance is just assumed to be zero.

The assumed mathematics is only basic algebra and simple probability theory, but the speed of the presentation really assumes prior familiarity with more than that. At one point Gillespie writes "If the concept of a mean is unfamiliar, read from the beginning of Appendix B through page 191", but anyone unfamiliar with the concept of a mean is most unlikely to be able to follow the explanation given there, in terms of the moments of random variables. One short appendix covers some important sequences and series and Taylor expansion; a second longer one covers important random variables and gives two derivations of more complex results. Similarly, only a very basic knowledge of genetics is assumed.

The assumed knowledge may not be great, but the presentation moves at
quite a fast pace. *Population Genetics: A Concise Guide* would be a
fine text for higher-level undergraduates or lay readers with the right
background. It is nicely organised and clearly presented, and recommended
to anyone after an introduction to the core ideas of the field.

Note: This second edition has "grown by about 20 percent ... the introduction of more material on stochastic processes in evolution, a new section on genetic load theory, and a new chapter on two-locus theory. The sections on effective population size and selection in a changing environment have been completely rewritten."

November 2011

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