This is a treatise on a mathematical approach to evolution, which reflects considerable progress that mathematical and computational means used in this field have made in recent time. This progress, also caused by an increasing flood of genome data of the last few years, has made these means more powerful, efficient and complex, and their conclusions more realistic. In fourteen survey chapters written by top researchers in the area, we find a compact summary of the state of mathematical techniques and concepts currently used in the field of molecular phylogenetics and evolution. The authors concentrate on fundamental mathematical concepts and research in current reconstruction methods. They describe probabilistic and combinatorial models that address evolution at different stages, from segments of DNA sequences to whole genomes. Methods of exploiting these models for reconstructing phylogenetic trees and networks are shown. It is explained how these reconstructions can be tested in a statistical sense and what the inherent limits of them are.

The book presents a number of mathematical results, which give an in-depth understanding of the phylogenetic tools. The book is of multidisciplinary nature, as it is a link between biology and mathematics. It will be of great value for graduate students and researchers in phylogeny and it offers a wide field of knowledge for applied mathematicians.

Reviewer:

jdr