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Introduction to theoretical population genetics. (English) Zbl 0839.92011
Biomathematics (Berlin). 21. Berlin: Springer-Verlag. xi, 369 p. (1992).
“This book covers the areas of theoretical population genetics that can be investigated rigorously by elementary mathematical methods” (from the Preface). The required basic genetics are presented in the text. Indeed, the reader only needs calculus, linear algebra, and elementary probability theory. However, good mathematical ability is required to follow through. The “major mathematical theme is the dynamical analysis of recursion relations.” The option on elementary mathematics makes the book appropriate for an advanced undergraduate or a graduate course for Biology majors or for a course for Applied Mathematics majors. Unfortunately, this leaves out some important topics such as, for example, diffusion approximation models when random genetic drift is present (although an introductory study by elementary methods is presented) or the study of the effects of environmental random variations.
However, the core of the subject is covered with extremely high standards on completeness, depth of coverage, generality, clear formulation of the biological assumptions, appropriate references, and careful and rigorous analysis (even when appropriate illuminating approximations are used). No textbook I know goes as far on those regards. This makes it a reference book everyone seriously interested on the subject should have. The list of chapters gives the spectrum of covered topics:
1. Introduction. 2. Asexual haploid populations. 3. Panmictic populations. 4. Selection at an autosomal locus (plus mutation, maternal effects, meiotic drive, and including density and frequency dependence). 5. Nonrandom mating. 6. Migration and selection. 7. $$X$$-linkage. 8. Two loci. 9. Inbreeding and random drift (including calculus of inbreeding coefficients from pedigrees). 10. Quantitative genetics.

##### MSC:
 92D10 Genetics and epigenetics 92-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology