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Mathematical theory of population genetics, fall 2012

Population genetics studies the genetic composition of biological populations, and its change under the influence of various factors, including natural selection, mutation, recombination and migration. Population genetics thus provides the basis for understanding the evolutionary processes that have led to the biodiversity we encounter today. 

In this course we get familiar with focal concepts and build a theoretical framework to gain proper understanding of the relevant evolutionary processes. Course will cover elementary population genetics (e.g. Hardy-Weinberg law, selection at single locus), mutation-selection models at two or more loci, equations for quantitative traits under selection and basic principles of coalescent theory.


Tadeas Priklopil


10 cu.


Advanced studies


Basic knowledge of dynamical equations (discrete dynamical systems and differential equations) and probability theory.


Weeks 36-42 and 44-50, Monday 14-16 in room C122 (note the change!) and Wednesday 14-16 in room B322. Two hours of exercise classes per week.

Note! Monday lecture 26.11 cancelled.


Date, time and place: 17.12.2012, 14.15 - 16.00, room C122.


Lecture notes will be mainly based on the book by Burger (2000): The mathematical theory of selection, recombination and mutation, and on the book by Wakeley (2009): Coalescent theory: an introduction. 


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Tadeas Priklopil


Below you will find a link to a feedback page, where you can express (anonymously) your thoughts about the course. In particular, it would be interesting to know whether some topics dealt in the course were too superficial/too detailed, or whether you have suggestions for future topics, or whether the course material should be improved (and if so, in which way), or etc.. ALL THE COMMENTS ARE WELCOME! Note, that you have a big influence on the content of the course, which will be given also in future semesters (those who give signed comments will be in the acknowledgments of the course material!).

Link to the feedback page   (note that the textbox can be enlarged by dragging the bottom right corner)

Course material

Lecture notes

week 1
5.9. Introductory lecture. Slides 1  
week 2
10.9. Hardy-Weinberg
12.9. Average effects
Exercise 1
week 3
week 4
24.9. Selection models - part I
26.9. Selection models - part II
Exercise 2
week 5
1.10. Protected coexistence - part I
3.10. Protected coexistence - part II
Exercise 3 





Lecture notes                                                                                                          Slides                                                Exercises                                  Solutions

                                                                                                                          5.9.2012  Lecture 1                          13.9.2012 Exercise 1

10.9.2012 Hardy-Weinberg (Lecture 2)                                                                10.9.2012 Lecture 2                         27.9.2012 Exercise 2                       Solutions 2 (corrected)

12.9.2012 Average effects (temporary notes, Lecture 3)

24.-26.9.2012 Selection models (Lectures 4-5 )                                                    26.9.2012 Lecture 6                         4.10.2012 Exercise 3                       Solutions 3

1.10.-3.10.2012 Protected coexistence (Lectures 6-8)                                           3.10.2012 Lecture 8                        11.10.2012 Exercise 4                       Solutions 4

8.10.-10.10.2012 Migration-selection (Lectures 9-10)  (corrected)                                                                                18.10.2012 Exercise 5 (corrected)      Solutions 5

15.10-17.10.2012 Mutation-selection (Lectures 10-11)                                        17.10.2012 Lecture 12                     1.11.2012 Exercise 6                         Solutions 6 Lynch 2010

29.10.-31.10.2012 Two loci (Lectures 13-14)                                                                                                               8.11.2012 Exercise 7                         Solutions 7 

5.11.-7.11.2012 Wright-Fisher, Moran (Lectures 15-16) (corrected)                                                                              15.11.2012 Exercise 8  (corrected)      Solutions 8     

12.11.-21.11 Standard coalescent                                                                                                                               29.11.2012 Exercise 9               Solutions 9

28.11 - 3.11. Notes based on Möhle 2000 and Kingman 1982

3.11-5.11 Properties of T_i and Human-Neanderthal couples                                                                                           13.12.2012 Exercise 10

Appendix I Perron-Frobenius - stability

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