Lecture by Prof. Dr. Joachim Krug

Exercises: Dr. Sungmin Hwang & Dr. Johannes Neidhart



General information

The course will be held on Mondays 14.00-15.30
and Wednesdays 10.00-11.30 in the conference room 0.01 of the Institut für
Theoretische Physik (new building).
Starting on April 20, every second Monday lecture will be replaced by an exercise class.
Exercise sheets will be handed out and can be handed in for correction.
See also.

Note: If you intend to choose this course as part of one of your master modules
you have to participate actively in the exercises.
Active participation will be defined in this course by a minimum score of 50% of the
exercise points. This means, that you have to hand in a (preferably
handwritten) copy of your solution of the exercises regularly and in time to get them graded.


Note: The lecture on (08.07) and the next problem session(13.07) are exchanged.


Exercise Sheets



Lecture Notes


There is no particular textbook which covers the content of this course, nevertheless,
there are several books and review articles which cover different chapters of this lecture.

Introductory slides
Coalescent theory
Sequence space and fitness landscapes
Error threshold: Error class frequencies
Clonal interference and the benefits of sex
A statistical properties of FGM


R. Durrett: Probability Models for DNA Sequence Evolution (Springer, 2008) link
M. A. Nowak: Evolutionary Dynamics (Harvard Univesity Press, 2006)
J. Wakeley: Coalescent Theory (Roberts & Company, 2009)


John W. Drake et al.: Rates of Spontaneous Mutation; Genetics 148 1667 (1998)
Kristina Crona et al.: The peaks and geometry of fitness landscapes; Journal of Theoretical Biology 317 (2013)
Frank J. Poelwijk et al.: Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes; Journal of Theoretical Biology 272 (2011)
Daniel M. Weinreich et al.: Sign Epistasis and genetic constraint on evolutionary trajectories; Evolution, 59(6) (2005)
A.J. McKane, D. Waxman: Singular solutions of the diffusion equation of population genetics; J. Theor. Biology 247 (2007)
Blythe & McKane: Stochastic models of evolution in genetics, ecology and linguistics; J. Stat. Mech. (2007)
Jain & Krug: Adaptation in Simple and Complex Fitness Landscapes;
from Bastolla et al.: Structural Approaches to Sequence Evolution; Springer (2007)
de Visser & Krug: Empirical fitness landscapes and the predictability of evolution; Nat. Rev. Genet. (2014)
Park et al.: The Speed of Evolution in Large Asexual Populations; J. Stat. Phys. (2010)