Universität zu Köln

Oros, Daniel (2022). Hypercubes, Peak Patterns and Universal Positive Epistasis. Masters thesis, Universität zu Köln.

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Abstract

Genes and their interactions with one another crucially affect reproductive success, commonly referred to as fitness. Biallelic models have been used in the past as a mathematical framework to model and explain these interactions. One approach is to represent L biallelic loci as hypercubic graphs, known as L-cubes. On these $L$-cubes, vertices model genotypes and the edges connect the vertices that differ by a single locus value. Assigning fitness values to genotypes gives edges a direction towards higher fitness. Local optimal genotypes, called peaks, then have a higher fitness than all their direct neighbors. Recently, researchers have introduced the notion of peak patterns, referring to the set of peaks that are unique up to relabeling of vertices. However, a complete characterization of all possible peak patterns has not yet been performed for L => 4. This work concerns itself with an analysis for L=4 regarding peak patterns and all possible instances of sign and reciprocal sign epistasis, substantiating the importance of peak patterns. Additionally a lower bound proportional to $2^{2^{L-1}}$ is provided for the set containing all possible peak patterns for a given L. Informed by this, all peak patterns up to L=6 are computed and joined with a variant of Fishers Geometric Model having a one dimensional phenotype. Moreover peak patterns are used to calculate the maximal number of peaks for the staircase triangulation up to L=8.

Item Type:	Thesis (Masters thesis)
Creators:	Creators Email ORCID ORCID Put Code Oros, Daniel daniel.aeg@gmx.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-633868
Date:	2022
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institut für Biologische Physik
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Peak Patterns English Fitness Landscapes English Geometric Theory of Fitness Landscapes English Shape English Staircase Triangulation English Epistasis English
Date of oral exam:	3 June 2022
Referee:	Name Academic Title Krug, Joachim Prof. Dr. Crona, Kristina Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/63386