Srivastava, Malvika (2018). Epistasis, Shapes and Evolution. Masters thesis, Universität zu Köln.

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Along with being consequential for evolution, epistasis is also quite prevalent in nature. Thus, it is important to study it. Till date, there exist many methods of inferring epistasis from experimental and theoretical fitness landscapes. The theory of shapes of fitness landscapes is another addition to that list. In this thesis, the shape theory of fitness landscapes is first introduced and then compared to pre-existing methods of gauging epistasis. From such a comparison for 3 locus landscapes, it turns out that landscapes of different interaction types differ in ruggedness, number of reciprocal sign epistasis motifs and presence of higher order epistasis. Next, the applicability of shapes in studying empirical fitness landscapes is explored. Here the theory proves to be useful because the additional tests suggested by the Markov basis further corroborate the diminishing returns epistasis hypothesis, especially for the β-lactamase landscape with synonymous mutations. Moreover, the triangulation of the landscape of large effect mutations has a particular genotype as vertex of every tetrahedra in the triangulation, indicating the presence of that genotype in all fittest populations. Finally, the effect of the shape on the evolutionary dynamics is discussed. For two locus landscapes, the equilibration time of the mutation-selection dynamics has a sharpness exactly at the transition point between the two shapes. Further, it was found that Eshel and Feldman’s results regarding the advantage of recombination in two locus permutation invariant landscapes can be extended to three locus landscapes. It turns out that in three out of the six shapes of permutation invariant landscapes, recombination is "advantageous", while in the other three, it is "dis-advantageous". This extensive analysis of its applicability indicates that the shape theory offers useful insights while studying empirical landscapes, however additional constraints are needed to predict evolution on landscapes of different shapes.

Item Type: Thesis (Masters thesis)
CreatorsEmailORCIDORCID Put Code
Srivastava, Malvikasmalvika95@gmail.comUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-94942
Date: 27 December 2018
Language: English
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects: Mathematics
Life sciences
Uncontrolled Keywords:
Fitness LandscapesUNSPECIFIED
Geometric theory of fitness landscapesUNSPECIFIED
Advantage of RecombinationUNSPECIFIED
Date of oral exam: 25 January 2019
NameAcademic Title
Krug, JoachimProf. Dr.
Refereed: Yes


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