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Generalized Moran process
Svoboda, Jakub ; Šámal, Robert (advisor) ; Balko, Martin (referee)
The Moran process is a model for simulating evolutionary dynamics. In that model, one mutant with higher fitness is introduced to a structured population. Evolution is simulated in rounds. In one round, individual is selected proportio- nally to its fitness and spreads to the place of a random neighbour. In this thesis, we motivate the Moran process, present basic results, and define our variant. We work in a vertex dependent model; every individual has fitness according to its type and occupied vertex. In the vertex dependent model we prove two theorems about the number of steps the process has to make to get to the stable state. We show that on the complete graph, the process takes only polynomially many steps and we find a graph where the process take exponentially many steps, but in the normal settings the number of steps is the same as on the complete graph. 1
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Evolutionary dynamics of rDNA clusters in arthropods with holocentric chromosomes
Tymich, Alexandr ; Šťáhlavský, František (advisor) ; Dalíková, Martina (referee)
Nowadays, rDNA clusters displayed by fluorescence in situ hybridization (FISH) are one of the standard cytogenetic markers used to identify chromosome homology, allowing the determination of mechanisms and possible rate of rearrangements during karyotypic evolution of the studied groups. This bachelor thesis presents a review of the variability of rDNA clusters in arthropods with holocentric chromosomes. Most of the groups studied so far (Odonata, Psocoptera, Hemiptera, Lepidoptera, Buthidae and the genus Rhipicephalus) show a conservative number and position of rDNA clusters. However, this fact may be due to the limited amount of data available. Nowadays, best studied is order Lepidoptera, in which a relatively large variability in the number and position of rDNA clusters has been found. This is probably due to chromosome fusion/cleavage, chromosome rearrangements, or transposition of rDNA clusters. Key words: rDNA clusters, holocentric chromosomes, fluorescence in situ hybridization, arthropods, evolutionary dynamics, NOR
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Generalized Moran process
Svoboda, Jakub ; Šámal, Robert (advisor) ; Balko, Martin (referee)
The Moran process is a model for simulating evolutionary dynamics. In that model, one mutant with higher fitness is introduced to a structured population. Evolution is simulated in rounds. In one round, individual is selected proportio- nally to its fitness and spreads to the place of a random neighbour. In this thesis, we motivate the Moran process, present basic results, and define our variant. We work in a vertex dependent model; every individual has fitness according to its type and occupied vertex. In the vertex dependent model we prove two theorems about the number of steps the process has to make to get to the stable state. We show that on the complete graph, the process takes only polynomially many steps and we find a graph where the process take exponentially many steps, but in the normal settings the number of steps is the same as on the complete graph. 1
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