Saakian, David BDavid BSaakianRozanova, OlgaOlgaRozanovaAndrei Akmetzhanov2021-03-162021-03-162008-101539-3755https://scholars.lib.ntu.edu.tw/handle/123456789/5529857 pagesWe introduce an alternative way to study molecular evolution within well-established Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the 1N accuracy, where N is the genome length. For a smooth and monotonic fitness function this approach gives two dynamical phases: smooth dynamics and discontinuous dynamics. The latter phase arises naturally with no explicite singular fitness function, counterintuitively. The Hamilton-Jacobi method yields straightforward analytical results for the models that utilize fitness as a function of Hamming distance from a reference genome sequence. We also show the way in which this method gives dynamical phase structure for multipeak fitness.animationQuantitative Biology - Populations and Evolution; Quantitative Biology - Populations and Evolution; Quantitative Biology - Quantitative Methodsjournal article10.1103/PhysRevE.78.041908189994562-s2.0-54549111432http://arxiv.org/abs/0908.1615v1