The dramatic decrease in time and cost for generating genetic sequence data has opened up vast opportunities in molecular systematics, one of which is the ability to decipher the evolutionary history of strains of a species. Under this fine systematic resolution, the standard markers are often too crude to provide a reliable phylogenetic signal. Nevertheless, among prokaryotes, genome dynamics (GD) in the form of horizontal gene transfer (HGT), the transfer of genetic material between organisms not through lineal descent, seem to provide far richer information by affecting both gene order and gene content. To the best of our knowledge, no rigorous statistical modelling for GD has been suggested. Here we provide a first statistical, two-level modeling and analysis, for GD under a very simple operation – the Jump operation. Under this framework, at the higher level, genome evolution is modeled as a random walk in the genome permutation state space. At the lower level, gene neighborhood is modeled as a birth–death–immigration process affected by the genes jumping across the genome. Using this modeling we can infer several innate properties for genomes evolving along a tree and analytically relate the HGT rate and time to the expected random variables that we define. Besides analytical results, we will also show results on real data conforming with existing biological knowledge. The talk assumes no background in Biology.   Related Papers 1) Katriel G., Mahanaymi U., Koutschan C., Zeilberger D., Steel M. and Snir S. 2023. Gene Transfer-based Phylogenetics: Analytical Expressions and Additivity via Birth–Death Theory, Accepted at Systematic Biology. A preliminary version is available at bioarxiv 2) Sevillya, G., D. Doerr, Y. Lerner, J. Stoye, M. Steel, and S. Snir. 2019. Horizontal Gene Transfer Phylogenetics: A Random Walk Approach. Molecular Biology and Evolution (MBE)37:1470–1479. 3) Shifman, A., N. Ninyo, U. Gophna, and S. Snir. 2013. Phylo si: a new genome-wide approach for prokaryotic phylogeny. Nucleic acids research (NAR)42:2391–2404.