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The 4D-Dynamic Representation of DNA/RNA Sequences, an alignment-free bioinformatics method recently developed by us, has been used to study the genetic diversity of Echinococcus multilocularis in red foxes in Poland. Sequences of three mitochondrial genes, i.e., NADH dehydrogenase subunit 2 ( nad2 ), cytochrome b ( cob ), and cytochrome c oxidase subunit 1 ( cox1 ), are analyzed. The sequences are represented by sets of material points in a 4D space, i.e., 4D-dynamic graphs. As a visualization of the sequences, projections of the graphs into 3D space are shown. The differences between 3D graphs corresponding to European, Asian, and American haplotypes are small. Numerical characteristics ( sequence descriptors ) applied in the studies can recognize the differences. The concept of creating descriptors of 4D-dynamic graphs has been borrowed from classical dynamics; these are coordinates of the centers or mass and moments of inertia of 4D-dynamic graphs. Based on these descriptors, classification maps are constructed. The concentrations of points in the maps indicate one Polish haplotype (EmPL9) of Asian origin.

4D-Dynamic Representation of DNA/RNA Sequences: Studies on Genetic Diversity of Echinococcus multilocularis in Red Foxes in Poland