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Besides, I specified that the bottleneck was in the number of species, not alleles.
"Bottleneck" in population genetics refers to a reduction in genetic diversity. Losing species (bottlenecks within genera) will indeed be one way that happens, as well as losing individuals within a species. In any case, we would expect to see genetic bottlenecks as a result of a catastrophe such as a flood. Furthermore, if it were a global flood, we would be able to detect bottlenecks dated to that time in the DNA of all extant species and genera world wide.