Yes, domestic cats are related to tigers. They are also related to all the other wild cat species including lions and leopards et cetera.
These days genetic material from the various wild cat species can be analysed using a range of molecular tests to figure out how closely related species are to one another. Greater divergence in the DNA of a species indicates that they have been separated for a longer time.
The family of cat species evolved fairly recently. Many wild cat species separated from one another quickly. These factors mean that there are small differences between the wild cat species and the domestic cat.
You can see the various lineages of the wild cat species (including the domestic cat) on this page.
A team of scientists sequenced the genomes of tigers, snow leopards and lions in the interests of conservation.
They found that the world’s largest felid (aka ‘cat’), the tiger, shared 95.6% of its DNA with the domestic cat.
They say that the domestic cat and the tiger diverged (in evolutionary terms) around 10.8 million years ago.
This information seems to clash with my information about the evolution and ancient history of the big cats. I concluded that the fossil history of the tiger goes back 1.5 million years. Of course that does not mean the tiger did not exist in a slightly different form before that.
The eight lineages of the 36 species of wild cats evolved within the past 10-15 million years.
As a comparison there is a 95% similarity between chimpanzees and humans according to a report in the Proceedings of the National Academy of Sciences dated 2003.
If that is correct, the difference between the tiger and the domestic cat is the same as the difference between the apes and humans. If you are not a creationist you’d agree that we are related to the apes.
Hope this helps.
Source for lineages: Wild Cats of the World by Mel and Fiona Sunquist.
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