How should the popular press compare similarity of genomes? Note this is a question from a lay reader.

I've read in the popular press that ~1-4% of the genome of non-African Homo sapiens is inherited from Neanderthals, or that Melanesians derive a similar amount from the Denisovans.

This seems like a lot, until you read (elsewhere!) that Neanderthals are 99.7% identical to humans, so most of the fraction inherited is identical in any case.

Or taking it another way, reading that two individuals will typically have 99.9% identical DNA seems pretty similar, until you realise you are only 0.3% 'different' from a Neanderthal, or 15% 'different' from your dog.

It seems to me this use of percentages is confusing, misleading, and open to abuse. When comparing species (for example) I would think that they should speak of differences in terms of  base pairs that we could not otherwise have had. 

How should the lay (or popular science) press best communicate similarities or differences in genomes when talking about individuals, races, or species?
1–4% is from an evolution point of view. 99.7% is from a sequence point of view. Because they are measuring different things, they can be compatible with each other. The correct interpretation is: 1–4% of a non-African genome is inherited from Neanderthals and the sequence of this 1–4% differs from modern human sequence by 0.3%. PS: so, for each non-African, Neanderthals contributed 1–4% * 0.3% of base pairs not present in modern human. This sounds tiny, but even a single SNP may lead to severe disease. This tiny fraction has known functional impact to diabetes and high-altitude adaption.



Others pointed out two related questions:


How many genes do we share with our mother?
Do apes and humans share 99% of DNA or 99% of genes? What is the difference?


These questions are really about the ambiguity in the definition of "gene". Importantly, traditionally in popular science and population genetics, a gene could mean an allele. This makes differences.

For example, by common uses of "gene" in biology, the answer to "how many genes do we share with our mother" would be nearly 100% – every human has nearly the same set of genes. However, clearly this is not what the asker wants. By gene, he/she really means allele. The expected answer is 50% – we inherit 50% of alleles from our mother.

In the end, what is a "gene" exactly? I don't know. Biologists can often figure out the meaning of word "gene" in the right context, but non-biologists will sometimes have troubles with the ambiguity.