Ok actual geneticist/ evolutionary biologist here: The two numbers (30,000 and 3 million) refer to different things.

The human genome is made up of about 3 billion nucleotides, like a string with 3 billion beads on it. Each of those nucleotides can be one of 4 variants: A, T, G or C - like having 4 different colours of beads.

There's inherent variation in the genome, different people will have different variants in different orders, so everyone has a unique string of nucleotides. However, that variation is not evenly distributed. There are some positions that are "polymorphic" (variable) where at a specific position different people have different variants, and there are positions that are "fixed" where virtually every person has the same letter at that position.

When we compare two people or two individuals of the same species we compare polymorphic sites, so if you pick two random people, on average 3 million of those 3 billion nucleotides at polymorphic sites will be different from each other.

When we compare species, we compare fixed sites. Those 30,000 differences between humans and neanderthals means that there are 30,000 sites in the genome where virtually all humans have one nucleotide, and virtually all neanderthals have a different nucleotide (eg, virtually all humans have a C while virtually all neanderthals have an A).

You're right to be confused, because that passage is extremely ambiguous. It looks like the author omitted whatever Pääbo said before “Our job is to find out which of those 30,000 are most important, because they tell us what makes us uniquely human”, where he presumably clarified what "those 30,000 [things]" actually are, and I haven't found a reference to the 30,000 figure in Pääbo's major publications.

Therefore, I'll have to make my best guess about what the 30,000 and 3 million figures signify. The first refers to variations between groups (all humans and all Neanderthals), while the second refers to variation within groups (individual humans). The number of differences between two humans has a straightforward interpretation: it's simply the number of nucleotides in two people's genomes which are not the same at each location. This intra-group variation is important to keep in mind, because it complicates the matter of calculating inter-group variation: if all humans are somewhat different, and all Neanderthals are too, how can we compare them?

Generally, we calculate the genetic variation between populations (which are different species in this case) by comparing the DNA sequences that are conserved (i.e. the same) within each population. For example, we'd find all the nucleotides that are shared among most or all humans and those that are shared among most or all Neanderthals, and then we'd compare those sets to each other and see how many differences there are between them. Those differences probably contain important mutations that, so to speak, make humans humans and Neanderthals Neanderthals. To use more technical vocabulary, we would say that these differences are alleles which are fixed (i.e. shared by all members) in each population.

There isn't. If there's 3 million different genes between me and you, a Neanderthal can't possibly be 30 thousand away from both of us. Where did the 3 million go? So the comparison probably ignores the variance between different humans and makes a comparison off what we do have in common. And it probably also ignores the same portion in the Neanderthal genome. Which means, when comparing the portion of the genome humans share with each other with the portion Neanderthals share among themselves, there's a 30 thousand gene difference.

I'm neither a biologist nor an anthropologist. But, it's fairly comprehensible if you consider the following three factors:

No. 1, there were way less homo running around the planet than there are today. So, in the modern human era, we had at least some time to diversify, now counting 8 billion individuals and more. Having said that, our DNA pool is still very small, which may not be a good thing if you want to calculate our chances of avoiding extinction. But it's also a testament of how specialized we are (which is also never a good thing in the long run).

The second is that we are easily tricked by the fact that only a few genes can vastly alter a creature's appearance. Think of skin color in humans or fur color in, I don't know, cats. This is evolutionary beneficial because it allows species to quickly adapt to their surroundings, even in an epi-genetic time-span. Foxes and hares are shown to completely change their fur color from brown to white when migrating to colder, icier regions within only a few generations. The same can be observed with the domestication syndrome, recently shown in foxes during a Russian study.

And thirdly, at least in Europeans, Neanderthal DNA makes up 2-3% of of their DNA already. So, part of it is "already included", if you will.

It is probably comparing 2 different things, there maybe 3 million single basepair differences between you and me.

And 30.000 gene differences between us and neanderthalers, but a gene that is different, can be a single basepair that is different, or a hundrend different basepairs.

I bet if you look at single base pair differences between us and neanderthalers it will greatly outnumber the differences between you and me.

Take this next part with a grain of salt. But i do remember the genetic similarity between you and me is 99.99%, and with us and neanderthalers our dna is 99.8% similar.

I think this is a case of "we can't tie those 3 million differences to neanderthals specifically". Maybe they also had them but we don't have enough sampling to know. What we do have is relic neanderthal genes that have mostly spread throughout all the population in the few hundreds of generations since they mixed in.

It is a misleading statistic. The extent of variation in neanderthals is poorly known simply because identification of that type of variation requires thousands upon thousands of samples to be analyzed, and we don't have that. All we have is enough data to say what all neanderthals had in common with each other (what makes them specifically neanderthal). The extent of variation in existing humans is well known because there are millions of analyses. Not really comparing the same details either (comparing apples to oranges, in a way). Major components that are unique to Neanderthals are being compared to major components of existing humans in the one case, and in the other, trace components among humans are being compared to trace components in other humans. They don't differ from other humans in the 10,000 ways (almost?) all humans differ from neanderthals.

Comparing apples and oranges and saying they are different in 10 easy to identify ways ways and then pointing out there are hundreds of varieties of apples, and then pretending that this proves that apples are more varied than oranges.

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Hes basically saying neanderthals didn't go extinct, humans absorbed them as part of our evolution.

Modern humans are extremely insanely diverse. There are billions of us and we are everywhere. We've beaten up natural selection and all had sex with each other.

Neanderthal genes have not evolved for tens of thousands of years. Meanwhile humans have been getting crazy. So we still have those neanderthal genes, and a bunch of new ones too.

Not sure about this specific case, but in general for this sort of thing (more difference between groups than within them):

Think of like a venn diagram with a large overlap. The difference between the groups is the distance between the two centers of the circles. The difference within the groups is the diameter of the circles. You can see how the former can be smaller than the latter, easily.

More accurately (and more mathy), think of two bell curves. The difference between the groups is the distance between the center of the two bell curves. The difference within the groups is proportional to the standard deviation or variance (4 standard deviations or whatever). Again you an imagine how by just putting the bell curves close together, they can remain clearly distinct while also having more difference within them than between the averages.

For an example more related to this, if you pick a trait like height for example. The difference in average height between people in your town vs the next town over (pretend you live in a town if you don't) is probably smaller than the difference in height between you and your sibling (pretend you have a same-sex sibling), despite the fact you are more closely related to your sibling.

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Reason for the genetic differences between humans and Neanderthals is that the two populations were separated for a long period of time, and evolved independently. Humans and Neanderthals likely diverged from a common ancestor around 600,000 years ago, and lived in separate geographic regions for hundreds of thousands of years.

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During this time, the two populations were exposed to different selective pressures, which led to the evolution of distinct physical and behavioral adaptations.Another reason for the genetic differences between humans and Neanderthals is that there was some interbreeding between the two populations. Studies of the Neanderthal genome have revealed that modern humans of non-African descent carry about 2-4% of Neanderthal DNA in their genome, indicating that there was some interbreeding between the two populations when modern humans first began to migrate out of Africa.

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Comparing two human individuals, the genetic differences would be much smaller. The human genome is about 99.9% identical from person to person, with the remaining 0.1% accounting for genetic variation that is responsible for differences in physical characteristics, such as eye and hair color, as well as differences in susceptibility to certain diseases.

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