If most of the people in North London have Israeli ancestry, did Israel conquer it?
Most of the people in North London probably have every possible ancestry, including Eskimo (probably just 0,1% or less of their DNA, but still). However, we are talking about Y-DNA which is only passed from father to son, and it is only a tiny portion of overall ancestry, but if some male lineage increases in number so much during such a short time then it is not a coincidence, but Genghis Khan or another conqueror - in this case those were Proto-Indo-Europeans.
Another thing is whether you want to apply the term "conquest" to times when states did not exist, but only tribes or other social groups. Maybe it was cultural domination, maybe they just accepted those newcomers as chieftains, without bloodshed. So "conquest" may or may not be a good term.
Another thing is that of course these theories which I describe here are not 100% certain, just 90% or so. We still know little about ancient DNA.
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There is also an indication that people with some Y-DNA lineages have a greater chance to conceive boys than girls. Some very small correlation was found, that for example one Y-DNA has a 0.5 chance to conceive a boy, and another Y-DNA has a 0.500000000000123 chance to conceive a boy. The difference is minimal but if you give it enough generations, then some statistical differences may show up, and of course these lineages will spread faster.
Because girls don't have Y-chromosome, obviously.
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As for the model of conquest.
Check for example this simulation - a population of "red-orange" ancestry with "R" Y-DNA conquers a population of "blue-azure" ancestry with "G" Y-DNA. After three generations the intermingled population has mostly "R" Y-DNA of conquerors, but in terms of overall ancestry is still mostly "blue-azure":
Autosomal refers to overall ancestry:
This is probably what happened in Europe and India - except that it took much longer than just three generations.
Overall ancestry of modern Europeans is mostly Stone Age, and of Indians mostly dates back to the Indus Valley Civilization.
But Y-DNA has been altered by some conquering warriors - though not to such a large extent as in this simulation.
If most of the people in North London have Israeli ancestry, did Israel conquer it?
The problem is that Europeans have mostly Stone Age ancestry and Indians also have mostly Pre-Aryan ancestry.
But their Y-DNA lineages are largely (some 35-45% of the total) from those conquering Indo-Europeans.