How large of an initial population would it take for these new traits to average out into the standard population of the world?

Question

Let's say, many years ago, hybrids between humans and other mammalians were created and introduced into the world for various purposes. They have the same cognitive abilities as the other humans, and are capable of interbreeding with them. They are generally treated as normal people with little discrimination apart from some small communities of purists. Their animal traits are a dominant gene, and these can span from just their eyes and facial features, to even having tails and digitigrade legs.

Given this takes place in the span of 2-3 thousand years, with enough of a spread across the world to facilitate this, how large an initial population of these hybrid people would be needed for animal traits, such as pointed and slightly furred ears, to become the norm amongst all humans?

First question here, let me know if I did anything wrong.

Answer 1

This depends on your definition for "the norm amongst all humans".

If you want absolutely 100%, every-single-human-of-billions, you can't reasonably achieve that on a global scale. There will always be outliers, isolated populations, purists, etc., that will spoil the idea of perfect coverage for basically any trait less critical than things like "born with a nose". Will migration over time from a single starting populace realistically reach and interbreed with every tiny community in the Amazon rainforest, on the Pacific islands a thousand miles from anywhere, and other such remote places?

However, if you're simply looking for "considered normal/ordinary" or perhaps "single most common trait of the options available", you've got a much more practical target, to the point where a starting population of a thousand hybrids would likely be severe overkill. Note that I'd recommend a minimum starting populace of hybrids of at least a few dozen for realism no matter what figure any mathematics give you, simply because you want to avoid the damage that a random accident in the first or second generation could do to the spreading efforts; any single individual can get an infected injury, suffer a bad fall down the stairs, be born infertile, get killed in a fight, and so on and so forth, and losing even one individual from a breeding population of four would be catastrophic.

For the former, the definition will be a little subjective, as there's no hard line on what overall percentage it takes for something to be considered "normal". Brown, black, and blonde hair are all considered "normal" in most regions (red hair being consistently a minority), and between them those represent the lion's share of humanity. Given that you're talking about upwards of a dozen possible animal traits that might manifest across however many different hybrid types you start out with (your question implies multiple species had human hybrids created), only one of which needs to show for any given individual to meet your goal, adequate coverage becomes easy.

For the latter scenario, of being the most common option, this generally depends on how many different categories are possible (like colours of hair, for instance). In your case, you're looking for a simple "has one or more animal traits" versus "has no animal traits", in which case your target for coverage is 50%. Given the example of Charlemagne provided by ETam in their answer (adequate coverage of Europe within about 1300 years or less), your timeframe of 2000 to 3000 years is eminently plausible with an initial populace of even a handful, and might be so even if you picked out a single specific trait, provided these hybrids did any serious migration.

Math time: You've specified these are all dominant traits, so not only will any child of a hybrid qualify, so will nearly all their future descendants for multiple generations even if no other hybrids enter the picture. This makes for exponential spreading power.

Let's say there are four possible traits of a given hybrid, and you've stated that your goal is met if even one of them shows in a person. I'm assuming a single gene for each trait to keep this simple (and ignoring edge cases like random mutation), although in practice genetic inheritance for a specific trait is often more complex. Every child will have one copy of all four relevant genes. Each grandchild has a 50% chance for any one of these genes. The odds of not having any of them are (1/2)^4 = 1/16, so only one in sixteen grandchildren will have zero (or all four): the average case is two traits, and there will be four with three traits and four with just one.

For the next generation, given the average case of two traits, the odds of inheriting none (or all) become (1/2)^2 = 1/4, so on average three-quarters of the great-grandchildren will have at least one trait even if everybody was marrying pure humans, and the chance of having one animal trait for a given great-great-grandchild still averages out to 50%. Realistically, some of those children will be marrying other hybrids or descendants of such (or even each other: marriages between first cousins or second cousins were historically fairly common, and are still practiced in a number of countries), so your set of animal traits will reinforce and proliferate themselves with impressive speed even if you only started with two or three hybrids in a given region.

Conclusion: If your target is "absolutely 100%", your goal is implausible unless you go back to near the start of homo sapiens. If your target is merely "widespread to the point of being unremarkable", your goal is almost trivial with your given conditions.

Note: I'm assuming that in your world, sufficient people were attracted to your hybrids to breed with them throughout the generations, that they weren't shunned as mates for being considered unappealing/unattractive, that they didn't get exterminated out of fear or racism, that their descendants didn't face serious purge efforts or witch hunts, etc.; in short, that social and cultural factors didn't mess with their chances to have children. Whether or not that would actually hold true is a topic for another question entirely: I'll merely point out that history shows a great many examples of persecution of groups for various differences of opinion or appearance, and your hybrids would certainly be a visible target for such efforts, so you should consider how that problem is addressed in your world.

Answer 2

It's totally up to you. The thing about evolution is that sexual preferences also make a difference. If men/women want to mate with something with digitigrade legs and a tail then it can happen with just a small number since it's a dominant trait. But only a very small minority these days find that attractive.

I personally would not be interested in either mating or producing offspring with such a creature and I assume that would go for most humans. That isn't discrimination, I have many friends and people I respect that I would have no interest in mating or having children with,

Answer 3

I have a cleaver solution. Let's simplify the question and have just one individual hybrid, who we'll call Adam. Adam will have children with normal humans, and those children will have more children with other humans etc, until all of humanity would be a descendent of Adam. When that happens, Adam would be the closest common ancestor for all of humanity.

Let's look to the past for a moment. When was the closest common ancestor for all currently living humans born? The answer is between 1,415 BCE and 55 CE. The large range comes from uncertainty the study's authors have about migration rates. So the answer is ~3,500 years if migration is very limited or ~2,000 years if migration is very common. This actually lines up almost perfectly with the range you gave. In the modern world, where travel is way more common than ever before, so the I would expect the timeframe to be even shorter.

That should be good enough for most writers, but I am a biologist and I unfortunately found a complication. Just because someone is your ancestor does not mean you share genes with them:

[B]ecause Charlemagne lived before the isopoint and has living descendants, everyone with European ancestry is directly descended from him. In a similar vein, nearly everyone with Jewish ancestry, whether Ashkenazic or Sephardic, has ancestors who were expelled from Spain beginning in 1492...
Not everyone of European ancestry carries genes passed down by Charlemagne, however. Nor does every Jew carry genes from their Sephardic ancestors expelled from Spain. People are more closely related genealogically than genetically for a simple mathematical reason: a given gene is passed down to a child by only one parent, not both. (source)

According to this post by a population genetic lab, the number of genetic ancestors you have going back k generations is about 2*(22+33*(k-1)). We can use the same equation to say how many people we would expect to an individual's genetic decedents. Set that equal to 8 billion (assuming human population size does not grow past that) and we get over 120 million generations until everyone shares DNA with Adam.

The only solution I see is that you are starting with a population of hybrids instead of just one individual. I am not sure how to calculate how many you would need to make it work perfectly.