That last one looks eerily familiar.
Anchorman math: 60% of the time, it works every time.
In terms of the feasibility, let’s look at some example math.
Constants -
Time frame: 10,000 years since the mutation occurred
Average turnaround per generation: 20 years
Average child count per family: 2.5
Math -
Generations since the mutation: 10,000 / 20 = 500
Total humans with mutation in 1st generation: 2.5^0 = 1
Either our person has 2 children or 3 children. Thus, on average, he has 2.5.
Total humans with mutation in 2nd generation: 2.5^1 = 2.5
Either we have 2 grandchildren with 2.5 children each (5 total) or 3 grandchildren with 2.5 each (7.5). On average, there are 6.25 great grandchildren.
Total humans with mutation in 3rd generation: 2.5^2 = 6.25
We can think of this like there being 3 out of 4 cases where there are 6 great grandchildren, and 1 case in 4 where there were 7. In the former case, we expect 15 gg-grandchildren and in the later 17.5. Skewing the average towards the lower number, we have an average expectation of 15.625 gg-grandchildren.
Total humans with mutation in 4th generation: 2.5^3 = 15.625
So the total expected descendants for generation n is 2.5^(n-1). This simple formula matches our expectation.
At generation 10, we’re up to ~3,815 people.
At generation 20, that goes to ~36,379,788. people.
At 30…it’s 346.9 billion. We currently think there’s only 8,2b people alive on Earth and we haven’t even gotten to generation 100, let alone the generation 500 that we’re targeting (that gets us to a number with almost 200 digits).
Now, obviously, the math doesn’t track reality too well since we’ve surpassed the entire population of the Earth. Due to how quickly the number grows relative to geographic constraints, most procreation doesn’t happen between 1 person with the gene and 1 person without the gene. In most scenarios where at least one person has the gene, the other person also has the gene. In that case, you’re not converting 1 person into 2.5 people, you’re converting 2 people into 2.5 (an expansion factor of 1.25). But even if we were somehow able to achieve this growth rate (allowing self-insemination for some individuals who can’t find a partner…or something), by generation 500 you’re still back over the entire population of Earth. We have to start looking to famines and wars as the only thing making the number of blue-eye mutation bearing people so low as to not just be everyone.
Among the descendants of those who survived, the only thing that could have constrained everyone from having a blue eye gene is physical inaccessibility. The disappearance of the land bridge between Siberia and Alaska might have prevented it from passing through into the New World until the 2nd millenium (1001 AD+). But with 500-1000 years to transmit, it would be very difficult for it to not have gotten to nigh everyone. You only need one missionary, one adventurer, one conquistador to go into some remote place and introduce his genetic legacy to some small tribe in the middle of nowhere, and then for one person within that tribe to migrate into another tribe, and a great-grandchild to migrate to another tribe, and so on…
In generally, you’d expect to see that the gene enters a population, quickly overtakes it within ~100 years, and at that point it will be sending off sparks towards neighboring populations.
We’re all blue-eyed people in potentia.
That neatly describes the difference between natural selection due to existing variation in phenotypes versus natural selection due to a novel mutation creating a change in phenotype. Some anoles have longer legs, or greener coloration. Those anoles move to the canopy, where they do better[1]. There’s no “long leg” mutation showing up, just the natural variability present in a trait.
In the E. coli example it isn’t that some do better on citrate than others, and the experimental selection caused the citrate ones to thrive, but rather that some extremely rare mutation event happened, which allowed survival on citrate.
This is just a poor headline writer, and has nothing to do with the actual scientific merits of the finding. The original paper says, “more than 97% of the analyzed persons with blue eyes carried the haplotype h-1…” It’s just the headline writer and journalist who use “all”.
Or the brown ones born in the canopy get eaten, or whatever the exact mechanism is ↩︎
Or the ones in the canopy that are greener with longer legs do better than the ones on the canopy that are brown with short legs. No particular specimen necessarily makes a specific choice, just the more fitting survival traits for that location win out.
One problem with your math. Blue eyes is a recessive trait. That means it takes two copies of that one mutant gene to express. So an average of 2.5 children per couple doesn’t take into account only a quarter will actually have blue eyes, but another two quarters will potentially have blue- eyed offspring.
The effect is that the rate of propagation will be slower than your math, but not so much slower that the end result is that the blue eye mutation has had time to spread to every corner of the globe (as the expression goes).
My favourite exchange from the earlier thread:
The math was for having inherited DNA from the person with the gene, not having blue eyes.
Correction to my previous post. A refresher on Wikipedia shows my info outdated and incorrect.
Eye color is not a simple Mendelevian trait, but a complex expression of several genes. There appears to be one gene for brown vs blue and another for green vs hazel.
Eye colors include the common brown (in dark and light variants), hazel, green, and blue of familiarity, but also include variants of gray and amber. This appear to be different than blue and light brown.
Be that as it may, the mathematical calculation about spread of a simple one gene main variant is accurate to the degree that one mutant source could explain all the blue eyes except for the rare cases of other pigment defect mutations that affect more than just eye color.
Ok, that’s fair.