A rational explanation for the "miracle" of Jacob's sheep

A guest post by NOYAMG

In the comments to this post by Chaim G. Le Brai de Fundie I, Chaim used Jacob’s sheep as an example of an overt miracle produced on demand, writing:

What about Yaakov? [Gen 30:37-28]

And Jacob took him rods of fresh poplar, and of the almond and of the plane-tree; and peeled white streaks in them, making the white appear which was in the rods
And he set the rods which he had peeled over against the flocks in the gutters in the watering-troughs where the flocks came to drink; and they conceived when they came to drink.

or was that all Gregorian [sic] genetic engineering?

In response, I said that, in fact, I think it was all genetics (I didn’t point out that the term is Mendelian, but it is), and that my frum Bio prof in YU very adroitly pointed out that this was very easily predictable through knowledge of genetics.

Someone asked “how.”

Here’s how:

Whiteness in sheep is dominant, color is recessive. What that means, essentially, is that there are sheep that will appear white that nevertheless carry a gene for color. They are called heterozygous. What Yaakov realized, being smart, astute and living with sheep and breeding them for years, is that even "pure" white sheep that bred sometimes had colored offspring (as would be expected in heterozygous white sheep).

Where this diverged from accepted breeding knowledge of the time was that the farmers thought that white was "pure" and that color would "spackle" the white, so to speak. Lavan thought that by removing all the colored sheep from the flock, there would be no color to "depurify" the white sheep. This was a mistake. In fact, had Lavan wanted to strip Yakov of all ability to profit, he would have made white sheep the payment, and removed all the white sheep from the flock. At that point, another white sheep would never have been born.

As Yakov selectively breeded (through the use of aphrodisiacs) the white sheep with the colored, he increased the incidence of heterozygous genotype/white phenotype sheep, which, in turn increased the incidence of colored offspring, until the majority of the sheep were colored, and there were no homozygous dominant left in the herd.

Think of this in terms of eye color, which may help explain it: Brown is dominant, blue recessive (this isn't entirely accurate, because eye color is controlled by more than one gene, but go with it). You can have a blue-eyed child born to parents who both have Brown eyes; if both parents are hybrid/heterozygous brown (Bb), an estimated 25% of their offpsring will be bb, and have blue eyes.

The same of the sheep. Pure White (W) is dominant. Taking out the ww sheep (the homozygous recessive spotted ones) still left Ww sheep in the flock. Heterozygous sheep tend to be stronger and more virile breeders. So, when Yakov mates the stronger sheep together, he’s mating heterozygous Ww. The expected result of such a pairing it that only one in four offspring will appear colored, but only one in four offspring will actually be “pure” white. The other three carry the recessive gene

Now, in the next generation, mate a Ww with a ww, and you get a 50% chance of ww offspring and 50% chance of Ww offspring, and 100% chance that you have NO WW (pure white) in the litter.

Over time and (sheep) generations, you can essentially eliminate the pure white WW from the flock, and continually increase the number of ww spotted sheep in the gene pool.

Finally, side point, even if you want to say that Yaakov didn’t know any of this, and he really thought his rods were having an effect (as opposed to just used as aphrodisiacs to selectively breed), still, that’s not a miracle produced on demand, since at no time does Yaakov call out to God to increase his sheep.