How many generations to lock in androgynous human characteristics?

Question

My story happens in fictional medieval age. There are the usual suspects of peasants, clergy, craftsman, merchants & aristocracy. There is also a specific class of hereditary servants. They work as domestic workers, and are above peasants and hired servants in class. Also they are more trusted, get better accommodations, more pay, and are usually better educated.

Hereditary servants are special since the aristocracy specifically bred them to look androgynous. They are normal humans but aristocracy selected the individuals with weakly pronounced secondary sex characteristics such hips, facial & body hair, Adam's apple, breasts etc. Males & females who didn't satisfy their specifications we removed from the genetic pool and were sterilized or had to change their class thus becoming normal peasants. Hereditary servants work only in households of aristocracy or very wealthy merchants.

Assuming below:

• Aristocracy wants to lock in androgynous traits, thus children of two servants need to look like a servant themselves. Thus children of two androgynous looking parents needs to be androgynous looking themselves.

• Aristocracy has enough people to start with, they could use peasants which are something like serfs, or war captives as starting stock.

• Aristocracy has knowledge of breeding animals, they've created different breeds of domestic animals such as dogs, horses, cows etc.

• Aristocracy has no one to prevent them from choosing who will have children with whom, among the household servants. If baroness Meghan want to breed Jane and Tom, they could either acquiesce or try to run away from the country. Since household servants are chattel property, they don't have any say in that matter.

How many generations of selective breeding would they need to lock in androgynous traits, since the start of their endeavour?

The question is from the year they started creating the breed of servants, from naturally occurring stock. If there was no servants in year 800, only peasants who looked somewhat androgynous, how many generations would it take the aristocracy to lock in those traits.

I need something like rule of thumb for dogs which says about 7 generations https://www.quora.com/When-making-a-new-breed-how-many-generations-until-the-new-breed-is-considered-locked

In the beginning they just started with most androgynous peasants / war captives they could find. Afterwards they've used selective breeding to improve their servants. If the children were too masculine/feminine they were send to become common peasants, or simply removed from the pool.

Aristocracy keeps a registry of servants, thus you are purebreed if both your parents are purebreed. However servants are defined by their look. Even you are purebreed you would lose your class if you are abnormally masculine/feminine for a servant. Also you could be accepted even from a non servant parents if you fit the specifications.

Answer 1

Let’s assume for starters that the desired phenotype (the outward appearance) is monoallelic (is carried by a single spot on the genome). Perhaps it is a malfunction in an important puberty pathway, maybe in the pituitary or something having to do with luteinizing hormone or follicle stimulating hormone. Let’s also assume for simplicity that the allele does not have an effect in a heterozygous individual with one working copy and one nonfunctional copy (the gene is purely recessive). Each of these assumptions may be false and in reality almost certainly will be but its a good starting place.

All we need to do to understand how the frequency of this allele will change over time is to define the starting characteristics of the population and the selection placed on them. Feel free to change these numbers however you want I’m just going to give some examples that I think make sense. Let’s say the desired allele has an initial frequency of 0.01. This means on average only 1 in 100 people has a single copy of this allele. Because it is recessive this means only 1 in 10000 people actually have 2 copies and therefore the desired phenotype. Let’s also assume for our purposes that the population is sufficiently large as to be infinite so we don’t have to worry about random chance butting in and messing with our perfect formulas. Finally, we need to quantify how effective the selection on this allele is. Essentially, how good are the aristocrats at filtering out individuals who don’t meet the desired criteria? If we say that the desired individuals reproduce with a rate of 1 I would suggest individuals who don’t have the phenotype reproduce at a fractional rate of say 0.2. This is strong selection, not as strong as it could be but in reality, humans aren’t machines and people will break the rules. What this is saying is that for every undesirable servant who reproduces into the servant pool there are 5 desirable servants who do so.

We now have everything we need to simulate the population. The math is relatively straightforward, but somewhat tedious to work out for each generation. Thankfully we don’t have to! There exists a tool to do just this calculation for us: https://www.radford.edu/~rsheehy/Gen_flash/popgen/. Here if we plug in the variables we defined above we get a highly variable mean time of fixation of roughly 30-40 generations. If you simulate finite populations, particularly small ones, there will be a high degree of randomness where sometimes the desired allele will be lost simply by random chance (you can avoid this by using an infinite population). If you increase the initial frequency of the allele or increase the strength of the selection this will be much faster.