Upper classes normally have fewer offspring than lower classes. In general, a couple will have as many children as they believe they can support in a lifestyle similar to their own.
"Parents sat down and consciously tried to decide, 'How many children can we afford to put through middle school,'" Low told LiveScience. livescience
Note that this citation assumes that children are planned; this is probably not the case in Ghengis Khan's myriad children, most of whom I believe did not arise from couples planning their mating and child rearing, but rather from rape.
Upper classes also normally limit their mating selection in order to preserve class structure; sex outside of class structure may occur, but the children are not recognized; it is impossible to predict the impact of illegitimate children on your hypothesis. Class selection of partners not infrequently leads to inbreeding and reduced fertility (e.g. Romanovs).
Ghengis Khan did not, so far I know limit his mating selection to an upper class individuals; his mating strategy was. (AFAIK) based on rape. It is difficult to discuss class structures when the ruler explicitly excludes the vanquished from any class structure at all. I suspect that the great Khan offered more respect to his horses than to the mothers of his children, or to the children. They were not Mongols, so they could not even be lower class. I don't think we have enough evidence to determine if he believed them to be human.
As I said above, I don't think there is enough formality in your analysis of genetics to measure similarity or dissimilarity. If we generate two sets of random numbers, there is no intrinsic way to compare them. 7 > 5 because we have a number line. Is (3,7,12) more or less similar to (29,128,7) than (7, 223,31)? It is impossible to observe "class" in genetic data.
And it would be an error to formulate any theory based on a dataset which is by definition an outlier. The Khan conquered the world. He is unique. At the moment I am sitting on a slowly moving train. Based on that dataset, I conclude that the entire universe is filled with a pervasive hum and vibration, that my location is effectively random, and that the universe is governed by conductors. Invalid conclusions, but if I trust an aberrant data set I cannot disprove them.
Last night my professional historian girlfriend pointed out that "class" is defined differently in different societies. In the USA class is strongly correlated with wealth, where as in the UK, there is no correlation (to the point that "impoverished nobility" is a trope.) Semaphore points out in this answer that status/class in Mongol society derives from the status of the mother. (and if I am correct, that most of Ghengis' children were born of women with lower status than his horses, that has significant implications on your thesis).
So in summary:
- Class is an imprecise term that your hypothesis does not define; at a minimum, if your hypothesis is to be tested there needs to be a way to reliably and transparently classify an individual as upper or lower class.Aside(Enter curmudgeon mode) The longer I think about this, the more convinced I am that "class" intrinsically conceals imprecision. I suspect that the meaning of the term shifts depending on the context, the speaker and the time period. Any argument built on these terms is flawed and needs exacting scrutiny.(End curmudgeon mode)
- The data set you are using to support your thesis is known to be non-representative; conclusions drawn from an outlier data set are suspect. If your hypothesis is to be taken seriously it needs to be tested against multiple other data sets.
- You haven't defined a methodology to compare sets of genetic data.
- You haven't supplied a genetic marker for "class" however that is defined.
- Your hypothesis relies on an assumption (Higher classes have higher reproductive rates) that is suspect (although I need to provide evidence to support my challenge).