Confucius [Kong Fuzi] say....

This hilarious article about "confirming" your descent from Confucius is making the rounds.

Now, my understanding is that the patrilineage of Confucius remains to this day. So the people who would seek confirmation would often have a tradition of descent from the great sage himself. But, I note tradition. We all know that "ancestors" can be concocted, and, we also know that sometimes patrilineages can be "interrupted." When English geneticist Bryan Sykes tested individuals with his surname across the British Isles he found that ~50% of individuals were of the same Y chromosomal lineage. That means that half of these "Sykes" were actually descended from the same man in the recent past (~1000 years ago, or less). But, what of the other 50%? Turns out that they were descended from a host of various different men. In other words, the pie chart of "Sykes" lineages would have shown a modal haplotype, and a diverse array of non-modal haplotypes. A plausible explanation for this pattern is that the other 50% are due to lineage introgression, a polite way of suggesting cuckoldry on the order of 1-2% per generation.

Unlike the Sykes lineage that of Confucius is of high prestige, and it seems plausible that in addition to misattributed paternity, there would be many individuals who would claim Confucian antecedants. On the other hand, one might contend that misattributed paternity would be somewhat lower in the Confucian lineage than the Sykes' lineage because of the higher status, and concomitant elevated vigilance of Confucian males (there is a positive correlation between lack of misattributed paternity and socioeconomic status). Additionally, Chinese traditions of filial piety place an importance on blood descendents (sons) maintaining ancestral graves and performing rites, so this might also mitigate against lineage introgression. Of course, the Confucian lineage is at least 2,500 years old. Assuming 99.5% fidelity and 100 generations (2,500 years divided by 25 years per generation) about 60% of the individuals claiming to be descendents of Confucius should carry the same Y haplotype. Drop it to 99% and it would be 36%. 95% and you drop to 0.6% carrying the Y lineage of Confucius! Of course, some researchers claim that the Kohanim priestly lineage, passed from father to son among Jews, seems to exhibit a modal haplotype on the order of 50% of Cohen lineages worldwide. But the difference between the Kohanim and the Confucian lineage is that the latter garners esteem from a wide swath of society, and it seems conscious defection would be low and introgression rather high because of the status of Confucius in East Asian society. In any case, my overall point is that if you believe in inference, you don't need to assay Confucius' remains, if a modal haplotype that coalesces to around 2,500 years into the past is found among reputed descendents, then I think one can say that the most parsimonious conclusion is that there is a genuine Confucian lineage extant.

Addendum: What we're talking about here are uniparental genealogies. The non-recombinant Y is passed from father to son intact, indefinitely (though with mutations). While it seems plausible that all Chinese, and possibly all Eurasians, can trace a line of descent back to the great sage, genomes are discrete, so most of these individuals may not carry DNA identical by descent from Confucius. On the other hand, since the Y is not diminished and is passed wholly from father to son, this signal can be discerned out of the noise of generations that have passed. Though most of the genomic material that is derived from Confucius is not found in the patrilineage (i.e., like all humans Confucius had 44 autosomal chromosomes in addition to the XY pair which determined his sex), scattered across humanity (though concentrated among Han Chinese) the Y chromosomal lineaeg is diagnostically tractable because it maintains its integrity because of its insulation from recombination.