Royal descent

A royal descent is a genealogical line of descent from a past or present monarch.
Both geneticists and genealogists have attempted to estimate the percentage of living people with royal descent. From a genetic perspective, the number of unprovable descendants must be virtually unlimited if going back enough generations, according to coalescent theory, as the possibility increases exponentially following every century back in time. In other words, the number of descendants from a monarch increases as a function of the length of time between the monarch's death and the birth of the particular descendant.
As for descendants of genealogical documented lineages, various estimated figures have been proposed. For instance, Mark Humphrys, a professor of computer science at Dublin City University in Ireland, and genealogy enthusiast, estimated the people of provable genealogical ancestry from medieval monarchs to millions. In any case, the percentage of genealogical descendants are bound to increase with time; not only with every new generation but also due to more extensive combination of individual efforts in genealogy software, including international services available online.
In genealogy, royal descent is sometimes claimed as a mark of distinction and is seen as a desirable goal. However, due to the incompleteness and varying uncertainty of existing records, the number of people who do claim royal descent tend to be higher than the number who can actually prove it. Historically, pretenders, impostors and those hoping to improve their social status have often claimed royal descent, some with fabricated lineages. The importance of royal descent to some genealogists has been criticized.
Logically, for every royal in a person's family tree, there are bound to be virtually an unlimited number of undocumented individuals whose births, deaths and lives went completely unrecorded by history. A truism that would naturally apply even to someone who is per se a living royal.
From a genetic, scientific perspective, it is theoretically true that "statistically, most of the inhabitants of Western Europe are probably descended from William the Conqueror; they are equally likely to be descended from the man who groomed his charger."
Europe.
There has been a long tradition for royalty predominantly to intermarry those of their own class. As a result, the ruling houses of Europe have tended to be closely related to one another, and descent from a particular monarch will be found in many dynasties – all present European monarchs, and a great many pretenders, are genealogical descendants of William the Conqueror (1028–1087), for example, and further back in time of Charlemagne (742/747/748–814). Through Charlemagne, some researchers have even speculated on descent from antiquity.
The practice of restrictive marriages has been noted as increasing over the years until the 20th century: the passage of time strengthened the conviction that royalty only allied with royalty, and from the 16th century marriages between royal and commoner became rarer and rarer. This is one reason why descent from more recent monarchs is rarer amongst commoners than from monarchs further back.
Members of untitled families today may be descended from illegitimate children of royalty as primogenitors. Since illegitimate children of royalty were seldom permitted to marry into other royal families because of their unacceptable status, these children tended to marry upper-class or middle-class families from their own country.
United States.
At one time, publications on this matter stressed royal connections for only a few families. One example included James Pierpont and others. Also, there are NEHGS articles on United States presidents and "tycoon" families and of royal descent that emphasize the discriminating notion, of which the "most royal candidate theory" is a notable result. That is, those of royal descent excel (to wit, Roberts' article on eminent descendants of Mrs. Alice Freeman Thompson Parke). Many, too, were at the forefront of social progress, for example Anne Marbury Hutchinson, who was banished from the Massachusetts Bay Colony for her progressive beliefs.
According to American genealogist Gary Boyd Roberts, an expert on royal descent, most Americans with significant New England Yankee, Mid-Atlantic Quaker, or Southern planter ancestry are descended from medieval kings, especially those of England, Scotland, and France. William Addams Reitwiesner documented many U.S. descendants of Renaissance and modern monarchs. Some Americans may have royal descents through German immigrants who had an illegitimate descent from German royalty.
Due to primogeniture, many colonists of high social status were younger children of English aristocratic families who came to America looking for land because, since given their birth order they could not inherit. Many of these immigrants initially enjoyed high standing where they settled. They could often claim royal descent through a female line or illegitimate descent. Some Americans descend from these 17th-century British colonists who had royal descent. There were at least 650 colonists with traceable royal ancestry, and 387 of them left descendants in America (almost always numbering many thousands, and some as many as one million). These colonists with royal descent settled in various states, but a large majority in Massachusetts or Virginia. Several families which settled in those states, over the two hundred years or more since the colonial land grants, intertwined their branches to the point that almost everyone was somehow related to everyone else. As one writer observed, "like a tangle of fish hooks".
Over time, opposing factors have affected the percentage of Americans who have provable royal descent. The passage of the generations has further intermingled the ancestry of the English colonists' descendants, thus increasing the percentage who descend from one of the immigrants with royal ancestry. At the same time, however, waves of post-colonial immigrants from other countries decreased the percentage who have royal descent.
Africa.
Royal descent plays an important role in many African societies; authority and property tend to be lineally derived. Among tribes which recognize a single ruler, the hereditary blood line of the rulers (who early European travelers described as kings, queens, princes, etc., using the terminology of European monarchy) is akin to a dynasty. Among groups which have less centralized power structures, dominant clans are still recognized. Oral history would be the primary method of transmitting genealogies, and both nobles and commoners base their status on descent. The royal blood is among the centralized power of all blood groups.
Asia-Pacific.
Many Asian and Oceanic or Pacifican cultures or civilizations have a veneration for royal descents. Many Muslims revere descents from Ali and his father-in-law, Muhammad. But further East than that, are India, Pakistan, Bengal(Bangladesh), Southeast Asia, Japan, Korea and China, respected such lines, even if there were no special merit attached to it. In China, a book of surnames was compiled, and updated most recently under the Ming. The Qing (Manchu) were more interested in subduing the indigenes; but there are still traceable descendants of Confucius, whose ancestors are traceable to the earlier dynasties of China. I, myself, though an Occidental, can trace my lineage back to the Tang. And through them, to the Sui, the Western Liang, The Zhou, and through the Persians to the Simas of Jin. And the Tangs also include descent from the Koguryeo royal family. Korean 'Ko' = Chinese 'Gao' or 'Go'.
Then there are also the pretenders to the thrones of Korea, Manchuria, the Grand Mughals, Viet Nam, Laos, Nepal and several Tibets. Bhutan, Cambodia, Thailand and Japan still have their royal or imperial families. And the former maharajas (great kings) of India, Sri Lanka, Bengladesh and Pakistan still exist, and India still recognizes them. 
There were or are similar stories for the South Pacific Islands. Tonga has three royal families. Hawai'i has gone through three royal dynasties, the Maori of New Zealand had several. Rapa Nui recognizes the descendants of the former royal line.
Proof of royal ancestry.
Royal descent is easier to prove than descent from less historically documented ancestors, since genealogies and public records are typically fuller, better known and preserved in the case of royal descent than in the case of descent from less noted individuals. Typically, it is only since the 20th century that family history has been an interest pursued by people outside the upper classes. Hence, the continuous lines of descent from royal ancestors are typically much better researched and established than those from other ancestors. Until the parish record system introduced in the 16th century, and civil registration in the 19th century, family records are fuller for landowners than for ordinary people.
Between 1903 and 1911, the Melville Henry Massue produced volumes titled "The Blood Royal of Britain" - which attempted to name all the then-living descendants of King Edward III of England (1312–1377) - were published. He gave up the exercise after publishing the names of about 40,000 living people, but his own estimate was that the total of those of royal descent who could be proved and named if he completed his work at that time was 100,000 people. His work, however, was heavily dependent upon those whose names were readily ascertainable from works of genealogical reference, such as Burke's Peerage and Landed Gentry.
The English geneticist Professor Stephen Jones estimates that 25% of the British population is descended from the Plantagenets.
Notably, the phrase "English descent" does not, of course, mean purely English descent: As soon as an immigrant family marries into an indigenous family, it acquires all the ancestors of its indigenous parent, and is therefore no less likely to be able to claim a royal descent than a non-immigrant family.