One of the things that lurks at the back of my genealogical / DNA research is the question of how rapidly lines of descent can be expected to increase.
My Murray grandfather had nine children by two marriages, seven of whom are still living; I am the oldest of his twenty-two grandchildren; between us we have I think twenty-eight great-grandchildren; and the first two of the next generation arrived in the last couple of years.
My Hibbard great-great-grandparents had five children, of whom one died young and another never married; ten grandchildren, five of whom have living descendants; sixteen great-grandchildren, ten of whom have descendants (and two are still living); and twenty-three great-great-grandchildren, including me and Sally Seaver.
It can go the other way of course. While my Hibbard great-great-grandfather has many living descendants, more than half of them are from his oldest surviving child (who also married early and thus got ahead of the game); his younger son’s living descendants are me, my two siblings and our five children, a total of eight after four generations.
These things are of course very dependent on time, place and social class, but I am hoping for a metric which would at least allow a rough comparison of rates of increase. One of the best chronicled lines of descent over the past 180 years, albeit of very rich white Europeans, is that of Queen Victoria and Prince Albert. Allan Raymond has a fantastic website investigating this, which appears to be complete up to early 2019. Vic and Al had nine children, all but one of whom had kids themselves; 42 grandchildren, 87 great-grandchildren and 142 great-great-grandchildren.
I’ve plotted the increase in both total and living descendants on a log scale in the graph above. Their first child, and therefore first descendant, was “Vicky“, the Princess Royal and later briefly Empress of Germany, born on 21 November 1840, nine and a half months after her parents’ wedding on 10 February. She had eight children, born between 1859 and 1872, and died on 5 August 1901, aged 61 (outliving her mother by less than a year).
Victoria and Albert’s tenth descendant was the first grandchild born after their nine children together, none other than Emperor Wilhelm II of Germany, the son of Princess Victoria and the short-lived Emperor Frederick III. He was born on 27 January 1859, a year after his parents’ wedding. He had seven children between 1882 and 1892, ruled Germany from 1888 to 1918 and died on 4 June 1941 aged 82.
Victoria and Albert’s hundredth descendant was born on 2 July 1903 as Prince Alexander of Denmark, though that is not how he is known to history. He was the only child of Princess Maud, the fifth of the six children of King Edward VII, and Prince Carl of Denmark. In 1905, Norway became independent and elected Prince Carl as the country’s new king; he ruled as King Haakon VIII until his death in 1957 at the age of 85. His son then ruled as King Olav V of Norway until his death in 1991 at the age of 87. (King Olav’s son, Harald V, inherited the throne and is still living; he turns 86 later this month.)
But in 1903, a number of Vic and Al’s descendants had already died, so the moment when Victoria and Albert’s living descendants exceeded a hundred was when Princess Ileana of Romania was born on 5 January 1909 (23 December 1908 by the old calendar). Her mother, Queen Marie of Romania, was the daughter of Prince Alfred, the second son of Victoria and Albert. Ileana was the fifth of Queen Marie’s six children. She had six children with Archduke Anton of Austria, born between 1932 and 1942. Ileana was exiled from Romania with the rest of the royal family after the Second World War, and died aged 82 in January 1991 in Youngstown, Ohio.
Victoria and Albert’s thousandth descendant is King Olav V’s great-grandson, Prince Sverre Magnus of Norway, born on 3 December 2005. Under Norwegian law his older sister Ingrid Alexndra is ahead of him in line to the throne, as is his father. By my calculation, extrapolating from Allan Raymond’s lists, the number of living descendants of Vic and Al will surpass a thousand later this year (2023) or early next year (2024).
|Total descendants||Living descendants|
|Time interval 1st to 10th||18.2 years||18.2 years|
|Time interval 10th to 100th||44.5 years||50.0 years|
|Time interval 100th to 1000th||102.4 years||~115 years|
I conclude two things from this. The first is that the rate of increase slows down dramatically after the first couple of generations. The second is that factors of ten are probably too blunt an scale to get a really good feel for the numbers.
Here’s the same graph, redrawn to powers of 2, with the 1st, 2nd, 4th, 8th, 16th, 32nd, 64th, 128th, 256th, 52th and 1024th descendants indicated, both living and total.
There are a few familiar names there. (And some unfamiliar ones: you may not have heard of Prince Alfred of Edinburgh and Saxe-Coburg Gotha, Vic and Al’s fourth child and second son, or his own unfortunate son, another Prince Alfred.) There’s also a small accounting issue – the birth of Tatiana Mountbatten in 1917 brought the number of living descendants of Victoria and Albert over 128, but it was almost immediately sharply reduced when the Russian imperial family were killed in the aftermath of the revolution, so it was not until the birth of Prince Philip of Greece, Tatiana’s first cousin, in 1921 that the number went permanently over 128.
Endogamy is not really an issue here. There have been only 22 marriages where both partners were descended from Victoria and Albert, and only three in the last 50 years (compared to seven such marriages in the 1930s when the pool of descendants was a lot smaller). I previously calculated that about a quarter of Vic and Al’s living descendants have more than one line of ancestry going back to them, but this proportion has been fairly stable for decades. So I don’t think it has a big impact on the growth rate.
If we do the same table as before, tracking the moments when the number of descendants doubled, we can see that it has slowed in recent decades.
|Total descendants||Living descendants|
|1st||Princess Vicky, Empress of Germany, 1840-1901||Princess Vicky, Empress of Germany, 1840-1901|
|1.0 years||1.0 years|
|2nd||Edward VII (1841-1910)||Edward VII (1841-1910)|
|2.7 years||2.7 years|
|4th||Prince Alfred, Duke of Edinburgh and of Saxe-Coburg-Gotha (1844-1900)||Prince Alfred, Duke of Edinburgh and of Saxe-Coburg-Gotha (1844-1900)|
|8.7 years||8.7 years|
|8th||Prince Leopold, Duke of Albany (1853-1884)||Prince Leopold, Duke of Albany (1853-1884)|
|11.3 years||11.3 years|
|16th||Princess Elizabeth of Hesse (1864-1918)||Princess Elizabeth of Hesse (1864-1918)|
|7.7 years||10.0 years|
|32nd||Princess Margaret of Prussia (1872-1954)||Alfred, Hereditary Prince of Saxe-Coburg and Gotha (1874-1899)|
|19.1 years||21.2 years|
|64th||Alexandra Duff / Princess Alexandra, 2nd Duchess of Fife (1891-1959)||George VI (1895-1952)|
|19.9 years||(22.0 years)|
|128th||Prince Alfred of Hohenlohe-Langenburg (1911-1911)||(Tatiana Mountbatten, 1917-1988)|
Prince Philip, 1921-2021
|30.5 years||38.7 years|
|256th||Infante Alfonso of Spain (1941-1956)||Prince Christopher of Yugoslavia (1960-1994)|
|28.3 years||26.4 years|
|512th||Princess Veronika Biron von Curland (b. 1970)||Prince Philipp of Prussia (b. 1986)|
|37.0 years||probably 39 or 40 years|
|1024th||Prince Gustav of Hohenlohe-Langenburg (b. 2007)||not born yet, likely in 2025 or 2026|
Just to grimly reflect that three of the above died by violence: Elizabeth of Hesse killed by Bolsheviks, the younger Prince Alfred probably as the result of a self-inflicted gunshot, and Alfonso of Spain accidentally shot by his brother (who later became King Juan Carlos).
To finish up with one more graph, this tracks the average annual increase in the number of descendants since 1900, both living and total. It is interesting that there is a visible cycle of higher and lower rates of increase; and the most recent years appear to show a continuing deceleration, with the lowest growth for a century. But I think it is unlikely that the number of living descendants will ever decrease, and of course it is impossible that the total number of descendants can ever do so.