How many Irish cousins: the impact of endogamy- Part 4 in Series

In previous posts I described the calculations used by several sources to predict the number of cousins we have at different degrees of cousinship (first, second etc). The calculations assume that our ancestors are not related to each other i.e. no first-cousin marriages or other types of inbreeding. If we have a significant number of ancestor couples who were in fact related, this has a two-fold impact on our own genealogy research.

First, it reduces the total number of cousins that we have. If our grandparents weren’t related then we gain different cousins from both sides of the relationship.

Second, it increases the genetic similarity between ourselves and our cousins. That skews the predictions of cousinship from DNA testing companies i.e. we would share similar amounts of DNA with our second cousins as other people share with their first cousins.

For Irish people trying to use DNA matching to build out their family tree and solve certain mysteries in their heritage, it’s important to know the likely incidence of genetic relationship amongst our recent and distant ancestors.

It’s worth defining a few academic terms used in research in this area.
“Endogamy” is the practice of marrying within a specific social group. It may be due to geographic isolation, or for religious reasons, or a sociological wish amongst a group to preserve traditions. The smaller the population of the group, the more likely that a proportion of couples will be related.

Consanguinity means being descended from the same ancestor as another person. So “consanguinious marriages” are marriages in which the couple are related.

Panmictic means random mating within a population i.e. free from influence of social, geographic or genetic preference. It is another stated assumption in the 23andMe research discussed in my previous post.

Okay, with those terms out of the way, let’s look at academic research which will determine whether the Irish can use with confidence the calculations and predicted figures of numbers of cousins.

Marriage between close family members is strictly illegal in Ireland. Marriage between first cousins is legal, but to be married in a Catholic church the couple must obtain a dispensation from the clerical authorities. If you see mention of a dispensation in ancestral marriage records, be sure to take a closer look.

bishopJ.G. Masterson studied the rate of first-cousin dispensations amongst Catholics in Ireland from 1959-1968. He found a rate of 1 in 720 for the entire island, and 1 in 625 for the Republic. That is less than 0.2%. Masterson also quotes a study from 1883 that simply asked people if they were the children of first cousins. A little less than 0.6% said that they were. I imagine that the falling trend over a hundred years was partly due to decreasing isolation of local populations (i.e. easier to travel).

So we can say in general that first cousin marriages are historically low amongst our Irish ancestors within the last hundred years.

The major exception is amongst a particular section of our population, the Travelling Community. Irish Government figures from 2003 reported that over 20% of marriages within the Travelling Community were between first cousins. This does mean that Travellers will have particular challenges in researching genetic ancestry. There are other endogamous communites taking great interest in similar research who may have useful methods for people from a Travelling background.

In 2017 Irish Travellers only account for about 0.6% of the Irish population. Therefore most Irish people researching their family history can assume a low level of first-cousin ancestral couples for well over a century. More distant consanguinity, such as third cousins, is more likely to be present due to limitations of travel. This will lower the numbers generated by the calculated model, but not with such signficance as experienced by populations with higher rates of endogamy.

I conclude that most Irish people can take as ballpark figures the calculated numbers of cousins by degree, as long as a realistic birth rate is used.

How many Irish cousins: according to AncestryDNA – Part 3 in Series

My previous blog post was on research by scientists at 23andMe on predicting our number of cousins. I applaud 23andMe for the publication of the research in detail.

AncestryDNA have also researched the topic but as far as I can find, they release the information through the marketing department with big headline numbers and not a lot of detail.

Their most recent release of information was to mark World DNA day in April 2018. Unfortunately some news outlets reported that the Irish have 14,000 cousins while others reported Ancestry as saying that we have 14,000 LIVING cousins up to a distance of 8th cousin. The living distinction is important, but I was more disillusioned on realizing this number is up to 8th degree. I’d like to see the breakdown estimates at each degree, as done by 23andMe, but cannot find the details for Ireland.

AncestryDNA did conduct a detailed study using British birth rates and census data to prouct statistics for the average British person, the numbers are shown here. The numbers are lower than in the 23andMe study by Denn et al. The formula used by Denn and Tim X to generate predicted number of cousins is 

If AncestryDNA used the same formula as 23andMe (Denn) and Tim Urban (as discussed in my blog post here), then figuring out the birth rate they utilized is a matter of solving a quadratic equation. I took a shortcut by using symbolab. Plugging in a result of 5 for first cousins and 28 for second cousins, I calculated that if they’d used the formula then their birth rate would have been 2.3. However, solving the same equation of their figures of 3rd and 4th cousins produced different birth rates.

I’m reluctant to repeat numbers for which I can’t explain the provenance, but for the sake of completeness – here are Ancestry’s estimates for British users:

Whatever birth rate and formula they used, the Irish birth rate was significantly higher than Britain prior to 1990 so I’m not particularly interested in the British predictions for the purpose of this post. The problem of course is that Ancestry state that they used census data and other statistics going back 200 years for their calculations, and these records are not generally available for Ireland (no fault of Ancestry here, the sad fact is that Irish records pre-20th century are very patchy).

So it looks like all we have on Ireland from AncestryDNA are their reported calculation of a total of 14,000 1st to 8th living cousins. How does that compare to the predicted totals from my previous posts – which don’t take into account whether these cousins are living or dead? Hard to say, as I can’t find any details as to how AncestryDNA calculated probability of living. There’s a pattern forming here. Even the ISOGG Wiki which have a page on cousin statistics have to cite the Daily Mirror as their source of AncestryDNA information. With all due respect to the Mirror, it’s a tabloid newspaper as opposed to the peer-reviewed journal that published the 23andMe research.

I do hope that AncestryDNA will produce the level of detail as done by 23andMe, but until then, their estimates are a bit of a bust for me. Knowing the assumed birth rate and other assumptions is important to assess whether the figures realistic for Irish users. In my next post in this series I’ll discuss some of the assumptions and caveats to be considered.

How many Irish cousins: according to 23andMe – Part 2 in Series

Yesterday I wrote a blog post based on an entertaining article from Tim Urban to calculate our number of cousins at various distances using birth rate statistics. Today’s post is based on an academic study by researchers from 23andMe (Henn et al) which covers a wealth of complex analysis that includes a table of “expected number of cousins” at degree of cousinship. This table is reproduced in several websites without the detail of the formula that arrived at the very specific numbers.

It took me a few reads to realize that the formula used by Henn et al is exactly the same as what Tim Urban devised. The formula is kinda buried near the end of the article under a section titled “Calculation of expected number of individuals sharing DNA IBD. Yep, that translates to “how many cousins do we have.”

Critically, this section specifies that a birth rate of 2.5 is used to produce the cousin numbers in the table. I’ll come to that later, as it may be more appropriate to the United States than to Irish people over a certain age.

I actually found the academic explanation easier to follow than Tim’s post. So now I’ll try to explain the formula as opposed to using it blindly to produce numbers. The formula is expressed using i as the degree of cousinship and z as birth rate. :

Why 2 to the power of i? For our first cousins, we share two sets of grandparents, therefore two couples. For our secound cousins we share four sets of great grandparents, therefore four couples. And so on up the generations, where the number of couples is equal to 2 to the power of the degrees of cousinship.

Why (z-1)? If one set of grandparents have four children, one of those children is our parent and that person’s children are ourselves and our average of three siblings so we need to remove 1 from the birth rate.

z to the power of i is the total number of non-ancestral cousins that stem from a particular ancestral generation. Thus the number of cousins from one set of ancestors is the product of (z-1) and z^i.  The full total is then achieved by multiplying by the number of ancestral couples for the degree of cousinship.

The table below has the totals for three different fertility rates in recent Irish history. The fourth line uses the fertility rate chosen by Denn et all for their numbers.

As befits a scholarly study, Denn et al also specify the assumptions that they made to simplify calculations. “Perfect survivorship” jumps out for me i.e. that every offsping at every generation lives to produce the average number of children. Given that the user base of 23andMe is predominantly American and with disposable income for personal DNA testing, this might be a reasonable assumption for their purposes. I do think we Irish need to pay some attention to the impact of our mortality rates up to the 1970s.

They also list other assumptions which I’d like to consider. But I’ll save that for another post in this “how many Irish cousins” series. In my next post I want to look at the quoted numbers from AncestryDNA.

How many Irish cousins: according to Tim Urban – Part 1 in Series

Tim Urban wrote an entertaining blog post in 2014 on calculating a ballpark number of cousins based on your country’s average birth statistics. His formula breaks down the totals by degree of cousin i.e. 1st/2nd/3rd/4th and outward.

Tim calculates numbers for USA, UK, Canada and a few other countries, but not Ireland – so I figured I’d crunch the figures for green.

Tim’s formula iswhere “n” is the fertility rate and “d” is the degree of cousin.

The 2013 fertility rates from NationMaster report fertility rates of 1.9 for the U.K, 2.01 for Ireland, and 2.06 for the U.S. Here are the totals for the three countries, with Ireland in the middle line.

Figures for 2013

For now, ignore the eye-watering totals at fifth cousin and beyond. I took one look at the predicted total of 4.1 for First Cousins and rechecked my calculation for a mistake. It just looked suspiciously low to me. My reaction wasn’t based solely on my own family. From the life-cycle of weddings, christenings, and funerals, you tend to have a passing familiarity of the family structures of your friends and neighbours.

A moment’s thought reminded me that Ireland’s birth rate has dropped in recent decades from one of the highest in Europe to closer to the average. The nearest published rate I could find for my birth year was 1970’s rate of 3.87 which predicts 22 first cousins using Tim’s formula. Quite the difference! The same publication reported fertility rates of 2.08 for 1989 and about 3.9 for 1950.

Here are the figures for Ireland only for those years:

figures Ireland 1970 and other yearsNow you can shift your eyes right, and look at the totals of more distant cousins. Again, I thought I’d got the calculations wrong, this time because those numbers were so big. Thankfully, John Reid of Anglo-Celtic Canada Connections has taken Tim’s formula and applied across a wide range of fertility rates, so a spot check stopped me from fretting.

I’ve seen other reported projections of numbers of cousins, including one from Ancestry and one from 23andMe. I’ll address them in other blog posts and compare them with Tim’s.

Your 5th cousin isn’t a DNA match? Don’t jump to conclusions!

In Ireland, the “townland” is a small area of land supporting a number of households. The townland of Creeny (or Creeney) is in County Cavan. In 1901 there were six households in Creeny. This reduced to five in 1911.


Two of the households have the surname of Gamble. Thomas and Mary Gamble sold their farm in 1920 and moved to the nearby town of Belturbet. They were my great grandparents, and I’m still trying to establish the precise relationship between the two Gamble families who were on neighbouring farms from at least the 1850s up to 1920.

My aunt told me the families were distant relations, but so far back that she didn’t know the common ancestry. So I built the Gamble line of both families as far back as Irish records allow, which unfortunately gets very sparse before the mid 1850s. I know that in 1855 there were two households headed respectively by John (my known ancestor) and Edward (ancestor of the “other” Gambles). Jump back to 1825 and there is only one Gamble in Creeny according to the tithe records: a Thomas Gamble. My guess was that John and Edward were the sons of Thomas, who subdivided his farm between them. But without paper evidence I’m stuck.

Enter DNA. Or the lack thereof.

I was very interested when I spotted the descendents of the “other” Gambles in a family tree on Ancestry. The owner of the tree told me that her brother had his DNA kit on Ancestry. I was crestfallen to find that he wasn’t in my DNA matches amongst the “5th-8th Cousins”. Does that mean there is no familial connection? That the proximity of two families of the same relatively unusual surname was by chance? No, not at all.

My theory is that her brother and I are descended from my great-great-great-great grandparents, so we would be fifth cousins. It just so happens that the Ancestry White Paper on DNA matching uses the example of 5th cousins to show clearly that some descendants at that distance may have matching segments, but some will not. This is due to the random nature of how DNA shifts around during transmission through the generations. The nicely illustrated example is in the early pages of the document and is worth a read.

The only conclusion that I can draw is that I can draw no conclusion from the absence of a DNA match at this distance. Of course, turning this on it’s head is more dispiriting. If the brother did have a small match to me, such as 6 CM, then it could also have been by chance.

In the case of the Gambles of Creeny, I personally attach weight to the family lore that the households were distant cousins. In rural areas it was important to keep track of such things. I’ve added the “other” Gambles to my family tree with a note that the connection is still speculation.