Sunday, 14 August 2016

How many cousins?

Children per family Degree of cousin
1st2nd3rd4th5th6th
1000000
1.25124102461
1.5251441122365
1.7539321133941,379
2416642561,0244,096
2.256251145132,30710,380
2.58381889384,68823,438
2.7510532911,6018,80748,441
312724322,59215,55293,312
3.5181238586,00342,018294,123
4241921,53612,28898,304786,432
5404004,00040,000400,0004,000,000
6607208,640103,6801,244,16014,929,920
7841,17616,464230,4963,226,94445,177,216
81121,79228,672458,7527,340,032117,440,512

This table is based on a blog post I stumbled on that gives a formula for the number of cousins of different degrees.

(n-1) 2d n

where n is the average number of children in a family and d is the degree of cousin.
That blog post uses the formula to give a general ballpark for the number of cousins using "your nation’s average number of children per family statistic." The number used for Canada is 1.58 children/family, for the UK 1.91 and for the USA 2.06 and is based on total fertility rate (TFR) statistics at www.nationmaster.com/graph/peo_tot_fer_rat-people-total-fertility-rate. TFR is "The average number of children that would be born per woman if all women lived to the end of their child-bearing years and bore children according to a given fertility rate at each age."

How good a ballpark estimate of the number of cousins is it?

The TFRs used are for 2013, typical family sizes are now much smaller that for earlier generations. Larger family sizes in earlier generation should mean more cousins.
Estimates of the TFR for back to the late 1800s are found in Fertility in Canada: Retrospective and Perspective by Anatole Romanluc in Canadian Studies in Population. Vol .18(2), 1991, pp.56-77.

The TFR for 1850, about 7, gives 230,500 fourth cousins, compared to about 60 using the 2013 TFR. Is that the same ballpark?
It's not as wide of the mark as the numbers suggest given that many of those born in the 1800s would have died before having their own children.


No comments: