Exploring the Odds

The parents of my great-grandfather Joseph Voisin (1858-1916) remain a mystery. Evidence indicates he was born in Ontario, Canada. He was related to Peter Joseph Voisin (1807-1892) of Saint Clements, Ontario. That was proven by a Y-chromosome DNA test with a known descendant. And by traditional genealogy, Joseph is related to Peter Joseph’s brother Henry Joseph Voisin (1801-1884) of Niagara Falls, Ontario. Both of the Ontario brothers went by their middle names, Joseph.

No birth, census or land records have yet uncovered Joseph Voisin’s birth or his parents, except for entries in his personal journal that show he was near both Saint Clements and Niagara Falls when he was young.

My father’s brother, my uncle Paul Voisin, was a grandson of Joseph Voisin. He took an autosomal DNA test and he matches several distant cousins who are also descended from the Voisin brothers in Ontario. Nevertheless I don’t know precisely how we are related. Since they are distant, the amount of shared DNA is low, and consequently there are several possibilities for relatedness.

To explore different hypotheses, I used the What Are the Odds tool at DNAPainter.com.¹ It provides some clues, but it by no means solves the mystery. I placed Joseph Voisin (red boxes) at several places in a family tree. Paul Voisin (blue boxes) was related to several cousins (tan boxes), who all have known lineages. The DNA shared between Paul and each cousin influences the probability that he, and thus Joseph Voisin, appears at a given hypothetical spot.

Some names are hidden for privacy. A “1/2” denotes a half-sibling relationship. Centimorgans (cM) is a measure of the amount of DNA two people share.

All hypothetical positions (blue boxes) in the tree are possible. Hypothesis 6, that Joseph Voisin was a son of Henry Joseph and Anne Marie (Ditner) Voisin, is the most likely. A few other hypotheses are also probable and cannot be ruled out.

DNA inheritance is fickle. Although John and Paul do not share a detectable amount of DNA, I am one generation removed from Paul and I share a relatively large amount, 44.4 cM, with John. Likewise Rebecca and Paul do not share DNA, but Rebecca shares DNA with William and Fred, both of whom share DNA with Paul. The inclusion of known cousins without shared DNA improves the probability estimate.

The probability of the relationships for each hypothesis is given by a percentage (see the following table). For hypothesis 6, the odds that Herman and Paul were actually second cousins, once removed (2C1R) is 51%. So it is still equally likely they didn’t have that relationship. Since the amounts of shared DNA are so low, the underlying statistical model cannot provide more accurate results. I used “version 2” probabilities, which improves the estimates for amounts of shared DNA below 40 centimorgans (cM).

Known Cousin	DNA (cM)	Hyp 1	Hyp 2	Hyp 3	Hyp 4	Hyp 5	Hyp 6	Hyp 7	Hyp 8	Hyp 9	Hyp 10	Hyp 11	Hyp 12
Herman	109.8	4C 0.50	4C 0.50	3C1R 3.04	3C1R 3.04	3C 20.08	2C1R 51.00	Half 2C1R 20.08	3C1R 3.04	Half 3C1R 0.50	4C 0.50	4C1R 0.26	5C1R 0.00
Thomas	56.8	4C1R 1.82	4C1R 1.82	3C2R 6.46	3C2R 6.46	3C1R 20.10	2C2R 37.00	Half 2C2R 20.10	3C2R 6.46	Half 3C2R 1.82	4C1R 1.82	4C2R 0.50	5C2R 0.50
Fred	25	4C1R 11.00	4C1R 11.00	3C2R 20.00	3C2R 20.00	3C1R 27.00	2C2R 22.00	Half 2C2R 27.00	3C2R 20.00	Half 3C2R 11.00	4C1R 11.00	4C2R 5.00	5C2R 4.00
William	23	3C1R 26.00	Half 3C1R 20.40	2C2R 20.40	Half 2C2R 26.00	4C1R 12.00	3C2R 20.40	3C2R 20.40	3C2R 20.40	Half 3C2R 12.00	4C1R 12.00	4C2R 6.00	5C2R 5.40
Norene	19.0	Half 3C 24.00	Half 2C 4.60	2C1R 4.60	Half 2C1R 17.20	4C 21.20	3C1R 24.00	3C1R 24.00	3C1R 24.00	Half 3C1R 21.20	4C 21.20	4C1R 14.00	5C1R 8.20
Larry	17	Half 3C 23.00	Half 2C 3.80	2C1R 3.80	Half 2C1R 15.60	4C 21.60	3C1R 23.00	3C1R 23.00	3C1R 23.00	Half 3C1R 21.60	4C 21.60	4C1R 15.00	5C1R 9.60
Craig	13.9	Half 3C1R 21.84	Half 2C1R 13.37	2C2R 13.37	Half 2C2R 21.53	4C1R 16.16	3C2R 21.84	3C2R 21.84	3C2R 21.84	Half 3C2R 16.16	4C1R 16.16	4C2R 10.31	5C2R 11.94
John	0	3C1R 19.00	Half 3C1R 21.00	2C2R 10.00	Half 2C2R 19.00	4C1R 17.00	3C2R 21.00	3C2R 21.00	3C2R 21.00	Half 3C2R 17.00	4C1R 17.00	4C2R 12.00	5C2R 17.00
Rebecca	0	3C1R 19.00	Half 3C1R 21.00	2C2R 10.00	Half 2C2R 19.00	4C1R 17.00	3C2R 21.00	3C2R 21.00	3C2R 21.00	Half 3C2R 17.00	4C1R 17.00	4C2R 12.00	5C2R 17.00
Carmen	0	Half 3C1R 21.00	Half 2C1R 10.00	2C2R 10.00	Half 2C2R 19.00	4C1R 17.00	3C2R 21.00	3C2R 21.00	3C2R 21.00	Half 3C2R 17.00	4C1R 17.00	4C2R 12.00	5C2R 17.00
Charles	0	Half 2C1R 10.00	Half 3C1R 21.00	2C2R 10.00	Half 2C2R 19.00	4C1R 17.00	3C2R 21.00	3C2R 21.00	3C2R 21.00	Half 3C2R 17.00	4C1R 17.00	4C2R 12.00	5C2R 17.00

The combined odds ratio measures the relative likelihood of each hypothesis compared to the others.

Ratio	Hyp	The hypothesis that Joseph Voisin was a(n)…
449,273.56	6	Son of Henry Joseph and Anne Marie (Ditner) Voisin. More likely than any other hypothesis.
117,934.21	7	Illegitimate son of Henry Joseph Voisin. (His children are half-siblings with Joseph.) Still relatively likely.
18,281.55	5	Son of Henry Joseph Voisin’s son Joseph Voisin.
4,250.62	8	Son of an unknown son of Vincent and Ann Eve (Denier) Voisin. Their known surviving sons were Henry Joseph and Peter Joseph.
1,739.21	4	Illegitimate son of Peter Joseph Voisin. (His children are half-siblings with Joseph.)
53.82	1	Illegitimate son of Peter Joseph Voisin’s son Jacob Voisin. (Jacob’s children are half-siblings with Joseph.)
16.79	10	Son of an unknown son, of an unknown son of Vincent and Ann Eve (Denier) Voisin. Their known surviving sons were Henry Joseph and Peter Joseph.
16.79	9	Son of an illegitimate son of Vincent Voisin. (Vincent’s legitimate children are half-siblings with another unknown son.)
4.24	3	Son of Peter Joseph and Catherine (Meyer) Voisin.
1.00	2	Illegitimate son of Peter Joseph Voisin’s son Anthony. (Anthony’s children are half-siblings with Joseph.)
0.00	11	Son of an unknown son of an unknown brother of Vincent Voisin. Vincent Voisin’s brothers were Joseph, Louis, Jean, Michel, and Etienne.
0.00	12	Son of an unknown son, of an unknown son, of an unknown brother of Ludwig Voisiné. No brothers are yet identified. Not statistically possible.

Another Angle

I am one generation further removed from Joseph Voisin than my uncle Paul. I created another probability tree (see below) using my own DNA test results. The shared DNA amounts are lower, but I am able to compare results with more cousins. The probability Joseph was a full son of Henry Joseph and Anne Marie (Ditner) Voisin is still the strongest conclusion. However the probabilities of his being an illegitimate son of either Henry Joseph or Peter Joseph are nearly equal, and rank a close second behind the strongest conclusion.

Conclusion

At this time, Joseph Voisin was most likely a full son of Henry Joseph and Anne Marie (Ditner) Voisin (hypothesis 6). However the evidence does not support that conclusion. At age 54 in 1858, it is unlikely Anne Marie gave birth to Joseph. The 1861 Canadian census lists Henry Joseph and Anne Marie (Ditner) Voisin, but not a three year old Joseph.

Three to four times less likely is that Joseph was an illegitimate son of Henry Joseph Voisin, that is, a half-sibling to his other children (hypothesis 7). Although less likely, it is still more likely than any remaining hypotheses. And, when I consider my chart, the odds dramatically improve that Joseph was an illegitimate son of Peter Joseph Voisin (hypothesis 4).

Perhaps most compelling however is that hypothesis 6 is more than one million times more likely than hypotheses 11 and 12. This effectively rules out that Joseph Voisin descends from a brother of Peter and Henry’s father Vincent Voisin, or from a brother of their grandfather Ludwig Voisiné. That seems to indicate there is not an undiscovered Voisin brother, uncle or cousin who also immigrated to the area.

Therefore I will concentrate my research on finding a child named Joseph in the company of his mother, living near either of the brothers.

In the coming years, as more distant cousins participate in DNA testing, the probabilities will improve. There are currently more cousins proven by DNA matches. I did not include them in the tree because I cannot determine their actual lineage. A small addition can change the odds significantly. And, the underlying statistical model itself may also improve in the future.

Footnotes

1. DNA Painter, What Are the Odds (WATO), beta V2, https://DNAPainter.com, March 2022.