The Universality of (Sephardic) Ethnicity, as Explained by Mathematical Genealogy

Last year, Spain announced that it would provide a fast track to citizenship for Sephardic Jews—Jews of Spanish descent (the Jews of Spain were expelled in 1492). While there hasn't been movement forward by the Spanish government on this proposal, it can serve as the basis for an intriguing thought experiment: how many Jews of Sephardic descent are there?

While only about 20% of Jews identify as Sephardic, what fraction of the Jewish population might actually be descended from Spanish Jews? Is it much higher than 20%? Joshua Weitz, a biologist at Georgia Tech, recently wrote a short paper posted on the arXiv that explores this from a mathematical perspective. Weitz makes the amount of historical mixing between Sephardic and Ashkenazi populations (Jews of Central European descent) a tunable parameter, and makes a simplifying assumption of how people choose their ethnic identification (chosen randomly if parents are of different ethnicity, as there is no gender in the model).

Some more assumptions from the model are below:

Further, the application of the model assumes that the Sephardic community was approximately 20% of the global Jewish population in 1492. Mating preference data spanning this historical period is not available in a comprehensive fashion. Instead, consider a highly conservative (and highly biased) mating scenario where α = 0.00124875, corresponding to a 1000:1 relative likelihood given one type-1 individual to mate with another type-1 individual rather than a type- 2 individual. Note that surveys of “inter-marriage” between Sephardic and Ashkenazi individuals in modern Israel suggest that within-ethnicity marriages account for approximately 90% of all marriages.

Weitz found that even if the likelihood of mating between Sephardic and Ashkenazi communities is incredibly low (less than 2%), in less than twenty generations all Jews are actually of Sephardic descent, even though only a small portion of the population might identify as such! The third frame of the figure below shows this:

So ultimately, descent and identity are quite different matters, and simple models can show this quite elegantly:

Instead, the model can be used to point out that policies linked to the identity of (distant) ancestors should be approached cautiously, given that the number of ancestors grows (nearly) exponentially. As a consequence, the identity-associated characteristic of ancestors need not be congruent with the identities of present-day individuals.

The original paper is highly readable and contains many more fascinating details.

Top image:Kent Wang/Flickr/CC