Surname Extinction

by Olivia Zhu

Every year, there comes a flood of articles regarding trends in baby names accompanied with charts and historical analyses. I’ve been tickled to see my own first name see rather significant increases popularity over the past decade or so—congratulations to my parents for being trendsetters!

Yet, equally interesting—if not perhaps even more interesting—is the modeling of surname trends over time, and it was that problem that captivated my collaborator Nicole Flanary (Nicole is the 152^nd most popular female baby name, by the way) and me. Surnames tell the stories of lineages, immigration, ethnic enclaves, feminism, assimilation, family planning, and more, whereas given names more typically reflect cultural fads. A study of surnames also offers up the idea of “surname extinction,” the fatalistically named phenomenon that British mathematicians Francis Galton and Henry William Watson modeled. In 1847, they explored the topic to determine whether aristocratic families might go extinct depending on the number of children they had—a process well-modeled since British high society at the time was fairly closed, homogenous, and patrilineal.

Galton and Watson might have found a few other societies interesting as well. Chinese, Korean, and Vietnamese populations are renowned for the lack of surname diversity—was there an extinction-style event at some point that eliminated names from the language altogether? Vietnam is a particularly interesting case, as 40% of the population share the same last name: Nguyen. Contrastingly, surname diversity and even inventiveness in other countries is also worth studying, especially since new last names may be easily and often added to the name pool.

Nicole and I had wanted to focus on Boston merchant names over a period of 80 years, beginning with 1845. We reached out to the Boston Athenaeum for information on census data that we needed to check the vigor of our model. Fortunately, the data not only included a list of each surname, but also how many individuals in the area possessed each surname. Moreover, the names are also associated with their occupation and address, as the city directories function as a type of phone book.

One consideration for the data involves the fact that it is not comprehensive, including only the names of individuals who were business owners. That is, families and women are generally not included. However, we believed that the city directory is representative of the greater demographic trends, and was a valid base for our analysis.

Looking at Boston meant we had to modify the Galton-Watson process in the following ways: first, we included true birth and death rate data for the region examined. Second, we inserted a new set of names each generation to account for natural rates of immigration that would add diversity to the surname pool. We did, however, keep the overall structure of the model relatively similar, and we also assumed a patrilineal passing down of names (where women take men’s names upon marriage, and therefore only sons can continue the surname line).

Why all this tinkering? Well, it was of interest to us whether we could approximate the average family size (really, the number of people that shared the same surname) and if we could determine and predict and extinction “rate” of names, which we ultimately discovered to be around 10-20%. That is, from one “generation” to another, 10-20% of all surnames disappeared—a surprisingly huge percentage.

We learned through completing this project that our model provides a reasonable framework for modeling name diversity in the United States in the 19th and 20th centuries. Opening a society (like American society been opened) fundamentally alters the Galton-Watson model as name diversity is very much driven by immigration—Galton-Watson assumes a closed society. From our model, we discovered that increasing name diversity is driven totally by name immigration numbers, which is unsurprising, but an important result nonetheless. We also learned how the rate of death could alter the surname makeup of a society; our results also indicated that birth and death rates clearly have long lasting effects on surname diversity as well.

It was a bit of a silly prompt to begin with (can we tell if surname extinction is actually happening?) and morphed into a project seeing how we could model how last name populations grow and decline. These are real names, tied to real lineages, and trends in this data is indicative of greater societal movements than the rising popularity of a first name like “Olivia” (however excited I may be about it).