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The title question is somewhat ill-defined because, of course, most Americans living today descended from immigrants from different years: one of your grandpas is a Mayflower descendant, another one's ancestors fled the Potato Famine, one of your grandmas escaped pogroms, and the other one fled from Nazis. To make the question better defined let's consider only Y-chromosome descendants, only male ancestry, so that almost every American would be a descendant from exactly one "ancestor immigration year", whether 1620 or 1848 or 1907 or 1938. Or, if you prefer, we could assign mitochondrial immigration year, IDK, as long as the the immigration year is well-defined.

I'd like to figure out the distribution of "ancestor immigration years" of today's US population. That would facilitate answering questions like "how many Americans descended from post-1865 immigration". In fact, the cumulative immigration descender count after 1865 is exactly what I am interested in.

Please advise how to go about finding such information.

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    @T.E.D., perhaps I wasn't clear on the question. I'd like to find out how many Americans descended from immigrants starting a certain year, which is a function of the year. If the year was 1498, you would be right. If the year was 2001, only those who were born to the 21st century immigrants would count.
    – Michael
    Aug 23 at 16:38
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    I find the question interesting. I think you'd have to start by graphing the change in US population each year, then estimate the split between changes due to migration and figure out how to allocate the births and deaths.
    – MCW
    Aug 23 at 16:58
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    So, for example, If my paternal grandfather immigrated in 1912, us 5 surviving siblings of my father and his brother would count as "1910"? Dang, yeah, that's a heck of a lot of researching and analysis. I guess whichever ancestral line you choose, the averages would come out in the wash, but there's also the 5-10% of not-the-real-father births to throw a wrench in the works. Aug 23 at 16:59
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    I think it should be possible to figure that out from migration policy data. Basically, for each decade take the immigration percentage over (birth rate + immigration percentage), and integrate over time.
    – Michael
    Aug 23 at 19:10
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    ALL Americans (other than those who actually immigrated themselves) are descended from immigrants.
    – jamesqf
    Aug 24 at 3:57
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I think it is impossible to answer this question without carrying out an extensive genetic sampling from the current US population. I am not aware that such data exist, but this is what one should be looking for.

Making inferences from demographics/migration data (as suggested in some of the comments) may be very misleading: genes (more precisely alleles) do not propagate through the population uniformly/proportionally even in absence of selection - due to genetic drift some Y-chromosomes may be overrepresented, while many have gone completely extinct. When selection is in play, the consequences can be even more spectacular - like 16 million descendants of Genghis Khan (see the links to research papers in this article).


Demographic approach
To perform a simple estimate we could define as nt the number of individuals that immigrated in year t from the beginning of the period of interest, so that n0 is the number of individuals that were already present in the beginning of this period. We assume that the period is T years long, and that the current population is N. The important parameter is the yearly increase of the population:

s=1+b-d

(b, d - rates of births and deaths), so that the number of the offspring produced by the immigrats from year t is

Nt = nt * s^(T-t)

The parameter s can be determined by summing all the Nt, which gives us the total current population in the US

N0 + N1 + N2 + ... + NT = n0*s^T + n1*s^(T-1) + n2*s^(T-2) + ... + nT=N.

This equation can be solved numerically or graphically. The fraction of the population descending from year t is then Nt/N.

Difficulties with the demographic approach
Stochasticity of birth and deaths
The OP suggest using Y-chromosome (only paternal descent) or mitochondrial genome (only maternal descent). This could be very useful, if we actually had the genetic data sampled from the current population, which are likely unavailable. It is necessary however to point out the complication which immediately arises in such a picture: the births and deaths are a stochastic process: some fathers/mothers left no children behind, whereas others have left multiple offspring. These fluctuations grow with the rate faster than s, and likely make the inference above meaningless (i.e., the standard deviations of Nt are of the order of Nt itself).

Diploidy
If we do not limit ourselves to only paternal or only maternaldescent then we have to account for another difficulty, as pointed in the comments by @jamesqf: since each person has a father and a mother, one has two anscestors in the previous generation, four ancestors two generations back, eight ancestors three generations back and so on. Thus, most persons cannot be said do descend from a specific immigration year - they likely have ancestors in many years. On thus could ask a question somewhat different from the reasoning suggested in the OP: what percentage of the current population have an ancestor that came with a certain immigration wave?

Update
The estimate actually works for the US population and not too small immigrant waves (e.g., Mayflower with its 100 passangers may be abit problematics). See the question and answer in the biology forum.

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  • If I understand you argument correctly, it proves than making inferences from genetic data may be very misleading, rather than demographics ?
    – Evargalo
    Aug 24 at 12:24
  • @Evargalo It depends on what kinds of inferences one tries to make. Tracing ancestries of the modern population to particular migration waves can be done rather unambiguously on genetic basis... if one can collect such data. On the other hand, using a demographic model will be likely very misleading. So it is the opposite of what you suggest in your comment... Aug 24 at 12:31
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    If I thought this question were actually about genetic data I would have downvoted and pushed back. I understood the reference to chromosomes as merely a symbol of a simplifying assumption - to model only through one line (either father or mother). If you track a single line, then each person has a (relatively) unambiguous number of generations since immigration. If you try to track both lines, then the "number of generations since immigration" for each person is a (bewilderingly) complex number.
    – MCW
    Aug 24 at 13:25
  • Genghis Khan died ~900 years ago. Assuming 25 years per generation, that's 36 generations, which means that someone alive today has something over 34 billion great^36 grandfathers. Even at the Civil War level, there are 32 possibilities.
    – jamesqf
    Aug 24 at 16:04
  • As @MCW mentioned, I'm not interested much in genetics as in rough estimate of when ancestral immigration happened. For example, if Roger and Vadim would be identical twins, one immigrated in 1980 and another one in 2020, from my point of view those would be two different cases because of two different immigration years, identical DNA notwithstanding.
    – Michael
    Aug 24 at 16:15
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Given the limitation in the actual phrasing of your question, I think what you're looking for is: the percentage of new immigrants in the US population, each year.

This is a solid data that could be "easily" found because immigration was registered (mainly). Overall, the situation is as follow for US population:

  • 18th century: mainly English and German (Hannover) immigrants. Arrival of slaves from Africa (not immigrants in the strict definition)
  • After the Independence war: mostly English still, but Scandinavian, Germans started to be more numerous
  • 1rst part of 19th century: Arrivals of European immigrants, from Ireland, Italy, Poland, Germany. Conquest of land occupied by Mexico triggers Latino presence (not immigrants in the strict definition)
  • 2nd part of 19th century: East Europeans came, as well as Chinese with the specific opening of China to Western trade
  • 1rst part of 20th century: More Europeans again, compared to less Asians because of the different wars
  • 2nd part of 20th century: Asian, especially linked to the Vietnam war, and South Americans. Also, a diversification to new regions such as Turkey or India.

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