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I've heard the argument that race is not a real scientific entity several times. Despite what on the surface look like very different traits, humans share significantly more DNA with each other than there are differences between them. Furthermore, the genetic variation within the continent of Africa is greater than what the variation between a typical Nigerian or Norwegian could be. However, I recently heard of a campaign in Israel to find a bone marrow donor for a woman suffering from Cancer. The campaign asked for anyone of Yemeni descent to provide a saliva sample in order to find a match.

So my question is if race does not exist then why are people of Yemeni descent more likely to be better bone marrow matches? What do you call the fact that they are more likely to be a better match if not race?

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What was once defined as 'scientific racism' is incompatible with what we know to be science or anthropology. Inter-group differences, supposed to be large in broad terms and used to qualify people, turned out to be much smaller than intra-group differences. And the classifications into 'better' or 'worse' turned out to be completely bogus.

But that does not mean that genetics do not exist or that systematic genetic differences do not exist. For societal classifications these turned out to be meaningless as well. For medical reasons there were some important variables identified that pertain for example to bone marrow transplants. Certain features of the immune system are more often grouped in similar ethnic groups than between dissimilar ethnic groups.

The National Marrow Donor Program summarises it as

How does a patient's ethnic background affect matching?
A patient’s likelihood of finding a matching bone marrow donor or cord blood unit on the Be The Match Registry ranges from 23% to 77% depending on ethnic background. Patients are more likely to match an adult donor of their own ethnic background.

Compare that to blood types. Yes, they exist. As do different colours of skin. But that doesn't mean that A is 'better' than B. They are just differently arranged molecules on blood cells.

Despite the large number of registered potential donors, the NMDP and unrelated HSC registries worldwide continue to face difficulties in identifying matched donors for some patients, in particular racial/ethnic minorities. (PUBMED)

Multiple dimensions of self-identification, including race/ethnicity and geographic ancestry were compared to classifications based on ancestry informative markers (AIMs), and the human leukocyte antigen (HLA) genes, which are required for transplant matching. Nearly 20% of responses were inconsistent between reporting race/ethnicity versus geographic ancestry. Despite strong concordance between AIMs and HLA, no measure of self-identification shows complete correspondence with genetic ancestry. In certain cases geographic ancestry reporting matches genetic ancestry not reflected in race/ethnicity identification, but in other cases geographic ancestries show little correspondence to genetic measures, with important differences by gender. However, when respondents assign ancestry to grandparents, we observe sub-groups of individuals with well- defined genetic ancestries, including important differences in HLA frequencies, with implications for transplant matching. While we advocate for tailored questioning to improve accuracy of ancestry ascertainment, collection of donor grandparents’ information will improve the chances of finding matches for many patients, particularly for mixed-ancestry individuals.
Hollenbach et al.: "Race, Ethnicity and Ancestry in Unrelated Transplant Matching for the National Marrow Donor Program: A Comparison of Multiple Forms of Self-Identification with Genetics", PLoS One. 2015; 10(8): e0135960.

They are not incompatible, as racism would describe it. The request with its specifics is just betting on the increased likelihood of finding a donor from a pool of a minority that has an increased likelihood of containing a match but a decreased likelihood of donors from that pool already registered. They might as well find a match from someone grouped into another ethnicity. It is a game of probabilities.

Directly about the situation in Israel:

HLA haplotype frequencies in a volunteer bone marrow donor registry should reflect the frequencies of potential transplant recipients served by that registry, a challenge in a country with diverse subethnicities of immigrants from Eastern and Western cultures, such as Israel. We evaluated the likelihood of finding suitable donors for hypothetical patients drawn from defined subethnicities in the Ezer Mizion Bone Marrow Donor Registry (EM BMDR) from donors both within and outside the registry now and during the coming decade. On average, bioinformatics modeling predicts that, given current donor recruitment trends, 6/6 high-resolution HLA match rates for Israelis, which currently stand at 40% to 55% for most subethnicities, will rise by up to 1% per year over the next decade. Subethnicities with historically lower rates of interethnic admixture are less likely to find matches outside of their designated group but will benefit from expansion of the registry, whereas ethnically directed drives will enhance matching rates for currently underrepresented subethnicities. Donor searches for the same cohort using a large extramural registry was of only slight benefit for most of the 19 EM BMDR subethnicities evaluated, confirming that local donor registries that reflect the ethnic diversity of the community being served are best equipped to serve the needs of their respective communities. Contemporary trends of an increasingly multiethnic admixture in Israel may impact the effect of ethnic profiling in assessing future match rates for EM BMDR.
Halagan et al.: "East Meets West—Impact of Ethnicity on Donor Match Rates in the Ezer Mizion Bone Marrow Donor Registry", Biology of Blood and Marrow Transplantation, Volume 23, Issue 8, August 2017, Pages 1381-1386, DOI.

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    Thank you for taking the time to write this detailed answer!
    – user27343
    Dec 5, 2018 at 17:48
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    @user27343 Well, I am so much more grateful that you had a genuine desire to know more about a complex topic that at first read I was unsure about whether it came from a less desirable part fo the spectrum or not. Dec 5, 2018 at 17:55

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