The answer is unknown because there is no research into genetic causes for the human phenotypes we associate with ethnic traits.
Actual genetic research has been looking for the causes of disease not aesthetics. This short paper Genetic determinants of phenotypic diversity in humans explains the issues involved in researching genetics: "The first disease traits to be ascribed to particular genes were Mendelian traits, which are controlled by a single gene and follow well defined models of inheritance…. The next, and more difficult, stage was to determine genes associated with the far more common complex (multigene) diseases…."
TL;DR diseases that are caused by one gene are rare because it's easy for the phenotype (the appearance) of the disease to be recognized, and the population will naturally select (breed) against it. But most genetic diseases are not simple, they are a pokerhand of gene combinations that we are only beginning to map, and an estimated 70% of these complex diseases also have environmental triggers that can turn them on and off. It may be decades before we have enough genetic data to understand multi-gene diseases, and these are life-and-death medical conditions getting priority funding (cancer, heart disease, diabetes, etc). While it's likely that some ethnic phenotype gene combinations will be discovered, that is not the goal of any serious gene research – and there are plenty of articles debunking the claims of home gene test kits that claim to tell your ethnicity or likelihood of disease. In cases where a genetic marker is known, the extra risk of developing the disease is usually within a few percentage points – in some cases the evidence is so vague that an increase of risk cannot be calculated. A complete map of what triggers each and every ethnic phenotype is a long way away, and will likely only be discovered though meta-studies that compare databases from many earlier research studies (a percentage of people who identified as African American statistically carry xyz gene groups in common, etc). Since almost all current gene data is from people of European descent, it will take even longer before we know what we need to know to answer our questions about ethnic diversity.
But it gets worse. Confirmation bias of the researchers has polluted genetic research from the start, and the notion that biodiversity is actually a good thing is unfortunately relatively new. The first century of gene theory reflected 19th Century ideas of "race entitlement" and fascist theories of dominance and submission, ethnic "superiority", and genetic determinism. It was accepted that evolution selects what is "best" and kills off traits that are "weak" – and no coincidence the theorists managed to conclude their own ethnic traits meant they were more evolved, while coincidentally other ethnicities were less evolved. Because researchers believed the philosophies of their age it influenced everything they observed, and even changed what they observed to fit the theory.
One myth I was taught in school that lingers today was when researchers tried to make eye color fit the emerging genetic theories. They decided there were 3 eye colors, blue, brown, and green – which was actually a kind of brown (um, what…?). They theorized there was a recessive allele for blue eyes, and everything else was the other color, not-blue. Blue-eyed parents always have blue-eyed children (which was what they were actually observing), except that's not true. This isn't how eye color works at all, and eyes aren't even "blue". Scientists actually denied that certain eye colors exist because it didn't fit the simple theory. Now imagine this scenario for each and every ethnic trait. Curly hair, nostril width, brow bone... Who decides which ethnic traits are "legitimate" to look for, and where are we looking? It's a hornets nest. I understand your scenario, but when you get specific about describing this it's all going to get ugly so don't go there. Imply a combination of traits or make your colonists like trendy cornchip flavors: Persian-Hawaiian, Bantu-Lakota, etc.
In reality, evolution is not a zero-sum game with clear winners and losers, and the environmental factors which help shape evolution are never constant. We now know environments can change drastically, even within a single lifetime. A new theory is emerging that biodiversity acts like a toolkit to respond to environmental changes, so here is your mandate for diversity in a space colony. Convince your colonists that biodiversity is the key to species survival, and you may be able to convince a generation that miscegenation is natural, healthy, and attractive. The fundamental goal of a colony is to survive, and you can land them with a crayola box of colors, but you need a philosophy that will get them through generations of plague, famine, war, mass suicide, and all the inevitable die-offs they will face. They may lose the technology to run a gene scan, but they can be taught to look for biodiversity in a mate. You could take that a step further and reinforce the beauty of biodiverse children, ergo mothers are discouraged from having children with similar-looking fathers. This assumes colonists are actually having children the old-fashioned way, beer and mood lighting, and not through family planning, lottery, or IncuBaby-9000™ – again, you have to plan for a worst-case scenario. If all technology fails, don't marry your brother.
Does this trigger the H&M Fashion Model Apocalypse? Mmmm mabey…
"This colony is humans of varying ethnicity": Can you distinguish between Turks, Kurds, Romanians, Bulgarians, Macedonians, Serbs, Bosnians, Croats, Hungarians, and Albanians by sight? I can assure you that all those are very distinct ethnicities. – AlexP – 2018-02-13T05:56:19.343
Ethnicity was probably not the most accurate word. I'll update with a better one and better description of what I mean. – Andon – 2018-02-13T06:03:10.097
Human races don't actually exist in nature. If you mean to say various eye colors, hair colors, hair types, levels of skin pigmentation, Rh factors, blood types, etc. just say so. I for one am curious to find out what exact physical attributes you have in mind. – AlexP – 2018-02-13T06:10:20.640
It's 1am and I'm trying to keep things simple. It is... not exactly working. I'm looking to see, largely: Will there still be such huge varieties in people's looks, or will things be more... uniform? – Andon – 2018-02-13T06:11:33.527
2You can't really ignore inbreeding in such situations. You either have to take it as a factor, or accept people looking for significantly different partners as a factor. – Mołot – 2018-02-13T09:22:07.603
1@Molot I didn't want to ignore inbreeding entirely I just wanted to ignore the "Minimum Viable Population* part which has been asked more than a few times. – Andon – 2018-02-14T00:00:35.840