We're a long way (2000km further North) from Bouvet Island, which we alighted on briefly in January. Tristan da Cunha is named for, indeed was named by, Portuguese explorer Tristão da Cunha who came up against them in 1506. That's more than 500 years ago, at the very dawn of the European voyages of exploration. Everyone knows that Columbus sailed the ocean blue in 1492 to discover the New World. Fewer appreciate that Vasco da Gama's voyage to India via the Cape of Good Hope came five years later in 1497. da Cunha was on his way to India when he discovered the archipelago of which we treat. It is really among the most remote places in the World and by all accounts there's not a lot for entertainment. If you want to take a gal to the dance for example, there isn't much choice: there are only 300 Tristanians all at all from tots to pensioners, and nobody wants to have a date with his own sister. There have only been eight surnames on the island: Glass, Green, Hagan, Lavarello, Patterson, Repetto, Rogers, and Swain who arrived there some time between 1816 and 1908, The Patterson line has 'daughtered out' and Mr Patterson's surname and Y chromosome is no longer to be found. Likewise, while history identified 7 ancestral females, whose surnames haven't come down to us, a study in 2003 showed that there were only 5 different mitochondrial genomes circulating. So two of those lines have gone too. You have to read the original paper to see how many instances of non-paternity there were South of the Line. Each Y chromosome has a characteristic genetic signature ('haplotype') which should be inherited with the surname. It looks like a Polish sailor left a boy behind shortly before WWI, for example. And of course boys and girls kick over the traces elsewhere, it's not unique to Tristan.
Thus although there has been an occasional instance of new gene variants coming into this small remote population, the fact of the matter is that the original in-comers were few in number and had a particular set of gene variants, some of which were deleterious [= not-so-good]. You and I and all people have about 23,000 protein-coding genes and many of these have known mutations that are harmless if you have one copy [masked by the other good gene] but can affect your health and well-being if you inherit one duff copy from The Da and another duff copy from your Mother. These are called recessive deleterious traits, and some classic back-of-an-envelope calculations in the 1930s suggests that we all carry a handful of them. Your handful will be different from my handful, but your cousin's selection of bad cards is likely to be similar to yours. Many of these defective genes are rare in the normal population, and all the copies of that gene are present in the carrier-state (aka heterozygous). Cystic fibrosis is 'carried' by about 1:20 of the population; Narcolepsy has a similar frequency; Tay-Sachs is rarer at about 1:300. The chances of having a child born with either disease is remote: both parents have to be carriers and they have to make a 1/4 draw of their chromosomes [explanatory diagram] for the child to inherit two mutant genes 1/20 x 1/20 x 1/4 = 1:1600.
But the case is decidedly altered if there are only 15 people in the population: 1:300 odds no longer apply. Such groups either have the trait, and at a much higher frequency than the rest of the world or they don't. This bottle-neck is called Founder Effect by geneticists and it's often quirky. The first small group of Asiatics who walked across the Bering Straits to people America just happened to be all blood group O, so none of their descendants have A or B antigens on the red blood cells. All Native South Americans are group O. Later sweeps brought in blood group A which is common among Athabaskans and some other groups in Canada and the US. Blood group B was effectively absent from the pre-Columbian New World. Tay Sachs is much more common among Ashkenazi Jews. It's like that for Tristanians, one or other of the original 15 carried a genetic predisposition to Asthma and another brought the genes 'for' retinitis pigmentosum a degenerative eye disease. So these maladies are way more common in the South Atlantic than hereabouts in South County Carlow. On the other hand, there are far fewer southpaws among the Tristanians than you'd expect. This is a problem in all small or endogamous populations.
All this poking and prying into the genetics and antecedents of the human guinea-pigs of Tristan and pushing it out into the public domain must make the poor data-providers feel like they are specimens in a large goldfish bowl. It certainly has me looking for a pinch of salt when historian Simon Winchester claims that he has been banned from the island for telling an old, and possibly true, love story that could have served as a model for Madame Butterfly. You may read that neat essay, with advantage, for its description of how a sure-I'm-right ethical position was gradually shaken into an appreciation that The Other is not only different, but may also be better.