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Is it caused by inbreeding of many generations within an isolated population?

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Short answer

Yes, you pretty much nailed it. Inbreeding of (and from) an isolated population.

Long answer

According to wikipedia > polydactyly, there are 39 known polmorphic sites underlying variance in polydactyly. It is therefore not a trait with a simple mode of inheritance.

There are two important (somehow related) concepts to understand to explain the relatively high frequency of polydactyly (and other genetic disease such as maple syrup urine disease) in Amish.

  1. High inbreeding
  2. Important population bottleneck

If you have no absolutely no background in biology, the following might be a little bit complicated. You might want to make sure you know some concepts (such as deleterious, recessive, dominant, homozygous, Hardy-Weinberg equilibrium, locus, allele and of course inbreeding and population bottleneck) by googling them.

Inbreeding

I will, here talk only about one mechanism by which inbreeding causes those diseases.

There is a positive correlation between how deleterious is a mutation and how recessive it is (the more deleterious, the less dominant, the more recessive). The post "Evolution of dominance of alleles" will probably help you to understand why this is true.

Inbreeding increases the frequency of homozygote loci and therefore, increase the probability of a locus which polymorphism explain variance for the disease to be homozygote deleterious. Using Hardy-Weinberg formula with Sewall Wright work, if at a given locus the allele A is deleterious and is present at frequency $p$, then the frequency of the homozygotes AA is $p^2$ without inbreeding (under Hardy-Weinberg assumptions). Taking inbreeding into account, this frequency becomes $p^2 + Fp(1-p)$ (where $F$ is the coefficient of inbreeding). In words, the higher is the inbreeding coefficient, the higher is the frequency of homozygotes (including homozygotes for the deleterious alleles).

In short, inbreeding matters because of dominance. There are other reasons why inbreeding matters though but that would be the subject of another post.

Bottleneck

In population biology, a bottleneck is is a sharp reduction in the size of a population. Imagine you have a population of size $N$ and you selection a fraction $\frac{N}{1000}$ of this population, you are going to lose a lot of alleles due to random sampling. Most of the times you are going to lose deleterious alleles (as they were already present at low frequency in the original population) but sometimes you are going to pick up a deleterious allele. The frequency of this deleterious allele was maybe 0.00001 in the original population and then suddenly its frequency jumps to 0.1. This is a big deal.

The Amish went though an important bottleneck, there was a time when the descendent of the modern-day Amish reproduced with everybody and at some point, they stopped doing so as they decided to create the amish community (I actually know little about the Amish history but I assume something similar happened). This community was formed by about 200 families only (according to this not-necessarily-trustable source, so very little genetic variance) in 1693 in Switzerland (according to wiki). They probably "won" by not having the alleles coding for clubfoot, sickle-cell and cystic fibrosis alleles (just to cite a few example) but they "lost" by drastically increasing the frequency of alleles coding for polydactyly (and some other diseases).

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  • $\begingroup$ Great answer. +1. One question: I thought that genetic drift was a slow random process nature.com/scitable/definition/… and that it has not a diect link to a sudden reduction in #individuals in a populaton? $\endgroup$ – AliceD Aug 17 '15 at 0:40
  • $\begingroup$ From wiki: Genetic drift (or allelic drift) is the change in the frequency of a gene variant (allele) in a population due to random sampling of organisms. A bottleneck is a sampling process where the number of individuals sampled is much lower than the number of individuals in the previous generation. I felt like it would lead to confusions though. I might as well just take my parenthesis away. Thnks $\endgroup$ – Remi.b Aug 17 '15 at 1:16
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Short answer
Yes, the high frequency of polydactyly in the Amish is caused by inbreeding.

Background
The polydactyly in the Amish is just one of the symptoms of Ellis-van Creveld (EvC) syndrome. EvC syndrome is an autosomal recessive disorder, involving polydactyly of the hands (see figure), short stature with shortening especially of the forearms and lower legs and, in at least half of all cases, congenital heart malformation. In the Amish of Lancaster County (Pennsylvania), EvC syndrome occurs at high frequency and is caused by mutations in the EVC gene.

Amish
Source: McKusick (2000).

The Amish have two characteristics that resulted in the high occurrence of EvC syndrome. First, they are descended from a limited number of founders who immigrated during the eighteenth century to the United States from Switserland, via Germany in the 1690s. Second, the Amish are endogamous, i.e., they marry only within their community. Hence, gene flow is exclusively centrifugal, i.e., members may leave the community but ‘outsiders’ do not join it and thereby introduce exogenous genes.

All EvC cases in the community are traceable to a single couple, Samuel King and his wife, who immigrated to Eastern Pennsylvania in 1744, thus demonstrating founder effect and a recessive pattern of inheritance.

Reference
- McKusick, Nature genetics (2000); 24: 203-4

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    $\begingroup$ Good answer, simple and without explanations of why inbreeding and founder effect can cause higher prevalence of a disease (but making a complete explanation would ask for writing a book). +1. Your first sentence says Yes, the mutation [..] is caused by inbreeding which is of course wrong. $\endgroup$ – Remi.b Aug 15 '15 at 16:05
  • $\begingroup$ @Remi.b - Thanks for the appreciation! And also thanks for pointing out that mistake :) I fixed it! $\endgroup$ – AliceD Aug 15 '15 at 22:19

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