If a gene mutation is associated with the development of Alzheimer's Disease (e.g. E280A), how might a high frequency develop in a population and why wouldn't natural selection decrease it?

A high frequency of mutation can be produced by having a small population, leading to high levels of inbreeding. When there is little interbreeding with different populations, the genetic diversity will remain low and the gene will become more prevalent within the population as it is passed from generation to generation, through various families sharing common ancestry. As Alzheimer's Disease doesn't develop until later in adulthood, survival to reproductive age is not affected. Thus, those affected will already have reproduced before disease onset and the gene mutation will be able to be passed down the generations without being reduced by natural selection.