Genetic flatlining of island foxes

Carl Zimmer’s article on “Foxes That Endure Despite a Lack of Genetic Diversity” is interesting and useful:

However the animals arrived on the Channel Islands, they adapted quickly. The oldest island fox fossils date back 7,000 years and show that they were small even then. The Great Shrinking required less than 2,200 years, it seems.
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Like other animals, island foxes carry two copies of each gene, inheriting one copy from each parent. In large populations with a lot of genetic variation, there can be many versions of any given gene. An animal may inherit two varying copies of a gene from its parents.
But the scientists discovered virtually no differences in the DNA the foxes had inherited. “We call it genetic flatlining,” Dr. Wayne said.

This is an extreme example of the situation that we consider likely to have generated substantial genetic load in Neandertals. In the foxes, there has been substantial phenotypic change but biologists do not yet know what negative or deleterious effects on the fox population may have resulted from the limited genetic variation. Several of the populations are endangered, and it is hard to know how much of their demographic challenge may be from their intrinsically low genetic variation as opposed to human disturbance to their habitat.

An even better hominin analog may be the Homo floresiensis situation, which was probably nearly as limited in genetic diversity, potentially for a much larger number of generations. Could a hominin population have persisted for thousands of generations in a “genetic flatline” situation?