Consider a population that becomes isolated at some point in time. Some catastrophic event may create a physical island from a peninsula, or human activity may isolate a forested region from surrounding areas, or an artificial island might be created when a small set of plants is selected to be used in a breeding program. For simplicity assume all individuals are originally perfectly healthy from a genetic standpoint, i.e. no individual carries a mutated gene when the island is created.
Over time new segregating mutations will be introduced into the population. Some will die out, but some will spread, and eventually a few will become fixed. From this point on other mutations will become fixed at a fairly steady rate. During this period the population becomes less and less healthy, since on average mutations are slightly harmful and when a mutation is fixed it becomes part of every individual in the population.
At this point an interesting question arises: will the population continue to decline at a steady rate, until sufficient mutations have accumulated so that at some generation no individuals survive and the population is extinct? According to computer simulations, the answer is ``yes'' for certain combinations of initial population size, mutation rate, and other factors.
Interestingly, the rate of decline in overall health of the population is not constant, but instead reaches a critical point. Up to this point the decrease in mean health is linear, but beyond this point the decline is drastic and extinction occurs within a very few generations. This phenomenon is known as a mutational meltdown.