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3.8 Analytical Model of Extinction Time

The buildup of mutations in a fixed-size population will take place in three phases, assuming the population begins with all individuals in perfect health:

  1. In a relatively short initial phase, mutations are introduced randomly into the population.

  2. In a longer second phase, mutations continue to build and start to become fixed.

  3. The final meltdown phase begins when enough mutations have accumulated that the population cannot replace itself, i.e. the number of survivors in a new generation is smaller than the carrying capacity of the island. Once this point is reached, extinction occurs in very few generations.

Ideally one could define an analytical model that would predict the expected number of generations to extinction as a function of initial population size, mutation rate, selection coefficient, and other parameters. However, this has proved to be very difficult for several reasons, not the least of which is that many simplifications are not valid for small populations.