# Genetic algorithm only using selection

Suppose you have a population of N individuals with fitness 1, 2, . . . , N (i.e., all individuals have a unique fitness value). Suppose you repeatedly apply tournament selection without replacement with tournament size s = 2 to this population, without doing crossover, mutation, and replacement.

In other words, you run a genetic algorithm with selection alone. After a certain number of generations you will end up with a population consisting of N copies of the same individual. Can you give an estimate of the number of generations needed to achieve that?

Is the answer to this just log(n) ?