Strong amplifiers of natural selection
Andreas Pavlogiannis, Josef Tkadlec, Krishnendu Chatterjee, Martin A. Nowak · IST PubRep (Institute of Science and Technology Austria) · 2016
Before presenting our proofs we first present detailed description of our model and the results.We then present the formal notations, then our negative results, and finally the positive results.2 Model and Summary of Results ModelThe birth-death Moran process.The Moran process considers a population of n individuals, which undergoes reproduction and death, and each individual is either a resident or a mutant [21].The residents and the mutants have constant fitness 1 and r, respectively.The Moran process is a discrete-time stochastic process defined as follows: in the initial step, a single mutant is introduced into a homogeneous resident population.At each step, an individual is chosen randomly for reproduction with probability proportional to its fitness; another individual is chosen uniformly at random for death and is replaced by a new individual of the same type as the reproducing individual.Eventually, this Markovian process ends when all individuals become of one of the two types.The probability of the event that all individuals become mutants is called the fixation probability.