Adaptation 1 Beneficial mutation 1 Beneficial mutations Branching process 1 Branching process model 1 Discrete time 1 Evolutionary rescue 1 Extinction 1 Population decline 1 Population dynamics 1 Population growth 1 Population statistics 1 Probability distributions 1 Simple++ 1 adaptation 1 article 1 evolution 1 extinction 1 gene frequency 1 genotype 1 model 1 mutation 1 mutation rate 1 population dynamics 1 population growth 1 probability 1 process model 1