We introduce a new parameter to discuss the behavior of a genetic algorithm. This parameter is the mean number of exact copies of the best-fit chromosomes from one generation to the next. We believe that the genetic algorithm operates best when this parameter is slightly larger than 1 and we prove two results supporting this belief. We consider the case of the simple genetic algorithm with the roulette wheel selection mechanism. We denote by ℓ the length of the chromosomes, m the population size, pC the crossover probability, and pM the mutation probability. Our results suggest that the mutation and crossover probabilities should be tuned so that, at each generation, the maximal fitness multiplied by (1 - pC)(1 - pM)ℓ is greater than the mean fitness.

We study a classical multitype Galton–Watson process with mutation and selection. The individuals are sequences of fixed length over a finite alphabet. On the sharp peak fitness landscape together with independent mutations per locus, we show that, as the length of the sequences goes to ∞ and the mutation probability goes to 0, the asymptotic relative frequency of the sequences differing on k digits from the master sequence approaches (σe-a - 1)(ak/k!)∑i≥ 1ik/σi, where σ is the selective advantage of the master sequence and a is the product of the length of the chains with the mutation probability. The probability distribution Q(σ, a) on the nonnegative integers given by the above equation is the quasispecies distribution with parameters σ and a.

An integro-differential model for evolutionary dynamics with mutations is investigated by improving the understanding of its behaviour using numerical simulations. The proposed numerical approach can handle also density dependent fitness, and gives new insights about the role of mutation in the preservation of cooperation.

Classical swine fever is a highly contagious disease that affects domestic and wild pigs worldwide. The causative agent of the disease is Classical swine fever virus (CSFV), which belongs to the genus Pestivirus within the family Flaviviridae. On the genome level, CSFV can be divided into three genotypes with three to four sub-genotypes. Those genotypes can be assigned to distinct geographical regions. Knowledge about CSFV diversity and distribution is important for the understanding of disease dynamics and evolution, and can thus help to design optimized control strategies. For this reason, the geographical pattern of CSFV diversity and distribution are outlined in the presented review. Moreover, current knowledge with regard to genetic virulence markers or determinants and the role of the quasispecies composition is discussed.

Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to replicate the best-adapted genotype, leading to a population composed of low replicating mutants that is eventually doomed. We propose a new branching model that shows that this is not necessarily so. That is, a population composed of ever changing mutants may survive.