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A quasispecies is the stationary state of a set of interrelated genotypesthat evolve according to the usual principles of selection and mutation.Quasispecies studies have invariably concentrated on the possibility of errorsduring genotype replication and their role in promoting either the survival orthe demise of the quasispecies. In a previous work [V. C. Barbosa, R.Donangelo, and S. R. Souza, J. Theor. Biol. 312, 114 (2012)], we introduced anetwork model of quasispecies dynamics, based on a single probability parameter($p$) and capable of addressing several plausibility issues of previous models.Here we extend that model by pairing its network with another one aimed atmodeling the dynamics of the immune system when confronted with thequasispecies. The new network is based on the idiotypic-network model ofimmunity and, together with the previous one, constitutes a network model ofinteracting genotypes and idiotypes. The resulting model requires furtherparameters and as a consequence leads to a vast phase space. We have focused ona particular niche in which it is possible to observe the trade-offs involvedin the quasispecies' survival or destruction. Within this niche, we givesimulation results that highlight some key preconditions for quasispeciessurvival. These include a minimum initial abundance of genotypes relative tothat of the idiotypes and a minimum value of $p$. The latter, in particular, isto be contrasted with the stand-alone quasispecies network of our previouswork, in which arbitrarily low values of $p$ constitute a guarantee ofquasispecies survival.

Quasispecies dynamics on a network of interacting genotypes and idiotypes: Formulation of the model