Observer design for phenotypic observation of genetic processes

In the paper a single-locus sexual population is considered, where the phenotypic selection process is described by an evolutionary game. First, in order to recover the genetic process from different observations, observability is guaranteed by the linearization method developed in earlier papers of the authors for systems with invariant manifold. Then, based on a known result of nonlinear systems theory, an observer system is constructed that makes it possible to asymptotically recover the solution of the original system from the observation. In the numerical illustrations the selection is described by a “rock-scissors-paper” type game widely studied in evolutionary game theory. For the corresponding evolutionary dynamics a Hopf bifurcation result is also obtained.