Learning by population genetics and matrix Riccati equation

A model of learning as generalization of the Eigen's quasispecies model in population genetics is introduced. Eigen's model is considered as a matrix Riccati equation, the error catastrophe in the Eigen's model (when the purifying selection becomes ineffective) is discussed as the divergence of Perron–Frobenius eigenvalue of the Riccati model in the limit of large matrices. Known estimate for Perron–Frobenius eigenvalue provides explanation for observed patterns of genomic evolution. We propose to consider the error catastrophe in Eigen's model as analogue of overfitting in learning theory, this gives a criterion for presence of overfitting in learning.