arXiv:2606.13323v1 Announce Type: new Abstract: We introduce a new simple model to study the fitness progress of Evolution Strategies (ES) in generic problems. In this model, we bypass the underlying fitness landscape and assume that the mutation of any individual produces an offspring whose fitness relative to the parent is given by an invariant distribution $Z$, such as a mean-shifted Gaussian. This serves as a prototypical model for the optimisation landscape when an evolution algorithm operates far from the global optimum. This simple model can be used to approximate the optimisation process for problems where it is intractable to model the exact fitness function, including tasks such as hyperparameter tuning in machine learning models. We rigorously analyse the expected growth rate $\mathcal{R}_{\mu}$ of the continuous steady-state $(\mu+1)$-ES in this model. Unlike comma-selection strategies, the steady-state $(\mu+1)$-ES maintains overlapping generations, introducing complex mat...