Percolation and depinning transitions in cut-and-paste models of adaptation

We show that a cut-and-paste model to mimic a trial-and-error process of adaptation displays two pairs of percolation and depinning transitions, one for persistence and the other for efficiency. The percolation transition signals the onset of a property and the depinning transition, the growth of the same property. Despite its simplicity, the cut-and-paste model is qualitatively the same as the Minority Game. A majority cut-and-paste model is also introduced, to mimic the spread of a trend. When both models are iterated, the majority model reaches a frozen state while the minority model converges towards an alternate state. We show that a transition from the frozen to the alternate state occurs in the limit of a non-adaptive system