Bijective construction of equivalent eco-systems

First, we explicit an infinite family of equivalent succession rules parametrized by a positive integer alpha, for which two specializations lead to the equivalence of rules defining the Catalan and Schroder numbers. Then, from an ECO-system for Dyck paths, we easily derive an ECO-system for complete binary trees, by using a widely known bijection between these objects. We also give a similar construction in the less easy case of Schroder paths and Schroder trees which generalizes the previous one.