The EDEN framework provides formal modelling and analysis tools to study ecosystems. At the heart of the framework is the reaction rules (RR) modelling language, that is equipped with an operational semantics and can be translated into Petri nets with equivalent semantics. In this paper, we formally define the RR language and its semantics, detailing the initial definition from [8] and extending it with a notion of constraints that allows to model mandatory events. Then, we consider in turn two classes of Petri nets: priority Petri nets (PPN), which are safe place/transition Petri nets equipped with transitions priorities, and extended Petri nets (EPN) which are PPN further extended with read arcs, inhibitor arcs, and reset arcs. For each of these classes, we define the translation of an RR system into a Petri net and prove that the state-space generated with the RR operational semantics is equivalent to the marking graph of the Petri net resulting from the translation. We use a very strong notion of equivalence by considering labelled transition systems (LTS) isomophism with states and labels matching.