A Computational Formal Model of the Invasiveness of Eastern Species in European Water Frog PopulationsSoftware Engineering and Formal Methods

European water frog populations are mainly composed by two species: Pelophylax lessonae (pool frog) and Pelophylax esculentus (edible frog). These populations are called L-E complexes. Edible frogs are a hybrid form between P. lessonae and Pelophylax ridibundus (eastern lake frog) and they reproduce in a particular way, called hybridogenesis. These frog populations have been studied in the contexts of evolution and speciation. In order to have stability of L-E complexes (namely self-maintainance of the population structure) some conditions are necessary. We present a computational formal model of European water frog population based on a variant of P systems in which evolution rules are applied in a probabilistic maximally parallel manner. Probabilities of application of rules will be computed on the basis of parameters to be associated with each rule. By means of our model we show how the stabilization of L-E complexes can be obtained. In particular, we show how the introduction of translocated eastern lake frogs in such complexes can lead to the collapse of the populations. The study of conditions for population stability and of possible threats to endangered species is of particular importance for the maintenance of biodiversity, which is an aspect of sustainable development.