We propose a new conceptual framework to study the dynamics of transposable elements. Based on a genetic algorithm, our model is designed as a self-organizing system. Our results show that transposable elements could emerge from a single endonuclease gene. The DNA repair mechanisms appear to condition the emergence success of class II TEs. Antagonist selective forces acting on transposable elements and their hosts induce by their opposition differences in the sequence evolution of the functional domains and of the copies.