Supplementary video 3 from Population dynamics of synthetic terraformation motifs

Ecosystems are complex systems, currently experiencing several threats associated with global warming, intensive exploitation and human-driven habitat degradation. Because of a general presence of multiple stable states, including states involving population extinction, and due to the intrinsic nonlinearities associated with feedback loops, collapse in ecosystems could occur in a catastrophic manner. It has been recently suggested that a potential path to prevent or modify the outcome of these transitions would involve designing synthetic organisms and synthetic ecological interactions that could push these endangered systems out of the critical boundaries. In this paper, we investigate the dynamics of the simplest mathematical models associated with four classes of ecological engineering designs, named Terraformation motifs (TMs). These TMs put in a nutshell different ecological strategies. In this context, some fundamental types of bifurcations pervade the systems' dynamics. Mutualistic interactions can enhance persistence of the systems by means of saddle-node bifurcations. The models without cooperative interactions show that ecosystems achieve restoration through transcritical bifurcations. Thus, our analysis of the models allows us to define the stability conditions and parameter domains where these TMs must work.