A generalized model for population dynamics where interactions change over time

Population dynamics has been modeled with differential equations since Malthus began their studies more than two hundred years ago. Conventional models always treat relations among species as static, denoting only their dependency for a fixed period of time, although it is well known that relations among species can, and in fact change over time. Here we propose a model for population dynamics that incorporates the evolution over time of the interactions among species. This model includes a wide range of interactions, from predator-prey to mutualistic relations, either obligate and facultative. The mechanism we describe allows the transition from one kind of relation among species to any other, according to some external parameters, fixed by the context. These transitions could avoid the extinction of one of the species, if it ends up depending too much of the environment or its relation with the other species.