Generic model of population dynamics

Population dynamics has been modelled using differential equations since Malthus, more than two centuries ago.
At this moment, there is no unified or general model that encapsulates all biotic interactions, given that the most used models, denominated as Holling’s types I, II and III functionals, involves too many variations and ad hoc premises.
Here we discuss a different approach in order to model ecological equations, based on the logistic-mutualistic model of Garc´ıa-Algarra et al. [1]. We propose that Holling’s types functionals reflect only a self-saturation limit and that Garc´ıa-Algarra’s model, once generalised, reflects both inter and intraspecific saturation limits. Any ecological model can be formulated by specific growth rate terms plus the competition terms that limits the population growth. Even when a complete ecological model surely must involve both limits, population dynamics tend to stay within only one of the regimes.
In this general model one can include in the equation of species i any species interacting with it, even itself. The interaction between individuals of the same species can be beneficial, namely, cooperation, or detrimental, as can be cannibalism or violent competition.