Generalized Lotka-Volterra Equation

The generalized Lotka-Volterra equations are a family of ordinary differential equations in mathematical ecology that extend the classic competitive and predator-prey Lotka-Volterra models to describe the population dynamics of an arbitrary number of interacting species at once. Each species' population change over time is written as that population multiplied by a function depending on an interaction matrix, which encodes competition and predator-prey relationships among all the species, together with a vector of intrinsic growth rates. The equations are prized for being analytically tractable, which makes them a useful theoretical tool for modeling food webs and for predicting how species yields change across mixtures of organisms such as algae, plants and protozoa; they have also been used to generate early warning signals of an impending population crash. Their main limitation is that, in their basic form, they cannot represent mutualism between species without risking runaway population growth, and they leave out ecological features such as predator preference and nonlinear responses to prey density. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/