The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:

Mutualism describes the ecological interaction between two or more species where each species has a net benefit. Mutualism is a common type of ecological interaction. Prominent examples are:the nutrient exchange between vascular plants and mycorrhizal fungi, the fertilization of flowering plants by pollinators, the ways plants use fruits and edible seeds to encourage animal aid in seed dispersal, and the way corals become photosynthetic with the help of the microorganism zooxanthellae.