Summary
Differential equations describing oscillating predator and prey populations.
In depth
dN/dt = rN - aNP (prey) and dP/dt = baNP - mP (predator). The model gives neutral oscillations; real systems add density dependence, refuges and other factors. Competition equations use competition coefficients.
Assumptions are unrealistic but the models gave insights into oscillations. Extensions add carrying capacity and functional responses (Rosenzweig-MacArthur).
Example: the lynx-hare cycle is shaped by predation and food limitation.
The model was developed independently by Alfred Lotka (1925) and Vito Volterra (1926), the latter motivated by the rise of predatory fish in the Adriatic Sea after World War I interrupted fishing. Predator and prey densities oscillate, with the predator peak lagging the prey peak. Isoclines (where growth is zero) help to analyse equilibria.
The competition version has two species with competition coefficients and predicts coexistence only if intraspecific competition exceeds interspecific competition for both species. Its simplified assumptions, such as no limits on prey, are not realistic, but it gave a framework used in epidemiology, economics and chemistry.
Example: the Hudson's Bay Company's pelt records for lynx and hares show cycles resembling the model, though experiments suggest food and predation both matter.
Frequently asked questions
What is Lotka-Volterra Models?
Differential equations describing oscillating predator and prey populations.
Which area of biology covers Lotka-Volterra Models, and how advanced is it?
Lotka-Volterra Models is one of the 54 topics in Ecology. It is rated Advanced, so it suits learners who want specialist depth. Related topics in this area include Logistic Growth, Limiting Factors, Predation.
Can you give an example of Lotka-Volterra Models?
Lynx and hare cycles of about 10 years.
What should I learn before Lotka-Volterra Models?
Work through the Beginner topics in Ecology first, such as Ecology, Ecosystem, Biotic and Abiotic Factors, then return to Lotka-Volterra Models. Advanced topics assume the Intermediate vocabulary.
What topics are related to Lotka-Volterra Models?
The closest topics to Lotka-Volterra Models are Logistic Growth, Limiting Factors, Predation, Carrying Capacity. Comparing them side by side is a good way to see how the ideas connect.
How can I check that I understand Lotka-Volterra Models?
Read the summary and the in-depth section, then use the quick check on the interactive lesson for Lotka-Volterra Models. To practise the whole of Ecology, use the Ecology quiz.
How is Lotka-Volterra Models different from Logistic Growth?
Lotka-Volterra Models: Differential equations describing oscillating predator and prey populations. Logistic Growth: Growth that slows as a population nears carrying capacity, forming an S-shaped curve. Read both side by side and note what each one explains.
How should I study Lotka-Volterra Models step by step?
First, read the summary and write the definition in your own words. Second, read the in-depth section and note any example. Third, compare it with Logistic Growth and explain the difference aloud. Finally, take the Ecology quiz and come back to this page for any question you miss.