Mathematical Equation Can Predict Population Levels In Predator/Prey Groups With Impressive Accuracy
The world is filled with different environments and ecosystems where plants, animals, and even microbes are constantly competing for survival. Sometimes this type of competition is conducted in pretty obscure ways, and other times it is very direct.
When it comes to animals that have a predator/prey relationship, the competition is fierce. For example, when looking at lions and zebra (and other prey animals), it may seem obvious that the lions have the clear upperhand.
This is true in many ways, but if the lions become too successful, the number of prey animals will drop significantly. This normally means only the strongest or fastest zebra are left to survive. When this happens, the lions have more trouble catching them and there are so many lions that it is hard to get enough food for them all.
Naturally, this leads to a decrease in the number of lions, which allows the zebra to repopulate. This generally goes in a cycle over the course of many years.
In the 1920’s, two mathematicians working independently came up with an equation to describe population levels in biological systems. Alfred Lotka was the first to come up with it, but his focus was on the autocatalytic chemical reactions rather than biological and chemical systems.
Later, Vito Volterra derived the same equations in order to describe populations in predator and prey systems.
A review of the methods was done by Dr. Sharon Kingsland in which she said:
“In both systems, all processes could be reduced to two kinds of changes: those involving exchanges of matter between the components of the system, and those involving exchanges of energy. In the chemical system the components were molecules. In the biological system the components were organisms plus the raw materials in their environment, and the exchanges of matter and energy took place through the web of food relationships, growth, and reproduction.”
At the time, many people, including Lotka himself, expressed surprise at how well these equations translated into the predator-prey relationship. They work so well that they continue to be used today.
In a 1920 paper, Lotka wrote:
“Periodic phenomena play an important role in nature, both organic and inorganic. In chemical reactions rhythmic effects have been observed experimentally, and have also been shown, by the writer and others, to follow, under certain conditions, from the laws of chemical dynamics. However, in the cases hitherto considered on the basis of chemical dynamics, the oscillations were found to be of the damped kind, and therefore, only transitory (unlike certain experimentally observed periodic reactions).”
“It seemed that the occurrence of […] permanent oscillations, the occurrence of purely imaginary exponents in the exponential series solution presented, would demand peculiar and very specific relations between the characteristic constants of the systems undergoing transformation; whereas in nature these constants would, presumably, stand in random relation. It was, therefore, with considerable surprise that the writer, on applying his method to certain special cases, found these to lead to undamped, and hence indefinitely continued, oscillations.”
These equations do not necessarily take all factors into account, of course. Specifically, when humans get involved through hunting, poaching, or destroying an environment, it will dramatically impact the population rates of the animals. This can throw off the results for years to come.
To see how these predator-prey cycles play out using this equation, check out this interesting video:
These mathematicians were surprised at how their work was able to be used.
Thought that was fascinating? Here’s another story you might like: Why You’ll Never See A Great White Shark In An Aquarium

Sign up to get our BEST stories of the week straight to your inbox.