Starving predators survive together, but maybe only in math-land

It is well-known that physicists believe that studying physics makes you qualified to carry out research in every field of scientific endeavor. Hence, there are physics journals and papers devoted to all manner of topics, including evolution and population dynamics. In fact, the mathematical toy models that physicists use are good at abstracting things like the relationship between species.

So, they can yield insights into what characteristics may be important to understand their interactions.

In a paper that fits nicely into this category, researchers have shown that starvation can help stabilize populations of predators (and I mean stable somewhere above a population of zero).

Predator vs. predator

Imagine that you have an ecosystem where two predators are also mutual prey: lions will eat tigers, and tigers will eat lions, while tigers don’t eat tigers, and lions don’t eat lions. A simple model will allow the animals to move around, eat each other, and reproduce. After letting the model run for a certain amount of time, you can examine the population density of each species.

You will normally find that one species has shuffled off its virtual mortal coil, while the second thrives. This is the case even when the two species are exactly evenly matched in terms of their ability to hunt their prey. This is probably not true in the real world, though. Scientists believe that mutual predatory systems exist: sperm whales and giant squid may be an example. So, what additional factor might allow a stable population of both species to exist?

The researchers added starvation to the mix. Essentially, if a predator fails to find prey after a certain amount of time, it dies. And, if it breeds while starving, then its offspring are similarly encumbered. But rather than changing the offspring’s hunting success, it comes into being partially starved, so it must find food sooner than its well-fed counterparts.

The researchers explored three basic scenarios. In the first case, two predators face off. The populations of the two predators are separated from each other with a common straight-line border. If no starvation can occur, then nothing much happens over the course of the run-time. Effectively, the border prevents the two populations from mixing, and, because there is no possibility to starve, the populations remain stable. If left long enough, however, one population would eventually gain the upper hand and annihilate the other.

Real predators starve

If starvation is a possibility, then, naturally the animals that are far from the border can’t get any food and die off. However, the border itself becomes quite mobile as the two populations begin to mix. Each species starts to form islands that are sparsely populated in the interior but heavily populated at the border.

In a second scenario, the researchers created a small island of one species and surrounded it with the second species. In this case, if neither population could starve, then the greater numbers took their toll on the besieged species. In short order, the encircled species was exterminated.

But, if starvation plays a role, the outcome is different. The minority species is not killed off and the two reach a stable equilibrium of numbers with the minority species remaining a minority, but hanging on quite nicely.

In a final test, the researchers introduce a third species, and again, the populations stabilize if starvation is introduced. In the absence of starvation, extinction for one or more species is even more rapid than the case for two species.

Do you learn from toys?

So, what does this tell us about real ecosystems and predator-prey, sorry, predator-predator relationships? Probably not a lot directly. Instead, these sorts of models give more general insights into how populations interact. They show that it is very difficult to predict the outcome of interventions that modify the relationships between species. This is, of course, evidenced by multiple attempts to control introduced pests by introducing new pests that make the situation far worse.

What I actually like about these models is not their practical usefulness, but their teaching value. It allows students to see that a seemingly simple set of equations cannot be solved on paper, but that set can be solved relatively quickly on a computer. And the solution exhibits all sorts of unexpected richness. (Trainee engineers will read this as ample opportunity to build non-functional and possibly unexpectedly lethal kit).

Europhysics Letters, 2019, DOI: 10.1209/0295-5075/126/68002 (About DOIs)