Focus: Evolution Sometimes Slows Things Down

Physics 8, 111
When a strongly cooperative species invades new territory, its spread can slow down or stop, according to a mathematical model, suggesting potential strategies against cancer and insect pests.
Invading and not cooperating. The cane toad was introduced in Australia in the 1930s to eradicate beetles that were decimating sugar cane crops. It has since invaded thousands of square miles in northeastern Australia.

Organisms that constantly try to spread into new territory, such as cancer cells or invasive weeds, seem to benefit from an ever-accelerating dispersal, which provides them with a steady supply of fresh resources. But a theorist has now shown that some spatial invasions can slow down and even stop completely, depending on the degree of cooperation among the invaders. The results of the study could potentially help researchers combat biological invasions such as agricultural pests or malignant tumors.

Invading species that disperse quickly and widely in a host or an environment are rewarded with favorable conditions—untapped resources, new habitats, and reduced competition among themselves—which promote even more rapid dispersal. This “survival of the fittest and fastest” has been demonstrated many times in nature, such as in the invasion of cane toads in northeastern Australia and the proliferation of feral pigs in the United States. But the observational and theoretical results showing a selection for rapid and widespread dispersal have been limited to organisms that function non-cooperatively, meaning that they exist largely independently of one another.

On the other hand, cooperativity is common. Cancer cells receive growth factors (growth-regulating proteins) from one another, and wolves rely on the pack for cooperative hunting and defense against predators. Cooperative groups are subject to competing forces: They require a minimum population density to survive—the so-called Allee threshold—but with limited resources, they can't become too numerous. So the invasion behavior of cooperative populations is complex and has remained largely unexplored.

Now Kirill Korolev of Boston University has investigated invasive organisms that exhibit cooperativity, using both exact mathematical techniques and computer simulations. Korolev's first approach was to set up direct competitions between pairs of organisms with different spreading rates. He used a standard mathematical model that predicts how population densities vary with time and space in a one-dimensional habitat. The equations also include the Allee threshold (minimum required population density) as a parameter determining the degree of cooperation, which was always the same for both "competitors."

With zero cooperation, and starting out with equal populations, the faster-spreading species eventually constituted essentially 100% of the population, as expected. But with high cooperativity (high Allee threshold), the slower species came to dominate for a significant range of the parameters. In a highly cooperative species, populations that “disperse too fast may end up dying more frequently” as they spread themselves too thin, Korolev explains.

In a second approach, Korolev ran simulations that began with a single species but allowed multiple mutations of the spreading rate “gene” to arise within the population and compete directly against one another. With low cooperativity, the spreading rate increased over time through Darwinian competition until it reached the maximum allowed value. But with high cooperativity, the spreading rate eventually decreased to zero, meaning that the population stopped spreading altogether. In this case, as Korolev puts it, evolution can be “survival of the slowest.”

An ability to slow down or even stop spatial invasions could be useful. For example, if researchers could intervene in the biochemistry of tumor cells in a way that raises the Allee threshold, natural selection could stop the cells' invasion, Korolev says. This technique may be better than killing cancer cells with chemotherapy, which can lead to drug resistance. He points to one recent study showing that raising temperature raises the Allee threshold and inhibits cancer cell growth [1]. As another example, Korolev cites a recent campaign against invasive gypsy moths that raised their Allee threshold and eradicated the insects from low-density populations by spraying artificial pheromones that prevented males from finding mates [2].

Korolev’s results are “a striking theoretical prediction that should motivate experimental biologists and field ecologists to pay more attention to the mechanisms of invasion,” says computational biologist Joao Xavier of the Memorial Sloan Kettering Cancer Center in New York. He adds that “we need more studies to identify mechanisms that can one day be manipulated to deter cancer progression.”

This research is published in Physical Review Letters.

–Katherine Kornei

Katherine Kornei is a freelance science writer in Portland, Oregon.


  1. S. Zhu, J. Wang, B. Xie, Z. Luo, X. Lin, and D. J. Liao, “Culture at a Higher Temperature Mildly Inhibits Cancer Cell Growth but Enhances Chemotherapeutic Effects by Inhibiting Cell-Cell Collaboration,” PLoS ONE 10, e0137042 (23015).
  2. Patrick C. Tobin, Christelle Robinet, Derek M. Johnson, Stefanie L. Whitmire, Ottar N. Bjørnstad, and Andrew M. Liebhold, “The Role of Allee Effects in Gypsy Moth, Lymantria dispar (L.), Invasions,” Population Ecology 51, 373 (2009).

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Interdisciplinary PhysicsBiological Physics

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