Journal · Simulation

The Red Queen hypothesis: running to stay in the same place

In 1973 a biologist noticed that old groups of species die out as readily as young ones. His explanation borrowed a line from Lewis Carroll. Watch it happen with foxes and rabbits below, then see where the same race runs today, from hospital wards to search results.

Highland Willow · Boone, North Carolina · 8 November 2026

The line from the book

In Through the Looking-Glass (1871), Alice runs hand in hand with the Red Queen until she is out of breath. When they stop, they are standing under the same tree they started from. The Queen tells her that in this country, "it takes all the running you can do, to keep in the same place."

A hundred years later that sentence became the name of an idea in evolutionary biology. It turned out to describe a great deal more than biology.

What Van Valen found

Leigh Van Valen, at the University of Chicago, gathered fossil records for thousands of groups of animals and asked a plain question: does a group that has already lasted a long time become safer from extinction? It seems as if it should. A lineage that has survived ten million years has presumably been well tested.

That is not what he found. When he plotted how long groups survived, the curves came out close to straight lines on a log scale. A straight line there means the chance of dying out in the next stretch of time did not depend on how long the group had already lasted. Old lineages were no safer than new ones. He called it the law of constant extinction (Van Valen, 1973).

His explanation is the Red Queen. Most of a species' environment is other species: its predators, its prey, its competitors and its parasites. They evolve too. A gain for one is usually a loss for another, so a faster rabbit makes life harder for the fox, and a faster fox makes it harder for the rabbit. Nobody gets ahead for long. Each side has to keep adapting just to hold its position against the others, and a side that stops adapting falls behind, however well suited it once was.

Try it: foxes and rabbits

The simulation below is the idea cut down to the minimum. There are 200 foxes and 200 rabbits, and each animal has one number: its speed. Every generation the animals are paired off at random, so each fox chases one rabbit and no two chase the same one. The faster the fox is compared with its rabbit, the likelier the catch. Caught rabbits leave no young. Foxes that catch leave more. Each newborn takes its parent's speed plus a small random change, and the sliders set how big that change can be.

Four things to try

1. Leave both sliders where they are and press Run. Both lines climb. By generation 400 both sides are about ten times as fast as they began. The lower panel wanders up and down but goes nowhere: about half the rabbits are caught at the start, and about half at the end.
2. Press Start again, drag "How fast rabbits can change" to 0, and run. The rabbits stop improving. They are no slower than before, and the catch climbs to nearly all 200 anyway, because the foxes kept going.
3. Set both sliders to 0. Nothing moves. The running in the first try was never about speed itself. It was needed only because the other side was running.
4. Give one side 0.6 and the other 0.3. The side that can change faster wins ground and holds it. In a Red Queen race, how quickly you can adapt matters more than any single improvement.

The run uses a fixed random seed, so the same settings from Start again give the same result on any device. Moving a slider mid-run changes the rate from that generation on.

What the model leaves out

Speed costs nothing here. In real animals it costs energy, muscle and risk of injury, which is why real arms races slow down and level off rather than climbing forever. Population sizes are fixed at 200, so a rabbit population that loses 190 animals a generation simply refills, where a real one would crash, and its foxes with it. Each animal has one trait. Real species have thousands, and a gain in one is often paid for in another. The model shows the logic of the idea and nothing about any real species.

Where else the Red Queen runs

The idea travels well beyond fossils, because its logic needs only three things. Your success is measured against someone or something else. That other side adapts to what you do. And a gain for one side is a loss for the other. Where all three hold, standing still means falling behind. Here is where they hold.

Medicine: germs, viruses and tumours

Every antibiotic selects for the bacteria that happen to survive it, and those survivors breed. Alexander Fleming warned of resistance in his Nobel lecture in 1945, the year penicillin was coming into wide use. Bacteria can divide in under an hour, so in the language of the simulation they have a very high slider, and new drugs are always racing them.

Flu works the same way. The virus keeps changing its surface proteins, so last year's immunity fits this year's virus less well. The World Health Organization reviews the make-up of the flu vaccine twice a year, once for each hemisphere, because a vaccine that stands still stops working.

Cancer treatment has borrowed the lesson in the other direction. A tumour under heavy treatment evolves resistance, much like bacteria. Robert Gatenby and colleagues (2009) proposed adaptive therapy, which doses to hold a tumour steady instead of trying to wipe it out, so that drug-sensitive cells survive and keep the resistant ones in check. It is an attempt to stop the race rather than win it.

Farming: pests, weeds and crop disease

Plant breeders put resistance genes into crops, and the diseases evolve around them. A strain of wheat stem rust found in Uganda in 1999, later named Ug99, overcame Sr31, a resistance gene carried by many of the world's wheat varieties (Pretorius and colleagues, 2000). Weeds do the same to herbicides and insects to pesticides. A farm that sprays the same product year after year is running the second try of the simulation, with the weeds as the foxes.

Technology: security, spam and machine learning

Computer security is a Red Queen race by design. A patched system is safe only until attackers find the next way in, and every defence teaches them what to try next. Spam filters and spammers, fraud checks and fraudsters, and tools that detect machine-written text and the tools that write it all run the same race.

Computer scientists have also used the race on purpose. Danny Hillis (1990) evolved programs that sort numbers, and found they improved faster when a second population of test cases evolved alongside them, hunting for the inputs the programs got wrong. Generative adversarial networks (Goodfellow and colleagues, 2014) train two neural networks against each other: one makes images, the other learns to tell them from real ones, and each improves because the other does.

Business: competitors, search and advertising

William Barnett and Morten Hansen (1996) carried the idea into organisations, in a study of banks. Firms that survive competition get better at it, which makes the competition harder for everyone else, who then improve in turn.

Search results are a race of this kind, because a page is ranked against the other pages for the same search. A page can slip from third to sixth without changing a word, when competitors improve theirs. Online ad auctions are the same: whether your ad shows depends on your bid and quality compared with everyone else's in that auction.

The practical lesson is about measurement. A figure that only tracks your own performance cannot tell you whether you are winning. Suppose your web pages now load in 2 seconds, down from 3. If the sites you compete with went from 3 seconds to 1.5 over the same months, you lost ground while improving. The second try in the simulation is that situation exactly. Put the comparison in the measure, so the question is how you stand against the others, not how you stand against last year.

Society: credentials, sport and arms races

When more people hold a degree, the same degree tells an employer less, and the next round of applicants needs more education to stand out. The sociologist Randall Collins described this credential inflation in The Credential Society (1979). Sport shows the race clearly when equipment changes: after a flood of swimming world records in full-body polyurethane suits, swimming's governing body banned them from 2010. And military arms races are the oldest example of all, where each side's new weapon is the reason for the other's.

Where it does not apply

The third try in the simulation is the other half of the lesson. A bridge has to carry its load, and the load does not evolve to beat the bridge. A month-end close has to balance, and the numbers are not trying to stop it. Where the target stands still, steady improvement really is progress, and there is no race to run. Knowing which kind of problem you have tells you whether to measure yourself against last year or against the others.

What this does not prove

Van Valen's constant extinction describes fossil records at the level of whole genera and families. Later analyses have found departures from it in some groups and some periods, so treat it as a strong tendency, not a law of nature. The examples from medicine, farming, technology and business share the logic of the idea. They are not evidence that each one follows Van Valen's law, and each field has its own research on how its race actually runs. The simulation demonstrates the reasoning. It is not evidence for it.

Sources

1. Carroll, L. (1871). Through the Looking-Glass, and What Alice Found There. Macmillan, chapter 2.
2. Van Valen, L. (1973). "A new evolutionary law." Evolutionary Theory 1, 1–30.
3. Fleming, A. (1945). "Penicillin." Nobel Lecture, 11 December 1945.
4. World Health Organization. Recommendations for influenza vaccine composition, issued twice a year.
5. Gatenby, R. A., Silva, A. S., Gillies, R. J. and Frieden, B. R. (2009). "Adaptive therapy." Cancer Research 69(11), 4894–4903.
6. Pretorius, Z. A., Singh, R. P., Wagoire, W. W. and Payne, T. S. (2000). "Detection of virulence to wheat stem rust resistance gene Sr31 in Puccinia graminis f. sp. tritici in Uganda." Plant Disease 84(2), 203.
7. Hillis, W. D. (1990). "Co-evolving parasites improve simulated evolution as an optimization procedure." Physica D 42, 228–234.
8. Goodfellow, I. and colleagues (2014). "Generative adversarial nets." Advances in Neural Information Processing Systems 27.
9. Barnett, W. P. and Hansen, M. T. (1996). "The Red Queen in organizational evolution." Strategic Management Journal 17(S1), 139–157.
10. Collins, R. (1979). The Credential Society: An Historical Sociology of Education and Stratification. Academic Press.

The simulation and its fox and rabbit drawings are made for this post and run entirely in your browser. Nothing you do in it is sent anywhere. None of its numbers come from any client.