Birthing the Red Queen
The Origins of an Evolutionary Law
Reading Length: 8 minutes
Keywords: Evolutionary Biology, Macroecology, Game Theory
In 1973 the biologist Van Valen made a startling discovery. Earnestly, he submitted the paper to the prestigious journal Nature but disagreed with the editorial comments suggested by their referees. Instead, Van Valen created his own journal, Evolutionary Theory.1
The paper, titled A New Evolutionary Law, became an influential landmark in the field of evolutionary biology. The thesis spilled over not only into macroecology but also game theory, organizational studies, and network studies more broadly. What was it that Van Valen found so startling?
Lindy?
Darwin theorized that organisms are forced to adapt to their environments in order to survive. Those species that are unable to adapt go extinct, or are naturally selected out of the environment. It would then be tempting to go one step further and surmise that organisms that are more able to adapt, for whatever reason, are less likely to go extinct.
Taking another step, we would then expect species that have been around for a long time to be particularly good at surviving, meaning that we would then expect them to stick around for a while longer, on account of how long they have already survived.
If something is expected to survive longer on account of how long it has already survived, this is called Lindy’s Law, or the Lindy Effect. The cultural critic Albert Goldman tells the story of barcrawlers who commented that comedians were more likely to make it in the industry the longer they could stick around:
the life expectancy of a television comedian is proportional to the total amount of his exposure on the medium.2
Goldman goes on to caution that “Lindy's Law, despite its awesome air of common sense, is more a cautionary fable than an accurate description or prognostic”, but the mathematician Mandelbrot and statistician-cum-trade-cum-author Taleb both took up the idea and ran with it more broadly.
The Lindy Effect is now a well-known phenomenon, to the point that a ‘Lindy Man’ who took the rule as a guideline for life was covered by the New York Times.3
On a more serious note, here is how the statistician Eliazar defines the Lindy Rule:
Lindy’s Law describes an antithetical behavior in which the likelihood of failure decreases with age. In other words, Lindy’s Law means ‘‘growing young’’ and ‘‘anti-aging’’.4
Where aging can simply mean how long something sticks around, not just in the strict biological sense.
Going back to Van Valen, he discovered while digging through the paleontological record is that species do not follow Lindy’s Law.
The Law of Constant Extinction
If Van Valen did not find conformity with Lindy’s Law, did he find the opposite? After all, it could be reasonable to assume that the longer a species lives on, the greater chance it has of going extinct because it has been ‘pushing its luck’ and could ‘run out’ of random mutations to adapt with.
Surprisingly, the data did not bear this hypothesis out either. Van Valen opens his paper with the striking conclusion:
All groups for which data exist go extinct at a rate that is constant for a given group.
That is, given a taxonomic group of species, the odds of going extinct are constant regardless of how long that species has been around. Van Valen shows this graphically by plotting taxonomic survivorship curves on a log scale:
Across the fossil record, the same linear pattern recurs, whether looking at mollusca and brachiopoda, protists, plants and inverebtrates, or mammalia. What does linearity mean?
For living taxa linearity of the distribution requires both constant extinction and constant origination. It further requires that both be more nearly constant over absolute time than does a distribution for extinct taxa.
In a corroborative follow-up paper decades later, the paleontologist Michael Benton confirmed that “modern species of mammals are just as likely to go extinct as their ancestors living 200 million years ago”.5
This fact, in itself, is striking and bears the name ‘The Law of Constant Extinction’.
All Rise for the Red Queen
Van Valen went one step further and hypothesized about what could cause the law of constant extinction to manifest so uniformly across vastly different species and millions of years.
First, Van Valen restates the law of constant extinction:
The effective environment of the members of any homogenous group of organisms deteriorates at a stochastically constant rate…A more neutral statement is that extinction in any adaptive zone occurs at a stochastically constant rate.
If organisms are able to adapt to their ‘effective environments’, it follows that after adapting, their probability of survival should improve until the ecological environment is perturbed. Whenever one species adapts to the environment, however, other species adapt as well in response. Van Valen draws upon game theory to illustrate this critical point:
We can think of the Red Queen’s Hypothesis in terms of an unorthodox game theory. To a good approximation, each species is part of a zero-sum game against other species. Which adversary is most important for a species may vary from time top time, and for some or even most species no one adversary may ever be paramount. Furthermore, no species can ever win, and new adversaries grinningly replace the losers. This is a direct generalization of game theory which I think has not been explored.
Where did the name Red Queen come from? Van Valen cites Lewis Carroll’s Through the Looking Glass, in which the Red Queen character states to the protagonist Alice:
Now here, you see, it takes all the running you can do, to keep in the same place.
The connection to evolutionary biology is obvious. Organisms may adapt to their environment to survive, but they are not actually improving their odds of surviving because they are locked in a zero-sum game with competitors that will also adapt and seize upon any advantage.
The Red Queen Hypothesis, then, serves as an explanation for the Law of Constant Extinction. In a retrospective of the paper, the biomathematician Ricard Solé describes the relationship as:
How are the Red Queen dynamics and the constant extinction trend related? In Van Valen’s picture, they are two sides of the same coin. Because of the intrinsic complexity of ecological interactions, community-level changes will sooner or later create negative effects on any species that will jeopardize survival.
The Red Queen Hypothesis is sometimes stated as an evolutionary arms race.
Survival of the (Momentary) Fittest
Another lesson Van Valen draws from the data is that evolution cannot be said to be the process in which organisms maximize their odds of survival. Rather, organisms are adapting to their momentary environment, but this could be to their detriment in the long term. Of course, randomly mutating genes are not blessed with farsighted opportunism and the ability to look around the corner and anticipate adversarial moves. Yet still, the common misunderstanding of evolution persists:
It is an almost universal mistake to think that evolution locally maximizes fitness…Selection at any level locally maximizes momentary fitness for that level, but the optima of different levels need not coincide.
In this sense it is a misnomer to call evolution a process of the survival of the fittest. What’s more, a constant rate of extinction implies that surviving does not even increase your odds of surviving in the future, which is why you have to “run fast just to stay in the same place”. Van Valen says in a footnote:
But on the next level, the Red Queen says that having one set of properties is not appreciably better than having another because the expected time to instinct ion is the same.
This striking statement is quite a departure from the common understanding of evolution.
Long Live the Red Queen
The Red Queen Hypothesis was controversial at its birth, and remains a contested theory today.6
The graph above shows the influence that Van Valen had, tracking the times that the term ‘Red Queen’ appears in written texts.7 The RHQ also inspired a family of new evolutionary laws by following researchers, such as The Red King, the Black Queen, the Court Jester, and the Suicide King.8
Based on the tone of Van Valen’s conclusion, and the bold decision to rebuke high-impact journals by creating his own, he had some sense of the influence his work would have for prosperity:
From this overlook we see dynamic equilibria on an immense scale, determining much of the course of evolution by their self-perpetuating fluctuations. This is a novel way of looking at the world, one with which I am not yet comfortable. But I have not yet found evidence against it, and it does make visible new paths and it may even approach reality.
The story is briefly recounted in Matthew Kosnick’s introduction to the republication of the paper for the 2014 book Foundations of Macroecology, available here.
The Lindy Way of Living, 2021. https://www.nytimes.com/2021/06/17/style/lindy.html
Eliazar, ‘Lindy’s Law’, 2017.
Benton, ‘Testing the roles of competition and expansion in tetrapod evolution’, 1996. The quote is from Solé, ‘Revisiting Leigh Van Valen’s “A New Evolutionary Law”’, 2021.
See, for example, Liow LH, Van Valen L, Stenseth NC (2011) Red Queen: from populations to taxa and communities. Trends Ecol Evol 26:349–358, cited by Solé.
The graph is taken from page 121 of Solé, infra.
For the Red King, see Bergstrom CT, Lachmann M (2003) The Red King effect: when the slowest runner wins the coevolutionary race.
For the Black Queen, see Morris JJ, Lenski RE, Zinser ER (2012) The Black Queen Hypothesis: evolution of dependencies through adaptive gene loss.
For the Court Jester, see Benton MJ (2009) The Red Queen and the Court Jester: species diversity and the role of biotic and abiotic factors through time.
For the Suicide King, see Dybdahl MF, Storfer A (2003) Parasite local adaptation: red queen versus suicide king.