Islands of Stability Evolution
How long do kinds of animals last? A law stated in 1973 says their age tells you nothing, which is proposition 3, fifty years early.
A genus is a group of closely related species, such as the oysters or the trilobite Paradoxides. It appears in the fossil record, lasts a while and disappears, and the record keeps the dates. The Paleobiology Database, built by hundreds of paleontologists, lists every genus they have entered with the rocks where it was found. This page takes the marine animals that left the richest records, eight groups and 23,191 genera over more than 500 million years, and asks the question proposition 3 asks: does a genus's age say anything about how long it has left?
On this page: Van Valen's law · When everything ends at once · The Red Queen · The propositions
Van Valen's law
In 1973 the paleontologist Leigh Van Valen plotted, for group after group, the share of its genera that had lasted at least so many million years, on a scale where a constant chance of dying out draws a straight line. The lines came out nearly straight. Within a group, he concluded, a taxon's chance of extinction does not depend on how long it has already lasted, and he called this the law of constant extinction. It is proposition 3, stated for taxa: exit is memoryless, and age is no evidence of remaining life.
The database gives both appearances for 23,191 valid genera of the eight groups. Of these, 6,982 (30 percent) were found in a single interval only, too briefly for the timescale to resolve, and are left out of the fits. Another 3,287 are alive today and count as still running. Half of a group's genera were gone within 9 million years for cephalopods and within 58 for snails. The Weibull shape sums up how the chance of dying out changes with age, 1 for Van Valen's constant chance and below 1 for a chance that falls with age, with 95 percent intervals: trilobites 1.01 (0.98 to 1.05), corals 0.92 (0.88 to 0.96), brachiopods 0.89 (0.86 to 0.91), bryozoans 0.87 (0.82 to 0.93), snails 0.84 (0.81 to 0.87), cephalopods 0.81 (0.79 to 0.84), bivalves 0.76 (0.73 to 0.79) and echinoderms 0.75 (0.72 to 0.78).
Trilobites follow the law. The other groups bend the same way: young genera die out faster than old ones. There are three explanations, and the first two are proposition 3's own alternatives.
- Frailty. Genera differ in depth, and the shallow ones go first, so the survivors of any age are the deep ones. Version 0.2 of the theory names this as no counterexample, provided it is shown.
- Memory. A genus becomes safer as it ages: more species, a wider range, more ways to survive a bad spell.
- The record. A short-lived genus is less likely to be found in more than one layer of rock, so short lives are counted less reliably than long ones.
Telling frailty from memory needs a measure of depth that does not depend on survival. Geographic range is the obvious one, since widespread lineages have long been known to survive better (Jablonski, Science, 1986), and the number of species in a genus is another. That test has been done, on this same database. Finnegan, Payne and Wang (Paleobiology, 2008) found that in most intervals of the marine record young genera were more likely to die out, and that range and species richness did not explain it away: a link between age and extinction risk remained after both were accounted for.
What this means for proposition 3. Version 0.2 says a falling hazard is no counterexample only where differences in depth are shown to produce it, and that otherwise it counts against the proposition. Here depth was measured, by range and richness, and the fall with age remained. In this domain, then, the published evidence counts against proposition 3, as far as range and richness capture depth. A defender could name other kinds of depth. The rule is that they must be measured, not assumed. A replication on today's larger database, with rules fixed in advance, has now run. It could not be blind to this result. Its verdict is below.
The re-run, with rules fixed in advance
Proposition 3 is killed by a hazard falling with age conditional on depth. A test deposited before it ran re-ran Finnegan and colleagues' analysis on today's database: does a genus's chance of extinction still fall with its age once its geographic range and species richness are held fixed? If it does, the proposition is killed here. If the fall disappears, it was a difference in depth, the exception the proposition names, and it survives.
The test ran once, on 8 October 2026, after its rules were deposited as 10.5281/zenodo.23248063. Its bootstrap seed comes from that identifier.
| Test | Bears on | Verdict | What was found |
|---|---|---|---|
| Does a genus's chance of extinction fall with its age once its geographic range and richness are held fixed? | P3 | killed | Across 10,368 genera found in more than one bin of 10 million years, 7,918 of which went extinct, each doubling of a genus's age multiplied its odds of extinction by 0.63 (0.61 to 0.66), with range and richness held fixed. A kill needed the interval's upper end below 0.90, and survival the whole interval within 0.90 to 1.11. All 1,000 resamples converged. |
Reported without a verdict, as the rules require:
- Without range and richness, the study's first finding: 0.63 (0.61 to 0.66).
- Without the five mass-extinction bins: 0.62 (0.60 to 0.65).
- With bins of 5 million years: 0.69 (0.67 to 0.71), over 11,854 genera.
- Class by class, for the 16 classes with at least 30 extinctions: Anthozoa 0.70, Asteroidea 0.75, Bivalvia 0.59, Cephalopoda 0.34, Crinoidea 0.61, Echinoidea 0.78, Gastropoda 0.78, Gymnolaemata 0.65, Holothuroidea 0.72, Lingulata 0.80, Ophiuroidea 0.72, Rhynchonellata 0.68, Stenolaemata 0.66, Strophomenata 0.48 and Trilobita 0.85. The 54 genera with no class given: 0.10.
- Of 707,897 occurrences, 616,431 were used, and 91,466 with an age range over 10 million years were left out. Of the genera, 10,558 were found in a single bin and left out, and 2,450 of those kept were censored, being alive today or last found in the youngest two bins.
Two deviations from the deposited document, neither of which can change the verdict. The database marks some occurrences with the class NO_CLASS_SPECIFIED, which the code counted as a class of its own instead of as missing. It is the most common class of 54 genera, 93 of the 44,185 rows at risk. And the run took 2 hours 27 minutes, not the hour the document estimated.
The interval lies far below 0.90. With range and richness held fixed, each doubling of a genus's age cut its odds of extinction by more than a third, as Finnegan and colleagues found in 2008. Holding range and richness fixed hardly moved the ratio, 0.63 either way, so as measured here they explain none of the fall. The fall holds without the mass-extinction bins and with bins of 5 million years, and its point estimate is below 1 in every class with enough extinctions to count. Under the deposited rules, proposition 3 is killed in the fossil record. Of the three readings of a falling hazard above, the test rules out frailty as range and richness measure it, and leaves memory and the record. What the kill means for the proposition's wording is the author's decision, pending.
When everything ends at once
Proposition 3's memoryless exit needs a steady disturbance. The fossil record has five times when the disturbance was anything but steady: the mass extinctions, when a large share of all genera disappeared together, whatever their age.
In a typical five-million-year bin, 172 extinct genera of these groups were last seen. In the bin holding the end-Permian extinction (251.9 million years ago), 1,071, the end-Ordovician extinction (445.2 million years ago), 707, the end-Cretaceous extinction (66 million years ago), 619, the Late Devonian extinction (372.2 million years ago), 304 and the end-Triassic extinction (201.4 million years ago), 252. The Late Devonian crisis was spread over several million years, and shows in more than one bin.
At these moments no age protects a genus. They are the paleontological version of the pandemic's quarter in the economy's record, and of the jumps a lake makes when pushed past its edge: exits imposed from outside, arriving for everyone at once. Any test of proposition 3 here has to allow for them, as Finnegan and colleagues did, by comparing genera only with others alive in the same interval.
The Red Queen
Van Valen explained his law with a line from Lewis Carroll. In Through the Looking-Glass the Red Queen tells Alice that here "it takes all the running you can do, to keep in the same place." Every species lives among others that are also evolving, competitors, predators and parasites, so its environment keeps getting worse unless it keeps changing too. If each group's fitness keeps being eroded at a steady rate, its chance of extinction stays the same at every age.
That is proposition 4 in biology's own words: depth held by continuous station-keeping against drift, lost when the running stops. The same 1973 paper holds a prior claim on propositions 3 and 4 together.
Cost line and fragility line
Cost line. A lineage pays continuously, generation after generation, in the selection that keeps it fitted to a world of other evolving species: the Red Queen's running.
Fragility line. A narrow range. In ordinary times, genera whose species were widespread, numerous or good at dispersing survived better. In the end-Cretaceous extinction those advantages stopped counting, and what helped was a lineage spread over a wide area (Jablonski, 1986).
How the propositions meet the fossil record
| Proposition | In the fossil record | Status |
|---|---|---|
| P3 Exit statistics | Van Valen's law of constant extinction is proposition 3 stated for taxa in 1973. Trilobites follow it. Seven groups of eight bend toward a hazard falling with age, which may be frailty, memory or the record. Mass extinctions break the stationarity condition. A published analysis of this database (Finnegan, Payne and Wang, 2008) found the fall with age remains when range and richness are accounted for, which by version 0.2's terms counts against the proposition here. Its re-run on today's database, with rules fixed in advance, came out killed. | killed |
| P4 Cost | The Red Queen: a lineage keeps its place only by evolving continuously against a world that also evolves. Station-keeping against drift, in Van Valen's own explanation of his law. Illustration. | illustration |
| P1, P2, P5, P6 | Not applied here. | not applied |
Source and method
Data: every genus the Paleobiology Database lists under Brachiopoda, Bivalvia, Gastropoda, Trilobita, Anthozoa, Echinodermata, Bryozoa and Cephalopoda, with first and last appearances, from its data service, retrieved 2026-09-29, SHA-256 0fa5b6f7d75cabdd57b7a394b2dcc62e26691e8d733c99fd4a5bad6935eca735, CC BY 4.0, credit to the Paleobiology Database and its contributors. The file's checksum is recorded, and the code refuses any other file.
Method. Valid genus names only, with both appearances recorded. A genus's first and last appearance are the midpoints of the intervals it is first and last found in. Its duration is the difference. Genera alive today are censored. Genera found in one interval only are left out, and the fits count from 1 million years. Survivorship is Kaplan-Meier. The Weibull shape is a maximum-likelihood fit with right censoring and a profile-likelihood interval. Extinct genera are counted by the end of the last interval they are found in, in bins of 5 million years. Description only.