A NEW EVOLI.NIONANY LAW

Leigh Van Valen Department of Biology The University of Chicago Chicago, Illinois 60537

ASSTRACT:

A11 groups for which data exist go extinct at a rate that is constant for a given group. When this is recast in ecological for:n (the effective environment of any homogeneous group of organisms d.eteriorates at a stochasti- ca11y constant rate), no tlefinite exceptions exist although a fev are possible. Extinction are similar within some very broad categories ancl vary regularly with"ates size of area inhablted.. A new unit of rates for discrete phenomena, the macarthur, is introduced.. Laws are appropriate in evolutionary biology. Truth needs more than correet pred.ictions. The Law of Extinction is evidence for eeological slgnifieance and. eomparability of taxa. A ncn- Markovian hypothesis to explain the law invokes mutually incompatible optima vithin an ad.aptive zone. A self*perpetuating fluctuation results vhich can be stated. in terms of an unstudied aspect of zero-sun gnrns theory. fhe hypothesis can be derived from a view that momentary fitness is the e,mount of control of resources, whieh rernain eonstant in total- anount. The hypothesis inplies that long-term fitness has only two eomponents and. that eventg of mutualism are rare. The hypothesis largely explains the observed pattern of molecu]-ar evolution.

Introduction

During a study (Van Valen, submitted.) on the effects of extinction I vanted to show that a modeL l was using was oversimplified.. It assumed no correlation of probability of extinction with age of the group, antl f thought that general1y more vulnerable groups should d.ie out first. A test using data from Simpson (1953) showed.to my astonishment that the assumption was reasonably correct in these cases. I d"id. not believe it could be generally true and so tested these and other cases in more detail-. The assr:nption proved to be consistent with all available data. Others (unpublished results) have now confir:ned this fincting for ind.ividual taxa. I will present a more extend.ed"treatment efsewhere; the present paper is contlensed..

The Evidence

Ttre method is an application of the survivorship curve of population ecology (includ.ing d.emography). It is a simple plot of the proportion of the original sanple that survive for various interval-s. In this case the sa,mple is the set of all known subgroups of some larger group, no matter when in absolute time each subgroup originatecl. A logarithmic ord.inate, stand.ard. in eeology, gives the property that the slope of the curve at any age is proportional to the probability of extinction at that age. Simpson (f9\\, 1953) compiled two well-knovn taxonomic survivorship curves but used an arittmetic ordinate (f-)+). The results (fig;.-1-5) for over 25'OOO subtaxa show aL:nost unifotrn linearity for extinct taxa except for effects attributabl-e to sa,npling error (216). Sa.mpl-ingerror is most noticeabl-e at the bottom of the graphs, where

Evol. Theory 1:1-30 (.lulY 1973) DINOFLAGELLATE . DINOFLAGELLATECYSTS 100 (ExrtNcr CYSTS '.. _aaaa^ GENERA) (EXTINCTSPECIES) raaaaa.

I tta"a a a a 10 tttaaaa

I l"ll o 50 100 M.Y. 150 DIATOMS (GENERA) 50 M.Y. 1oo{i r v EXTrfrtCT,CENTRALES. ^ ^ x | t. o o ou 'VIilG.CENTRALESo o o oo tvrno, PEt{ilALEsx

COCCOLITHOPHYCEAE oa (EXTINCTGENERA) a a O3 taa

a oaaaaa otttaa 20 40 M.Y. o CENTRALES (SPECIES)

L TorALEXTIt{cr r -qqL^ EXCEPT LATE PERMIANi -o EXTIIICTION$ ^- -

EXTINCTPLANKTONIC X EXTINCTBENTHONIC o FORAMINIFERA LIVINGo 100 "".... (EXTINCTSPECIES)

oa tooor

olo20 M.Y. 30 o 200 M.Y. 600 for protists. Fig. 1. Taxonomic survlvorshiP curves BRACHIOPODA BRACHIOPODA (EXTINCT FAMILIES) (EXTIi.ICTGENERA)

tt, a ta t', JLATEPERMIAN lX - IEXTINCTIONS oor xx ?o .OTHERARTTCULATA tx ' .r xxx ?oot x OTHERINARTICULATA ax t t8 a ... XCLUDING lo ATEPERMIAN t, ooo xl XTINCTIONS oo

x ooo xx a xXx ooo PELECYPODA O (GENERA) M.Y. 200 ""f r PELECYPODA BRYOZOA a .EXTINCT 100 (FAMILIES) a (FAMILIES) a . LIVING a 100 ra '{'** 1- \*, O-t a \e** a t-t L. 10 -' . . EXTINCT x'o.aw , LIVING Ff-Frt!4, -"7 a 200 M.Y. 400 NAUTILOIDEA

a RUDISTS . EXTINCTGENERA 100 ( HIPPURITACEA) 100 ttt (GENERA) XEXTINCT FAMIL]ES

t\ ".o \- "**- ?rf 10 ^*q *_ e_ a . rALL 'rrw ll@-i aI x 'MAesrnrcxrtan, EXTTNCT BEFORE I -]tO 20 40 M.Y. 60 100 200 M.Y. 300 AMMONOIDEA ARCHAEOGASTROPODA t t l ruoruoPLAcoPHoRA (GENERA) . FAMILIES r^?:. {o) . aLL Exrrrcr XGENERA ^i9 (ExrtNcrExcEPT o + LATE ^o..t -JM|DDLE a X r ^IPERMIAN o'o ^?. o {ExrlNcrloNs xa oooo"i.. o LIVING xo xx. x oa- aa oo Xr - I- a ooo"x xl a aa x ooo I I. "::.

M.Y, r50 o 200 M.Y. 300 o 100

for Mollueca and BrachloPoda. FiC.2. Taxonomic survivorshiP curves PTERIDOPHYTA GRAPTOLITHINA too (GENERA) (SENSU LATO) . ro (FAMILIES) 100 t .ALL a r xxrr:x'xxx Iexcepr(FTNAL) xxxxxxx : r x E?llllft I xIPENNSYLVANTAN aa xx ^ I lEXTlNCTlot.l aa a a xxxxxxrxxxxr xolo . aa xxxo aa x aaaa ' r""aaaaa oa t'l I roo 200 M.Y. 300

100 M.Y. ECHINOIDEA (FAMILIES)

XXX. a--t...5xxxrl<

.X a xx tt. T \

M.Y.

ZOANTHARIA (GENERA) MALACOSTRACA TOTALEXTINCT . (FAMILIES) r EXTINCTEXCEPTI ^'^ LATEPERMIAN IX SItt** OOI EXTINCTIONS) ta -l?. XXxxxxx LtvtNGo a- XXXX o6t3 -o o x ^ lo a xx taa aa xx a o' . xx EXTINCT .. xxx @O0(...o XLIVING I 200 M.Y. 400

100 M.Y. . . MALACOSTRACA x x (GENERA)

""! a oo Xao Xa a x Xlo^^ 10 taoo x oo o LIVING . . .TOTALEXTINCT xx. xEXTINCT DECAPODA r'ti' o 50 'r@ M.Y. r50 o

Flg. 3. Taxonomic survivorshiP curves for pl"ants and invertebrates. OSTEICHTHYES (FAMILIES}

100 M.Y.

o OSTEICHTHYES (exltNcr GENERA) 200 M.Y. 300

OSTEICHTHYES (EXTINCTGENERA)

1-r-r-+-e--J o 100 M.Y. 150

REPTILIA (FAMILIES)

TOTALEXTINCT o EXTINCTEXCEPTT LATE CRETACEOUSIx EXTINCTIONS) LIVINGo

. EXTINCT XLIVING

20 M.Y. 30

loo EDENTATA PROBOSCIDEA (XENARTHRA) (EXTINCT GENERA) (EXTINCTGENERA)

aaaa aaa 10 aaaaaaa

tttttttt aaaq I I I o 10 M.Y. 20 o 10 M.Y. 20 Flg. 4. TaxonomLc survivorship curves for vertebrates. rrMajor therian ordersrr are those nith lndlvidual plots. 1000 CARNIVORA+ HYAENODONTA (GENERA) aaaaa r. ' EXTINCT -".- x LIVING xxxxx -o. oa a xxx xxxxx t. 10 *rrrri. a xx.xx aa

I I o 10 20 M.Y. 30 1000 ARTIODACTYLA .... (GENERA)

a a POLYPROTODONTA 100 a .... (EXTINCTGENERA) 100 -... 'EXTINCT xxxx ".. xLlVlNG tta .. aa ttaaaa- taaa tta

XXXxxxX r

aaa aa

I I' I 1-f-_ I I 'l o 10 20 M.Y. 30 o 10 20 M.Y. 50 1000 PERISSODACTYLA (EXTINCT GENERA) 100 .... PRIMATES aaaaaa ... (EXTTNCTGENERA) 100 tOr -a aa a 10 a a a a 10 aa aa 'i aaaaa '15 aaa M.Y.

rl to 20 M.Y. 30 NOTOUNGULATA+ . . . LITOPTERNA o (GENERA) loo oa

O3 ttaa 10

aa t

1 l" o Fig. 5. Taxonomic survivorship cr.lrves for manunals. For Primates, Madagascar genera are omitted because the island lacks pre- Pleistocene fosslls' Polyprotodonta lncludes caenotestoldea. A NEI^IEVOLUTIONARY LAI^I

a few taxa have disproportionate weight, and at the left sid.e, where inaccuracies in dating are most ircportant (T). Usually, the more taxa included the cl-oser is the approach to linearity. For living taxa linearity of the d-istribution requires both constant extinetion and constant origination. It further requires that both be more nearly constant over absol-ute time than does a d.istribution for extinct taxa, which nonnally spans many overlapping half-l-ives of taxa, and that probability of discovery not d.ecrease appreciably vith age of strata. It is therefore surprising that many even of these d.istributions are linear (8). Linearity is not an artifact of the method.. Most survivorship curves for ind"ividuals are either markedly concave or markedly convex (9). Most smal-l passerine bird.s are exceptional in having l-inear survivorship curves. The very wide d.iversity (biotogically and stratigraphica[y) of groups plotted. here argues against any kind of special artifact. The sources of data usually d.o not distinguish between real extinction of a lineage and pseudo-extinction by evolution of one taxon into a successor taxon (Sinpson, 1953). The latter proves to be negligible. Most taxa which give rise to suecessor taxa continue in their original form for an appreciable period. after the branching. For farnilies of mannals, for which I am familiar with the phylogeny, a maximum (and surely inflated.) estinate is 20 per cent pseudo-extinction; a more likely estimate is ! per cent. Anmonites (!) give 5 per cent (I2 of l8B taxonomic extinctions for fa.rnilies). A1l- other available phylogenies give similar results. The pattern of constant extinction remains r:nchanged whether pseudo-extinctions are included or excluded.. AdditionalJ-y, it is plausible that even pseudo-extinction usually implies the end of an ad.aptive mod.e and so woufd fit into the hypothesis given below. Pseudo- exbinctions are probably more eomnon at lower taxonomic l-evel-s, d.espite the counter-claim made or inplled by Ruzhentsov (rg5S), MacGillavry (1958), and Eldrefue (lgtf; Eld"redge and Goul-d.,1972) that they do not occur for species. Any example of an ancestral taxon co-existing with a descendant taxon viol-ates a basic premise of cladistic systematics (Hennig, 1966). As noted, such exa,mples not merely exist but greatly predominate.

Apparent Exceptions

There are some real and some sptrrj-ous exceptions to constant extinction rates. As noted above, the ages of living taxa are not directly cornparable to those of extinct taxa. Sa.npling error al-so causes d.eviations from linearitY. Some short intervals of geologic time have had massive extinctions of some kinds of organisms (Newell-, 1963, 1967, 1971). A11 graptolites became extinct in the Pennsylvanian and al-rnost all stony corals (Zoantharia) aia so in the l-ate Permian. This is clearly a different sort of event from the usual- process of extinction and does not fit the general explanation given below. In the late pernian, aL:nost everything in the ad.aptive zone of stony corals was el_iminated (10). The ad.aptive zone itself was demolished for a while. If ve eliminate such extinctions as being different from events within an adaptive zone (d"one supplementarily in parts of Fi5.. 1-l+)rlinearity is never reduced ancl sometimes, as with corals, increasea (ff). When, as with brachiopod. genera, extinctions at such a time are suffieiently numerous to be plotted separately, the slope is less than for: others, as for the ages of genera living today and for the same trivial reason. There is no accepted cfassification of coral-s at the famlly level-. Two more or fess orthogonal classifications are plotted in Figure 6. One is linear, the other convex. This gives some evidence that the Treatise 1000 x TRILOBITA loo X TRILOBITA x (GENERA) , (FAMtLlEs) - a -ool-" a ORIGINCAMBRIAN ORI tlr EARLYORDOVICIAN I^ ltt. 100 ORIGINLATER . 10 ol o a x' aa x o ORIGINLATER x x x Xa a XORIGIN t 10 CAMBRIAN t"" too M.Y.

100 I r"l o 50 M.Y. 100 MAMMALIA(THERIA) 100 (EXTINCTFAMILIES) MAMMALIA(THERIA) (FAMILIESORIGINATING BEFORELATE EOCENE) 10 rl

I o 20 40 M.Y. - a?

I 60 GASTROPODA '. (oRtGlNATtNGtN PALEOZOC) taa

100 a ooooo^^'aa xxxxxilooooooo (f)oooooooof,6 tx ^',,tllriiilooooo xxxrxPl?ge ^tt""aaa x 10 t... ll^--rttdx a xxx . t..- qD EXTINCT(TREATISE) GENERA LIVING(TREATISEI OO'!" O ALL FAMILIES xEXTINCT(FOSSIL RECORD) ooxx EXCEPT .....o.. ^IPERMIAN'JFAMILIESEXTINCTIONS 1 I ' J- 100 M.Y. 200 200 M.Y 300 FORAMINIFERA x (GENERAORIGINATING IN PALEOZOIC) 100 .xxx a txxx*t ol ^xXxxxxxxxxxxr aa^ ttaa X ALL . EXTINCT

aaaaa aaaaaaaa

o

Fig. 6. Taxonomic survivorship curves for apparent exceptlons to linearity. See text. Zoantharia families are from very different c lass i ficat ions . A NEI^IEVOLUTTONARY LAW

classification is ecoJ-ogically more realistico but a decision must ultirnately come from phylogeny. Manmalian fa.mil-ies also give a convex curve (fig. 6). As shorm by plotting only fanilies (extinct and. living) origlnating before the late Eocenen hovever, this is an artifact of the short duration of the Cenozoic in relation to the durations of many fanilies. Living fa^noilies seem similar to extinct oneq because they jointly d.eter':nine a single linear curve. This is al-so true for gastropod.s but not for foraniniferans. This d.ifference in fora,minj-ferans of some living ta:ra from most extinct ones also occurs elsewhere, notably in the Pterid.opffia. ft is ind.ete:minabl-e from these d.ata whether reaf exceptions are involved or whether the deviant taxa occupy sufficiently different ad.aptive zones as not to interact appre- ciably with the maJority of related taxa. Simpson (fg\t+) noted this pheno- menon for pelecypod.s and mad.e it the basis of his bradytelic evoluti.on. Deviant adaptive zones are obvious for genera of most of the d.ifferent mammal-ianord.ers (Van Valen, I97I) and. al-so for rud.ists, coral-like peleeypod.s which forrned reefs i-n the late Cretaeeous and seem to have caused the extinction of many coral-s while d.oing so (fe). Their extinction rate is greater than that of no:maI pelecytrlods o althor:gh also greater than that of genera of corals, which may not be taxonomically similar (f:). Anmonite and nautiloid generao but not fanilies, give ostensibly concave crlrves. When grouped into more homogeneous classes (fig. 7)' approximate linearity results. This also applles to the lengths of the tentinal branches (after each final branch-point) of the phylogeny of e.nmonite fanil-ies (ll+). Removal of the Late Devonian extinctions has a similar effect for genera as for tenninal branches but is not plotted. I d.id. not try to subd.ivicle the nautiloids. I further suspect that pseudo-extinction is more cotlmon for nmmonite and perhaps nautiloid genera than is true elsevhereo which would increase eoncavity by increasing short-lived. ta:ra at the expense of longer-lived lineages. The need to separate Pafeozoic and Mesozoic ammonites shows that there is at least a d.escriptively real exception here. The extinction rate is definitely not constant throrrghout the existence of the group. The sa,meis true for trilobites (fig. 6), the separation here being in the Ordovician. Linearity again hold.s for each segment. I d.o not know what caused either change' but it may be refevant that effeetively alf Mesozoic ammonites d.escended from one paleozoic lineage and that trilobites declined greatly in the Ord.ovician. In each case the d.ivision time found. for extinction rates corresponds to the greate* separation in the group on other criteria (U.)' Moreover, because of preservational bias and incomplete collecting and stuctyn short-1ived taxa will be found. l-ess often than long-1lved taxa. However, for equally frequent groups the effect of this bias will be a red.uction in observed longevity by a constant absofute ainount. This will leave linearity and even the slope of the curve unchanged.. Rarer groups will have a greater expected. reduction in observed longevity than cotmoner groups. Any effect of this property clepends on whether rarity is correfated with longevity, and I know of no relevant clata. Any combination of subgroups with unequal constant extinction rates produces a concave resul-tant curve. The a.mount of inequality can be estimated by thls concavity, but unfortunately any concavity manifests itself most in the regions of greatlst sanpling enor. Linearity is nevertheless sufficient that exceptions must be rare or slight. Abrupt end.s to tiistributions, as with echinoid families' ;;;.* when (as we have seen with ma:nmalfa,nilies) tne stratigraphic range of the group inplnges on the possibility of long-1ived taxa having already become extinct. Linearity is unaffeeted. by muttiplication or ad.dition with a logarith- mic (ordinate) or Lrithmetic (abscissa) constant' 10

AMMONOIDEA (GENERA)

. MESOZOTC (MESOZOICEXCEPT 'IMAESTRICHTIAN(EXTINCTIONS O PALEOZOIC

o t*-'a8 uxegsroa

o o a -E M.Y,

Fig. 7. Taxonomic survivorship curves for annonites. See text. The graph on the lower left is for ter-minal twigs of a phylogeny of fa,nilies. tt** We see that the exceptions are either spurious, rare, slight, doubtful, or exceptions only in part. The pattern is therefore sufficiently general that the minor exceptions are best explained by unusual circurstances pecu- liar to each case. There is a strong first-order effect of linearity, and it is this, rather than its perturbations by special and diverse circrrnstances, that deserves prlmary attention.

Related Phenomena

The constancy of extinction in terms of survivorship does not imply constancy over geological time, and vice versa. Any form of survivorship curve has a mean, as d.oes any pattern of extinction rates over absolute time, and this is the only formal connection between the two phenomena. fhere may nevertheless be a d"eeper causal connection. I give some extinction and origination curves over geological time to illustrate their variability in the measurement framework proposed. here (Fig. B). There is an extraord.i.nary exponential d.ecrease in origination rate of mnmmalian femilies, by two orders of magnitud.e, from the beginning of the Cenozoic. An inverse phenomenon occurs in d.iatomso where the species of Pennales (a largely benthonic groups, unlike the Centrales) have increased exponentially, as in the 1og phase of bacterial culture, in the sane intervaf (f5; Fie. 1). We can l-ook at Figure 8F inversely: there is a nearly linear increase in the propor- tion of fanilies that had. originatetl by a given time a^ndthat are now extinct. Large foraniniferans (f1) trave originated about hl tines independently from smaller fora.miniferans, almost always from much smaller ones. About 33 of these clades have existed. since the end of the early Cretaceous, when an approximate equilibrir:m was establ-ished. Figure p shows that the numbers of clad,es and genera present simr:ltaneously have followed nore or less Iog-no:mal 1200 11 r;CENTRALES BENTHONIC. PENNALES t;ORIGINATION FORAMINIFERA 1100I (EXTINCT EXTINCTION GENERA) I 1000 I ,t lcoo{1l

roo ]

100

300 M.Y.8.C.200 or I 50 -- zoo--l I . exirrucrroru o ORIGINATION

=20 I il, {. 40 30 1020 . M.YB.C. "li/400 300 M.Y.B.C.200 MAMMALIA ( FAMILIES)

60 50 40 30 20 10 40 20 M.YB.C M.Y. B.C.

Fig. 8. A: Orlgination and extlnction rates for species of diatoms. B: Extinctlon rates for genera of benthonic foraminiferans. C: Orlgination and extlnction rates for famllies of anrnonites. High originatlon rates precede hlgh extinction rates except for the Permlan and latest Cretaceous. D3 Extinction rates of mammallan famiLy lineages, and orlgination rates for mammalian famlLles now surviving. E: Origination rates for all mammaLian famllles (new famllles per famtly ln previous age per unit time). F: For manrnalian families, (cumul-ative recent families originated)/ (cumuLative total families originated). L2 LARGEFORAMINIFERA

. EXTINCTCLADES XEXTINCT GENERA

a

10 15 20 25 30 NO.SIMULTANEOUSLY PRESENT ?-?-?-?-?- 100 M.Y. 150

Fig. 9. Survivorship curves for genera and clades of large foraminifers,ns, and d.istribution of m:mber of genera and clades simultaneously present after the early Cretaceous (Rrlian). **tt d.istributions since that time. Survivorship curves for clades and genera of this taxonomically very heterogeneous, but ecologically rather homogeneous, group are linear within sa,mpling error and d.iffer from the curve for genera of all benthonic foraniniferans. It woul-d be useful- to knov vhether the extinction of entire lineages al-so occurs at a constant rate, or if some taxa can avoid it by evolving suecessor taxa. fhis appears to represent an unsol-ved problem in graph theory (18).

Measurement of Rates

I propose a general unit of rates for phenomena which can be treated as d"iscrete. A macarthur (na) is the rate at which the probability of an event per !00 years is 0.5. Robert H. MacArthur showed.the importance of extinction in ecolory (U.). Let P be the probability per t thousand. years.

ma = -logr(r-gegy (r)

With respect to extinctlon, one macarthur is the rate of extinctlon (fl) giving a half-life of 500 years. With respect to origination, one macarthur is the oceuruence of one origin per thousand. years per potential ancestor. With respeet to molecular evolution, one millimacarthur (nna) is the rate giving one substitution per million years (eO). Apparent equilibriun extinction rates of bird. species on islands that have been stud1ed (21) are 0.5 to 10 ma. Ma.rnnalspecies in the late Pleistocene of Florid.a (Martii-and. Webb, i.n press) naa a rate of regional turnover (time frori of about (r'is. 10). irnnigration to locaI extinction) ? 'ma Table 1 gives estimated extinction rates for the taxa stud.ied.. The sedentary marine benthos is remarkably homogeneous, and notile marine organlsms have somewhat higher rates less similar among themselves. Me.rnnalian Senera (and. Mesozoic annonites) have the highest rates, but rateg for reptlllan fa,nllles are as high as those for manrmalian families. For everlrthlng except manmals the extinctlon rate for fa.rnilies is about haLf that for genera. Groupe ln relatively new adaptive zones (at least to them) usually have hlgher ratee than long-established groups. Not surprlsingly, ecology ls a better predlctor of evolutionary rate than is a^nor:nt of inforrnation-bearlng DNA (eZ), ff genera of a fa.nily go extinct ind.epend.entl-y, the extlnctlon rate of fanilies will d.epend.directly on the number of contemporaneous genera per fanlLy A NEW EVOLUTIONARYLAW 13

TABLEl: Extinction Rates (in Ana). Abbreviations: fa.m.o fa.uaily; gen., genus; sp., speci.es

GROUP RATE

fam. gen. sp.

Fterid.ophyta 20 d.iatoms 50 90 Coccolithophyceae 25 DinoflagelJ-ata 20 55 Foraninifera 10 benthonic 20 planktonic 30 100 large 50 0stracoda 10 25 GraptoJ.ithina 30 Bryozoa T Brachiopoda L5 Articulata t+j fnarticulata 25 Malacostraca 12 30 Trilobita early 20 80 ].ate 10 35 Echinoidea 10 2' Zoantharia 10 25 Anmonoiclea Paleozoic 20 35 Mesozoic 75 150 Nautiloidea 15 30 Arehaeogastropoda + Monoplacophora 20 Gastropod.a Paleozoie h 20 Pelecypod.a R 20 rud.ists 50 'lq 0steichthyes 30 Teleostei 20 35 Holostei + Chond.rostei t2 25 Sarcopterygii 30 Acanthodii 30 ReptiJ-ia 30 Ma^umalia (Tueria) 30 150 Polyprotod.onta 150 Primates 220 Rodentia 150 Carnivora + Hyaenodonta 120 Edentata 180 Proboscidea 5o Notoungulata * LitoPterna 1?o Perissodactyla 120 ArtiocLactyla 120 Cetacea 200 L4 100

'oooool ojo 10

' 6' 5b T.Y. 100

pig. lO. Regional survivorship curve for ma.wtalian species in Fl-orid.a d.uring the late Pleistocene. * * if there is no origination of new genera in the fanily. Rough estimates ' weighted by the number of taxa in each interval, give 2.9 contemporaneous genera per fanily of Ostracod.ar 2.S for Echinoid.ea, and5.l- and5.8 species per genus respectively for pennate and centric diatoms. With 2.9 genera pu" irroify, independent extinction w:ill give an extinction rate per genus 2.6 tlmes that per fa:nily. This ratio would" be 2.5 for echinoids and.3.5 for average d.iatom speeies. I take the expected. time of farnily extinction to be when the expected. number of genera per fa,nlly reaches 0.!. With branching (origination of new genera), the fa,milies will of course have longer expected longevity and so the expected ratio will increase. If the rate of branching equals that of extinction, simrrlation in the above range indicates roughly a doubling of the expected ratio, although a high variance aJnongfa.nilies in genera per fa.nily probably increases it more. Table 1 shows that genera of echinoids and ostracod.es have about 2.5 times the extinction rate of fanilies, a result ind.istinguishable from that on the assumptions of ind.epencience and no branching. Because branching exists, some degree of correlated. extinction of genera within fanilies seems probable. Ttre observed rate for species of diatoms is only twice that for genera, much less than the expected value of 3.5, so there i.s a strong correlation in extinction here even without consid.ering branching.

Contemporaneous Subgroups

Extinction rate obviously depends on the area consid.ered as velL as on the inhabitants. Fig. 11 gives a relation between area and. extinction rate, using all available d.ata (Zf). Approximate linearity holds over 11 orders of magnitud.e on a 1og seaIe. With the extinction rate in 1oglo macarthurs and A the area in logln sq. km, the regression is J) = -Q.669+ 1.53 when calculated from the birds and-manmals and excluding the worl-d. fauna. A regression from complete data would presumably differ somewhat. As expected, the arthropods on Simberloffia seem to require less area for the sa^ne exti.nction rate than d.o vertebrates (ef). A continent seems to be the largest area in which organisms can interact more or J-ess as they do in any smaller area that is large enough for a population. Therefore species and higher taxa occupying smaller areas, as will often be the case when they originate, have an expectecl rate of extinction greater than that of more wid.espreacl taxa. Sinilarly, as Smalf (fg)+5, 19h8b) noted. in 15

2

co

-2 A ARTHROPODS BIRDS o MAMMALS \" -4 -2 o24 LOGrc AREA

Fie. 11.. Extinction rate (f[nin loglo ma) of species as a function of area (sq. lon.). a different context for tliatons, genera with fewer species have a higher probability of extinction than do genera with more species. This is of course because branching at the specific l-evel inereases the probability of survival of the entire sub-tree n since the species will usually have different ecologies. For these and other, less well-documenteti, reasonso there are definabfe and large subgroups that have a higher extinction rate than others, and moreover these subgroups should be relatively most frequent among younger taxa. Therefore a concave survivorship curve should. result. How can it be that the curves are nevertheless linear? There are two possibilities: incorrect assr:mptions and. eompensatory feedback. ft nay be that, by the time taxa have an appreciable probability of appearing in the fossil record, they have the sa.memean area oceupied as ol-der taxa. fhis sort of rapid increase may also be true, although it doesnrt seem as 1ikeIy, for nr:mber of speeies in a genus. Enough data.are probably availabfe to resolve the latter point. Conpilations by Sloss (f950) ana Sinpson (fg:S)n Smallf s studies (e.e. 19h6) on d.iatomso and" d.ata by Berggren (tg6g) and others on planktonic foraminiferans, suggest that there is indeed usually an appreeiable lag before the number of subordinate taxa approaches its maximum value. The kind.s of evidence in these papers are by no means conclusive on the present point, however. Fr.rrthermore, there may well be a threshol-d. (tite those folnd by MacArthur lryfZl and others for population size in simplified models of colonization) above which survival is virtually assured and below which rapid extinction is likely. Other possible inad.equacies of the assr:mptions, that the effects are too smaLl to be deteeted or that they affect only a small proportion of taxa, are clearly unrealistic. Even if an initial concavi.ty in survivorship curves is avoided by the rapid. ehanges invoked above, there still remains a major heterogeneity anong the surviving taxa with respect to area, nr:mber of species or genera, and other faetors relevant to survival. There must then be some kind. of compensa- tory feedback to give the observed. degree of linearity. Two kind.s of feedback seem possible. There might be an interaction between age and area (or nu:nber of species) such that older and younger toca have d.ifferent effects of area on probability of extinction. No simple mod.el fits this biol.ogically inplau- sible alternative. However, if for new ta:ca small area and low nr:mber of species were not ha:mful , or as har"nful as later, the expected initial concavity would be reduced. or eliminated. L6 L. VAN VALEN

The other kind. of feedback is by the continual appearanee at a1l- a,ges of taxa of low area and. other characters giving greater susceptibility to extinc- tion. fn fact this could. be regard.ed.as an aspect of the extinction process: taxa would. become more susceptible at a constant average rate per taxon per time. This transforuation need. not be by feedback per se, but it d.oes require that the production of greater susceptibility be part of the sarne process as the extinction. There j.s no requirement that eaeh subord.inate taxon be equally likely at any given time to beeome more susceptible, but the overall control- must eompensate for survival by greater susceptibility at some other time or for some other species. fhis second. aLternative is plausible (given linear sr:rvivorship) but largely untested. ft pred.icts that, at least after a short initial period o criteria of susceptibility will have a steady-state distribution i-n survivorship time ind.ependent of the age of the taxon. Smal-l (fgl+6, l9\7, 191+8arc) found. such a steady-state distribution in real- time for generic sizes of d.iatons through the Cenozoic.

An Evolutionary Law

The effective environment (el+) of the menbers of any homogeneous group of organisms d.eteriorates at a stochastically constant rate. This law goes a bit beyond the observations in postulating the cause to be extrinsic rather than intrinsic n like nucl-ear d.ecay. There is of course much other evid.ence (Sinpson, 1953) for such a step. The law is also stated in terms of reaf time rather than survivorship timeo although lt appties to both and. ties them together. A more neutral statement is that extinction in any adapti-ve zone occurs at a stochastically constant rate. ttHomogeneoustt is a necessarily arnbiguous word., and its meaning in a partl- cular case must depend. on the particular cj.rcunstances and on the d"egree of precision desired. Pal-eozoic and Mesozoic amrtonites nay d.iffer sufficiently to be nonhomogeneous, but the entire marine benthos could be treated. together aLmost as well- as subdivid.ing it. This d.oes not lead to circularity; no subdivision of a group with racial senescence (25) would give a set of linear survivorship curves. The homogeneity required. (and so its verification) is entireJ-y ecologicaf and is in terms of ultimate regulatory factors (Van Va1en, 19?3) of population d.ensity. Mice and fruit-eating flies night be honogeneous with each other but not with blood"-sucking flies, although a scaLing problem vould remain. We could say that there always exists a degree of homogeneity at which the law is true, a4d try to measure it ind.ependently. Homogeneity d.oes not inply equality of abil-ity to respond to the d.eterioration; but counterexamples to a eonstant d.istribution of such abilities would. disprove the 1aw in its first form as a universal phenomenon (e5) Like a^ny 1av (ZT), the effects of the lav of extinction a,re observable only under eppropriate cond.itions (here, persistence of the wid.th of the ad.aptive zone). Un1ike many laws (e8), it nay not be universal. If it ls not universal, it should be possible to limit its domain in an obJeetive manner. Such limita- tion should. d.erive from an understand.ing of the causal basis for the law. ft is not fashionabfe to speak of l-aws in evolutionary biology or for historical proeesses generally. I think this is baged on both a misunderstand.lng of the regularity of actual processes (A) and on an over-reaction to poorly fonrulated. laws of earlier workers (30). Laws are propositions that specify sufficient cond.itions for a result; Sven the condiiions, the result will- occur, although some of the eonditions (ttre bounds of the d.onain) may be inplicit. Ttre clegree of confirnation of a law is of course a different matter from whether a proposition is (or represents) a law in this sense. Any general statement of the nature of a causal process states a faw (ff1. A NEW EVOLUTIONARYI.AW T7

The Red Queenrs Hypothesis (3e)

fhe probability of extinction of a taxon is then effectively ind.epend.ent of its age. This suggests a randomly acting process. But the probatifity ts strongly related. to ad"aptive zones. This shows that.a randomly acting process eannot be operating unifor:nly. How can it be that extinction occurs rand.omly v"ith respect to age but nonrand.omly with respect to ecology? We can consi-der the situation in te:rns.of an ensemble of mutually ineompa- tible optima. It is selectively advantageous for a prey or host (includ.ing plants) to d.ecrease its probability of being eaten or parasitized.. ft is often selectively ad.vantegeous for a predator or parasite species, an4 much more often for a predator or parasite ind.ividual, to increase its expected rate of capture of footi. It is selectively advantageous for a competitor for resources in short supply (fooct and space in the broadest senses, and sometimes also externally supplied. ad.juncts'bo reproduction or d.ispersat) both to i-nerease its own effect on its competitors and to d.ecrease the effect of its competitors on itset-f (Sf ). Rvery species d.oes the best it can in the faee of these pressures. Probably all species are affected. importantly by them at least over intervals of a few generations. Response to one kind of pressure may well deerease resistance to some other, at that time weaker, kind.. The various species in an ad.aptive zone (Van Va1en, J.97l-), whether or not this zone is sharply d.elimited from others, can be considered together. We can assume as an approximation that a proportional a^urountw of suecessful- response by one species prod.uces a total negative effect oT v = w on other species Jointlyo usually less than v for any one of these spEcieF. For n speeies, the mean d.ecrement of fitness per species is v/n. For m suc"esiful responses simultaneously (in an intervalt), the *ean ToTal decr6nent per species i-s sg/g. Over some interval t (in units of t), the d.eerenent is then gob-/". To maintain itself as before, the species must increase its fitness by Fa.ilount gnnb-/g. Since each d.ecrement generates a responser g =.g.. Most species will be abl-e to recoup their loss o more or less while it occurs, but in doing so they Jointly prod.uee another d.isadvantage of v for the avera.ge species. fhis process of successive o'rerlapping d.ecrements of v may continue indefinitely. Species at feast 1oca1ly new may replace those for which the rate of environ- mental deterioration has been too great. For the momentary fitness F of a rand.om species o

dq= $ = m(w-v) dt

For a given species, { will of course vary from time to time as its specific decrements and possible responses covary. However, since w = I on the average, E(0 ) = O, i.e. the mean fitness in the adaptive zone is constant in the long run. If we take a standard average fitness f1, the real average fitness will = of b. & If - fr because any response one speeies above $ will bring a corresponding deerenent from the cortnter-response of other species. v is the environmental loacl. Thus, even for a single speeies, the total selecTion pressure is constant over intervals that are long enor:gh to average out irregu- larities. { is of course itsel-f a variable anong the species at any time, and its variation (or that of E) w111 determine the extinction rate in the ad.aptive zone. Species may (anT d.o, but to an unknolrn extent) aiffer in the epectral 18 L. vAN vALEN

(Reyrnent threshold T and Van Valen, 1969) of S or lts components to which they can no longer respond successfully and. at vhich they therefore become extinct. Which speci-es have which values of + and T wiJ-l change markedly with the nature of the stresses at a given time. The observed. pattern of extinction seems to inply that the stresses are sufficiently diverse that they affect most species simil-ar1y over a very long interval. Assumeo as Justified. in part by the Central- Linit Theorem, that both $ and T are normally d.istributed., r+-ith neans y',1 and.y, respectively. Then, since-toth distributions range over the sa.meset-of spedies and so have the s€,tnearea, the rate of extinction is the overl-ap of the d.istributions. In the case of equal varianceg for f and !o

J'9 (^) = (3) -r 4, - €Lt

Uncompensated. d.epartures from no:mality and from equal variances in the d.istribution will of course affect the accuracy of this expression but not the dependence ofil on the real area of overlap. On this self-contained system we must now impose the physical environ:nent and irregular biotie perturbations. Almost all changes in the physical environ- ment of an ad.aptive zone will- be deleterious to its inhabitants, either directly or by pe:mitting the establ-isiment of other species which can then survive there. Therefore regular changes in the physical environment ean be treated. as constant factors of p . The observed. constancy of fl is evid.ence that such a treatment is pernissible. Important perturbations clo, however, occrr, from both biotic anil physical causes. They can be treated together. The probability of extinction is not constant over geological time, as Fig. 8 anct the extinctions at the end. of the Cretaceous suffice to remind us. When maJor perturbations occur wel-I within the geological range of a group, as for brachiopod.s in the late Permiann Paleozoic ammonites at the end of the Devonian, or coccoliths at the end of the Cretaeeous, it happens that if we ignore the subgroups that bece.me extinct then, the remainder show a constant rate of extinction (34). There is no irnportant lasting effect of the unique event, unless total extinction occurred., nor d.o its effects extend d"etectably beyond. the subgroups prematr.rely eliminated. Newly appearing subgroups after the event continue in the sr.me way as those that l-ived through it. Smal-ler perturbations occur much more frequentlyn however (fig. 8), and. it is the very resultant of these perturbations that d.etermines the long-term cgnstancy. Therefore the effects of these minor perturbations are not ind.epend.ent of each other over time. If they wereo they should not be distributed. about a constant mean. The rate of d.eterioration of the effective envirorunent has what we can d.escriptively call the property of homeostasis. A large change in one i.nterval is compensated for by a smaIl one latero on the average, and. vice versa; the mean itself d.oes not undergo a rand.omwalk. ft is the organisms in the adaptive zone that can l-ink the perturbations across tine in that the effects of one perturbation may d.epend on the effects of those before it. Species easily removed by one kind. of perturbation are not there if it comes again soon, and may accumulate if it d.oes not come for a long time. Meanwhile other kinds of perturbations are taking their own toll-, more or less indepen- dently of the first kind (35). We see here a maJor d.ifference from the usual theory of genic selection. The l-atter depends only on the current distributlon of frequencies of alleles and their interactlons with each other and the environment. It d.oes not depend A NEWEVOLUTIONARY LAW 19 at all on the process by whieh the current d.istribution was obtained.. fn forual languager it is a Markov process. But any process can be made Markovian by choice of a suitable leveI of analysis. With extinction we can see that a non-Markovian analysis,of selection is appropriate. This is probably true for the general case arso (35). The Red Queen does not need. changes in the physical environment, although she ean accommodate them. Biotic forces provid.e the basis for a self-d.riving (at this leveI) perpetual motion of the effective envlrorulent and so of the evolution of the species affected by it (SZ). fne Red. Queenrs Ilypothesis is a sufficient explanation of the law of extinction but not one that is yet d.erivable with confidence frcm lower-l-evel knowled.ge of the causes of ind.ivid.ual extinctions anci the nature of species interactions. There may be other sufficient explanations that I have not been inaginative enough to see, anil pred.ictions by the Red. Queen may be duplicated. by such und.iscovered explanations. Disproof of the Red Queenfs Hypothesis is possible in several ways, but f'ully adequate confirmation must await d.erivation of it from what we can reasonably regard as facts. We can go a step further by thinking of an ad.aptive landscape in a resource space (Van Valen, l-971). The a,moun+.of resources is fixed and. ean be thor:ght of as an incompressible ge1 neutrally stabl-e in configuration, supporting the peaks and ridges. ff one peak is diminished. there must be an equal total increase elsewhere, in one related peak or more unifonoly. Similarly, increase in a peak results in an equal d.ecrease elsewhere. Species occupy thi-s land.scaFe and can be thought of as trying to maxi- mize their share of whatever resource is scarcest relative to its use and. availability. fhis resource will- take the role of the geI, and the momentary fitness of a species wil-l be proportional to ihe a^mountof ge1 r.md"erits areaTttre smount of the liniting resource it controls). To a sufficiently close approximation this momentary fitness seems to be what natural sel-ection maximi:zes. fhe lanilscape is changing continuously, at three levels. Species d.isplece each other from areas of the aclaptive surface. This can be by resistance to predation as wel-l as other means, and some parts of the land.seape may in this way or others (e.S. severe weather) be under-occupied.. Incorrpatible optirna maintain d.iversity. Secondly, the d.istribution of gel within the land"scape changes, as with cLimatic change or (for herbj"vores) when the flora changes. Fi.nally, the total a.mount of ge1 (or the amount in fact useci.) can change. This can occur by another necessary resou.rce beconing limiting, bJr constraints on occupation of the ad.aptive zone, or by a change ln the arnowt of the sa,me liniting resource. fhe entire lanclscape can in this way d.isappear. The first two kinds of change ln the land.scape lead" to the the Red Qrreents Hypothesis, while the third. is, without compensatory changes, inconsistent with it. Enpirically extinction is less independent of age when extinctions caused by maJor constrictions of adaptive zones are includ.ed. The observed. d.egree of independence suggests that the third. kind of change is rel-atively unimportant on the evolutionary time scal-e. We can hard.ly regard such a conclusion as established, but it d"oes show that the question of variation in the size of maJor ailaptive zones is firnd'amental.

Molecul-ar EVolution

The Red Queenfs Hypothesis provid.es reason to expeet a long-tera approxi- mate constancy in the rate of evolution of ind.ividual proteins within ar5r single adaptive zone (38). It does so without ad hoc assumptions, although 20 L. VAN VALEN

such assunptions could be invoked. to explain away exceptions Just as they have been invoked (Clarke, 1970) to explain away constancy by the usual selective frarroework. Constancy of the rates of protein evolution is often regarded as the most important evidenee for what Kirrg and. Jr:kes OgAg) called. non-Darwinian evolution, despite serious misinterpretations (-:g). A further pred.iction is that rates of protein evofution will be related monotonically to rates of taxonomic evotrution, to the extent that the subtaxa in d.ifferent groups are comparable (r3rl+O). Some eviaence ()+1) is available that rates are not always constanto and. preliminary results f obtained long before d.iscovering constant extinction suggest that the mean rate of protein evolution during the relatively short time while the orders of placental me.mmalsd.iverged. from each other was greater than that later ()+2). Lingufa, a brachiopod genus present since the Ord.ovician or Silurian, anil Triops cancriformiso a branchiopod. (q[ t"""hiopod.) species not detectably changed since at least the early Triassic (1), would. be expected. to have proteins more similar to those of the eonmon ancestor than would- their more d.ivergent relatives. The evid.ence for approxinately constant evoLutionary rates of proteins comes from organisms (nainly vertebratels) whieh have all evolved. appreciably since their separati-on from eaeh otherr fhe Red. Queen in her simplest gown also predicts a perhaps real pheno- menon, which Ohta and Kimura (fgff ) noted as mysterious: that iregularities in the rate of molecular evol-ution seem to be more or less caricelled. out over long intervals by a seemingly negative autocorrelation.

Implications of the Red. Queen

Thod.ay (fg:S) propcrsed.a concept of fitness as the probability of survival of a lineege to some very dlstant tine in the future. More generally, we can take @r F= I *(t )r(t )at ()+) z* J ---- o where p(t) is the probability (h:) at time O of survival to time !r and w(t) is a weightlng functlon (the sarne for all lineages and perhaps integrating to l for scale) for whlch I vould choose exponential decay a*, a 1ow rate (lrh). Tlme 0 :ls the varlable present. The Red Queen propoees that thle fltnesn has only two components for a"lmoet any real lineage: whlch adaptlve zone J.s occupled. and what the probabillty cllstrlbutlon ls of new sublineages occurring by branching. Artiodactyls have largely replaced perissod.actyls in the sa.mead.aptive zone, yet their extinction rates are id.entical (Tables 1,2). It is the rates of branching that are d.ecisive. Monotreures sti11 llnger on in two isolated sutrzones, one of vhich has already been invaded. by marsupials. The gradual extinction of nulti- tubercul-ates (Van Valen and Sloan, 1966) occurred. by herbivorous placentals d.iversifling lnto parts of the Joint ad.aptive zone foranerly held by multi- tubercufates. One multituberculate survived. 1l or 20 million years after the rest of the extinction was eompleted (h5); the fatter had. taken only about 10 nillion years. fhe Red Queents proposal implies that extinction of lineages (subtrees) will prove not to be constant when j.t can be measured. For the Red Queen, curiously, does not d.eny progress in evolution. By group seLectlon such as thls, as weJ.J.as by ind.ividual selection, properties of conmunities can change in a clirectional manner. It may well be that the everage Cenozoie species could. outcompete the average Ca^:nbrianone; some informatlon on this can probably be derived from ftrnctional analysis. It is A NEI{ EVOLUTIONARYLAW 2T

TABLE 2: Extinetion and. origination rates (in ma) for genera of two competing orders of ma:nmals. E: early; M: middle; L: late

E}MTNCTION ORTGTNATION

Epoch Perissodactyla Artiod.actyla Perissodactyla Artioclactyla

E. Eocene 120 150 1300 500 M, Eocene 80 9o 3+0 920 L. Eocene 120 9O 290 260 E. Oligoeene r20 100 An 150 M. Oligocene 100 150 l+o 130 L. Oligocene 170 130 BO E. Miocene 9o 130 130 260 M. Miocene 30 9O 90 90 L. Miocene l+o 6o 60 100 E. Plioeene 90 130 90 320 L. Pliocene 90 BO 20 7o l8 t3 * well known (cf. Roner ftgee]) ttrat such fi.mctional progress has occurred in vertebrate evoluti"on. The Red Queen measures environmental d.eterioration on a scale that is deter:nined. by the resistance of eontempory species to it, so the scale and real d.eterioration themselves may weJ.l change without a change in the measured cleterioration. Darrinrs example of wolf and deer exemplifies this. The RecI Qu.een proposes that events of mutualism, at least on the sa.rne trophic leveL, are of l"ittle importance in evolution in comparison to negative lnteractions, although she does not consid.er other cases where mutualism is so great that the mutuallsts function as an evolutionary unit, as with fichens. and perhaps chloroplasts. She consitiers the usual contrary view to be a result of wlshful thlnklng, the imposition of hr:man values on nonhrrnan processes. The existenee of the law of extinetion is evj.d.ence for ecological signi- ficance and. ecological comparability of tarca from species to fa,mily, within any adaptive zone. We can think of the Red Queenrs Hypothesis in terms of an unorthodox game theory (l+5). To a good" approximati.on, each species is part of a zero-sum ga,ne against other species. Which ad.versary is most important for a speei.es may vary from time to timen and for some or even most species no one adversary may ever be para,nowrt. Furthermore, no species can ever win, and new ad.versaries grinningly replaee the fosers. This is a d.irection of generalization of ga,me theory which I think has not been explored. From this overlook we see dyna.nic equilibria on an immense scale, deter- nining much of the course of evolution by their self-perpetuating fluctuations. This is a novel way of looking at the world, one with which f a:n not yet com- fortable. But f have not yet found. evid.ence against it, and it does make visible new paths and. it may even approach reality.

Aeknowled.gments

I thank the National Science Foundation for regularly reJecting my (honest) grant applications for work on real organisms (cf. Szent-Gy8rgyi, L972), thus forcing me Lnto theoretical work. Thls paper has been circulating in glzdat since December, 1972, and. I have given talks based on it before and after then. I thank Dr. R. A. Martin for unpublishetl d.ata and Drs. P. BillingsJ-e;rr J. Cracraft, 22 L. VAN VALEN

J. F. Crow, D. H. Janzen, T. H. Jukes, S. A. Kauffinano H. W. Kerster, M. Kimr:ra, E. G. Leigh, J. S. Levintotro R. C. Lewontin, J. F. Lynch, V. C. Maiorane, J. Maynard Snith, P. Meier, D. M. Raupo G. A. Sachero T. J. M. Sehopfo and. E. O. Wilson for d.iseussion. The Louis Bloek Fund. of the University of Chicago paid. for the preparation of the figures.

Notes

(f). fhe taxonomic d.ata I used are from the following sources: For vertebrates, Romer (tg66), with a few modifications from vari.ous later work. For invertebrates and genera and fanil-j.es of Foraninifera, R.C. Moore (ed.), Treatise on Inverlebrd.te Paleontology (goutaer, Colorado: Geologi- cal- soe .TAGA;TrAs), 1953-present, ineluding revisions (C. feictrert, ed..), with supplementation or (for Bryozoa) substitution from fhe Fossil Rdcord (W. S. Harland et a1., ed.s.; London: Geological societyaT ffi TltdTI). r deliberately lgnored. later pertinent work (e.g. Yochel-son ltg6gl) on invertebrates. Pberidophytes and coccoliths are also from The Fossil Record. For species of Forarnini-

rers.- Bersgrenvvro (tg6g). ror n-norlffialil-s-irJeant (ig6l). For diatoms, -vrer Snall- (rg\:,191+5). (l-gtZ); Q) . irhe time scal-e I used is from the following sources: Berggren Anonynous (rg5l+); Everndon, Savage, Curtis, and Jemes (lgeb); Everndon and Curtis (t955); Kauffman (1970); and Van Valen and Sloan (1966). Experiments show that the results are robust to reasonable changes in the time scafe. (:). Various conventions are necessa.ry in any such compilation. Some general ones I used are the following: I took the d.uration of a tarcon as from the nid.dle of the epoch (or other shortest interval) before the first recorcl, to the mid.trLe of the epoch of the last record. I ignored. ques- tioned. record.s and unrecognizable taxa. For d.ata accurate only to period. I plotted the range as ending in the niddle unit of the period,. f used all d.ata regardless of degree of precision (unless imprecise beyond a period.) but used then to the precision allowable. A1so, summaries of ranges (even of ind.ividual taxa) are too often inaccurate, as shovn by rmquestioned record.s of subordinate tarca beyond the stated limits o so whenever possible I compiled d.ata at the level of genus. (!.). f knew of this deficiency for manyyears but saw no reason to pursue it, as I expected" the shape of the culn'es to renain concave. In hind.sight one could. also expect that the group as such might have a progressively higher probability of extinction as the biota around j.t evolves vhile it d.oes not. This woufd. give convex survi"vorship curves. (:.). In ad.d.ition to the d.ata plotted, I mad.eseveral- d.ozen plots of subsets of the sa,medatao using such criteria as exclusion of a maJor extinetion or subtaxon, or restriction of the time interval used. A11 important deviations from the total d.istribution are includ.ed in the figures given here. There is a bias in using all extinct subta:ca of a living group in that the longer-lived of subtaxa originating reeently are still- al-ive. Tests show that this effect is negligible for long-ranging groups (not, e.g. r for fa,milies of ma.wtals or echinoids) and obviously al-l living anci erbinct subtaxa cannot be eombined. into one useful cr:rve (Sinpson, 1953). (5.). I used. all gror:trrs for wtrich ad.equate data were available. Omissiona are due to poverty of the fossil record or its study (e.g. Insectivora), small number of extinct taxa, error of d.ating being a substantial part of estimatecl tlurations (e.g. Archaeocyatha) o or lack of adequate compila- tion (e.g. Gtrrnnospe:ruae). A NEWEVOLUTIONARY LAW 23

(1). This is the reason for the apparently flat tops of some distributions. (g). The initial figure in parentheses in distributions of most livlng taxa represents the total now aliven includ.ing those not known as fossil-s. Many living tarca in some groups are not easily fossil-izable, and. our knowled.ge of the present fauna is better than that at any other time even aside fron this. (g). UxelnFJ.escan be found in the following: Pearl (fgZ8); A11ee, Thtersonr Park, Park, and Schmidt (191+9); Kurten (fg:S); Od"rrn(fgff ). (fO). Coral-like brachiopod.s of the Permian also becane extinet, as d.id. many other organisms superfieially less simil_ar to corals. (ff1. Tests are necessarily weak, but data from several groups give no indica- tion that a major extinction affects taxa of d.ifferent ages to a d.ifferent extent. (re). A third (fT or 51) of the fainilies of stony corals present in the late Cretaceous beca,me extinct then, but only one of these d.id so at the no'lnr anigis at the end of the Cretaceous. The Fossil Record. famiLies are the only ones with aciequate d.ata on this point. Rud.ists diversified. throughout the late Cretaceous and abruptly d.isappeared at its close. (fS). f give several ways of evaluating comparability of taxa elsewhere (Van Valen, in press). (rt+). The plrylogeny is from the Treati?g (1) and excludes ! fe.nrilles of unknown ancestry. Schinctewolf (1961-1968) has given a rather different phylogeny, but parts of it are not d.etaiLed enough for this application. (f:). A brief d.iscussi.on of possible factors in the crisis for trilobites can be for:nd. in The FoSSil Record (1) p. 51+. Sone other curves also probably exhibit real deviations from linearity,' but the ones discussed. are the largest. (f6). Small (fghg,l?r2).noticed this exponentiaL increase for some individual genera, as Sma]l (1950) and Tappan and Loeblich (fgff) d"id for the entire group. (U.). I arbitrarily d.efine these as having a maxj.mu:nd.ianeter of at l-east 5 m. Most are highly complex internally, and most are discoid.aL, fusifo:m, or low conical. (rB). llhat is necessary is the expected. d.istribution of the d.urations of all sub-trees, incJ-uding parts of larger sub-trees o given a constant extinc- tion rate and a branching rate that varies from time to tine. Harris (f953, p. 32) considereti the problem for a constant branching rate and for:nd it intractable. It would further be useful if some sub-trees could be ignored as effectively infinite (extending an unknown arnowrt beyond. some absolute d.ate such as the present). The point is directly resolvable by simulation, but this requires more money for computer use than f have. (U.). MacArthur died. (at the age of \e) two weeks after the discovery of constant extinction. (eO). I ma is the reciprocal of a half-life of 5OOyears; in generaln ma = (naff-fife in units of 5OOy"ars)-r. Macarthurs apply also to phenomena (such as origination rates) for which half-lives are inappropriate. Applications in the text are to phenomenavariously with and without replacement of the iten sampled.; the d.erivations therefore differ in = aetait. Some conputational aids: . ma. (1og1921-1(-Ioelg(f -p2!.1 ;, Pn-s(l ctay) = 183 kilomacarthurs (t

factor of e per million years. Kimura (tg6g) d.efined. a unit of rates for molecular evolution: a pauling is, in this context, the seme as a mil]-inacarthur. (2f1. For bird.s, the d.gta are for islands and. of variable quality: MacArthur e"ndWilson (t967); Lack (rghe); Dianond, (t969,1971). The island.s are, in ord.er of size, Los Coronados, Santa Barbarao Anacapa, St. Kild.an the Scillies, Krakatoa, San Miguel, San Nicolas, San Cl-ementenSanta Catalina, Santa Rosa, Santa Cruz, Karkar, Mann and. the Orkneys. For arthropods, Simberloff and Wilson (tg6g) have approximate d.ata from mangrove islets. fhe inaccuracy of the estimated extinction rates for bird.s and arthropod.s, in the present contexto is about an orcler of magnitucle. Estimates for both groups are probably too high, but I use available val-ues. Manmal data are from Kurten (f968) for Europen Martin and Webb (in press) for Florida, Webb (tg6g) for North America, and the data of Table l for the world. There are nolr about I+ species per genus of me.mnal-sin both North Ameriea and" the world; if they go extinct lnd.epend.ent1y, the extinction rate of species is three times that of genera. This inaccurate assunp- tion, which ignores the correlation between number of species present and number of new species produced"o is reasonable at the seale used.. The grouping of bird"s and ma,:rm.alsinto one equation is less defensible but is supported. by the Florida d.ata. The sa,me is true for grouping d.ata from islands, a peninsula, and two partly isolated continents. (ZZ). Treatments of evolutionary rates in paleontology not in other notes can be found in, e.g., the books by SchindewoLf (fgfO), Zeuner (fg:8), and Kurten (rg58); a syrnposir.un(.1. Paleont. 26: 297-39\ l].9fZl); anct papers by willia.ns (195?), Kurten (rg5o), Bone (rg5f), Lerman (tg6S), House (:?6t), Newel1 (ry6f), valentine (1969), Lipps (rgfo), Kurten (r9?r), Olsson (tglZ) o and Cooke and Maglio (tgTZ). DNA estlmates are readily accessibl-e in the At1as (Dayhoff, L972); various guesses exist on the proportions that are info::national. (eg). A more extreme divergence from the regression wou-l-d.be expected for smaller organisms. Cairns, Dahlbergo Dickson, Smith, and Wal1er (f959) in fact give d.ata for protozoans on bfocks of an artificial substrate in a l-ake. An extinction rate of about 12 kma [P(extinction) = O.Oh3 per species per d.ay] can be derived from their data. However, the substrate was a foa,n and so the effective area is unknovn; the area of the top was 5 x 10-9 sq.. 1gn. Furthe:more, the extinction rate may be higher than that in naturally occurring isolated. substrates of the se.meeffective areao and the experiment tasted. only a,bout l+Od.ays. The glass slides that Patrick (lg6l) used as isfand.s for diatoms would seem an excel-lent model system for such estimations, especially because the effect of area itself can be isolated from that of spatial heterogeneity and. both stuilied. together. 1'he estimated. extinction rate on Simberloffia nay also be higher than a rate comparable to that for vertebrates; Sinberloff and Wilson (1959) trextinctionsrt say that most seem to have been of species that coulclntt colonize the islets und.er any circr:mstances, so no real populations of them existeti to become extinct" This is a serious bias even if one d.ifficult to overcome, and ilLustrates the d.anger of letting what we can easily measure d.etermine what we think we want to measuret the tyranny of epistemology on ontology. (Van (Zl1)[email protected]. t{:e efiectilq environment- of any organism is its ad.aptive zone Valen,

(Z>). A hypothesis recently revived in terns of DNA by Bachmann' Goin and Goin ( L972). (26). ff we look at too nanow a part of the zone' with only a fev tanca, discrete A NEIIIEVOLUTIQNARY LAW 25

single events will be inclividually noticeable, as with argr rand.om process in the real vorld.. In a causal wtiverse a claim of randomness is a bad.ge of ignorance. With evolutionary d.iversification the causes of seemingly random patterns nay well be important and. cliscoverable (Van Valen and. Sloan ltgtZl give an exanple). The Iaw of extinction is on the next 1evel of abstraction from such causes. (Zl). Gravitation does not cause an obJect resting on the floor to fa1l. Lakatost critique (tg6l-tg6h) of mathematieal proof is based on the ilifficulty of d.elimiting d.omains obJ eetively. (28). But liker e.8., Mendelrs Lavs or the gas 1aws. (29). I have treated this subJect elsewhere (Van Valen , 1972). (30). For instance, E.D. Cope proposed a farnous law in the nineteenth century that prinitive taxa have a greater expected longevity than their d.escen- dants. This has never been aciequately tested. and should be re-formul-ated. in terms of d.egree of primitiveness (assuming a threshold. is absent) and a d.efinition of prirnltiveness by entrance to en adaptlve zone. (Sf). A lar.r need not be quantltative (although the 1aw of extinctlon is). The contrary tradition ls a rlyth derived, as Egbert Lelgh has eaid, from physics enry. (:Z). ttNowherer you.see, it tekes all the running you can do, to keep ln the sannep].ace.tr (t. Carroll-, lhroueL the Looking Glaes.) (:f). Fisher (r9:o) and others, including Darwin ancl especially Lyell (:-B:e), foreshadoved. the Red Queenrs Hytrlothesis but had no reason to impose the crucial- constraint of constancy, and d.id. not do so. I regartl interference competition as causally a mechanism of resource competition, a proximal rather than ultimate regulator. (3I). Whether the total- group does also depentls on the d.istribution of longevities of the subgrouPs omitted-. (::.). On one leveI, the probability of extinction of a group is related to its own properties beeause d.ifferent groups go extinct for different reasons and so at d.ifferent times. But on the next level, the Red Queen says that having one set of properties is not appreciably better the.n having another because the expected. time to extinction is the se.me. (rg5t+) showed experimentally tor Drosgphilp (36.). Levine and Van Valen !!:t natural selection has rather non-Markovian aspects. Lewontin (1955) later elaborated. the point theoretically but without specific results. (:f). Origination-extinction equilibria are implicit in $frnFsonrs work (fghl+,1953), ancl in Lyel.lrs (fBfZ). I realize that the Red Queenrs Hypothesis is at feast a sirnplification of reality. ft is d.irectly analogous to Newtonrs third lalr of motion. (SA). That the Recl Queen in her simplest gown implies long-term constancy in total evolutionary rate is obvious. For any slngle protein we mugt invoke an analogue of the Central- Limit Theorern: pervasive pleiotropy makes the rate for one protein roughty proportional to that for a1lo or linkage effects have a similar resul-t. For i.nstancer many proteins are to some ertent attachedo ancl the other components of the attachment may change for extraneous reasons, making the previous structure nonoptimal. Dickerson (fg?f) antt others have made a similar point from the other end of the microscoPe. I'the (-fg.) . Stebbins and Lewontin ( L972) actually think that entire argunent is based upon a confilsion between an average and a constant.tt What is remarkable is, however, precisety that the avergge rate (over shorter segnents of a ptrylogeny) is so nearly constant (anong these segments) for a given proteino rather than reflecting a branching rand.om walk or some other Process' 26 L. VAN VALEN

(!9.). More precisely, the precliction is of a monotone relationship of the average rate of protein evolution with the average rate of change arnong phenotypic characters (including the origin of netr eharacters). (hr). Horne (rg6f)n Kohne (rgfo), ohta and Kirnr:ra (r9?r), uzze11 and Pilbeam, (fgtf), Jukes and Hol-mquist (L972). Also, constancy predicts the salne e:cpected. nr-mber of changes in eaeh lineage after the latest conmon ancestor. The data for hemoglobins in the Atlas (Dayhoff, 1]72) seem inconsistent with this expectation. The assumption of total constancy leads to the expecta'tion, presented seriously by D. Boulter (tglZ) and. Ranshav ei al-. (1972) that angiosperms originated. in the early or mid.d.le Paleozoic. (l+2). The approach used the protein sequenee data of the &fes-'195p edition, a^ndprobability estimates of various alternative placental phylogenies as determined. bY mYself. (hf). Probability in the sense of a propensity, a property of any single lineage. groupe wlth respect can depend. on the (!.L). the rank-order of d.ifferent io & choice of w(t). It is an almoet univereal raisteJre tU think that evolutlon 1oca]Iy marcimlzes fitness. Evolutionary fitness le ft except to some populatlon geneticists, but evolutlon doesnrt marclmizE it. Selection at any 1evel local1y maxinizes momentary. fltness for that level' but the optima of different levels need not eoincide. Thrs is obvlous betneen prezygotic and inclividual selection trut is equally true for higher levels. Indivictual selection, the most important evolutionary force' can decrease F1 until extinctlon by, e.B. r foz'cing the occupation of only a temporary rrfche. record-h3l_lo* been for,md.by J.F. University of l(ansas (!t). The tatest futtgn* (tatts at l-971 and. L972 meetings of the Society of Vertebrate Paleontology). 46). Lewontfn (f96f), Warburton (f96?), ancl Maynaril Snith (fgre) harre mad.e applications of gane theory to evolution within the usual evolutionary r'ranework.

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