Survival and Selection Biases in Early Animal Evolution and a Source of Systematic Overestimation in Molecular Clocks

Home , Amiskwia, Death march, Gnathostomulid, Gwynia, Gwynia capsula, Molecular clock

Survival and selection biases in early animal evolution and a source of systematic overestimation in molecular clocks

Graham E. Budd1 and Richard P. Mann2,3

1 Dept of Earth Sciences, Palaeobiology, Uppsala University, Villavägen 16, Uppsala, Sweden, SE 752 36. [email protected] 2Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom. [email protected] 3The Alan Turing Institute, London NW1 2DB, United Kingdom

1 Abstract

2 Important evolutionary events such as the Cambrian Explosion have inspired many

3 attempts at explanation: why do they happen when they do? What shapes them,

4 and why do they eventually come to an end? However, much less attention has

5 been paid to the idea of a “null hypothesis” – that certain features of such diver-

6 siﬁcations arise simply through their statistical structure. Looking back from our

7 own perspective to the origins of large groups such as the arthropods, or even the

8 animals themselves, will expose features that look causal but are in fact inevitable.

9 Here we review these features with particular regard to the Cambrian explosion. We

10 conclude that the fossil record of the late Ediacaran to Cambrian is very likely to

11 be recording a true evolutionary radiation at this time; and show how the unusually

12 rapid nature of this event leads to characteristic over-estimation of its time of origin

13 by molecular clock methods - an artefact that is likely to apply to other unusually

14 fast radiations too.

16 Keywords: Crown groups, diversiﬁcation rates, the push of the past, molecular

17 clocks, Cambrian explosion.

1 18 Introduction

19 The early evolution of the animals remains a remarkably contentious topic, with a lack

20 of agreement even on fundamental issues such as when it took place. The majority view

21 in the ﬁeld is probably that animals evolved considerably before their undoubted fossil

22 record commenced (e.g. [1][2][3][4][5]). Such a view is based on several lines of evidence:

23 (1) molecular dates, that have consistently placed the timing of (for example) bilaterian

24 origins tens to hundreds of millions of years before the Cambrian [2][4]; (2) biomarkers

25 that have been used to place the origin of sponges in the Cryogenian [6]; (3) a general

26 view about timing involving a necessary period of evolution being required before the

27 fossil record (and its biogeography) can be generated [7][8]; and (4) a view that the fossil

28 record is in general patchy and unlikely to be reliable in any useful way for documenting

29 the precise timing of animal origins (see discussion in [5]).

30 Standing against this sort of view is what is probably the minority one that the fossil

31 record of early animals can be read more or less “as is”, despite its obvious imperfections

32 [9][10][11][12]. In particular, the origin of bilaterian-like trace fossils from later than 560

33 Ma in the late Ediacaran [13] is seen as an important marker that provides a backstop

34 for the latest time of origin of crown-group bilaterians, and which probably indicates the

35 time of entry of stem-group bilaterians into the fossil record. The rapid, but resolvable,

36 appearance of body and trace fossil taxa in the succeeding Terreneuvian Series is thus

37 seen as the unfolding of the crown group bilaterian radiation.

38 It seems remarkable, on the face of it, that so well a documented phenomenon as the

39 Cambrian explosion can be open to such divergent interpretations. One reason why this

40 might be the case is that the basic “ground rules” are diﬀerent in each sort of view. In

41 particular, there is an ancient tradition of viewing the animal phyla as being distinct

42 entities that cannot be easily compared to each other. Thus, it has become quite com-

43 monplace to argue that their morphological origins are essentially independent from each

44 other. Whilst such a view has been articulated in various ways by many people, one

2 Figure 1: A classical image of the parallel emergence of the phyla around the time of the early Cambrian from relatively simple (and thus unfossilisable) ancestors. Reprinted with permission from Bergström (1989) [14].

45 classical image is the striking one of Bergström 1989 (Fig.1; [14]) that shows a series

46 of phyla emerging from a small, slug-like organism (a “procoelomate”) during a “forma-

47 tive interval” (c.f. Valentine’s “roundish ﬂatworm” [15] and the "small, thin" ancestors

48 of Sperling and Stockey [4]). A more extreme version of such ideas is that the earliest

49 bilaterians closely resembled the planktonic larvae of the extant clades (e.g. [16], drawing

50 on the tradition that can be ultimately traced to Haeckel [17]). Buttressed by various

51 geological and developmental arguments, this hypothesis posits that such small, and by

52 their very nature hard-to-preserve tiny animals are meant to persist up many, if not all

53 stem groups that lead to the modern-day crown-group phyla. Hence, the appearance of

54 undoubted bilaterian fossils represents in each case the transition from the unfossilisable

55 proto-phylum member to a full-blown fossilisable taxon. Such a transition could be trig-

56 gered either by an environmental stimulus (typically oxygen levels rising) or presumably

57 by some necessary level of ecological complexity being reached.

58 It is surprisingly diﬃcult to unpack the entire set of assumptions and traditions that

59 lie behind the ﬁrst of these views, but some features stand out and can be critically

3 60 examined. The ﬁrst is the assumption that for all or at least many bilaterian clades,

61 the ancestral state was a small body size which would be diﬃcult to record in the fossil

62 record [18]. Small organisms often lack key features such as complex musculature, body

63 cavities and appendages, and it seems that the critical body length for these purposes is

64 around 1 mm (see discussion in [11]). Many living protostomes are indeed tiny, and some

65 phylogenetic reconstructions have suggested this is ancestral for the clade as a whole [19].

66 Without a reliable and fully-resolved protostome phylogeny, such a view is diﬃcult to

67 assess. Nevertheless, in recent years some relatively large Cambrian members of clades

68 that today consist of meiofaunal organisms have been discovered. Of course, simply

69 ﬁnding a single large member of a clade is not equivalent to demonstrating that large body

70 size is the ancestral state, but it does (considerably) weaken the assumption that small

71 body size must be, especially given evidence that old fossils preserve more plesiomorphic

72 character states than recent taxa do (having had less time to shed them; [20]). Another

73 point of dispute has been the placement of the “Xenacoelomorpha”, a clade that consists

74 of Xenoturbella and acoel and nematodermatid ﬂatworms; diﬀerent analyses have placed

75 them either as the sister group to all other bilaterians [21][22], or as sister group to the

76 Ambulacraria (echinoderms and hemichordates) [23]. It should be stressed, however, that

77 even if such a clade is the sister group to all other bilaterians, it does not immediately

78 follow that its simple morphology must represent the ancestral condition for bilaterians as

79 a whole (as in [21]). Determining this would require detailed character reconstruction at

80 the base of the rest of the bilaterians, which is currently a matter of considerable dispute,

81 and reference to the cnidarian outgroup. In order to present more crisp hypotheses, we

82 shall brieﬂy examine the current evidence for various clades:

83 Annelids, phoronids, sipunculans, brachiopods, molluscs

84 This, the classical “Lophotrochozoa” grouping, may also include entoprocts, bryozoans

85 and nemerteans (for a recent discussion of all of the lophotrochozoans in their broadest

86 sense, see [24]). Most of the included clades have tiny members (e.g. the so-called

4 87 ‘archiannelids’ [25], Gwynia capsula [26] etc) but a secondary derivation of these seems

88 most likely (see e.g. [27][28] for annelids). In general, the lively debate around the origins

89 of this group includes the distinct possibility that fossilisable morphological features such

90 as sclerites and setae are plesiomorphic within them [10][29][30][31].

91 Other spiralians

92 Other protostomes (excluding the ecdysozoans - see below) include the Gnathifera (gnathos-

93 tomulids, rotifers, micrognathozoans, and, it seems, chaetognaths [32]), and the “Roupho-

94 zoa” [33] consisting of platyhelminths and gastrotrichs; these two clades together may

95 be paraphyletic and give rise to the lophotrochozoans (see e.g. the summary of re-

96 cent progress in [34]). Such a reconstruction has been considered to suggest a primitive

97 small body size for the protostomes as a whole [19][33]. In particular, it has been

98 argued [33] that the coelomate condition in the spiralians is conﬁned to the lophotro-

99 chozoans (i.e. annelids, brachiopods, molluscs etc) and arose from within a clade of

100 acoelomate, ﬂatworm-like animals. Once again though, some recent molecular and fossil

101 discoveries have suggested the situation is not so simple. The inclusion of the relatively

102 large, and potentially fossilisable and coelomate chaetognaths within or as sister group of

103 the Gnathifera throws into question the primitive state in this clade ( [35]; c.f. [32][36]);

104 and even in the Rouphozoa, recent suggestions of large (> 10 cm) gastrotrichs in the

105 Cambrian [37] must bring the primitive character state in this clade under question as

106 well.

107 Ecdysozoans

108 The last common ancestor of onychophorans and euarthropods (at least) was a large

109 organism [38][39]. The placement of tardigrades remains uncertain [40][41], but once

110 again a single clade of tiny organisms cannot be automatically assumed to reveal ances-

111 tral states. The plesiomorphic state in the cycloneuralian worms, whether or not they

5 112 are monophyletic, remains uncertain. Of the living clades, it is reasonable to assume that

113 the priapulans are primitively large, and that the loriciferans and kinorhynchs small.

114 However, large Cambrian representatives of both the latter groups have recently been

115 described (i.e. [42][43], although the status of the kinorhynch remains to be conﬁrmed),

116 with the suggestion that the ancestral scalidophorans were also of large size. Even with

117 the assumption of primitive small body size in the nematoideans (nematodes plus ne-

118 matomorphs) then, a large body size for the entire Ecdysozoa is, on the basis of present

119 evidence probably most likely. In addition, the presence of sclerotized cuticle within

120 the entire clade makes its appearance in the small carbonaceous fossil record entirely

121 plausible.

122 Deuterostomes

123 Despite the recent description of a putative meiofaunal deuterostome from the early

124 Cambrian [44], and the possible presence of the Xenacoelomorpha in the clade [23]), an

125 ancestral large body size in at least echinoderms, hemichordates and chordates seems

126 most reasonable. Thus, overall an ancestrally large body size seems most likely for the

127 deuterostomes.

128 It should be clear from the above that an ancestral small body size for large clades

129 of bilaterians cannot straightforwardly be inferred from present day body sizes, and this

130 conclusion becomes even less secure once the fossil record is considered. For example,

131 such a view seems to be directly contradicted by the reconstruction of the stem group in

132 the arthropods, where we know that, far from being tiny, many stem group arthropods

133 were in fact very large [45][46][47].

134 Body size is by no means the only marker for preservability, and perhaps not even

135 a very good one. However, the trace fossil record is one that is tied to body size, and

136 it is indeed diﬃcult to imagine a high abundance of relatively large bilaterians existing

137 without any sort of perceivable trace fossil record. Even if (as has been argued) ancestral

138 deuterostomes, for example, were sessile or semi-sessile [48], it does not follow that no

6 139 trace of them would be left in the record. Furthermore, even if an ancestral small organism

140 (or one that could not leave trace fossils) was inferred, it would be required to stay in

141 this state without any ecological innovation for many millions of years. Trace fossils from

142 the terminal Ediacaran are not always particularly small [49], and – if we accept that

143 they represent stem-group, or even early crown-group bilaterians – it follows that some

144 of these were of large size too.

145 Even if we accept that ancestral bilaterians were small, the implication for the fossil

146 record would be that as the stem-group members of many phyla crossed into the Cam-

147 brian, they would simultaneously each have to develop into large animals, in a highly

148 unparsimonious way. Finally, it should be noted that at least putative trace fossils of

149 meiofaunal organisms have been reported from Brazil [50], suggesting (if correctly as-

150 signed) that even tiny organisms might leave traces.

151 The problem of suggesting multiple attainments of large and fossilisable body size

152 as a solution to the problem of the lack of Ediacaran crown group bilaterians is partly

153 concealed by the low sampling of present day diversity in summary cladograms, because

154 phyla are often (and perforce) represented by a single lineage (see e.g. [5]). However,

155 if the crown group of any particular clade of large animals is thought to have emerged

156 before the Cambrian, then all crown group lineages of that phylum crossing the boundary

157 would themselves have to independently develop large (and complex) organisation. This

158 itself is striking: why would be the case that of all the implied crown group bilaterian

159 diversity in the Precambrian, no lineage ever hit upon a way of attaining large body

160 size? Such arguments have recently gained new potency because of the growing and

161 widespread recognition that the large Ediacaran organisms indeed lie within stem groups

162 to various animal groups (cnidarians, ctenophores, bilaterians, etc [51][52] [53][54]).

163 If, then, the presence of large stem-group animals (complete with their at least putative

164 trace fossils (e.g. [55][56]) is acknowledged during the Ediacaran, why are there no crown-

165 group bilaterians? We believe that the combination of these factors makes the presence

166 of bilaterians deep in the Ediacaran or even earlier very unlikely indeed.

7 167 Such a view receives substantial support from birth-death modelling [57][58], which

168 suggests that under most conditions, crown groups emerge rapidly and swamp their stem

169 groups in short order. In such a view, if the crown group bilaterians emerged during the

170 early Ediacaran (c.f. [2]), then modelling would suggest that by the time of the opening of

171 the Cambrian, there should be many thousands of species, diversiﬁed into many diﬀerent

172 crown group lineages. Yet, somehow, not a single body fossil of an indisputable crown-

173 group bilaterian has ever been found before the Cambrian. Just as strikingly, when

174 animals do appear in the fossil record in the Cambrian, the fossil record develops in a

175 way that makes it look as if a real diversiﬁcation is going on (see e.g. [59][60][61][62][63];

176 a pattern that is consonant across the small skeletal, carbonaceous and trace fossil records

177 [63]). Such a pattern has also been noted in the unfolding of the early angiosperm fossil

178 record [64], despite molecular clock evidence for a deeper origin [65][66]. No satisfactory

179 explanation of such patterns has been undertaken. In the rest of this contribution, then,

180 we take as our view that crown-group bilaterians emerged late (probably just before the

181 beginning of the Cambrian). We wish to examine two features of this emergence, both

182 through birth-death modelling: i) why do body plan features appear to emerge so rapidly

183 in the Cambrian, and ii) why might molecular clocks be overestimating the timing of the

184 origins of clades?

185 Birth-death models and their biases

186 Patterns of diversiﬁcation have been long studied through birth-death models, with im-

187 portant early papers being [67] and [68]; with very signiﬁcant early contributions by

188 Raup, whose 1983 paper [69] on the early origins of major groups is an underappreci-

189 ated classic (for an update of this work, and a general discussion of the fossil record and

190 birth-death models, see [58]. Recent important developments in this general area include

191 e.g. [70][71]). Simple homogeneous birth-death models assign constant rates of extinction

192 and speciation to a group; an end member is the so-called Yule process that has only

8 Figure 2: Two "gambler’s ruin" simulations with an exponential birth-death process. A Starting with 1 species; B starting with 10 species. Red lines are successful clades that manage to escape from the absorbing boundary of extinction; black ones, clades that go extinct. In the case of initially small clades (A), most rapidly go extinct without reaching a substantial size. Initially larger clades (B) more often survive; note that those that go extinct tend to behave like the survivors until they rather rapidly collapse to extinction.

193 speciation and no extinction [72]. However, despite the presence of these constants in

194 the models, a wide range of stochastic outcomes can emerge from them (compare: even

195 if one has a constant 1 in 6 chance of rolling a 6 with an unbiased die, the number of

196 sixes actually rolled in a trial set of 20 rolls will vary greatly from one trial to the next).

197 In particular, if there is any sort of signiﬁcant extinction rate, then clades are logically

198 unlikely to survive for long. Clades that do survive to the present from a distant time

199 in the past (as Cambrian clades would represent) thus represent a small subset of all

200 possible clades. Such survival can be compared to a classical "gambler’s ruin" process

201 (c.f. page 45 ﬀ. of ref. [73]), with the critical diﬀerence being that in an exponential

202 process (as opposed to the simple random walk of Raup), it is possible (rarely) to escape

203 from the absorbing boundary that extinction represents (Fig.2).

204 Such survivors thus represent a very biased subset of all possible outcomes of the

205 birth-death process, and the most important component of their peculiar characteristics

206 was identiﬁed by Nee et al.(1994) [67] as the “push of the past”. Essentially, the push

9 207 of the past is the chance higher-than-normal rate of diversiﬁcation present in the early

208 species of a successful clade. As discussed by Budd and Mann (2018) [58], this early burst

209 of diversiﬁcation can be seen by considering the observed rate in species as a whole (i.e.

210 including both extinct species and lineages leading to modern groups).

211 The push of the past has been almost entirely ignored because most phylogenetic work

212 involving birth-death models has involved the modelling of the so-called reconstructed

213 evolutionary process. This essentially involves the modelling of the “lineages” that give

214 rise to modern day diversity, and which can be reconstructed backwards in time through

215 the coalescence process (e.g. [74]). Such lineages are, in short, those represented by

216 the terminal and internal branches of a phylogeny. Rather surprisingly these lineages,

217 although speciating twice as fast as the background rate [74][58], show little variation of

218 rate until the present is nearly reached, and thus show no “push of the past” eﬀect, at least

219 as deﬁned by [67][58], even though early diversiﬁcation rate changes along lineages are

220 sometimes referred to as such (e.g. [75]). Early high rates of lineage creation, then, must

221 rely on a diﬀerent feature. Various explanations have been posited for observed instances

222 of such early bursts of lineage diversiﬁcation [76][77][78][79], and the general pattern has

223 been referred to as the “large clade eﬀect” (LCE [58]). Whatever their underlying causes,

224 early bursts can again be seen as features of the general stochasticity of birth-death

225 processes ( [58]; c.f. [80]). Nevertheless, this is not a survivorship bias, because all clades

226 that have lineages must tautologically have survived to the present day. Survivorship

227 could occur by only one lineage of a particular clade living in the present day, or by

228 many thousands, even with the same diversiﬁcation parameters. If one examines only

229 the large examples out of these many possibilities, it will be seen that they will generally

230 have created a larger-than-expected number of lineages early on in their history, giving

231 a characteristic “bulge” in the lineage-through-time (LTT) plot of the clade (Fig.3; c.f.

232 ﬁg. 7 of Budd and Mann 2018). This, then, is a selection, not survivorship bias of the

233 process (c.f. [81], who discusses the perils of treating large clades as representative of the

234 evolutionary process as a whole).

10 Figure 3: The exponential probability distribution of Yule-process generated crown group sizes for crown groups of age 100 Ma, mean size of 200 and birth rate of 0.0530. The distribution is broadly divided into small (left), medium (middle) and large (right) clades. The middle section runs from clades that are twice too large to half too large, and contains half of all the trees. Representative lineage-through-time (LTT) plots are provided for each sector (compare Fig.6) with retrospective time in Myrs on the x axis and the number of lineages of the y axis.

11 235 A few papers have explicitly examined these early diversiﬁcation bursts considered

236 as features of unusually large clades (e.g. [58][80] [82]). However, they are normally

237 subsumed under a diﬀerent sort of category, i.e. “diversity-dependent” diversiﬁcation.

238 Such models make the assumption that as a characteristic carrying capacity of a particular

239 clade is reached, the rate of diversiﬁcation will asymptotically slow down, until a steady

240 state is reached. Although we are rather skeptical towards the biological reality of the

241 ecological underpinnings of such models, we note that in any case the typical patterns

242 of the LCE and DDD closely resemble each other, and it is not clear that the two can

243 be easily distinguished ( [58][57]). Two sorts of bias can thus be distinguished in birth

244 death modelling of the evolutionary process: the push of the past survivorship bias of the

245 process as a whole, and the large clade eﬀect selection bias that further emerges by only

246 examining unusually large living clades. We now wish to explore some of the features

247 that these biases introduce into patterns of evolution, in particular the rapid formation

248 of body plans and the concept of “key innovations”; and how they might aﬀect molecular

249 clocks.

250 Body plans and key innovations

251 In order to introduce the rates of morphological (and, indeed, molecular) evolution into

252 discussions about trees based on birth-death models, it is probably necessary to make

253 a further assumption, i.e. that there is some sort of relationship between rates of spe-

254 ciation and rates of molecular and/or morphological change. Such a relationship seems

255 intuitive, because eventually all species must be distinguished by certain morphological

256 and molecular synapomorphies, but the empirical evidence for this has been mixed (see

257 e.g. [83]). One potential reason for this is that molecular phylogenies are perforce based

258 on the reconstructed evolutionary process which cannot include extinctions within it (lin-

259 eages, by deﬁnition, cannot include extinction). Any examination of rates of molecular

260 or phenotypic change in such trees can thus only examine the relationship between such

12 261 rates and the rate of lineage production; and the latter will bear little resemblance to

262 the rate of true speciation that includes all extinct taxa too. Only if extinction rates are

263 very low will there be a reasonably close relationship between the two, because then any

264 speciation event in the past will have a good chance of giving rise to a lineage.

265 Early bursts of molecular and morphological evolution: the case

266 of the arthropods

267 We explore some of the problems discussed above by examining the important study of

268 rates of evolution of arthropods by Lee et al. 2013 [84]. They showed that if the time of

269 origin of the arthropods was ﬁxed by the fossil record at around 555Ma, then arthropods

270 evolved very rapidly during the Cambrian, with initially high rates of both molecular

271 and morphological change across the early lineages. Arthropods, above all other clades,

272 are likely to be a “large clade” in the sense of [58], given that they are much larger than

273 any other clade of a comparable age that does not include them. This view is supported

274 by the LTT plot that can be reconstructed from the data of Lee et al. 2013 [84] (Fig.

275 4), showing a large early bulge. In addition, because of the inevitably very low sampling

276 rate (c. 50 taxa across the probable millions of extant species), the LTT shows a rapid

277 ﬂattening out as the present is approached (i.e. given true present day diversity, one

278 would except many more lineages actually to have been created as the present day is

279 approached).

280 A notable feature of the data provided by Lee et al. (2013) [84] is that when one

281 compares the rate of lineage creation to the rates of molecular/morphological evolution,

282 they counter-balance each other, so that the mean number of molecular (or morphological)

283 changes per lineage creation remains constant through time. Thus, the curve showing

284 the rate of decline of lineage creation (Fig.4B) is very similar to their curves showing

285 the rate of decline of morphological/molecular change (their ﬁg. 3). Furthermore, they

286 show that the size of the initial burst of evolution is dependent on where the root of

13 Figure 4: A The "lineage-through-time" (LTT) plot reconstructed from the data of Lee et al. 2013 [84]. Note, owing to (inevitable) undersampling, that the LTT plot flattens out towards the recent, but that it starts with a pronounced bulge characteristic of large clades. B The reconstructed rate of lineage production through time. Each point is the inverse of total branch length between successive lineage creations; a 50 Myrs smoothed average line is also included. Compare this effect with that rate of slow-down of molecular and morphological rates of change in Lee et al. 2013, fig. 3.

287 tree is placed; if deeper, the initial rates are lower. These patterns imply that lineage

288 creation rate (as opposed to speciation rate) and evolution rates are not independent

289 (c.f. [85][86]). Why might the creation of a lineage be accompanied a ﬁxed amount of

290 molecular and morphological change?

291 If one makes the assumption that rates of morphological/molecular change correlate

292 in some sense with rates of speciation (see above and discussion in [58]), it follows that

293 the large clade eﬀect would not predict such a slowing down of rates along the lineages,

294 which only have a slightly elevated initial speciation rate in large clades compared to

295 normal ones [58]. Several other possibilities present themselves, however. The ﬁrst is

296 that the root of the arthropods is really much deeper than the fossil record suggests (but

297 see below), and that artiﬁcially compressing their early evolution has the side eﬀect of

298 increasing early rates of evolution too. The second is that there really is a large clade

299 eﬀect (i.e. early arthropod lineages do appear much faster than expected), and that the

14 300 algorithms used for distributing character change across the tree do not take this into

301 account (and thus distribute character change to lineages as if they all had the same mean

302 length). Finally, there is the possibility that there is an as yet poorly-understood lower-

303 level process (involving ecology, competition etc) that really does connect rate of lineage

304 creation with that of underlying evolutionary change. Although we have not managed

305 to penetrate this question adequately, we suspect that the second of these possibilities

306 is likely to be correct, and that, along with other artefacts that we demonstrate below,

307 standard treatment of large clades will generate artefactual high rates of evolutionary

308 change along their early branches. Despite the diﬃculties of understanding what happens

309 along the lineages of a clade, it nevertheless remains likely that successful clades will show

310 high rates of evolutionary change in their early history when averaged across both plesions

311 and lineages, because of the overall push of the past eﬀect [58], but concentrated into the

312 early lineage(s). Such rapid early evolution will however, be a necessary feature of the

313 emergence of a successful clade, and not its cause, as in the ‘key innovation’ concept (see

314 discussion in e.g. [38]). One further selection bias may enter here. Phyla are commonly

315 thought of as (often) large clades that are morphologically distinct from each other.

316 Unusually large clades should have short stem groups [58][57], and all thing being equal

317 this should imply a relatively short period of time for evolutionary change to accumulate;

318 yet the distinctness criterion for phyla suggests the opposite, since the accumulation of

319 distinctiveness occurs by extinction in the stem group [59][87] and therefore selecting

320 phyla through distinctiveness selects in favour of longer stem groups. Although the overall

321 eﬀect of such a bias is uncertain, it should probably be considered as an important factor

322 when trying to understand the disparity diﬀerences between phyla when considered as

323 distinct evolutionary units (e.g. [87]).

15 324 Molecular clocks and the large clade eﬀect

325 Because almost all molecular data are from living organisms, it follows that they bear

326 largely upon the reconstructed evolutionary process. A further consequence is thus that

327 molecular data are in principle not aﬀected by changes in rates of speciation, which are

328 largely constant along the lineages, even in large clades (until the recent is approached at

329 least [58]). However, we have previously suggested that molecular reconstruction might

330 nevertheless be more subtly affected by the large clade effect [58]. Whilst this influence

331 is potentially wide-ranging, here we focus on one part of it, which is the inﬂuence of the

332 LCE on molecular clock estimates.

333 Modern-day molecular clocks [88] are typically (but not universally – e.g. [89]) con-

334 structed using approaches that simultaneously estimate a phylogenetic reconstruction,

335 branching model and rate of substitution along the lineages, often employing so-called

336 “relaxed clock” methods (e.g. [90][91]). It is rather noticeable that in many cases, molec-

337 ular clocks considerably over-estimate times of clade origins when measured against the

338 fossil record, and the origin of the bilaterians has been one of several classical instances

339 of this pattern (for the case of angiosperms, see e.g. [64] and the particularly trenchant

340 discussion by [92]). Often such mismatches arise through rather imprecise or inadequate

341 calibration of clocks [93][94], and indeed better attention to calibration has certainly

342 narrowed the fossil-molecular clock gap in many instances (see e.g. [95]). Even so, de-

343 spite rather close interrogation, molecular clock estimates of bilaterian origins, although

344 exhibiting a considerable range of possible dates, still ﬁrmly place them deep in the

345 Ediacaran or even earlier, even when the error bars on the estimates are taken into

346 account [5][2].

347 Many possible reasons for problems with molecular clocks have been discussed, includ-

348 ing those concerning heterogeneous molecular evolution [96], date calibration [93][97] and

349 various issues of sampling and tree priors [98][99][100][101]. Without denying any of

350 these issues, many of which can and have been accounted for, we wish here to take

16 351 a somewhat broader perspective of the relationship between tree model and molecular

352 clock results. Given our reasoning above, we are led to ask the question: “given an ap-

353 parently reliable fossil record of animals, why might molecular clocks be systematically

354 inaccurate here?”, which we appreciate is the opposite of the one normally taken, which

355 is, rather, to examine ways in which the fossil record might be misleading. Here, then,

356 we wish to focus on one topic in particular: the role of unusual clade size in molecular

357 clock bias.

358 Lineage-through-time plots and times of origins: general consid-

359 erations

360 By reconstructing a tree, and with some dating constraint on it (by estimating some

361 combination of the rate of molecular change, ages of tips or of nodes), the lineage-through-

362 time (LTT) plot should be expected to yield an estimate of the base of the clade (Fig.

363 5). For normally-sized clades, the LTT plot when not close to the present is a straight

364 line on a semi-log plot, with slope λ − µ (where λ is the unit rate of speciation and µ the

365 unit rate of extinction). However, in an unusually large clade, the early part of the LTT

366 shows a much higher slope than that of the central part (which remains of slope λ − µ),

367 implying the lineages accumulate faster than one would expect. Extrapolation from the

368 central part of the plot might thus be expected to yield an erroneously deeper origin of

369 the clade (Fig.5). In the case of the Yule process, this is a straightforward calculation

370 as the expected time to produce a clade of N species is ln(N)/λ and to produce a clade

371 of αN species is ln(αN)/λ; the expected time diﬀerence is thus ln(α)/λ.

372 Bayesian phylogenetic inference packages such as BEAST and BEAST2 can employ a

373 birth-death (or Yule) model for their clade inference (it has recently been shown, however,

374 that initial model selection has little eﬀect on the results obtained from BEAST2 at

375 least [102]). Such inference discovers the most (a posteriori) likely trees for any given set

376 of input data. A priori, this will favour trees with an early straight-line LTT, because this

17 Figure 5: The possibilities of poor inference from unusually large clades. The solid line represents the true LTT plot for an usually large clade that would normally have been expected to produce c. 60 species in the present after diversifying for 100 Ma (diversiﬁcation rate 0.0407), but in fact produced 200. Extrapolating the asymptoptic slope of of the curve at the recent backwards assuming the clade was a normal size (dashed line ending in blue dot) would imply an origin at 130 Ma. For simplicity, we have chosen a Yule process, but a similar principle would hold for a birth-death model too. The dotted line might be inferred if the root was known, but not the diversiﬁcation rate.

18 377 is the central outcome of the birth-death (or Yule) process. If the true process led, however

378 to an unusually large (or small) clade, then the molecular data may be in tension with this

379 central expectation. In other words, the shape of the tree, and the rate of accumulation

380 of change upon it, will be telling diﬀerent stories. In such a scenario (we predict), the

381 inferred time of origin of the clade will emerge as a compromise between the two, with

382 the exact balance being determined by the relative weight given to each and the relative

383 ﬂexibility of each prior. Even if the time of origin of a clade is well known, and its number

384 of species in the present, the true extent of the LCE might not be inferred, because it

385 is possible to reconstruct the generating process by a higher background diversiﬁcation

386 rate.

387 BEAST2 recovery of simulated data

388 We have chosen to examine the inﬂuence of the LCE on molecular clocks by a simulation

389 approach. Using the TreeSim package in R [103] we ﬁrst simulated eight sets of ﬁve trees

390 (Table1), each with 200 terminal taxa. Each tree was ﬁxed to a height of 100 Myrs (to

391 the most recent common ancestor). The diversiﬁcation rate in each set was chosen so

392 that the actual 200 taxa in each of the sets of ﬁve trees represented 20, 10, 5, 2, 1, 0.5, 0.2

393 and 0.1 times the number that would be expected given the diversiﬁcation parameters

394 chosen. For further simplicity, a Yule process (i.e. with no extinction) was chosen for the

395 tree generation. After generating these trees we further simulated a process of molecular

396 evolution along the branches from the most recent common ancestor to the terminal taxa.

397 For each tree we simulated 1000 nucleotide sites, with a homogeneous Poisson process

398 for nucleotide substitutions, utilising a substitution rate of 0.03 per site per million years

399 (i.e. 0.01 per possible transition), using the phytools R package [104].

400 For the BEAST2 recovery of the simulated data, we set a strict clock rate to the

401 true value of 0.03, a Yule process tree prior, and a MCMC chain of 10,000,000 samples,

402 thinned to 10,000 trees for further analysis with Tracer [105].

403 For illustrative purposes, we show an exemplar simulated clade of each set, together

19 Set nr. Nr. of taxa Tree height Div. rate (d) Expected nr. of taxa given d 1 200 100 0.0220 10 (clade 20× too big) 2 200 100 0.0294 20 (10×) 3 200 100 0.0366 40 (5×) 4 200 100 0.0459 100 (2×) 5 200 100 0.0530 200 (1×) 6 200 100 0.0599 400 (0.5×) 7 200 100 0.0691 1000 (0.2×) 8 200 100 0.0760 2000 (0.1×)

Table 1: The parameters of each set of ﬁve simulated Yule-process trees (giving forty simulations in total).

404 with its LTT plot (Fig.6; (d) is the expected clade size for the given diversiﬁcation rate).

405 Note that in the smaller-than-expected clades (Fig6 a-c), there is a delayed lineage

406 diversiﬁcation, leading to a depressed early LTT; whereas in the larger-than-expected

407 clades (6 e-h), the opposite pertains: more lineages emerge early on, and there is an

408 increasingly pronounced bulge in the early LTT plot.

409 Results

410 We show the results of inference of tree height on all 40 sets of simulated data in Fig.7,

411 grouped by (true) relative clade size. In each set of ﬁve, we show the 95% High Posterior

412 Density (HPD) interval and the mean of the ﬁve means. In addition, we plot the naïve

413 expected value of the tree height based on Fig.5. All the outputs reached a satisfactory

414 value (i.e. >200) of eﬀective sample size (ESS) for the tree height parameter. All the

415 other parameters for all runs had satisfactory ESS except for two of the twenty-times

416 too large clades. The most notable result of the plot is that in the large clade cases, the

417 tree height is consistently overestimated, and in the small clade cases, underestimated,

418 with a clear trend of eﬀect between them. In each case, as predicted, the mean of the

419 mean plot falls between the true value of 100 Myrs and the height calculated from a naïve

420 extrapolation of the recent diversiﬁcation rate as shown in Fig5. We note two signiﬁcant

421 sources of stochasticity: that of the individual HPD intervals, and variation between

20 Figure 6: Representative trees and LTT plots for clades that are (A) 0.1 (B) 0.2 (C) 0.5 (D) 1 (E) 2 (F) 5 (G) 10 and (H) 20 times too large for their diversiﬁcation parameters (see Table1). Note how the LTT plots move from concavity to convexity.

21 422 the ﬁve simulations of each parameter set that result from the inherent stochasticity of

423 the Yule process. Despite these sources of variability though, the overall trend from

424 larger-than-expected to smaller-than-expected clades is very clear.

425 Discussion

426 As predicted, choosing to examine trees with known unusual features exerted pressure

427 on the reconstruction process (c.f. the closing comments of [96]), and the clear outcome

428 was that larger-than-expected clades had their heights overestimated by BEAST2, with

429 smaller-than-expected clades being underestimated. Although the values we chose for our

430 simulations were illustrative, the scale factors are absolute, and the time scale is arbitrary,

431 in the sense that one time unit can represent any amount of real time. It is thus possible

432 to translate our results directly into a timescale that would be comparable to that of the

433 Cambrian explosion. For example, for a clade that was ﬁve times too big and had its real

434 origin at c. 540 Ma, our results suggest that an origin at c. 650 Ma would be inferred

435 (the extrapolated value from Fig5 would be c. 800 Ma, which represents an approximate

436 maximum expected molecular clock overshoot).

437 For any given birth-death or Yule diversiﬁcation process, there is, from Fig.3, an

438 exponential distribution for the size of surviving clades. Approximately half of all these

439 trees lie between 0.5 and 2 times the expected clade size. Larger or smaller clades rapidly

440 become less likely: for example, the x20 example is, in our model, exceptionally unlikely.

441 However, other clades are much more likely: approx. 14% are at least 2 times too large;

442 and 5% are at least 3 times too large. On the small side, almost 40% of clades are less

443 than half the mean size, and 28% are less than one third the mean size.

444 The relative commonness of small clades means that the deviation from the true tree

445 height value is less than that for the equivalent large clade (in our examples, the 10 times

446 too small clade is approximately 10 Myrs underestimated, whereas the 10x too large clade

447 is c. 50 Myrs overestimated. This might lead one to the expectation that molecular clocks

448 should consistently underestimate clade origin times, rather than overestimate them as is

22 Figure 7: Inference errors of tree height in BEAST2. Eight groups of five inferences corresponding to the diversifications in Table1 are shown as a plot of inferred tree height (i.e crown group age) against relative clade size. The true tree height in each case is 100 Ma (dashed line). The red dots represent the mean of the means of the five runs in each set, and the blue dots represent the extrapolated inferred tree height from Fig.5. Note that in each case (except the normal sized clade where all three are close), the red dots lie between the real value and the blue dot. The vertical black lines represent the 95% HPD intervals in each run.

23 449 commonly supposed. However, three important features suggest this would be unlikely.

450 The ﬁrst is that the smaller eﬀect of small clades is less likely to be noticeable; the second

451 is that because large clades have so many species in them, a randomly chosen species is

452 likely to fall within one (indeed, the expected size of a clade from which any randomly

453 chosen species is selected from is twice the average [58]). The third, and most important

454 reason, is that large and charismatic clades are consistently studied at the expense of

455 the smaller, less interesting ones. Whilst it is understandably sometimes stated that

456 these sorts of clades are representative of the diversiﬁcation process as a whole (e.g. [84]),

457 our results show clearly that they are not. Whilst we have not carried out a survey of

458 empirical clade sizes versus molecular clock mismatches of their origins, it is notable that

459 many clades that exemplify this phenomenon are notably larger than their sister groups.

460 For example: animals have millions of species, but choanoﬂagellates c. 125; birds have c.

461 10,000 and crocodylians c. 23; angiosperms c. 300,000 and gymnosperms c. 1,000. This

462 selection bias means that large, charismatic clades are precisely those that will show the

463 most striking pathologies in their molecular clock behaviours. Indeed, molecular clock

464 dating for conifers [65] and crocodylians does not exhibit the same sort of mismatch (for

465 crocodylians, the molecular clock might even underestimate [106] the fossil record, as

466 might be predicted).

467 In the light of our results, the mismatch between fossil-based estimates of perhaps

468 crown group bilaterians at c. 545 Ma compared to a cautious molecular clock estimate

469 of 630 Ma [2] could be explained with bilaterians being 3-5 times too large given their

470 diversiﬁcation parameters. However, even this estimate is likely to be generous to molec-

471 ular clock estimates, because our simulations used a strict clock that we also used in our

472 BEAST2 inferences. In reality, such BEAST2 analyses would not know the true rate, nor

473 would it likely be to be strict.

474 We note that, although the direction of this eﬀect is clear from our results, its precise

475 value will depend on a set of features that we have not explored. For example, the degree

476 of inﬂuence of the clock prior versus the tree prior will be aﬀected by the amount of useful

24 477 molecular data included in the analysis. In addition, most molecular clock analyses are

478 calibrated by tip or node dating (or some combination) rather than a direct estimate of

479 the clock rate, which will typically be relaxed. In general, a relaxed clock will considerably

480 increase the LCE overestimate of clade heights, because the more ﬂexible and less-well

481 constrained molecular clock rate will do a less good job of compensating for the rapid

482 appearance of early lineages. How such overestimation is compensated for by accurate

483 fossil-based dating of early nodes remains to be investigated.

484 Large clades of more than 3 times the expected size represent some 5% of all surviving

485 clades in our simulations. However, the Yule process, or even homogeneous birth-death

486 process, may not necessarily reﬂect the true dynamics of clade diversiﬁcation. For exam-

487 ple, if the popular diversity-dependent diversiﬁcation model [77] is an intrinsic part of the

488 diversiﬁcation process, then, rather than outliers of the diversiﬁcation process (albeit not

489 particularly rare ones) such clades with their distinctive early LTT bulge would be normal

490 clades, and thus, we would expect these sorts of pathologies to be very widespread. In

491 other words, present day methods assume a central expectation of an exponential process

492 with constant rate of lineage rate, but any source of over-dispersion relative to this prior

493 expectation (whether statistical or ecological/evolutionary in origin) is likely to produce

494 systematic errors of the sort we have outlined here.

495 Summary

496 Despite its imperfections, the fossil record of early animal evolution is highly unlikely to

497 be as grossly in error as many molecular clock estimates indicate. In particular, neither

498 small size nor rarity are at all likely to account for the purported non-appearance of crown

499 group bilaterians in the Ediacaran or earlier. In addition, the apparent orderly appearance

500 of taxa in the Cambrian is strongly suggestive of a real-time evolutionary event being

501 recorded. Here we have outlined a variety of survival and selection biases that can aﬀect

502 our understanding of major evolutionary radiations such as the Cambrian explosion, that

25 503 include the disparity of the phyla. Most importantly, such biases include clade size for

504 charismatic taxa such as the bilaterians and indeed animals as a whole; our analysis here

505 suggests that without taking into account their usual features, molecular clock estimates

506 will tend to be biased in a way that can potentially explain the mismatch between fossil

507 and molecular clock origins of large clades. In other words, the problems with molecular

508 clocks might not just revolve around adequate calibration [95] from the fossil record, but

509 also include oversight of fundamental aspects of the statistics of phylogenetic inference

510 that may be harder to account for [96].

511 Acknowledgements

512 We are very grateful to Tanja Stadler, Rachel Warnock and Tim Vaughan for discussions

513 about inference and BEAST/BEAST2, and in particular for their suggestions about how

514 to test large clade biases. This work was funded by the Swedish Research Council (VR:

515 grant 621-2011-4703 to G.E.B.).

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