31 J. Paleont., 78(1), 2004, pp. 31–38 Copyright  2004, The Paleontological Society 0022-3360/04/0078-31$03.00 SIMULATIONS OF EVOLUTIONARY RADIATIONS AND THEIR APPLICATION TO UNDERSTANDING THE PROBABILITY OF A CAMBRIAN EXPLOSION JEFFREY LEVINTON, 1 LINDSEY DUBB, 2 AND GREGORY A. WRAY 3 1 Dept. of Ecology and Evolution, State University of New York, Stony Brook 11794, 2 Dept. of Genome Sciences, University of Washington, Seattle 98195, and 3 Dept. of Biology, Duke University, Durham, North Carolina 27708 ABSTRACT—A molecular survey of animal phylogeny (Wray et al., 1996) recovered the presumed correct temporal order of the phylogenetic splits Protostomata-Deuterostomata, Echinodermata-Chordata, and Agnatha-Gnathostomata in studies of six of seven gene sequences. This result raised the question of how this order could be recovered if all of the phyla had appeared in a Cambrian ‘‘explosion’’ of less than 10 m.y., given the expected erratic nature of the molecular ‘‘clock.’’ We simulated trees, and molecular sequence evolution along the trees, under different evolutionary radiation scenarios, with different periods of radiation, relative to times of subsequent evolution. Simulations and phylogenetic analyses of sequences derived from a simulated ‘‘Cambrian explosion’’ of 10– 35 million years did not allow the successful recovery of the correct tree, using neighbor-joining, maximum likelihood, or parsimony methods. Success in recovering phylogenies under a Cambrian divergence scenario (520 million years ago) did not exceed 80 percent without an extended divergence time interval of at least 100 m.y. An increased substitution rate during the initial radiation improved the ability to recover correct phylogenies, especially when the rate was 8–10 times the rate following the radiation. Our results militate against the likelihood of an Early Cambrian or slightly longer explosion of the animal phyla, as apparently supported by the fossil record. Some limitations to these conclusions are discussed. INTRODUCTION W RAY ET AL. (1996) used molecular data to test the Cambrian explosion hypothesis and concluded the divergence of the protostomes and deuterostomes occurred much earlier than the Cambrian, perhaps as deep as 1.2 billion years ago. The echino- derm-chordate split was estimated at approximately one billion years and was separated from the protostome-deuterostome di- vergence by an interval greater than 100 m.y. Thus the divergence of animal phyla was neither Cambrian nor explosive. Subsequent molecular estimates of the Protostome–Deuterostome split have all yielded Precambrian ages; all but two of 13 cited in Levinton (2001) were deeper than 800 m.y.a. (see for example: Ayala et al., 1998; Nikoh, 1997; Bromham et al., 1998; Gu, 1998; Wang, 1998; Hausdorf, 2000; Levinton, 2001). The ages from these es- timates, despite being all Precambrian, cover a discouragingly broad range, which is a probable reflection of differences of meth- odology, different genes employed, and likely real variation in rates and variance of rates of evolution along different branches of the evolutionary tree. We can calculate from the data in Wray et al. (1996) a proba- bility of getting the correct order of appearances of the proto- stome-deuterostome, echinoderm-chordate, and agnathan-gna- thostome evolutionary splits from the seven sequences (Table 1). For example, there are six permutations of order of appearance for the three evolutionary splits mentioned above. Therefore any analysis will get the correct order by chance one out of six times (for some of the genes, we only have two splits, which yield only two permutations). If the genes are independent, the probability of getting the order of appearance of splits correctly is the product of the individual probabilities. Such assumption of independence of estimates among genes yields a probability of 0.00016 that the order of splits we got were achieved by chance alone. If rates of the mitochondrial genes are correlated owing to linkage, but the nuclear genes are independent of each other and independent of the mitochondrial genes, then the probability of obtaining the or- der of evolutionary splits found for the different divergences is 0.0348. This latter assumption is overly conservative, since great spans of time would tend to reveal differences related more to differences in substitution rate among the genes, which are con- siderable. Given the vagaries of the molecular clock, we would not expect to get a correct order of appearance in calculations from such different genes if the animal phyla diverged in just a few million years, as is suggested by the Early Cambrian fossil record, cali- brated by radioisotopic estimates (Bowring et al., 1993). We now have simulated both evolutionary trees and nucleotide sequences and find that it is unlikely that any correct resolution of a tree would be possible under a strict Cambrian explosion scenario. Indeed our evidence suggests that the divergence of the animal phyla likely occurred over a protracted period, possibly greater than 100 million years, which fits previous molecular results (Wray et al., 1996). There are three separable conceptions of the extent of the pe- riod of the diversification of the animal phyla. The extreme Cam- brian explosion hypothesis (Gould, 1995, p. 681) argues that the divergence of the animal phyla ‘‘. . . lasted only 10 million years (from 530–520 million years ago) and featured the first appear- ance in the fossil record of effectively all modern animal phyla, including annelid worms and chordates.’’ This interpretation is based upon a literal interpretation of a large number of animal phyla in the Precambrian, which corresponds to a time interval of 10 million years (Bowring et al., 1993). The late Precambrian divergence hypothesis, in contrast, restricts the divergence of the animal phyla to the latest Vendian and Early Cambrian, which encompasses a rapid appearance of trace fossils and identifiable triploblastic metazoans (Valentine et al., 1996). This hypothesis restricts the protostome-deuterostome branching and diversifica- tion of derived triploblastic metazoan clades to a period of about 35 m.y. (565–530 m.y.a.). Finally, the deep Precambrian hypoth- esis argues that the divergences predate the Vendian, and that the divergences of the triploblastic metazoan clades may have ex- tended over a significant period of time, perhaps over 100 m.y. (Wray et al., 1996; Fortey et al., 1996). The timing and temporal extent of the radiation of the Metazoa must affect our ability to resolve evolutionary relationships of the animal phyla with molecular data (Philippe et al., 1994). With increasing age of the divergence, multiple hits at specific nucle- otide or amino acid sites are more likely, which obscures the informative sequence substitutions needed to resolve relation- ships. Furthermore, as a series of divergences are confined to shorter and shorter periods of time, it stands to reason that the informative amount of evolutionary change will be small, relative to subsequent evolution of the divergent lines. Thus an ancient