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Supplementary Information 1 Supplementary information for “Bayesian Morphological Clock Methods Resurrect Placoderm Monophyly and Reveal Rapid Evolution in the Early History of Jawed Vertebrates.” Benedict King, Tuo Qiao, Michael S.Y. Lee, Min Zhu, John A. Long Contents 2-5 Figures S1-S4 6 Prior distributions 7-13 Taxon list 14 Stratigraphic ranges used in sampling test 15-63 Character list 64-70 Supplementary references 2 Figure S1. Weighted mean evolutionary rates in each time slice in a BEAST2 analysis in which placoderms are constrained to be paraphyletic. The overall pattern of rates is the same as the unconstrained analysis, with higher rates in the Silurian and a subsequent decline. 3 Figure S2. Weighted mean evolutionary rates in each time slice in a BEAST2 analysis in which certain taxa are given an age range rather than a fixed age. The overall pattern of rates is the same as in the focal analysis, with higher rates in the Silurian and a subsequent decline. 4 Figure S3. Weighted mean evolutionary rates in each time slice in a BEAST2 analysis in which all taxa occurring after the Frasnian are deleted. The overall pattern of rates is the same as in the focal analysis, with higher rates in the Silurian and a subsequent decline. 5 Figure S4. Comparison of rate heterogeneity patterns between a tree with placoderm monophyly (constrained) and placoderm paraphyly (constrained). This figure shows that the pattern in figure 6D was not an artefact of constraining the topology. A and B) Guide trees showing the branches on which rates of evolution would be expected to be affected between the two trees (A placoderm monophyly, B placoderm paraphyly). Both topologies were constrained such that the only difference is the root position. Dark grey branches (triangles) would be shortened in the paraphyly tree and black branches (diamonds) lengthened, thus increasing and decreasing rates respectively. Star (with arrow) indicates the root in placoderm paraphyly. C) The pattern of rate heterogeneity in the constrained placoderm monophyly tree resembles that of the unconstrained placoderm monophyly tree (fig. 6D). This shows that the pattern of rate heterogeneity in the constrained paraphyly tree is due to paraphyly and not an artefact of topological constraints. Single and double headed arrows indicate weighted and unweighted mean rates respectively. 6 Priors Origin: Uniform 0-1000 Birth Rate: Lognormal with mean (real space) 0.14 and standard deviation 0.9 The prior on birth rate matches the distribution rates found across living ray-finned fish (Rabosky et al. 2013). Death rate: Exponential with mean 0.1 Sampling rate: Exponential with mean 0.03 The proportion of known species included in the analysis can be used to place an upper bound on the sampling rate. (Sallan and Galimberti 2015) list 1124 Devonian-Mississippian taxa, said to be ~90% of named species, and 531 from the Lochkovian to the Frasnian. The dataset contains 107 and 97 taxa from taxa from these intervals respectively, placing an upper bound in the sampling proportion of between 0.0856. and 0.164. The exponential distribution employed here places the 97.5% quantile at 0.111. This amounts to an uninformative prior since the number of named species is still much lower than the true diversity. Gamma shape: Uniform 0-10 Mean rate: Exponential with mean 0.003 and offset 0.0016 The offset of the exponential sistribution is placed at the rate calculated by taking the mean number of steps per character from the parsimony analysis and dividing by the total branch length obtained when the parsimony tree is time-scaled in R using timePaleoPhy in the R package paleotree (Bapst 2012) with minimum ghost ranges. This provides a minimum rate estimate. The exponential is broad enough that the 95% quantile is at 0.0106, 6.3 times the estimated rate from parsimony. The median of this distribution is 0.0037, the rate generated by dividing the minimum estimate by the proportion of non-missing data. Ucld standard deviation: Exponential with mean 1 7 Taxa, sources formations and age used in analysis Taxon Source(s) Formation Age for analysis Hemicyclaspis (Stensiö 1932) Ludlow, Shropshire. 421 murchisoni Downtownian (Pridoli) Zenaspis salweyi (Stensiö 1932) Lower old red 412 sandstone. Skirrid Fawr, Senni/St Maughans formation Cephalaspis lyelli (Stensiö 1932, White Lower old red 412 1958) sandstone, Glammis Benneviaspis (Janvier 1985a) Ben Nevis formation, 413 holtedahli Red bay group. Boreaspis (Janvier 1985a) Wood bay formation 411 macrorhynchus Norselaspis glacialis (Janvier 1981) Wood bay formation 411 Nectaspis areolate (Wängsjö 1952, Janvier Wood bay formation 411 1981) Procephalaspis (Robertson 1939, Saaremaa, Estonia. 427 oeselensis Denison 1951, Janvier Wenlockian and 1985b) Ludlowian Tremataspis (Robertson 1938a, Saaremaa 427 mammillata Robertson 1938b, Denison 1947, Denison 1951, Janvier 1985b) Waengsjoeaspis (Wängsjö 1952, Janvier Fraenkelryggen 416 excellens 1985a) formation Escuminaspis laticeps (Janvier et al. 2004) Escuminac formation 380 Eugaleaspis changi (Liu 1965, Zhu and Gai Xitun formation, 412 2007) Liaojaoshan Hanyangaspis (Zhu and Gai 2007) Guodingshan 436 guodingshanensis formation. Telychian Polybranchiaspis (Liu 1965, Liu 1975) Xishancun and Xitun 415 liaojiaoshanensis formations Bannhuanaspis (Janvier et al. 1993) Bac Bun formation 411 vukhuci Wenshanaspis (Zhao et al. 2001) Posongchong 409 zhichangensis formation, Wenshan. Pragian Shuyu zhejiangensis (Gai et al. 2011) Maoshan formation. 433 Late Telychian to early Wenlock Polybranchiaspid sp. (Wang et al. 2005) Xishancun and Xitun 415 (histological samples) formations Yunnanolepis sp. (Zhang 1980, Zhu 1996) Xishancun and Xitun 415 (various taxa from formations same formations) Parayunnanolepis (Zhang et al. 2001, Zhu Xitun formation 412 xitunensis et al. 2012) 8 Microbrachius dicki (Hemmings 1978, Long Eday flagstone and 386 et al. 2015) John O’Groats sandstone. Lower- Middle Givetian Bothriolepis sp. (Young 1984) Gogo formation 383 MVP230985 Bothriolepis (Downs and Donoghue Escuminac formation 380 canadensis 2009, Béchard et al. 2014) Pterichthyodes milleri (Hemmings 1978) Achanarras horizon, 389 under upper Stromness flagst. Late Eifelian Remigolepis walkeri (Johanson 1997) Canowindra. 366 Famennian Diandongpetalichthys (Zhu 1991) Xishancun formation 417 liaojiaoshanensis Quasipetalichthys (Liu 1991) Kunming; Shixiagou 385 haikouensis formation, Ninxia. Givetian Eurycaraspis incilis (Liu 1991) Haikou formation. 385 Givetian Lunaspis broili (Gross 1961) Hunsrueck slate. Late 408 Pragian to early Emsian Macropetalichthys (Stensiö 1925, Stensiö Onondaga limetone. 390 rapheidolabis. 1963b, Stensiö 1969) Eifelian (including Macropetalichthys sp. specimens used in 1963 and 1969) Wuttagoonaspis (Ritchie 1973, Miles and Mulga Downs group. 393 fletcheri Young 1977). Emsian-Eifelian AMF53610, AMF53631, AMF53591, Groenlandaspis sp. MVP48873(AMF59808) , Mt. Howitt 385 AMF59814, MVP48877/8 (AMF59811/2), AMF62534A, AMF59809 Cowralepis mclachlani (Ritchie 2005, Carr et al. Merriganowry shale. 383 2009) Late Givetian to early Frasnian Gavinaspis convergens (Dupret et al. 2009) Xitun formation. 412 Sigaspis lepidophora (Goujet 1973) Wood bay formation 412 (extreme base) Kujdanowiaspis (Stensiö 1963a, Dupret Dnister series, Podolia. 411 podolica 2010) Upper Lockhovian- lower Pragian Dicksonosteus arcticus (Goujet 1975, Goujet Wood bay formation 411 1984) 9 Buchanosteus (Burrow and Turner Buchan. Mid-late 408 confertituberculatus 1998, Long et al. 2014) Pragian Parabuchanosteus (White and Toombs Taemas-Wee Jasper 401 murrumbidgeensis 1972, Young 1979, Burrow and Turner 1998) Holonema westolli (Miles 1971) Gogo formation 383 Coccosteus cuspidatus (Miles and Westoll Achanarras and 388 1968) edderton fish bed. Eifelian-Givetain boundary Incisoscutum ritchiei (Dennis and Miles 1981, Gogo formation 383 Giles et al. 2013) Eastmanosteus (Dennis-Bryan 1987) Gogo formation 383 calliaspis Compagopiscis (Gardiner and Miles Gogo formation 383 croucheri 1994) Materpiscis (Long et al. 2008, Gogo formation 383 attenboroughi Trinajstic et al. 2012) Austroptyctodus (Long 1997a) Gogo Formation 383 gardineri Campbellodus (Long 1997a) Gogo formation 383 decipiens Rhamphodopsis (Miles 1967, Long Edderton fish beds. 388 threiplandi 1997b) Eifelian-Givetian boundary Brindabellaspis (Young 1980). Taemas-Wee Jasper 401 stensioi ANUV3247 Romundina stellina (Ørvig 1975, Dupret et Lockhovian. Prince of 415 al. 2014) Wales island. Jagorina pandora (Stensiö 1969, Young Kellwasserkalk, Bad 375 1986) Wildungen. Late Frasnian Gemuendina stuertzi (Gross 1963) Hunsrueck slate 408 Entelognathus (Zhu et al. 2013) Kuanti formation 424 primordialis Janusiscus schultzei (Giles et al. 2015b) Lower member, 415 Kureika formation. Middle Lockhovian. Ramirosuarezia (Pradel et al. 2009) Icla formation. Early 392 boliviana Eifelian Acanthodes bronni (Gross 1935, Watson Lebach ironstone. 298 1937, Miles 1973b, Early Permian Miles 1973a, Coates 1994, Davis et al. 2012, Brazeau and de Winter 2015) Brachyacanthus (Watson 1937) Lower old red 415 scutiger sandstone, Farnell. Lockhovian 10 Brochoadmones milesi (Hanke and Wilson MOTH 415 2006) Cassidiceps (Gagnier and Wilson MOTH 415 vermiculatus 1996) Cheiracanthus (Watson 1937, Miles Middle old red 388 latus/murchisoni 1973a) sandstone, Moray firth. Nodular fish beds, Eifelian-Givetian Climatius reticulatus (Watson 1937, Miles ‘Turin hill’ 415 1973a) Culmacanthus stewarti (Long 1983) Mt Howitt 385 Euthacanthus (Watson 1937, Miles ‘Turin hill’ 415 macnicoli
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