C S D T Tracy A. Heath Ecology, Evolution, & Organismal Biology Iowa State University Taming the BEAST Workshop Engelberg, Switzerland July 1, 2016 A T-S M Phylogenies with branch lengths proportional to time provide more information about evolutionary history than unrooted trees with branch lengths in units of substitutions/site. Oligocene Miocene Plio Pleis 0.03 substitutions/site 20 0 Time (My) (silhouette images from http://phylopic.org) A T-S M Phylogenetic divergence-time Historical biogeography Molecular evolution estimation • What was the spacial and climatic environment of ancient angiosperms? (Nabholz, Glemin, Galtier. MBE 2008) • How has mammalian body-size Diversication changed over time? (Antonelli & Sanmartin. Syst. Biol. 2011) • Is diversification in Caribbean Trait evolution anoles correlated with ecological opportunity? • How has the rate of molecular evolution changed across the Tree of Life? Anolis fowleri (image by L. Mahler) (Lartillot & Delsuc. Evolution 2012) (Mahler, Revell, Glor, & Losos. Evolution 2010) Understanding Evolutionary Processes P N T Sequence data are only informative on relative rates & times Node-time priors cannot give precise estimates of absolute node ages We need external information (like fossils) to calibrate or scale the tree to absolute time Node Age Priors C D T Fossils (or other data) are necessary to estimate absolute node ages no information There is in ABC the sequence data for 10% absolute time 10% Uncertainty in the 20% N 200 My placement of fossils 10% 400 My C D Bayesian inference is well suited to accommodating uncertainty in the age of the calibration node Divergence times are calibrated by placing ABC parametric densities on internal nodes offset by age N estimates from the fossil 200 My record Density Age A F C Misplaced fossils can affect node age estimates throughout the tree – if the fossil is older than its presumed MRCA Calibrating the Tree (figure from Benton & Donoghue Mol. Biol. Evol. 2007) F C Age estimates from fossils can provide minimum time constraints for internal nodes Reliable maximum bounds are typically unavailable Minimum age Time (My) Calibrating Divergence Times P D C N Common practice in Bayesian divergence-time estimation: Parametric distributions are typically off-set by the age of the oldest fossil assigned to a clade Uniform (min, max) Log Normal (µ, σ2) These prior densities do not (necessarily) require Gamma (α, β) specification of maximum bounds Exponential (λ) Minimum age Time (My) Calibrating Divergence Times (figure from Heath Syst. Biol. 2012) P D C N Describe the waiting time between the divergence event and the age of the oldest fossil Minimum age Time (My) Calibrating Divergence Times P D C N Overly informative priors can bias node age estimates to be too young Exponential (λ) Minimum age Time (My) Calibrating Divergence Times P D C N Uncertainty in the age of the MRCA of the clade relative to the age of the fossil may be better captured by more diffuse prior densities Exponential (λ) Minimum age Time (My) Calibrating Divergence Times P D C N Common practice in Bayesian divergence-time estimation: Estimates of absolute node ages are driven primarily by the calibration density Uniform (min, max) Log Normal (µ, σ2) Specifying appropriate densities is a challenge for Gamma (α, β) most molecular biologists Exponential (λ) Minimum age Time (My) Calibration Density Approach (figure from Heath Syst. Biol. 2012) I F C Domestic dog Spotted seal Zaragocyon daamsi We would prefer to Ballusia elmensis Ursavus brevihinus eliminate the need for Ursavus primaevus Giant panda Ailurarctos lufengensis ad hoc calibration Agriarctos spp. Kretzoiarctos beatrix prior densities Indarctos vireti Indarctos arctoides Indarctos punjabiensis Spectacled bear Calibration densities Giant short-faced bear Sloth bear Brown bear do not account for Polar bear Cave bear diversification of fossils Sun bear Am. black bear Asian black bear Fossil and Extant Bears (Krause et al. BMC Evol. Biol. 2008; Abella et al. PLoS ONE 2012) I F C Domestic dog Spotted seal Zaragocyon daamsi We want to use all Ballusia elmensis Ursavus brevihinus of the available fossils Ursavus primaevus Giant panda Ailurarctos lufengensis Agriarctos spp. Kretzoiarctos beatrix Example: Bears Indarctos vireti Indarctos arctoides 12 fossils are reduced Indarctos punjabiensis Spectacled bear to 4 calibration ages Giant short-faced bear Sloth bear Brown bear with calibration density Polar bear Cave bear methods Sun bear Am. black bear Asian black bear Fossil and Extant Bears (Krause et al. BMC Evol. Biol. 2008; Abella et al. PLoS ONE 2012) I F C Domestic dog Spotted seal Zaragocyon daamsi We want to use all Ballusia elmensis Ursavus brevihinus of the available fossils Ursavus primaevus Giant panda Ailurarctos lufengensis Agriarctos spp. Kretzoiarctos beatrix Example: Bears Indarctos vireti Indarctos arctoides 12 fossils are reduced Indarctos punjabiensis Spectacled bear to 4 calibration ages Giant short-faced bear Sloth bear Brown bear with calibration density Polar bear Cave bear methods Sun bear Am. black bear Asian black bear Fossil and Extant Bears (Krause et al. BMC Evol. Biol. 2008; Abella et al. PLoS ONE 2012) I F C Domestic dog Spotted seal Zaragocyon daamsi Ballusia elmensis Ursavus brevihinus Because fossils are Ursavus primaevus Giant panda Ailurarctos lufengensis part of the Agriarctos spp. Kretzoiarctos beatrix diversification process, Indarctos vireti Indarctos arctoides we can combine fossil Indarctos punjabiensis Spectacled bear Giant short-faced bear calibration with Sloth bear Brown bear birth-death models Polar bear Cave bear Sun bear Am. black bear Asian black bear Fossil and Extant Bears (Krause et al. BMC Evol. Biol. 2008; Abella et al. PLoS ONE 2012) I F C Domestic dog Spotted seal Zaragocyon daamsi This relies on a Ballusia elmensis Ursavus brevihinus branching model that Ursavus primaevus Giant panda accounts for Ailurarctos lufengensis Agriarctos spp. Kretzoiarctos beatrix speciation, extinction, Indarctos vireti Indarctos arctoides and rates of Indarctos punjabiensis Spectacled bear fossilization, Giant short-faced bear Sloth bear Brown bear preservation, and Polar bear Cave bear recovery Sun bear Am. black bear Asian black bear Fossil and Extant Bears (Krause et al. BMC Evol. Biol. 2008; Abella et al. PLoS ONE 2012) P N “Except during the interlude of the [Modern] Synthesis, there has been limited communication historically among the disciplines of evolutionary biology, particularly between students of evolutionary history (paleontologists and systematists) and those of molecular, population, and organismal biology. There has been increasing realization that barriers between these subfields must be overcome if a complete theory of evolution and systematics is to be forged.”. Reaka-Kudla, M.L. & Colwell, R.: in E.C. Dudley (ed.), The Unity of Evolutionary Biology: Proceedings of the Fourth International Congress of Systematic & Evolutionary Biology, Discorides Press, Portland, OR, p. 16. Two Separate Fields, Same Goals P N Two Separate Fields, Same Goals C F E D Statistical methods provide a way to integrate paleontological & neontological data Two Separate Fields, Same Goals C F E D Combine models for sequence evolution, morphological change, & fossil recovery to jointly estimate the tree topology, divergence times, & lineage diversification rates Time Tree Model Substitution Model Substitution Model Site Rate Model DNA Data Morphological Data Site Rate Model Branch Rate Model Branch Rate Model Fossil Occurrence Time Data C F E D Until recently, analyses combining fossil & extant taxa used simple or inappropriate models to describe the tree and fossil ages Time Tree Model Substitution Model Substitution Model Site Rate Model DNA Data Morphological Data Site Rate Model Branch Rate Model Branch Rate Model Fossil Occurrence Time Data M T O T Stadler (2010) introduced a generating model for a serially sampled time tree — this is the fossilized birth-death process. (Stadler. Journal of Theoretical Biology 2010) P FBD This graph shows the conditional dependence structure of the FBD model, which is a generating process for a sampled, dated time tree and fossil occurrences speciation rate λ ψ fossil recovery rate µ extinction rate origin time x0 ρ sampling probability time tree T fossil occurrence times F P FBD We re-parameterize the model so that we are directly estimating the diversification rate, turnonver and fossil sampling proportion s fossil sampling proportion diversification rate d r turnover speciation rate λ ψ µ extinction rate fossil recovery rate origin time x0 ρ sampling probability time tree T fossil occurrence times F d rd s rd λ = μ = ψ = 1 r 1 r 1 s 1 r − − − − T F B-D P (FBD) Improving statistical inference of absolute node ages Eliminates the need to specify arbitrary calibration densities Useful for ‘total-evidence’ analyses Better capture our statistical uncertainty in species divergence dates All reliable fossils associated with a 150 100 50 0 clade are used Time (Heath, Huelsenbeck, Stadler. PNAS 2014) T F B-D P (FBD) Recovered fossil specimens provide historical observations of the diversification process that generated the tree of extant species 150 100 50 0 Time Diversification of Fossil & Extant Lineages (Heath, Huelsenbeck, Stadler. PNAS 2014) T F B-D P (FBD) The probability of the tree and fossil observations under a birth-death model with rate parameters: λ = speciation μ = extinction ψ = fossilization/recovery 150 100 50 0 Time Diversification