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SVP 2012 Talk: Time-Scaling Trees in the Fossil Record
This document discusses various methods for time-scaling phylogenetic trees constructed from fossil occurrence data. It introduces a new method called sampling rate conditioned time-scaling that randomly scales branches based on the estimated fossil sampling rate to account for uncertainty. Simulation results show this method generally outperforms previous approaches in estimating divergence times, trait evolution rates, and model selection. Accounting for the incompleteness of the fossil record through probabilistic time-scaling methods improves analyses relying on time-scaled trees.
SVP 2012 Talk: Time-Scaling Trees in the Fossil Record
- 1. TIME-SCALING TREES IN THEFOSSIL RECORD David Bapst University of Chicago Geophysical Sciences (Pretty figure taken from Ted Garland’s website)
- 2. Phylogeny in theFossil Record G H E K F J I D C Time B L A
- 3. Sampling in theFossil Record G H Sampling Event E K F J I D C Time B L A
- 4. What We Have AH KG E ID A K IG H D E Time
- 5. What We Want AH KG E ID A K IG H D E Time A K IG H D E Time Original
- 6. Of Time andTrees: ‘Basic’ Method • Clades are as old as earliest observed descendent A K IG H D E A K IG H D E Time OriginalBasic Method Smith, 1994
- 7. Of Time andTrees: ‘Basic’ Method • Creates zero-length branches (…nuisance) • Common fix: Extend branches a small amount • No measurement of the uncertainty involved A K IG H D E A K IG H D E Time Nodes Separated by Zero-Length Branches OriginalBasic Method
- 8. Dealing with Uncertainty: StochasticAnalyses • Example: Dealing with Discrete Intervals K D TimeIntervals t.1 t.2 t.3 t.4 t.5 t.6 A IG H E K D A IG H E Lloyd et al., 2012
- 9. Dealing with Uncertainty: StochasticAnalyses • Example: Dealing with Discrete Intervals K D TimeIntervals t.1 t.2 t.3 t.4 t.5 t.6 A IG H E K D A I G H E Randomly Drop FADs and LADs Lloyd et al., 2012
- 10. Dealing with Uncertainty: StochasticAnalyses • Example: Dealing with Discrete Intervals K D A I G H E K D TimeIntervals t.1 t.2 t.3 t.4 t.5 t.6 A IG H E K D A I G H E Repeat! K D A I G H E Lloyd et al., 2012
- 11. Stochastic Time-Scaling • Randomlyselect new node ages across a cladogram – Give lower bounds by starting with root (with loose lower bound) and work up, node by node • Rinse, repeat many times to produce a large sample of trees ? Time
- 12. Stochastic Time-Scaling: Extensions •Stochastically infer ancestor-descendant relationships by allowing node ages to occur after the earliest taxon appears Time
- 13. • Stochastically resolvesoft polytomies by iteratively placing lineages over multiple steps C B A ?? B A C B A C B A Time Stochastic Time-Scaling: Extensions
- 14. Stochastic Time-Scaling • Expectmore uncertainty in poorly-sampled fossil records • Weight selection of node ages via probability model of the unobserved evolutionary history at a node Time Pr(Σ gaps)
- 15. A Probabilistic Modelof Gaps • Total minimum unobserved evolutionary history is dependent on sampling rates – Can obtain via methods such as the freqRat Time
- 16. A Probabilistic Modelof Gaps • But also dependent on diversification: branching and extinction rates – Unsampled ‘twigs’ matter! • Node ages need to be calibrated with three rates – Cal3 time-scaling method – Probability of unobserved twigs derived with Matt Pennell and Emily King Foote et al., 1999; Friedman and Brazeau, 2011 Time
- 17. A Probabilistic Modelof Gaps • But also dependent on diversification: branching and extinction rates – Unsampled ‘twigs’ matter! • Node ages need to be calibrated with three rates – Cal3 time-scaling method – Probability of unobserved twigs derived with Matt Pennell and Emily King Foote et al., 1999; Friedman and Brazeau, 2011 Time But how good is the time-scaling?
- 18. A Probabilistic Modelof Gaps • But also dependent on diversification: branching and extinction rates – Unsampled ‘twigs’ matter! • Node ages need to be calibrated with three rates – Cal3 time-scaling method – Probability of unobserved twigs derived with Matt Pennell and Emily King Foote et al., 1999; Friedman and Brazeau, 2011 Time Let’s do some simulations to find out!
- 19. So, How Goodis the Time-Scaling? Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res Median of Median Error in Per-Node Ages 100 Simulation Runs Samples of 20 Trees ~50 Taxa; Budding p= q = r = 0.1 per Ltu Disc. Intervals = 5 tu Rates est. via ML Using R library paleotree (Bapst, 2012; MEE)
- 20. Squared-Error: Cal3 hasMore Error Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res Median of Median Squared-Error in Per-Node Ages Using R library paleotree (Bapst, 2012) 100 Simulation Runs Samples of 20 Trees ~50 Taxa; Budding p= q = r = 0.1 per Ltu Disc. Intervals = 5 tu Rates est. via ML
- 21. Better Estimator ofUncertainty? Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res Proportion of True Node-Ages within 95% Age Quantiles Using R library paleotree (Bapst, 2012) 100 Simulation Runs Samples of 20 Trees ~50 Taxa; Budding p= q = r = 0.1 per Ltu Disc. Intervals = 5 tu Rates est. via ML
- 22. Similar Patterns withTerminal Branch Lengths Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res Proportion within 95% Age Quantiles Median of Median Squared Error Using R library paleotree (Bapst, 2012) 100 Simulation Runs Samples of 20 Trees ~50 Taxa; Budding p= q = r = 0.1 per Ltu Disc. Intervals = 5 tu Rates est. via ML
- 23. 100 Simulation Runs Samplesof 20 Trees ~50 Taxa; Budding p= q = r = 0.1 per Ltu Disc. Intervals = 5 tu Rates est. via ML Using R library paleotree (Bapst, 2012) Similar Patterns with Terminal Branch Lengths Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res Proportion within 95% Age Quantiles Median of Median Squared Error But this isn’t what we’re interested in most often…
- 24. Analyses of TraitEvolution Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res True Phylogeny Median Estimated Rate of Trait Change (Log-Scale Axis) 100 Simulation Runs Samples of 20 Trees ~50 Taxa; Budding p= q = r = 0.1 per Ltu Disc. Intervals = 5 tu Rates est. via ML
- 25. Analyses of TraitEvolution Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res True Phylogeny AICc Weight of BM vs OU (for Trait Simulated Under BM) 100 Simulation Runs Samples of 20 Trees ~50 Taxa; Budding p= q = r = 0.1 per Ltu Disc. Intervals = 5 tu Rates est. via ML
- 26. Conclusions • New time-scalingmethod: cal3 (paleotree v1.5) – Time-scaling calibrated with estimated rates of sampling, branching and extinction • Fidelity of time-scaling can be decoupled from fidelity of comparative analyses – Why? A certain je ne sais quoi of the time-scaling? • Frequency of int. ZLBs? Balance of total BrLen distribution? – If analytical performance cannot be easily extrapolated or predicted, simulations are key Thanks to M. Foote, E. King, J. Felsenstein, A. Haber, M. Pennell, G. Hunt, G. Lloyd, M. Friedman, P. Wagner, M. Webster, D. Jablonski, M. LaBarbera, K. Boyce, J. Mitchell, P. Harnik, G. Slater and the R-Sig-Phylo Email List!
- 28. Slightly Better PolytomyResolver Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors timeLadderTree 100 Simulation Runs 20 Trees Samples ~50 Taxa; Budding p= q = r = 0.1 per Ltu Interval Length = 5 tu Rates est. via ML Proportion of Collapsed Clades Correctly Resolved
- 29. Fidelity of VCVMatrices: All High Cal3 w/ Ancestors Cal3 w/o Ancestors 100 Simulation Runs 20 Trees Samples ~50 Taxa; Budding p= q = r = 0.1 per Ltu Interval Length = 5 tu Rates est. via ML Median Random Skewer Similarity of VCV Matrices to True VCV Matrix Cal3 w/o Ancestors Rand-Res Basic Rand-Res
- 30. Samp. Rate Cond.gives best est across samp rates 100 trees each (not SRC), ~50 taxa (Lmy-1)
- 31. Model Fitting AtOther Parameters Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res True Phylogeny AICc Weight of BM vs OU (for Trait Simulated Under BM) 100 Simulation Runs 20 Trees Samples ~50 Taxa; Budding p= q = r = 0.1 per Ltu Interval Length = 5 tu Rates est. via ML p=q =0.1 r=0.5 per Ltu
- 32. Model Fitting AtOther Parameters Basic Rand-Res Cal3 w/ Ancestors Cal3 w/o Ancestors Cal3 w/o Ancestors Rand-Res True Phylogeny AICc Weight of BM vs OU (for Trait Simulated Under BM) 100 Simulation Runs 20 Trees Samples ~50 Taxa; Budding p= q = r = 0.1 per Ltu Interval Length = 5 tu Rates est. via ML Bifurcating Cladogenesis
- 33. A Model ofUnobserved History Time Using R library paleotree (Bapst, 2012)
- 34. A Model ofUnobserved History • Best fit with gamma models Time Using R library paleotree (Bapst, 2012)
- 35. A Model ofUnobserved History • Importance of Diversification: Twigs Matter! • Calibrate with Three Rates: ‘Cal3’ time-scaling – Sampling, branching and extinction rates Time (Derived with Matt Pennell and Emily King)
- 38. Of Time andTrees • Usually start with data like this… – (Thanks to Melanie Hopkins for this example data!) Taxon Ranges Unscaled Topology Hopkins, 2011 (Strict Consensus Tree)
- 39. Of Time andTrees • Usually start with data like this… – (Thanks to Melanie Hopkins for this example data!) Taxon Ranges Unscaled Topology Hopkins, 2011 (Strict Consensus Tree)
- 40. Of Time andTrees Time • …but want a time-scaled tree for analyses • How do we time-scale? Effect on analyses? Note: Time = Strat meters for Hopkins (2011)
- 41. Of Time andTrees Time • One solution uses morph ‘clock’-like approach • But what about trees with no char change info?
- 42. Previous Approaches • Unit-lengthbranches • “speciational” scale • No actual time-scale! – Is setting all branches equal a good approx? • Soft polytomies have to be randomly resolved beforehand – (True of most methods) Scaled Consensus Tree from Hopkins, Polytomies Rand-Res. # of Obs Branching Events
- 43. Previous Approaches • BasicApproach • Clade age = age of earliest obs desc • Creates many zero- length branches (ZLB) – Unrealistic – Singular varcovar matrices: math for BM, etc. doesn’t work Time Time-Scaled Consensus Tree from Hopkins, Polytomies Rand-Res.
- 44. Previous Approaches • AddingX to all branches (ABA) or just very short branches – X = A Number • Avoids singularity • Similar: MinBrLength • Widely used but how to pick X? • Can push root back unrealistically far Time Time-Scaled Consensus Tree from Hopkins, Polytomies Rand-Res.
- 45. Previous Approaches • ‘Equal’Method – Graeme Lloyd • Pull root down by X, redistribute time on earlier branches along ZLBs – X = A Number • Widely used, but how choose X? Time Time-Scaled Consensus Tree from Hopkins, Polytomies Rand-Res.
- 46. New Method: Sampling RateConditioned • Est samp rate r • Randomly pick ‘gaps’ in evol history to scale branches, using P(gaps|r) as weights • Repeat many times… Time Time-Scaled Consensus Tree from Hopkins, Polytomies NOT Rand-Res.
- 47. New Method: Sampling RateConditioned • Est samp rate r • Randomly pick ‘gaps’ in evol history to scale branches, using P(gaps|r) as weights • Repeat many times, make many trees! – No single answer! • Resolve polytomies, identify ancestors 25 Time-Scaled Trees, Polytomies NOT Rand-Res.
- 48. New Method: Sampling RateConditioned • Est samp rate r • Randomly pick ‘gaps’ in evol history to scale branches, using L(gaps|r) as weights • Repeat many times, make many trees! – No single answer! • Resolve polytomies, identify ancestors – Stratolikelihood-esque But How Do These Methods Perform? 25 Time-Scaled Trees, Polytomies NOT Rand-Res.
- 49. New Method: Sampling RateConditioned • Est samp rate r • Randomly pick ‘gaps’ in evol history to scale branches, using L(gaps|r) as weights • Repeat many times, make many trees! – No single answer! • Resolve polytomies, identify ancestors – Stratolikelihood-esque Let’s Run Some Birth-Death- Sampling Simulations and Find Out! (…For Some Stuff) 25 Time-Scaled Trees, Polytomies NOT Rand-Res.
- 50. Obs Data Est PDF (KDE) TrueSim Value (OUR TARGET) Quick Guide to Beanplots! Sampling Rates Methods Value Using R library beanplot
- 51. Samp. Rate Cond.gives best est across samp rates 100 trees each (not SRC), ~50 taxa (Lmy-1)
- 52. Signal estimate badacross the board; bias for zero 100 trees each (not SRC), ~50 taxa (Lmy-1)
- 53. 100 trees each(not SRC), ~50 taxa • Implications for trait evol model-fitting in fossil record? • Bias for low-signal models like OU? Signal estimate bad across the board; bias for zero (Lmy-1)
- 54. 100 trees each(not SRC), ~50 taxa High correlation generally; SRC performs worst Only Fully Extinct Clades(Lmy-1) 1 MY timebins
- 55. • Similar resultsfor FirstDiffs • Corr increases with time step size used • Obs ranges good – True under diff sampling model? – Clades with living desc? • Lane et al. 2005 100 trees each (not SRC), ~50 taxa High correlation generally; SRC performs worst Only Fully Extinct Clades(Lmy-1) 1 MY timebins
- 56. Samp. Rate Cond.better than randomly resolving 100 trees each , ~50 taxa ~50% of Nodes Removed (Lmy-1)
- 57. • Results – Newmethod: Sampling Rate Conditioned – Good for BM rate, not so good for diversity curve – No method unbiased for estimating phylo signal • Future Work – Compare fidelity with poorly resolved trees – Test possible bias in trait model-fitting analyses • Simulations necessary to understand the reliability of methods in paleobiology • Code to be released soon in R library Thanks for Code: G. Lloyd, G. Hunt Thanks for Data: Melanie Hopkins Thanks for Comments and Ideas: M. Foote, M. Webster, D. Jablonski, E. King, P. Wagner, J. Mitchell, M. Friedman, G. Slater, M. Pennell, L. Harmon and the R-Sig-Phylo Email List! Results and Future Work
- 61. – Effect ofrandom zombie lineages on div corr – Time-scale with joint L(gaps,morph) – Integrate with birth-death models of branch length distribution for paleo trees
- 62. • Move uptree, node by node – calculate likelihoods for each possible position of a node – Randomly sample a position, using likelihoods as weights • Repeat to produce large sample of time-scaled trees B A B A B A B A B A L ( obs gap of length t ) = r * exp (- r * t) r = instantaneous sampling rate Time (Bapst, in prep. C)
- 63. • Move uptree, node by node – calculate likelihoods for each possible position of a node – Randomly sample a position, using likelihoods as weights • Repeat to produce large sample of time-scaled trees B A B A B A B A B A Time Pick One by Weighted Random Sampling (Bapst, in prep. C) L ( obs gap of length t ) = r * exp (- r * t) r = instantaneous sampling rate
- 64. Time-scaling Difficulties • Inan extinct clade of fossil taxa... – Temporal placement of nodes constrained only by appearance of descendant taxa Time B A C B A C
- 65. Time-scaling Difficulties • Inan extinct clade of fossil taxa... – Ancestors are potentially among our sampled taxa (particularly in well-sampled clades) Time B A C B A C ‘Budding’ Anagenesis
- 66. Zipper Method: AStochastic Solution • Produces stochastic samples of time-scaled trees • In each run, samples many hypotheses of branch lengths and (also) anc-desc relationships, weighted by sampling probabilities • Cannot reconstruct multi- budding scenario • Requires integrated phylogenetic inference method • As many truly interesting things do
- 67. Problems Created bya Really Big Supertree of Dead Plankton • Dealing with topological uncertainty – Need to resolve soft polytomies for time-scaling – Randomly resolving can produce poor overall fit to observed sequence of appearances A B C D A B C D Time
- 68. Problems Created bya Really Big Supertree of Dead Plankton • Dealing with topological uncertainty • Developed alternative method based on stochastic sampling(Bapst, in prep. B) – Uses sampling rates in the fossil record, estimated from range data (Foote, 1997) – Reconstructs more nodes correctly than randomly resolving nodes in simulated trees • Evolutionary analyses must be repeated over large samples of potential topologies • Additional uncertainties in time-scaling phylogenies of fossil taxa