The Impact of Time-Scaling Methods

on Phylogenetic Comparative

Methods in the Fossil Record

David Bapst

South Dakota School of Mines and Technology

Evolution 2013 06/23/2013

Phylogeny in the Fossil Record

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Sampling in the Fossil Record

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Time Intervals in the Fossil Record

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What We Have

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Tiffanian

Cloudian

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What We Want

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Original

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Original Basic

Smith, 1994; Laurin, 2004

Time-scaling Methods

• Clades are as old as earliest observed descendent

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Original Basic

Smith, 1994; Laurin, 2004

Time-scaling Methods

• Creates zero-length branches (…nuisance)

Nodes Separated by Zero-Length Branches

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Original Basic Min. Branch Length

Smith, 1994; Laurin, 2004

Time-scaling Methods

• Creates zero-length branches (…nuisance)

• Common fix: Extend branches a small amount

• No measurement of uncertainty of node ages

ZLBs

Time

Stochastic Time-scaling

Bapst, Accepted, Methods in Ecol. Evol.

• Randomly select new node ages across a cladogram

• Repeat many times to get large sample of trees

Stochastic Time-scaling

Bapst, Accepted, Methods in Ecol. Evol.

• Also can allow for ancestor-descendant relationships

• Also, resolve soft polytomies

Time

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Pr(Σ gaps)

Stochastic 3 Rate-Calibrated Time-scaling

Bapst, Accepted, Methods in Ecol. Evol.

• Weight node age selection by

probability density of total inferred unobserved evolutionary history

• Birth, death, sampling rates

• cal3 in R package paleotree

(From in prep work with Matt Pennell and Emily King)

Time

Pr(Σ gaps)

Stochastic 3 Rate-Calibrated Time-scaling

Bapst, Accepted, Methods in Ecol. Evol.

• Weight node age selection by

probability density of total inferred unobserved evolutionary history

• Birth, death, sampling rates

• cal3 in R package paleotree

(From in prep work with Matt Pennell and Emily King)

But does cal3 improve our time-scaling?

• Simulate diversification, differentiation and sampling

• Transform to get true time-scaled phylogeny of sampled taxa

– Dependent on times of observation of populations

– Different times = different branch lengths and topology

Comparing Time-Scaling Methods

• Get sampled ranges and put in arbitrary discrete intervals (more realistic)

Comparing Time-Scaling Methods

• Transform set of relationships to ideal cladogram of sampled taxa (Bapst, 2013, PLoS One)

– All intrinsically resolvable clades

Comparing Time-Scaling Methods

• Apply time-scaling methods to cladogram and ranges to get ‘empirical’ time-scaled trees

Comparing Time-Scaling Methods

Comparing Time-Scaling Methods: A Wizard Could Do It

Comparing Time-Scaling Methods

Compare and Contrast!

Set Differentiation

Model With Extant

Taxa? Time of

Observation Sampling Rate

(per Ltu) Interval Length

A Budding No Last Appearance 0.1 5 B Budding No First Appearance 0.1 5 C Budding No Random 0.1 5 D Budding No Last Appearance 0.05 5 E Budding No Last Appearance 0.5 5 F Budding No Last Appearance 0.1 Cont. Time G Budding No Last Appearance 0.1 1 H Budding No Last Appearance 0.1 10 I Budding Yes Last Appearance 0.1 5 J Bifurcation No Last Appearance 0.1 5 K Terminal-Taxa No Last Appearance 0.1 5 L Terminal-Taxa No First Appearance 0.1 5 M Terminal-Taxa No Random 0.1 5 N Terminal-Taxa No Last Appearance 0.1 Cont. Time O Terminal-Taxa Yes Last Appearance 0.1 5

Don’t panic! I’ll only talk in reference to the baseline A

See Bapst, 2013 and Bapst, Accepted for Diff. Models

100 Simulation Runs ~50 Sampled Taxa Samples of 20 Empirical Trees

Baseline (Budding) Higher Sampling

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Budding

Basic gives better point estimates of branching times under budding …except at high sampling

Bapst, accepted, MEE Bapst, in review, Paleobio.

Baseline (Budding) Higher Sampling Terminal-Taxon

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Budding Terminal-Taxon

Node ages over-estimated with budding, but under-estimated in terminal-taxon simulations

Bapst, accepted, MEE Bapst, in review, Paleobio.

100 Simulation Runs ~50 Sampled Taxa Samples of 20 Empirical Trees

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K Budding Terminal-Taxon

Stochastic samples of cal3 trees more likely to bracket uncertainty in true node ages

100 Simulation Runs ~50 Sampled Taxa Samples of 20 Empirical Trees

Bapst, accepted, MEE Bapst, in review, Paleobio.

A

K Budding Terminal-Taxon

Stochastic samples of cal3 trees more likely to bracket uncertainty in true node ages

100 Simulation Runs ~50 Sampled Taxa Samples of 20 Empirical Trees

Bapst, accepted, MEE Bapst, in review, Paleobio.

But how does this impact phylogeny-

based analyses?

Last Appearance First Appearance Random Times of Observation

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• Earlier times of observation lead to over-estimated rates of trait evolution

• Effect is mitigated under cal3 time-scaling Bapst, in review. Paleobiology

Last Appearance First Appearance Random Times of Observation

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Bapst, in review. Paleobiology

• Also leads to incorrectly inferring OU when true model of trait evolution is BM, but not under cal3 time-scaling

• The culprit: zero-length branches (or just very short branches) in the wrong places

Bapst, in review. Paleobiology

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Test with some Very Simple Simulations…

Wait, what about testing for OU?

• No problem here!

Comparing Time-Scaling Methods

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alpha = 1/10 of the step variance (i.e. the ‘rate’ parameter in BM)

Conclusions

• A stochastic time-scaling method: cal3

– Provides better summary of uncertainty in node ages

• Fitting models of trait evolution sensitive to artifacts of time-scaling phylogenies of fossil taxa

– cal3 is generally method that performs best, but can show some bias, in some cases

• Need to account for uncertainty in time-scaling

– We can’t pinpoint the true time-scaled tree

Thanks to the following for advice: M. Foote, E. King, M. Pennell, G. Slater, G. Lloyd, P. Smits, M. Villarosa Garcia, A. Haber, G. Hunt, P. Wagner, M. Friedman, J. Mitchell

Stochastic Time-Scaling: Extensions

• Infer ancestor-descendant relationships by allowing node ages to occur after the first appearance of the earliest taxon

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A New Time-Scaling Method: cal3

• Stochastically resolve soft polytomies by iteratively placing lineages over multiple steps

– Allow us to at least consider those relationships that aren’t intrinsically resolvable

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Stochastic Time-Scaling: Extensions

A New Time-Scaling Method: cal3

A Probabilistic Model of Gaps

• Total inferable unobserved evolutionary history is

– Can obtain via methods such as the freqRat

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A New Time-Scaling Method: cal3

Probability of Sampling an Extinct Clade of Unknown Size

(100 combos of 3 rates; 300 runs each)

(a) p=q=r=0.1; budding (b) p=q=0.5 ; r=0.1; budding (c) p=q=r=0.1; bifurc (d) p=q=0.1; r=0.5; budding

A Density Function for Total Inferred Unobs Evol History: Simulations

• For example, estimating the diversity curve… – Adding a phylogeny, regardless of time-scaling

method, only makes slight improvements (if at all)

– cal3 with ancestral inference does provide the greatest benefit

High Sampling Rate

Cont Time Ranges

Bapst, in prep. Paleobiology Comparing Time-Scaling Methods

Drop Modern Only Taxa

• Pull of the recent… Sort of!

• Extant taxa sampled only at the modern can add many ZLBs to the phylogenies

Budding Terminal-Taxa

Comparing Time-Scaling Methods

• Pull of the recent can also screw up PGLS