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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
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Phylogeny in the Fossil Record
G
H
E
K
F
J I
D
C Time
B
L
A
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Sampling in the Fossil Record
G
H
Sampling Event
E
K
F
J I
D
C B
L
A
Time
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Time Intervals in the Fossil Record
G
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Sampling Event
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K
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J I
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C B
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Time
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What We Have
A H K G E I D
Tim
e In
terv
als
Tiffanian
Cloudian
Barrettian
Yuffiean
Aerisean
Cidian K
D
A
I G H E
Time
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What We Want
A H K G E I D
A
K
I G
H D
E
Time
Original
K
D
A
I G H E
Time
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A
K
I G
H D
E
Time
A
K
G
H D I
E E
Original Basic
Smith, 1994; Laurin, 2004
Time-scaling Methods
• Clades are as old as earliest observed descendent
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A
K
I G
H D
E
Time
A
K
G
H D I
E E
Original Basic
Smith, 1994; Laurin, 2004
Time-scaling Methods
• Creates zero-length branches (…nuisance)
Nodes Separated by Zero-Length Branches
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A
K
I G
H D
E
Time
A
K
I G
H D
A
K
G
H D
E E I
E E
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
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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
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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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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)
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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?
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• 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
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• Get sampled ranges and put in arbitrary discrete intervals (more realistic)
Comparing Time-Scaling Methods
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• Transform set of relationships to ideal cladogram of sampled taxa (Bapst, 2013, PLoS One)
– All intrinsically resolvable clades
Comparing Time-Scaling Methods
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• Apply time-scaling methods to cladogram and ranges to get ‘empirical’ time-scaled trees
Comparing Time-Scaling Methods
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Comparing Time-Scaling Methods: A Wizard Could Do It
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Comparing Time-Scaling Methods
Compare and Contrast!
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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
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100 Simulation Runs ~50 Sampled Taxa Samples of 20 Empirical Trees
Baseline (Budding) Higher Sampling
A E
Budding
Basic gives better point estimates of branching times under budding …except at high sampling
Bapst, accepted, MEE Bapst, in review, Paleobio.
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Baseline (Budding) Higher Sampling Terminal-Taxon
K A E
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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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.
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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?
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Last Appearance First Appearance Random Times of Observation
Bu
dd
ing
Term
inal
-Tax
a
A
K L
B C
M
• Earlier times of observation lead to over-estimated rates of trait evolution
• Effect is mitigated under cal3 time-scaling Bapst, in review. Paleobiology
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Last Appearance First Appearance Random Times of Observation
Bu
dd
ing
Term
inal
-Tax
a
A
K L
B C
M
Bapst, in review. Paleobiology
• Also leads to incorrectly inferring OU when true model of trait evolution is BM, but not under cal3 time-scaling
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• The culprit: zero-length branches (or just very short branches) in the wrong places
Bapst, in review. Paleobiology
A
Test with some Very Simple Simulations…
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Wait, what about testing for OU?
• No problem here!
Comparing Time-Scaling Methods
A
alpha = 1/10 of the step variance (i.e. the ‘rate’ parameter in BM)
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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
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Stochastic Time-Scaling: Extensions
• Infer ancestor-descendant relationships by allowing node ages to occur after the first appearance of the earliest taxon
Tim
e
A New Time-Scaling Method: cal3
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• Stochastically resolve soft polytomies by iteratively placing lineages over multiple steps
– Allow us to at least consider those relationships that aren’t intrinsically resolvable
C
B
A
? ?
B
A
C
B
A
C
B
A
Tim
e
Stochastic Time-Scaling: Extensions
A New Time-Scaling Method: cal3
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A Probabilistic Model of Gaps
• Total inferable unobserved evolutionary history is
– Can obtain via methods such as the freqRat
Tim
e
(a)
A New Time-Scaling Method: cal3
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Probability of Sampling an Extinct Clade of Unknown Size
(100 combos of 3 rates; 300 runs each)
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(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
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• 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
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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
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• Pull of the recent can also screw up PGLS