brian o ’ meara http:
DESCRIPTION
Brian O ’ Meara http:// www.brianomeara.info. http://www.youtube.com/watch?v=9R8hpPY_9kY. Get out laptop, fire up R. install.packages("ctv"). library(ctv). install.views ("Phylogenetics") install.packages (" corHMM "). Model selection. Likelihood ratio test. - PowerPoint PPT PresentationTRANSCRIPT
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Brian O’Mearahttp://www.brianomeara.info
http://www.youtube.com/watch?v=9R8hpPY_9kYGet out laptop,
fire up R
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install.packages("ctv")library(ctv)
install.views("Phylogenetics")install.packages("corHMM")
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Model selection
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Likelihood ratio test
test statistic = 2(ln L1 - ln L0)
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Likelihood ratio test
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Posada and Crandal 1998
Likelihood ratio test
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Akaike information criterion
AICi = -2 ln Li + ki
“Truth drops out as a constant” -- Burnham and Anderson 2004
AIC is estimator as distance between truth and approximating model
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Bayes Factors
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Reversible jump MCMC
Model 1
Model 2 Model 2
Model 1
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Organize by:Question Method
• Correlation of herbivory with group living
• Crepuscular foraging being intermediate between nocturnal and diurnal
• Biogeography • Causes of
diversification• Rate of trait evolution• What limits the number
of species
• Continuous time Markov Chain
• Birth death process• Multivariate normal• BiSSE and friends• Tree stretching
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Flour, sugar, egg, butter, leavening, liquid
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Continuous time Markov chain finite state space
A, T, G, Cwoody, herbaceous
susceptible, infected, recovered
herbivorous, omnivorous, carnivorous
0, 2, 4, 6, 8, ..., 100 legs
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Per day:
What is probability of it leaving the store that day?If it leaves, what is the probability it was paid for?What is the probability it stays in the store ≥
two days?
Action Bought by adult
Bought by child Stolen
Probability 0.20 0.10 0.05
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Per ∆t:
Action Bought by adult
Bought by child Stolen
Probability
0.20 /scaling
0.10 /scaling
0.05 /scaling
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Per ∆t:
Action Bought by adult
Bought by child Stolen
Rate radult rchild rstolen
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Per ∆t:From \
To Store Adult Child Thief
Store - rstore-adult rstore-child rstore-thief
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Per ∆t:From \
To Store Adult Child Thief
Store - rstore-adult rstore-child rstore-thief
Adult
Child
Thief
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Per ∆t:From \
To Store Adult Child Thief
Store - rstore-adult rstore-child rstore-thief
Adult radult-store - radult-child radult-thief
Child rchild-store rchild-adult - rchild-thief
Thief rthief-store rthief-adult rthief-child -
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From \ To Store Adult Child Thief
Store - rstore-adult rstore-child rstore-thief
Adult radult-store - radult-child radult-thief
Child rchild-store rchild-adult - rchild-thief
Thief rthief-store rthief-adult rthief-child -
From \ To Store Adult Child Thief
Store - rstore-adult rstore-child rstore-thief
Adult radult-store - radult-child radult-thief
Child rchild-store rchild-adult - rchild-thief
Thief rthief-store rthief-adult rthief-child -
Does the store ever get Twinkies back? [Do people return Twinkies for a refund?]
H0: r*-store = 0H1: r*-store > 0
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From \ To Store Adult Child Thief
Store - rstore-adult rstore-child rstore-thief
Adult radult-store - radult-child radult-thief
Child rchild-store rchild-adult - rchild-thief
Thief rthief-store rthief-adult rthief-child -
Do adults give to kids at the same rate kids give to adults?H0: rchild-adult = radult-child H1: rchild-adult ≠ radult-child
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A B C DA - rAB rAC rAD
B rBA - rBC rBD
C rCA rCB - rCD
D rDA rDB rDC -
•Hypotheses about rates for a single character (are some equal? are some zero?)•Hypotheses about correlation between characters•Tree inference•Ancestral state inference
From this basic model:
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Continuous time Markov chain finite state space
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Currie et al. 2010 Nature
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Currie et al. 2010 Nature
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Currie et al. 2010 Nature
From \ To Store Adult Child Thief
Store - rstore-adult rstore-child rstore-thief
Adult radult-store - radult-child radult-thief
Child rchild-store rchild-adult - rchild-thief
Thief rthief-store rthief-adult rthief-child -
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Currie et al. 2010 Nature
From \ To
A(acephalous)
sC(simple
chiefdom)
cC(complex chiefdom)
S(state)
A - rA-sC rA-cC rA-S
sC rsC-A - rsC-cC rsC-S
cC rcC-A rcC-sC - rcC-S
S rS-A rS-sC rS-cC -
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Currie et al. 2010 Nature
From \ To
A(acephalous)
sC(simple
chiefdom)
cC(complex chiefdom)
S(state)
A - rA-sC rA-cC rA-S
sC rsC-A - rsC-cC rsC-S
cC rcC-A rcC-sC - rcC-S
S rS-A rS-sC rS-cC -
0
0
0
0
0 0
0 0
0
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Currie et al. 2010 Nature
From \ To
A(acephalous)
sC(simple
chiefdom)
cC(complex chiefdom)
S(state)
A - rA-sC rA-cC rA-S
sC rsC-A - rsC-cC rsC-S
cC rcC-A rcC-sC - rcC-S
S rS-A rS-sC rS-cC -
0 0
0
0
0 0
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Currie et al. 2010 Nature
From \ To
A(acephalous)
sC(simple
chiefdom)
cC(complex chiefdom)
S(state)
A - rA-sC rA-cC rA-S
sC rsC-A - rsC-cC rsC-S
cC rcC-A rcC-sC - rcC-S
S rS-A rS-sC rS-cC -
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Currie et al. 2010 Nature
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Currie et al. 2010 Nature
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Currie et al. 2010 Nature
From \ To
A(acephalous)
sC(simple
chiefdom)
cC(complex chiefdom)
S(state)
A - med small small
sC med - large med
cC med large - med
S med med med -
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0
1
A
01 A
B
B
No sex play
No sex play
Yes sex play
Yes sex play
No social play
No social play
Yes social play
Yes social play
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From \ To 0A 0B 1B 1A
0A - r0A-0B r0A-1B r0A-1A
0B r0B-0A - r0B-1B r0B-1A
1B r1B-0A r1B-0B - r1B-1A
1A r1A-0A r1A-0B r1A-1B -
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From \ To 0A 0B 1B 1A
0A - r0A-0B r0A-1B r0A-1A
0B r0B-0A - r0B-1B r0B-1A
1B r1B-0A r1B-0B - r1B-1A
1A r1A-0A r1A-0B r1A-1B -
0
0
0
0
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0
1
A
01 A
B
B
No sex play
No sex play
Yes sex play
Yes sex play
No social play
No social play
Yes social play
Yes social play
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0
1
A
01 A
B
B
No sex play
No sex play
Yes sex play
Yes sex play
No social play
No social play
Yes social play
Yes social play
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Pagel 1994
From \ To 0A 0B 1B 1A
0A - r0A-0B 0 r0A-1A
0B r0B-0A - r0B-1B 0
1B 0 r1B-0B - r1B-1A
1A r1A-0A 0 r1A-1B -
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Barker & Pagel 2005
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0
1
1
01 1
0
0
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Barker & Pagel 2005
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Barker & Pagel 2005
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 a
2 a b
3 b c
4 c d
5 d e
6 e f
7 f g
8 g h
9 h i
10 i j
11 j k
12 k l
13 l m
14 m n
15 n o
16 o
... up to maximum number of genes
...
......
where a, b, etc. are just f(i, j, birthdeath rate)
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Ree & Smith 2008
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Ree & Smith 2008
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Courtesy Nicolas Salamin
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Joint: Choose values for x, y, z, w that together maximize likelihood
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Joint: Choose values for x, y, z, w that together maximize likelihood
Marginal: Choose value for x (and repeat for others) that maximizes
likelihood while integrating over all values for y, z, w
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Joint: Choose values for x, y, z, w that together
maximize likelihood
Marginal: Choose value for x (and
repeat for others) that maximizes likelihood while
integrating over all values for y, z, w
Henry Hargreaves
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Finnigan, G. C., V. Hanson-Smith, T. H. Stevens, and J. W. Thornton. 2012. Evolution of increased complexity in a molecular machine. Nature 481:360-U143.
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Courtesy Nicolas Salamin
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Equal: all states equally likely
Empirical: count the proportion of each state in the tip taxa
Fixed: make them up (ideally, based on knowledge)
Equilibrium: what they'd be if the process ran forever
This assumption can have a major effect on results
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Schluter et al. 1997
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Beaulieu, O'Meara, and Donoghue, 2013
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Beaulieu, O'Meara, and Donoghue, 2013
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Beaulieu, O'Meara, and Donoghue, 2013
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Beaulieu, O'Meara, and Donoghue, 2013
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Tree stretching
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Continuous
- rAB × t
rAC × t
rAD × t
rBA × t - rBC ×
trBD ×
t
rCA × t
rCB × t - rCD ×
t
rDA × t
rDB × t
rDC × t -
e( )
Discrete
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Lambda = multiply internal branch lengths1
0.5
0
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Delta = speed up or slow down
1
1.5
0.5
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Kappa = raise each branch to kappa.
Punctuational models.
0.5
0
1
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Eldredge and Gould 1971
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Eldredge and Gould 1971
¿=?≠
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Schematic illustration of evolution of one phenotype on a phylogeny leading to three extant species. Cladogenetic change appears as vertical lines as it is modeled here as an instantaneous event on a geological time scale. Anagenetic change appears as Brownian motion of the phenotype on a logarithmic scale. Sh indi- cates the speciation events that do not appear on a reconstructed phylogeny but did contribute to phenotypic evolution of the extant species, and S◦ indicates a speciation event that can be “ob- served” in a reconstructed phylogeny. In the resulting “branching Brownian motion,” species E and F are separated by three speciation events of which two contributed to the phenotypic difference between E and F. F and G are separated by four events that all four contributed to the present phenotypic difference between F and G.
Bokma 2008
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Bokma 2008Eldredge and Gould 1971
=
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Two rate: apply different rate before and after some point
(in this case, midpoint)
1
2after
0.2after
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What questions can we answer with tree stretching?
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Heterogeneity
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Smith and Donoghue. Rates of Molecular Evolution Are Linked to Life History in Flowering Plants. Science (2008)
Trees/shrubs
Herbs
Subs
titut
ions
/MY
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Meredith et al. 2011, Science
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O’Meara 2012
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O’Meara 2012
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O’Meara 2012
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O’Meara 2012
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Yang 1994
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O’Meara 2012
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Pagel and Meade 2004
Familiar
Mixture model
Note: likely used a window, not
mentioned, though
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O’Meara 2012
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O’Meara 2012
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Tree stretching
Heterogeneity
Tree stretching + Heterogenei
ty
Continuous methods Y some some
Discrete methods Y nope nope
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O’Meara 2012
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library(geiger)?fitContinuous?fitDiscrete
#Look at some Geospiza examples. Is the rate of beak depth evolution dropping in Darwin’s finches?
http://www.youtube.com/watch?v=BZG14R5p6Kg http://www.youtube.com/watch?v=h6fqrDShlMM
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MADDISON. Confounding asymmetries in evolutionary diversification and character change. Evolution (2006) vol. 60 (8) pp. 1743-1746
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MADDISON. Confounding asymmetries in evolutionary diversification and character change. Evolution (2006) vol. 60 (8) pp. 1743-1746
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MADDISON. Confounding asymmetries in evolutionary diversification and character change. Evolution (2006) vol. 60 (8) pp. 1743-1746
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MADDISON. Confounding asymmetries in evolutionary diversification and character change. Evolution (2006) vol. 60 (8) pp. 1743-1746
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0 1q01
q10
speciation0 speciation1
extinction0extinction1
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MADDISON. Confounding asymmetries in evolutionary diversification and character change. Evolution (2006) vol. 60 (8) pp. 1743-1746
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MADDISON. Confounding asymmetries in evolutionary diversification and character change. Evolution (2006) vol. 60 (8) pp. 1743-1746
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MADDISON. Confounding asymmetries in evolutionary diversification and character change. Evolution (2006) vol. 60 (8) pp. 1743-1746
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MADDISON. Confounding asymmetries in evolutionary diversification and character change. Evolution (2006) vol. 60 (8) pp. 1743-1746
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Goldberg et al. 2010