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Transcript of 2 6 19 13 8 16 18 12 - ib.berkeley.eduib.berkeley.edu/courses/ib200/lect/mar18_DA_slides.pdf ·...
28
616
16
1114
8.59
11.511
1918
1312a
b
R = 0.74
511
1317
914
412
610
1010
1615
28
616
16
1114
8.59
11.511
1918
1312
48
108
32
-6-6
65
2-2
86
a
b c
R = 0.74 R = 0.92
Oakley and Cunningham 2000
Oakley and Cunningham 2000
A21223Fig. 2
3. Tempo and mode of evolution
phylogeny and ages from Renner et al. 2008 Syst. Biol.
~3 Ma
~40 Ma
Striped Sugar Mountain Silver Red Ash-leaf Dipteronia
Blomberg’s K – measure of phylogenetic signal
Blomberg et al. 2003 Evolutionexamples from Ackerly 2009 PNAS
K = 0.18 K ~ 1 K = 1.62
low brownian high
phylogenetic signal
Data diagnostics
• do traits fit Brownian model? can we use model fitting to answer evolutionary questions?
• pattern vs. process table
Brownian motion – assumptions and interpretations
Evolutionary models
Brownian motion – assumptions and interpretations
Evolutionary models
∞
-∞
Ornstein-Uhlenbeck model (OU-1)
Evolutionary models
the math:brownian motion + ‘rubber band effect’
change is unbounded (in theory), but as rubber band gets stronger, bounds are established in practice
repeated movement back towards center erases phylogenetic signal, leading to K << 1
0 50 100 150 200 250 300
-15
-50
510
15
time
trait
valu
e
see Hansen 1997 EvolutionButler and King 2004 Amer. Naturalist
Ornstein-Uhlenbeck model (OU-1)
Evolutionary models
the math:brownian motion + ‘rubber band effect’
change is unbounded (in theory), but as rubber band gets stronger, bounds are established in practice
repeated movement back towards center erases phylogenetic signal, leading to K << 1
0 50 100 150 200 250 300
-15
-50
510
15
time
trait
valu
e
see Hansen 1997 EvolutionButler and King 2004 Amer. Naturalist
Harmon et al. 2010
Harmon et al. 2010
Assign proportional weighting of alternative models that best fit data
Rates of phenotypic diversification under Brownian motion
time
var(x)
1 felsen = 1 Var(loge(trait))
million yrs
Rates of phenotypic diversification under Brownian motion
time
var(x)
higher rate lower rate
Diversification of height in maples, Ceanothus and silverswords
~30 Ma
~45 Ma
rate = 0.015 felsens 0.10 felsens 0.83 felsens
Ackerly 2009 PNAS
~5.2 Ma
Evolutionary rates
Rates of phenotypic diversification (estimated for Brownian motion model)Ra
te (f
elsen
s)
Leaf sizeHeight
Acer
Aesculu
sAr
buto
ideae
Ceanothus
lobeli
oids
silve
rswo
rds
North temperateCaliforniaHawai’i
Acer
Aesculu
sAr
buto
ideae
Ceanothus
lobeli
oids
silve
rswo
rds
±1 s.e.
Ackerly, PNAS in review