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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