The Elephant in the Dark:Resolving evolutionary patterns across timescales

…One by one, we go in the dark and come out

Saying how we experience the animal

One of us happens to touch the trunk.“A water-pipe kind of creature.”

Another, the ear. “A very strong, always movingBack and forth, fan-animal.”

Another, the leg. “I find it still, Like a column on a temple.”

Another touches the curved back. “ A leathery throne”

Another, the cleverest, feels the tusk. “A rounded sword made of porcelain.”

He’s proud of his description.

Each of us touches one placeAnd understands the whole in that way.

The palm and fingers feeling in the dark areHow the senses explore the reality of the elephant

If each of us held a candle there,And if we went in together,

We could see it.

-The Elephant in the DarkRumi (Translated by Coleman Barks)

Another, touches extant populations,…

“A very strong, always moving back and forth [process]”

Another, the fossil record, …

“I find it still, like a column on a temple [with occasional punctuations]”

Another, the phylogeny…

…Brownian Motion might be a good approximation.

How can the evolutionary pattern be all these things?

Contemporary field studies

• Rapid evolution

• High genetic variation

• Strong selection

Fossil record

• Stasis over millions of years

• Geographic variation

• Extinction and species turnover

Comparative methods

• Variance increases through time

• High morphological diversity

• Brownian motion fits reasonably

How can we see the pattern across scales of time?

All studies of phenotypic evolution measure comparable

quantitiesAllochronic

We measure two quantitaties:(1) “time for evolution”

(2) Δ mean

Pop Bmean(z)

Pop Amean(z)

Time interval

Pop X

Synchronic

Pop Bmean(z)

Pop Amean(z) Time interval

Estes and Arnold 2007

Field StudiesFossil Record

Historic

Divergence isn’t dependent on time?

Why is there no time-span effect?

• How can this be consistent with strong phylogenetic signal for body size traits?

Thomas F HansenUniversity of Oslo

Body size is known to have a strong phylogenetic signal

Smith et al. 2004. Phylogenetic heritability of body size between sister species of mammals

(think of the plot like a sib-sib regression)

Estes and Arnold 2007

Field StudiesFossil Record

Historic

Divergence isn’t dependent on time?

Estes & Arnold (2007)

• Neutral drift in trait or adaptive optimum

• Stabilizing selection

• Displaced optimum

• Moving optimum

• White noise motion of the optimum

• Peak shift

Estes and Arnold 2007

Time (Raw timescale)

Example: Brownian Motion process

Time (Raw timescale)

Example: Brownian Motion process

Time (Raw timescale)

Example: Brownian Motion process

Time (Log timescale)

Let’s combine with comparative data:• Log-scaled linear body size traits

• e.g. ln(height) or ln( mass1/3)

• Taxa- Many, but mostly vertebrates

• Field and historic data (e.g. Hendry et al. 2008)

• Fossil record (e.g. Gingerich 2001)

• Comparative data:• Time-calibrated phylogenies &

body size databases• Mammals, Birds & Squamates

Microevolutionary data

Fossil data

Comparative dataMammals

Comparative dataBirds

Comparative dataSquamates

Comparative dataMammalian, Avian and Squamate body size

Comparative dataMammalian, Avian and Squamate body size

“The Evolutionary Blunderbuss” ™ Stevan J Arnold

Study bias?

Models must explain:

“The Stasis Distribution”and

Longer term trends of accumulating variance

Two-layer process

Stochastic modelsBounded Evolution (BE)Brownian Motion (BM)Single-burst (SB) – Exponential time to displacementMultiple-burst (MB) – Poisson Point Process

All datasets- Microevolutionary, Fossil and Phylogenetic:

Model Parameter estimates AIC

White Noise -2940.53

Brownian motion -7877.97

Displaced optimum 1/ =107.4438 -9018.03

Poisson process 1/ =107.3976 -9142.54

Poisson process model fit to subsets of the data:

Dataset Parameter estimates

Microevolutionary & Fossil 1/ =106.1642

Phylogenetic 1/ =107.3375

Multiple-Burst Model• Punctuational change• Stasis distribution:

± 10% linear size change (1 SD)(ME + phenotypic plasticity +

evolutionary change + genetic drift)• Burst distribution:

± 30% linear size change (1 SD) Average time to displacement =

25 my

Multiple-Burst Model:bootstrapped over studies

Parameter estimates and AIC scores for three model fits to the data. Models tested include a bounded evolution model (BE), a Brownian motion model (BM), a single-burst model (SB) and a multiple-burst model (MB). In all models, standard deviations are in units of the natural log size difference. The inverse of the rate parameters (1/ ) for the exponential distribution and Poisson distribution in the single-burst and multiple-burst models, respectively, can be interpreted as the average number of years until a displacement. Details of each model may be found in the SI text.

Dataset Model Parameter estimates

AIC

Microevolution & Fossil BE = 0.1417 -5740.28

BM = 0.0974 1.60e-4 -8298.53

SB = 0.0885 0.396 1/ =106.2990 -8687.00

MB = 0.0874 0.249 1/ =106.1642 -8793.06

Phylogenetic only BE = 0.2986 1106.31

BM = 0.1000 4.61e-5 0.66

SB = 0.1182 0.4451 1/ =107.7344 -171.30

MB = 0.0857 0.2166 1/ =107.3375 -363.26

All data less than 500,000 years

BE = 0.0976 -8493.74

BM = 0.0976 1.94e-7 -8491.74

SB = 0.0260 0.106 1/ =102.276 -8960.72

MB = 0.0872 0.327 1/ =106.337 -8758.38

All data greater than 500,000 years

BE = 0.2997 1417.48

BM = 0.1946 3.99e-5 599.30

SB = 0.1558 0.508 1/ =107.8724 105.76

MB = 0.1480 1/ =107.7482 45.82

Why millions of years?

What process accounts for this pattern?

What pattern makes evolution look like Brownian motion over macroevolutionary time?

• Genetic drift (Lande 1976)?– No, parameters do not work

• Drift of a local adaptive peak? – No, or we could never measure selection

• A statistical pattern in need of an interpretation

What then, is randomly walking?

• “Niches”• Not a real answer• We need more focus on

interpretation and causation!

Is there anything significant about 1-5 milllion years?

• Species life-spans for mammals are ~1-5 million years (Alroy et al. 2000; Liow et al. 2008)

• Marine inverts 2.5-10 my (Foote, 2007)

• Taxon cycles are suggested to occur on the order of 0.1-10 my(Ricklefs & Bermingham 2002)

Liow et al. 2008

Liow et al. 2008

Foote 2007

What role could demography & extinction play?

• Similar to models proposed by Eldredge et al. (2005)

• As fitness-related mean trait value deviates from θ, mean population fitness declines according to a Gaussian function.

• Let the population grow at a multiplicative growth rate, Rt, such that:

and, otherwise .

Population growth (Burger & Lynch 1995)

tt WBR

KN t KN t when where B is the maximum population growth rate and K is the carrying capacity.

1 ttt NRN

G/(ω2 +1)=0.01 σ2ө = 2.25 B=1.025

λ = 1/250 N0 = 10000

Constant population size:

Divergence increases with time

Addition of demography:

Divergence decreases with time

G/(ω2 +1)=0.01 σ2ө = 2.25 λ = 1/250,

Linear increase in average divergence expected

From adaptive landscapes & G-matrices to phylogenetic stochastic models

• Need to account for the scaling from populations species

• e.g. Futuyma’s ephemeral divergence model• Demography, and the dynamics of species

ranges over time (including speciation) can be factored in to explain shifts in species means

• The ultimate “cause” of evolutionary change is change in adaptive landscapes