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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