Fossil Mammals in Time (and Space)

Bob O'HaraBiK-F, Frankfurt am Main, Germany

http://blogs.nature.com/boboh/2012/07/04/ISEC2012

Kiitoksia..

Mikael ForteliusJussi Eronen

– University of Helsinki

I want to play with thefossil record

Some obvious statistical issues

The fossil record has holes

Where are the missing lynx?

There's a process here somewhere

The real distribution?

Extinction & Speciationin the fossil record

• How do they vary?– can we blame climate change?

• Who dies?– Related to traits?

Bad News

I won't answer either question

Good News

There is some progress, and there might be more before the next ISEC

Where I am Now

Where I am Now

• Sundvollen

© Andres Lopez-Sepzulcre

No, where the research has got to?

• Got the simple model working• Starting to puzzle over the full model

The problems

• Estimating dates of sites– many based on fossils, not external data

• Estimating actual extinction and speciation times– mark recapture

The First Problem

Getting some data

A database. Woooo!

http://www.helsinki.fi/science/now/database.html

Data

• 282 Species• 347 locations

– Europe (not Russia)

• Covers last 25m years

The DataSpecies Date Dating

MethodI II III IV

Site 1 1 0 1 0 12-14 C

Site 2 1 1 0 0 12-15 C

Site 3 0 0 0 1 1-3 MN

Site 4 0 1 0 0 5-12 OI

Site 5 0 1 0 1 2-7 MN

Independent Dating

• Paleaomagnetic

• Oxygen Isotopes

Bloggy explanation:http://tinyurl.com/ctskvmx

Wikipedia explains:http://en.wikipedia.org/wiki/Oxygen_isotope_ratio_cycle

http://en.wikipedia.org/wiki/File:Phanerozoic_Climate_Change.png

The Model I: Species

Now 25 mya

ExtinctionU(0, Speciation)

SpeciationU(Extinction, 25)

The Model II: Sites

Now 25 mya

DateU(min, max)

DateU(0, 25)

If dating uses independent data

If dating uses fossil data

The Model III: Observations

Pr(Observed|Extant) ~ Species + Site

Logistic regression

Now 25 mya

Estimating extinction/speciaiotn

Now 25 mya

Pr(Observed|Extant) ~ Species + Site

Logistic regression

Model Fitting

• OpenBUGS– MCMC

model { for(l in 1:NLocations) { for(s in 1:NSpecies) { Presences[l,s] ~ dbern(p[l,s]) logit(pSTAR[l,s]) <- mu + al.Loc[l] + al.Sp[s] p[l,s] <- pSTAR[l,s]*step(Age[l]-Extinct[s])*step(Speciate[s]-Age[l]) } Age[l] ~ dunif(MinAge[l], MaxAge[l]) al.Loc[l] ~ dnorm(muL,tauLoc) } for(s in 1:NSpecies) { Speciate[s] ~ dunif(Extinct[s], 25) Extinct[s] ~ dunif(0,Speciate[s]) al.Sp[s] ~ dnorm(muS,tauSp) }

sdLoc ~ dunif(0,10); tauLoc <- pow(sdLoc,-2) sdSp ~ dunif(0,10); tauSp <- pow(sdSp,-2)

mu ~ dnorm(0,2) muL ~ dnorm(0,2) muS ~ dnorm(0,2)}

Estimated Site DatesLooks OK

Not good(& doesn't converge)

Not goodBut no calibration

Time (mya)

Speciation & Extinction Rates

What Next?

• Calibration needs improvement?– also spatial effects

• Extend the model to look at trait effects– frailty models

http://blogs.nature.com/boboh/2012/07/04/ISEC2012

Credit: Dr. H.G of Cromer

But I'm an effing Bison!

http://blogs.nature.com/boboh/2012/07/04/ISEC2012

Credit: Dr. H.G of Cromer