1. Fossil Mammals in Time
(and Space)
Bob O'Hara
BiK-F, Frankfurt am Main, Germany
http://blogs.nature.com/boboh/2012/07/04/ISEC2012

2. Kiitoksia..
Mikael Fortelius
Jussi Eronen
– University of Helsinki

3. I want to play with the
fossil record
Some obvious statistical issues

4. The fossil record has holes
Where are the missing lynx?

5. There's a process here
somewhere
The real distribution?

6. Extinction & Speciation
in the fossil record
• How do they vary?
– can we blame climate change?
• Who dies?
– Related to traits?

7. Bad News
I won't answer either question

8. Good News
There is some progress, and there
might be more before the next ISEC

9. Where I am Now

10. Where I am Now
• Sundvollen
© Andres Lopez-Sepzulcre

11. No, where the research has
got to?
• Got the simple model working
• Starting to puzzle over the full model

12. The problems
• Estimating dates of sites
– many based on fossils, not external data
• Estimating actual extinction and
speciation times
– mark recapture

13. The First Problem
Getting some data

14. A database. Woooo!
http://www.helsinki.fi/science/now/database.html

15. Data
• 282 Species
• 347 locations
– Europe (not Russia)
• Covers last 25m years

16. The Data
Species Date Dating
I II III IV Method
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

17. Independent Dating
• Paleaomagnetic
Bloggy explanation:
http://tinyurl.com/ctskvmx
• Oxygen Isotopes
Wikipedia explains:
http://en.wikipedia.org/wiki/Oxygen_isotope_ratio_cycle
http://en.wikipedia.org/wiki/File:Phanerozoic_Climate_Change.png

18. The Model I: Species
Now 25 mya
Extinction Speciation
U(0, Speciation) U(Extinction, 25)

19. The Model II: Sites
If dating uses
Date independent data
U(min, max)
Now 25 mya
Date
U(0, 25)
If dating uses fossil data

20. The Model III: Observations
Now 25 mya
Pr(Observed|Extant) ~ Species + Site
Logistic regression

21. Estimating
extinction/speciaiotn
Now 25 mya
Pr(Observed|Extant) ~ Species + Site
Logistic regression

22. Model Fitting
model {
• OpenBUGS for(l in 1:NLocations) {
for(s in 1:NSpecies) {
Presences[l,s] ~ dbern(p[l,s])
– MCMC Age[l])
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] ~ 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)
}

23. Estimated Site Dates
Looks OK
Not good
But no
calibration
Not good
(& doesn't
converge)
Time (mya)

24. Speciation & Extinction
Rates

25. What Next?
• Calibration needs improvement?
– also spatial effects
• Extend the model to look at trait
effects
– frailty models

26. http://blogs.nature.com/boboh/2012/07/04/ISEC2012
Credit: Dr. H.G of Cromer

27. http://blogs.nature.com/boboh/2012/07/04/ISEC2012
But I'm an
effing Bison!
Credit: Dr. H.G of Cromer